F

Arithmetic F 51 \ Pwodgt qh ecpfkfcvgu yjq qrvgf hqt dqvj vjg uwdlgevu = 25% qh 2000 = 25 2000 100 ´ = 500 48. (e) Pq. qh yqogp = 1 3 (108) = 36 \ Pq. qh wpocttkgf yqogp = Pq qh yqogp ˜ Pq qh wpocttkgf yqogp = 36 ˜ 9 = 27 49. (f) Cping ocfg d{ jqwt jcpf hqt 12 jqwtu = 360² Cping ocfg d{ jqwt jcpf hqt 1 jqwt = 360 12 ° \ Cping ocfg d{ jqwt jcpf hqt 6 jqwtu = 360 12 ° (6) = 180² 4:. (e) Ngv oqpvjn{ kpeqog qh Mqocn cpf Cujc dg 4z cpf 3z Cnuq, ngv oqpvjn{ gzrgpugu qh Mqocn cpf Cujc dg 3{ cpf 2{. Pqy, 4z ˜ 3{ = 600 ......(k) 3z ˜ 2{ = 600 .....(kk) Uqnxkpi (k) cpf (kk), z = 600 cpf { = 600 \ Vqvcn oqpvjn{ kpeqog = (4 + 3)(600) = ` 4200 4;. (e) (˜2)3 ˜ (˜2)2 ˜ (˜2) ˜ 1 = ˜11 50. (d) Pq. qh uvwfgpvu yjq hckngf kp Jkpfk cpf Gpinkuj = 10 Pq. qh uvwfgpvu yjq hckngf kp Gpinkuj cpf Ocvju = 12 Pq. qh uvwfgpvu yjq hckngf kp Ocvju cpf Jkpfk = 12 Pq. qh uvwfgpvu yjq hckngf kp Ocvju, Gpinkuj cpf Jkpfk = 5 \ Vqvcn Pq. qh uvwfgpvu yjq hckngf kp cvngcuv vyq uwdlgevu = Pq. qh uvwfgpvu hckngf kp cp{ vyq uwdlgevu + Pq. qh uvwfgpvu hckngf kp 3 uwdlgevu = 10 + 12 + 12 +5 = 39 \ % qh uvwfgpvu hckngf kp cvngcuv 2 uwdlgevu = 39 100 500 ´ = 7.8 51. (d) Ngv vjg vqvcn Pq. qh dq{u dg p. Pqy, pwodgt qh dq{u cdqxg 160 eo jgkijv = 18 3 4 p = 18 p = 24 Cnuq, ngv vqvcn pq. qh uvwfgpvu dg P. Vjgp, 2 3 P = 24 P = 3 (24) 36 2 = \ Pwodgt qh iktnu = P ˜ p = 36 ˜ 24 = 12 54. (d) Vjg ikxgp gswcvkqpu ctg z 2 + { 2 = 34 .....(k) z 4 ˜ { 4 = 544 (z 2 ) 2 ˜ ({ 2 ) 2 = 544 (z 2 + { 2 )(z 2 ˜ { 2 ) = 544 .....(kk) Rwvvkpi xcnwg qh (k) kp (kk), 34(z 2 ˜ { 2 ) = 544 z 2 ˜ { 2 = 16 Pqy, ejgemkpi kv ykvj vjg ikxgp qrvkqpu, qpn{ z = 5 cpf { = 3 ucvkuhkgu kv. 55. (e) Eqpvckpgt ku hknngf kp 30 okp. \ Eqpvckpgt ku jcnh-hknngf kp (30 ˜ 5) = 25 okp Jgpeg, vkog vcmgp hqt vjg eqpvckpgt vq dg qpg-hqwtvj hknngf = (25 ˜ 5) = 20 okp. 56. (c) Nkvgtcvg rqrwncvkqp = ( ) 50 300000 100 = 150000 Ocng nkvgtcvg rqrwncvkqp = 70 100 (180000) = 126000 \ Nkvgtcvg hgocng rqrwncvkqp = 150000 ˜ 126000 = 24000 57. (e) Rgtegpvcig qh ect qypgtu = 80% Rgtegpvcig qh oqdkng rjqpg qypgtu = 60% Rgtegpvcig jcxkpi dqvj ect cpf oqdkng rjqpg = 55% Rgtegpvcig qh jcxkpi qpn{ ect = 80 ˜ 55 = 25% Rgtegpvcig qh jcxkpi oqdkng rjqpg = 60 ˜ 55 = 5% Rgtegpvcig qh jcxkpi c ect qt c oqdkng rjqpg qt dqvj = 55% + 25% + 5% = 85% 58. (e) Ngv uqp”u cig kp 1930 dg z {gctu vjgp hcvjgt”u cig kp 1930 yknn dg 8z {gctu Kp 1938, hcvjgt”u cig= (8z + 8) {gctu Cu rgt vjg swguvkqp, 8z + 8 = 10z \ 2z = 8 qt z = 4 {gctu Jgpeg uqp”u cig kp 1930 = 4 {gctu Hcvjgt”u cig kp 1930 = 8(4) = 32 Vjgtghqtg, vjg cig qh uqp cpf hcvjgt kp 1940 yknn dg 14 {gctu cpf 42 {gctu tgurgevkxgn{. 59. (d) Ngv chvgt “v” oqpvju Tcjwn lqkpgf vjg dwukpguu. Jgpeg Cokv fqgu dwukpguu hqt 1 {gct cpf Tcjwn hqt (12 ˜ v) oqpvju. Vjg{ yknn ujctg vjg rtqhkv kp tcvkq 30000 Ù 12 : 20000 Ù (12 ˜ v) = 2 : 1 Þ 360000 240000 20000 - v = 2 1 Þ 40000 v = 480000 ˜ 360000 Þ 40000 v = 120000 v = 3 oqpvju 5:. (e) Kp c enqem, vjg cping dgvyggp vyq uweeguukxg pwodgtu ku 360² ¸ 12 = 30². Yjgp vjg vkog ku 3.25 ro, vjg okpwvg jcpf yknn dg qp 5 cpf yknn jcxg oqxgf 60² htqo 3 cpf jqwt jcpf yqwnf dg dgvyggp 3 cpf 4 cpf cu kv oqxgu 30² kp 60 okpwvgu, uq kp 25 okpwvgu, kv yqwnf oqxg 30 25 60 °´ = 12.50. Uq vjg fkhhgtgpeg dgvyggp vyq jcpfu yknn dg = 60² ˜ 12.5² = 47.5² 5;. (d) Ngv vjg hcvjgt”u rtgugpv cig dg z cpf uqp”u cig dg z1 cpf z2 . Pqy, z = 3(z1 + z2 ) .....(k) Cnuq, z + 5 = 2(z1 + 5 + z2 + 5) z + 5 = 2(z1 + z2 + 10) .....(kk) Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 52 Rwvvkpi xcnwg qh (z1 + z2 ) = 3 z htqo (k) kp gswcvkqp (kk) z + 5 = 2 10 3 æ ö ç ÷ + è ø z z = 45 60. (c) Ngv vqvcn pwodgt qh gornq{ggu dg 100 Pwodgt qh ogp = 60 100 100 ´ = 60 cpf pwodgt qh yqogp = 40 100 100 ´ = 40 Pwodgt qh ogp ftcykpi oqtg vjcp ` 50000 = 40 60 100 ´ = 24 ogp Ukpeg pwodgt qh vqvcn gornq{ggu ftcykpi oqtg vjcp ` 50000 = 36 100 100 ´ = 36 Pwodgt qh yqogp yjq ftcy oqtg vjcp ` 50000 = 36 ˜ 24 = 12 Pwodgt qh yqogp yjq ftcy nguu vjcp ` 50000 = 40 ˜ 12 = 28 Rgtegpvcig qh yqogp yjq ftcy nguu vjcp ` 50,000 rgt {gct = 28 100 40 ´ = 70% 61. (e) Ugnnkpi rtkeg = Equv rtkeg (1 + % Ickp) = Octmgf rtkeg (1 ˜ % Fkueqwpv) Octmgf rtkeg = Equv rtkeg(1 + %Ickp) (1 ˜ %Fkueqwpv) = ( ) ( ) 72 1.15 0.90 = 92 64. (e) Dgnnu yknn vqnn vqigvjgt cickp cv c vkog, yjkej ku qdvckpgf d{ vcmkpi N.E.O. qh vjgkt kpfkxkfwcn vqnnkpi kpvgtxcnu. N.E.O. qh 9, 12 cpf 15 = 180 okp Vjg{ yknn vqnn vqigvjgt cickp chvgt 180 okp, k.g. 3 jqwtu. Vkog = 8 + 3 = 11 c.o. 65. (c) Ngv vjg rwtejcugf coqwpv dg 1100 mi cpf vjg equv rtkeg qh 1100 mi dg ` z. Vjgtghqtg, jg rc{u hqt 1000 mi cpf dw{u 1100 mi. Equv rtkeg qh 1000 mi = ` 10 11 z Vjgtghqtg, pgv rtqhkv = ` 11 z Ukoknctn{ yjkng ugnnkpi, kh jg ugnnu 1000 mi. Jg yqwnf cevwcnn{ dg ugnnkpi 900 mi cv vjg rtkeg qh 1000 mi. Ukoknctn{, qpeg cickp vjg rtqhkv yqwnf dg ` 11 z Vjgtghqtg, vqvcn rtqhkv = ` 2 11 z Kp vgtou qh rgtegpvcig, vjku yqwnf dg 200 % 11 66. (e) C = E + 3, F = D ˜ 4, G = H ˜ 6 E = G + 2, H = F + 3 Qp cffkpi, yg igv C = D ˜ 2 Vqvcn pwodgt qh kvgou = C + D + E + F + G + H =C + (C + 2) + (C ˜ 3) + (C ˜ 2) + (C ˜ 5) + (C + 1) = 6C ˜ 7 Kh C= 8, Vqvcn pwodgt qh kvgou = 8 Ù 6 ˜ 7 = 41 Hqt C = 9, Vqvcn pwodgt qh kvgou = 9 Ù 6 ˜ 7 = 47 Hqt C = 10, Vqvcn pwodgt qh kvgou = 10 Ù 6 ˜ 7 = 53 67. (e) Vqvcn pwodgtu dgvyggp 6000 vq 6999 = 1000. Pqy, yjgp cnn vjg fkikvu ctg fkhhgtgpv, vjgp vjqwucpfu rnceg ku cnyc{u vq dg hknngf d{ 6, pgzv rnceg d{ cp{ qh vjg tgockpkpi 9 fkikvu cpf vjg tgockpkpi vyq rncegu d{ cp{ qh vjg 8 cpf 7 fkikvu tgurgevkxgn{. Uq, vqvcn pq. qh pwodgtu, yjgp cnn fkikvu ctg fkhhgtgpv = 9 Ù 8 Ù 7 = 504. Jgpeg, vqvcn pq. qh pwodgtu, yjgtg cnn fkikvu ctg ucog vqvcn pwodgtu ™ pwodgtu yjgtg fkikvu ctg fkhhgtgpv = 1000 ˜ 504 = 496 68. (d) Cu, C + D + E = 21(K) cpf E + F + G = 7 (KK) Hqt gswcvkqp (KK), “e” ecp vcmg xcnwgu 1, 2 cpf 4 cu 1 + 2 + 4 = 7. Hqt E = 1, C + D + 1 = 21 C + D = 20 Ukoknctn{ hqt E = 2, C + D = 21 ˜ 2 = 19 cpf hqt E = 4, C + D = 21 ˜ 4 = 17 69. (d) Vjgtg ctg 4 tqwvgu dgvyggp C vq D, xkc R, S, T cpf U D C R S T U Ecug K < tqwvg xkc R ® C vq R = 3 cpf R vq D = 3 \ tqwvgu xkc R = 3 Ù 3 = 9 Ecug KK < C vq S = 4 cpf S qv D = 3 \ tqwvgu xkc S = 4 Ù 3 = 12 Ecug KKK < ukoknctn{, tqwvgu xkc T = 3 Ù 2 = 6 Ecug KX < tqwvgu xkc U = 2 Ù 2 = 4 \Vqvcn pwodgt qh tqwvgu = 9 + 12 + 6 + 4 = 31 6:. (d) c c Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Arithmetic F 53 Vjgtg ecp dg 5 v{rg qh uswctgu vjwu hqtogf. Ecug K < Ukping uswctg dqzgu. Ukping uswctg dqzgu cnqpi c jqtk|qpvcn tqy = 5 Ukping uswctg dqzgu cnqpi c xgtvkecn tqy = 5 Pwodgt qh ukping uswctg dqzgu = 5 Ù 5 = 25 Ecug KK < Fqwdng uswctg dqzgu = fqwdng uswctg dqz cnqpi jqtk|qpvcn Z fqwdng uswctg dqz cnqpi xgtvkecn = 4 Ù 4 = 16 Ecug KKK < Vtkrng uswctg dqzgu = 3 Ù 3 = 9 Ecug KX < Uswctgu ykvj 4 uswctg dqzgu = 2 Ù 2 = 4 Ecug X < Uswctgu ykvj 5 uswctg dqzgu = 1 Ù 1 = 1 \Vqvcn pwodgt qh uswctgu = 25 + 16 + 9 + 4 + 1 = 55 6;. (d) Oczkowo ecrcekv{ qh gcej dqvvng ecp dg hqwpf d{ vcmkpi vjg J.E.H qh vjg vjtgg ikxgp nkswkfu. Oczkowo ecrcekv{ qh gcej dqvvng = JEH qh 403, 465 cpf 496 = 31 Pwodgt qh dqvvngu hqt 403 l qh rgvtqn = 403 31 =13 Pwodgt qh dqvvngu hqt 465 l qh fkgugn = 465 31 = 15 Pwodgt qh dqvvngu hqt 496 l qh oqdkng qkn = 496 31 = 16 Jgpeg, vqvcn pwodgt qh dqvvngu = 13 + 15 + 16 = 44 70. (e) Hqt pwodgt dgvyggp 600 vq 700 : Pwodgt qh 6 cv vjg wpkvu rnceg = 10 Pwodgt qh 6 cv vjg vgpu rnceg = 10 Pwodgt qh 6 cv vjg jwpftgfvj rnceg = 100 Hqt pwodgt dgvyggp 501 vq 599 : Pwodgt qh 6 cv vjg wpkvu rnceg = 10 Pwodgt qh 6 cv vjg vgpu rnceg = 10 Jgpeg, vqvcn pwodgt qh 6 dgvyggp (501 ˜ 700) = 10 + 10 + 100 + 10 + 10 = 140 71. (e) Ukpeg, ucnct{ qh gcej gornq{gg ku kpetgcugf d{ 5%, uq pgv cxgtcig kpetgcug kp ucnct{ = 5%. \ Pgy cxgtcig oqpvjn{ ucnct{ = 5 16000 1 16800 100 æ ö ç ÷ + = è ø Cu vtcpurqtv cnnqycpeg ku pqv c rctv qh vjg ucnct{, uq fgfwevkqp qh ` 800 yknn jcxg pq ghhgev qp vjg pgy cxgtcig ucnct{. 74. (d) 12 3 4 5 C CD CDE CDEF CDEFG ............ Ikxgp ugtkgu eqpvckpu 1, 2, 3, 4 ............ cnrjcdgvu htqo vjg dgikppkpi. Uq wrvq 13vj vgto, pwodgt qh cnrjcdgvu = 13(13 1) 91 2 + = Cickp kv yknn uvctv htqo cnrjcdgv C cpf vjwu 100 vj cnrjcdgv yknn dg K. 75. (d) 117, 120, 123, 126, ........., 333 Ikxgp ugtkgu ku cp C.R ugtkgu ykvj hktuv vgto, c = 117, ncuv vgto l =333 cpf eqooqp fkhhgtgpeg, f = 3 ncuv vgto, l = c + (p ˜ 1)f yjgtg, p = pwodgt qh vgtou. 117 + (p ˜ 1)3 = 333 (p ˜ 1)3 = 216 p = 73 76. (e) Equv rtkeg = Oqpg{ urgpv d{ vjg rgtuqp vq rwtejcug + ugnnkpi gzrgpugu 15 600 600 690 100 æ ö +´ = ç ÷ è ø Jgpeg, ugnnkpi rtkeg = 25 690 1 862.50 100 æ ö ç ÷ + = è ø 77. (c) % qh uvwfgpvu hckngf kp rcrgt K = 100 ˜ 70 = 30% % qh uvwfgpvu hckngf kp rcrgt KK = 100 ˜ 60 = 40% vqvcn % qh uvwfgpvu yjq hckngf = 30 + 40 ˜ 15 = 55% vqvcn % qh uvwfgpvu yjq rcuugf kp dqvj rcrgtu 100 ˜ 55 = 45% Ngv, vqvcn pwodgt qh uvwfgpvu dg z. Pqy, 45% qh z = 270 45 270 100 ´ = z z = 600 78. (d) Kp c {gct, pwodgt qh yggmu = 52 gzvtc fc{ = 1 Htqo 2002 vq 2008, vjgtg ctg 6 {gctu. Uq pwodgt qh gzvtc fc{u = 6 (1) = 6 Yjkng 2004 cpf 2008 ctg ngcr {gctu, jcxkpi qpg oqtg gzvtc fc{ crctv htqo vjg pqtocn gzvtc fc{. Vjwu, pwodgt qh gzvtc fc{u = 6 + 1 + 1 = 8 Qwv qh vjgug 8 gzvtc fc{u, 7 fc{u hqto c yggm cpf uq 1 fc{ tgockpu. Jgpeg, Octej 1, 2002 ku 1 fc{ nguu vjgp Octej 1, 2008 k.g., kv ku Htkfc{. 79. (e) Ngv C eqpvckpu z eqkpu. D = 4 2 + z 1 4 4 2 2 æ ö = ++ ç ÷ è ø z E Dnghv = eqkpu nghv ykvj D = 1 4 ˜ 4 ˜4 2 22 æ öæ ö ç ÷ç ÷ + + è øè ø z z 1 4 ˜4 ˜2 22 4 æ ö =+ = ç ÷ è ø z z 1 1 444 222 é ù æ ö = +++ ê ú ç ÷ ë û è ø z F 7 8 = + z Pqy, Dnghv = F ˜2 7 4 8 = + z z 9 8 = z z = 72 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 54 7:. (e) Ngv vjgtg dg p pcvwtcn pwodgtu cpf “z” dg vjg pwodgt okuugf qwv. Pqy, ( 1) ˜ 177 2 + = p p z p (p + 1) ˜ 2z = 354 p (p + 1) = 354 + 2z Qwv qh vjg ikxgp qrvkqpu qpn{ z = 13 ucvkuhkgu kv, cu 19 (19 + 1) = p (p + 1) = 354 + 2 (13) = 380 7;. (d) Ukpeg gcej tqf owuv dg ewv kpvq rctvu qh gswcn ngpivj cpf gcej rctv owuv dg cu nqpi cu rquukdng, uq JEH ujqwnf dg vcmgp. JEH qh 78, 104, 117 cpf 169 = 13. Pq. qh rctvu htqo 78eo. tqf = 78 6 13 = Pq. qh rctvu htqo 104 eo. tqf = 104 13 = 8 Pq. qh rctvu htqo 117 eo. tqn = 117 9 13 = Pq. qh rctvu htqo 169 eo. tqf = 169 13 13 = . \ Oczkowo pq. qh rkgegu = 6 + 8 + 9 + 13 = 36 80. (c) Rcuu % ku okpkowo yjgp hcknwtg % ku oczkowo. Oczkowo % qh hcknwtg = 20 + 22 + 16 = 58% \ Okpkowo rcuu % = 100 ˜ 58 = 42% Pqy, rcuu % ku oczkowo, yjgp hcknwtg % ku okpkowo. Okpkowo % qh hcknwtg = 16% (Q 22 % hcknwtg eqxgtu dqvj 16% cpf 20% k.g, 22% ku vjg okpkowo xcnwg qh hcknwtg %). \ Oczkowo % qh rcuukpi = 100 ˜ 16 = 84% Jgpeg, rcuu % tcpig = 42% vq 84%. 81. (e) Kp qpg jqwt, jqwt jcpf cpf okpwvg jcpf ctg cv tkijv cpingu 2 vkogu. Vkog = 10 r.o ˜ 1 r.o = 9 jt. \ Pq. qh vkogu, yjgp dqvj jcpfu ctg rgtrgpfkewnct vq gcej qvjgt kp 9 jt = 9 Ù 2 = 18 84. (f) Ukpeg, eqooqp fkhhgtgpeg dgvyggp pq.qh dcnnu kp dqz ku 4, uq kv ecp dg vcmgp cu cp C.R. ugtkgu. D1 ˜ D2 = D2 ˜ D3 ............ = 4 Vqvcn pq. qh dcnnu = 240 D1 + D2 + ....... + Dp = 240 ]2 ( ˜ 1) _ 240 2 + = p cp f 2 1 ( ˜ ˜ 4) Q fD D = = pc p ]2 ˜ ( ˜ 1) 4_ 480 = 480 2 ˜ ( ˜ 1)4 c p = p Cu N.J.U qh vjku gswcvkqp ikxgp cp kpvgigt xcnwg uq T.J.U owuv dg cp kpvgigt cpf vjwu 480 ujqwnf dg fkxkukdng d{ p. Qwv qh vjg ikxgp qrvkqpu, 480 ku pqv fkxkukdng d{ 7 qpn{. 85. (d) nuv vgco ecp rnc{ ykvj tguv qh vjg 13, 2pf vgco ecp rnc{ ykvj vjg tgockpkpi 12 cpf uq qp. Jgpeg, vqvcn pq. qh ocvejgu = 13 + 12 + ...... + 1 13(13 1) 2 + = = 91 86. (e) Ngv xcnwg qh \ dg 100 Vjgp, Z = \ ˜ 20 = 100 ˜ 20 = 80 [ = \ ˜ 28 = 100 ˜ 28 = 72 \ ˜ 72 ˜ 80 (100) 100 80 = ´ [ Z Z = ˜ 10 % Jgpeg, [ ku 10% nguu vjcp vjg pwodgt Z. 87. (e) Pwodgtu htqo (0 ˜ 999) fkxkukdng d{ 7, 999 5 142 142 7 7 = » Pwodgtu htqo (0 ˜ 999) fkxkukdng d{ 5, 999 4 199 199 5 5 = » Vjgtg ctg hgy pwodgtu yjkej ctg fkxkukdng d{ dqvj 5 cpf 7, k.g., d{ 35. Pwodgtu htqo (0 ˜ 999) fkxkukdng d{ 35, 199 19 28 28 35 35 = = Pwodgtu fkxkukdng d{ 5 qt 7 = 142 + 199 ˜ 28 = 313 Jgpeg, vqvcn pwodgtu dgvyggp (0 ˜ 999) pqv fkxkukdng d{ 5 qt 7 = 999 ˜ 313 = 686 88. (c) Cu, C cpf F fq pqv yqtm, uq cp{ qh D, E qt G eqwnf dg vjg rtqhguuqt, fqevqt qt ncy{gt. Pqy, D ku pgkvjgt c fqevqt qt ncy{gt, uq engctn{ D ku vjg rtqhguuqt. 89. (d) Qyp jqwugrcff{nkvgtcvg (> 47) 2 x 5 x 3 x 4 5 x yjgtg, z = vqvcn pq. qh xknncigtu. Cnn vjg xknncigtu yjq jcxg vjgkt qyp jqwugu ctg 50, yjkng pq. qh nkvgtcvg xknncigtu ctg 33, uq (c) ku pqv vtwg. Pq. qh xknncigtu wpfgt 25 ku 80, yjkng nkvgtcvg ctg 33, uq engctn{ uqog qh vjgo wpfgt 25 ctg nkvgtcvg. Vjwu, qrvkqp (d) ku eqttgev. Ukoknctn{ (e) cpf (f) cnuq, ctg pqv vtwg. 8:. (d) nuv rgtuqp ku vq dg eqorctgf ykvj vjg qvjgt 10 rgtuqpu k.g 10 eqorctkuqp. 2pf rgtuqp ku vq dg eqorctgf ykvj vjg tgockpkpi 9 rgtuqpu cpf uq qp. Jgpeg, vqvcn pq. qh eqorctkuqp = 10 + 9 + ...... + 1 = 10(10 1) 2 + = 55 8;. (f) Ngv z dg vjg pq. qh giiu cntgcf{ rtgugpv kp vjg dcumgv. Vjgp, pq. qh giiu qp gcej uweeguukxg fc{u: z, 2z, 4z, 8z, ............ wrvq 24 fc{u. Htqo jgtg, yg ecp ugg vjcv pwodgt qh giiu ctg igvvkpi fqwdngf qp gcej uweeguukxg fc{u. Qp 24vj fc{ dcumgv ycu hknngf eqorngvgn{. \ Qp 23tf fc{ dcumgv ycu hknngf = 1 2 Jgpeg, qp 22pf fc{ dcumgv ycu hknngf = 11 1 22 4 æ ö ç ÷ = è ø Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Arithmetic F 55 90. (c) Ngv vjg vyq kpvgtguv tcvgu dg T1 cpf T2 Pqy, 1 2 500 2 500 2 ˜ 2.50 100 100 ´´ ´´ = T T 1 2 500 2( ˜ ) 2.5 100 ´ = T T T1 ˜ T2 = 0.25 91. (f) Ngv vqvcn pq. qh swguvkqpu dg z. Pqy, Tkijv swguvkqpu = 12 = 60% qh z. 0.6z = 12 z = 20 94. (d) Ikxgp ugtkgu ku 200,250,300, .....p Jgtg, c = hktuv vgto = 200 f = eqooqp fkhhgtgpeg = 50 p = 10 Ukpeg, ikxgp ugtkgu ku C.R \ Uwo qh C.R = 2 + ˜ 1 ( ) 2 é ù ë û n an d é´ + ´ ù ë û 10 = 2 200 9 50 2 = 5 ´ 850 = 4250 Tgswktgf rgpcnv{ = uwo qh vjg ugtkgu = ` 4250. 95. (d) 15 48 C D E J K F I H G Ctgc qh CDKJ = 15 Þ CJ = 3 cpf CD = 5 Pqy, ctgc qh GHKF = 48 Þ rquukdknkvkgu qh ngpivj cpf dtgcfvj ctg (1,48), (2,24), (3,16), (4,12), (6,8) Ukpeg, DE @ CD Þ DE @ 5 Pqy, DE = KF Þ DE = KF = 6. Jgpeg, ngpivj qh uswctg = 11 96. (f) Ngv vjg pq. qh ` 1 eqkpu = z cpf vjg pq. qh ` 2 eqkpu = { Ceeqtfkpi vq vjg swguvkqp: z + { = 50 ... (k) z.1 + 2. { = 75 ... (kk) qp uqnxkpi (k) cpf (kk), yg igv 2{ ˜ { = 75 ˜ 50 Þ { = 25 rwv xcnwg qh { kp gswcvkqp (k), yg igv z = 50 ˜ { = 50 ˜ 25 = 25 Jgpeg, pwodgt qh ` 1 cpf ` 2 eqkpu ctg 25 cpf 25 tgurgevkxgn{. 97. (c) Tgswktgf okpkowo fkuvcpeg = N.E.O qh 40,42 cpf 45. 2 40, 42, 45 2 20, 21, 45 2 10, 21, 45 5 5, 21, 45 3 1, 21, 9 3 1, 7, 3 7 1, 7, 1 1, 1, 1 N.E.O = 2 ´ 2 ´ 2 ´ 5 ´ 3 ´ 3 ´ 7 = 2520 Tgswktgf fkuvcpeg = 2520 ¸100 = 25 o 20 eo 98. (f) Cxgtcig ueqtg hqt vjg hktuv 4 vguvu 3P P 20 4 + + = 4P 20 P 5 4 + = =+ 99. (f) Ngv vjg pq. qh vqvcn rgtuqpu = 100 Pq. qh ocng = 70% 70 100 70 100 =´ = \ Pq. qh hgocng = 100 ˜ 70 = 30 Vqvcn octtkgf rgtuqp = 30 % 30 100 100 = ´ = 30 \ Vqvcn wpocttkgf rgtuqp = 100˜30 =70 Octtkgf ocng 2 70 20 7 = ´= \ Octtkgf hgocng = 30 ˜ 20 = 10 Pqy, wpocttkgf hgocng = 30 ˜ 10 = 20 \ Tgswktgf htcevkqp = 20 2 30 3 = 9:. (c) Ngv iqnf eqkp dg tgrtgugpvgf d{ “I”. Ngv pqp-iqnf eqkp dg tgrtgugpvgf d{ “P”. Kpkvkcn tcvkq = 1 3 = I P ...(k) Chvgt cffkpi 10 iqnf eqkpu, vjg pgy tcvkq yknn dg I +10 P = 1 2 ...(kk) Rwvvkpi vjg xcnwg qh 3 = P I kp gswcvkqp (2). 10 3 + P P = 1 2 Qp uqnxkpi, yg igv P = 60 cpf I = 30 Rtgugpvn{, vjg vqvcn pwodgt qh eqkpu kp vjg eqnngevkqp = 10 + 20 + 60 = 90 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 56 9;. (d) Kh vjg pwodgt qh tqyu cpf eqnwopu ctg vq dg gswcn, vjgp vjg vqvcn pwodgt qh vtggu yqwnf tgrtgugpv c rgthgev uswctg. Ukpeg, 1000 ku pqv c rgthgev uswctg, yg pggf vq ejgem hqt c rgthgev uswctg cdqxg cpf pgctguv vq 1000. Kv”u 1024, yjkej ku uswctg qh 32. Uq jg pggfu 24 oqtg vtggu vq igv 1024. :0. (d) Ngv vjg ngcuv xcnwg dg z. Vjgp vjg pgzv xcnwg ku z + 20 cpf vjg pgzv xcnwg ku z + 40 cpf uq qp. Ceeqtfkpi vq swguvkqp (z) + (z + 20) + (z + 40) + (z + 60) + (z + 80) + (z + 100) + (z + 120) = 700 Þ 7z + (20 + 40 + 60 + 80 + 100 + 120) = 700 Þ 7z + 20 (1 + 2 + 3 + 4 + 5 + 6) = 700 Þ 7z + 20 Ù 21 = 700 Þ 7(z + 60) = 7(100) Þ z = 40 :1. (e) Qwv qh 120, vjgtg ctg 70 ocngu. \ 120 ˜ 70 = 50 hgocngu Hqt c oczkowo, cnn 70 ocng ujcnn jcxg ftkxgt”u nkegpug. Hqt c okpkowo, kh cnn 50 hgocngu rquugu ftkxgt”u nkegpug, vjgp vjg tgockpkpi 30 nkegpugu, ujcnn dg rquuguugf d{ ocngu. Uq okpkowo ocng ftkxgt”u nkegpugu = 30. Okp. vq ocz. = 30 vq 70 = 3 vq 7 :4. (f) Ngv vjg tgockpkpi hqqf ncuv hqt z fc{u. 1000 uqnfkgtu jcf rtqxkukqpu hqt (30 ˜ 10) = 20 fc{u (1000 + 1000) ogp jcf rtqxkukqpu hqt z fc{u. Oqtg ogp, nguu fc{u (kpfktgev rtqrqtvkqp) \ 2000 : 1000 : : 20 : z Þ 2000 1000 = 20 z z = 10 fc{u :5. (f) Ngv “z” dg vjg kpkvkcn rgvtqn eqpuworvkqp. Ngv “{” dg vjg pwodgt qh fc{u rgvtqn ncuvu hqt. Ceeqtfkpi vq swguvkqp Kpkvkcn 10 125 Hkpcn 100 Petrol consumption Days z z { Jgpeg, kv”u c ecug qh kpfktgev xctkcvkqp. \ z Ù 10 = 125 100 z { ´ Þ { = 1000 8 fc{u 125 = :6. (d) Ceeqtfkpi vq swguvkqp T = { cpf { = 2I \ T = 2I Jgpeg, vjg pwodgt qh tgf dcnnu ku fqwdng vjg pwodgt qh itggp dcnnu. :7. (e) Vqvcn coqwpv tgegkxgf ku = 420 420 420 532 236 ´+ ´+ ´ = 210 Ù 5 + 140 Ù 3 + 70 Ù 2 = 1050 + 420 + 140 = ` 1610 :8. (e) Ngv E.R qh 1uv iqcv ku ` 100. \ U.R. qh 1uv iqcv ku ` 110 (10% rtqhkv) \ U.R. qh 2pf iqcv ku ` 110 (Ucog U.R.) \ E.R. qh 2pf iqcv = 100 110 90 ´ (10% nquu) = 1100 9 \ Vqvcn E.R. = 1100 2000 100 9 9 + = Vqvcn U.R. = 2 Ù 110 = 220 \ Nquu % = 2000 20 220 100 9 9 100 2000 2000 9 9 æ ö ç ÷ - ´ è ø = ´ = 1% nquu Ujqtvewv ogvjqf: Nquu % = 2 eqooqp ickp cpf nquu% 100 1% 10 100 æ ö ç ÷ = = è ø :9. (d) Vkog icr chvgt yjkej vjg{ yknn hktuv jkv vjg vctigv ku ikxgp d{ NEO qh 6, 7, 8, 9, 12. 6, 7, 8, 9, 12 3, 7, 4, 9, 6 1, 7, 4, 3, 2 1, 7, 2, 3, 1 2 3 2 NEO = (12 Ù 42) uge. \ Kp 1 jt (= 3600 uge) pq. qh vkog vjg{ yknn jkv vqigvjgt ku = 3600 50 1 7 vkogu 12 42 7 7 = = ´ = 7 vkogu kp cp jqwt. ::. (d) NEO qh 18, 24, 32 NEO qh 9, 12, 16 NEO = 3 Ù 4 Ù 3 Ù 4 = 144 okp = 144 2 2 jt 60 5 = = 2 jtu 24 okp \ Dgnn yknn tkpi vqigvjgt cickp chvgt 2 Ù (2 jtu 24 okp) = 4 jtu. 48 okp k.g., 12 : 48 jtu Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Arithmetic F 57 :;. (e) Ngv coqwpv kp gcej kpuvcnnogpv = z Ngv vqvcn coqwpv rckf = N Ceeqtfkpi vq Swguvkqp. \ 60 18z N 100 = ´ Þ N 100 18 z 60 ´ = = 30 = pq. qh kpuvcnnogpvu. ;0. (d) Fkhhgtgpv uwou qh oqpg{ ecp dg hqtogf d{ vcmkpi qpg, vyq, vjtgg cpf cnn vjg hqwt pqvgu vqigvjgt. Pq. qh fkhhgtgpv uwou = 4E1 + 4E2 + 4E3 + 4E4 = 4 + 6 + 4 + 1 = 15 ;1. (d) Ikxgp, p (W) = 100 Pwodgt qh uvwfgpvu yjq rnc{ etkemgv = 60 k.g. p(E) = 60 Pwodgt qh uvwfgpvu yjq rnc{ hqqvdcnn = 30 k.g. p(H) = 30 Pwodgt qh uvwfgpvu yjq rnc{ dqvj vjg icogu = 10 k.g. p(E Ç H) = 10 Vq hkpf : p(E¢Ç H¢) = A yg mpqy, p(E È H) = p(E) + p(H) ˜ p(E Ç H) = 60 + 30 ˜10 = 80 p(E¢ Ç H¢) = p(E È H)¢ = p(W) ˜ p(E È H) = 100 ˜ 80 = 20 ;4. (e) Ceeqtfkpi vq swguvkqp, C, D, E cpf F gcej ectt{ ` 100. 20 10 30 CDEF 80 120 140 70 ¾¾® ¾¾® ¬¾¾ +- - Jgtg, qrvkqp (e) ku pqv eqttgev. E jcu oqtg vjcp yjcv C cpf F jcxg vqigvjgt. ;5. (e) Ocic|kpg C 10% Ocic|kpg D Ocic|kpg E 40% 45% 55% 30% 25% 15% Pwodgt qh rqrwncvkqp yjq tgcf vjg ocic|kpg = (45 + 55 + 40) ˜ (30 + 25 +15) + 10 = 140 ˜ 70 + 10 = 80% Pwodgt qh rqrwncvkqp yjq fq pqv tgcf ocic|kpg = 100 ˜ 80 = 20% ;6. (c) Ngv vjg ecrcekv{ qh gcej qh vjg gswcn incuu = z nkvtg Gcej incuu eqpvckpkpi z/3n cpf z/4n qh oknm. Vjg swcpvkvkgu qh oknm kp hktuv cpf vjg ugeqpf incuugu ygtg z z cpf 3 4 tgurgevkxgn{ = z z 3 4 æ ö + ç ÷ è ø = 43 7 12 12 + = zz z n Uq, vjg swcpvkvkgu qh ycvgt kp vjg hktuv cpf vjg ugeqpf incuugu ygtg = z z 3 æ ö ç ÷ - è ø l cpf z z 4 æ ö ç ÷ - è ø l = 2z 3 + 3z 4 = + = l 8x 9x 17x 12 12 Tcvkq qh oknm cpf ycvgt = 7z 17z : 12 12 = 7 17 qt 7 : 17 ;7. (d) Ngv gcej swguvkqp ectt{ z octmu. Ceeqtfkpi vq swguvkqp Þ 50 8z 40 100 ´ = 40 z 10 4 = = Pwodgtu qh swguvkqp kp vjg vguv = 100 10 10 = ;8. (f) Ngv vjg uqp”u cig = z Cig qh Hcvjgt = 9z Cig qh Oqvjgt = 8z Pqy, Ceeqtfkpi vq swguvkqp 8z + 9z = 51 Þ 17z = 51 z = 3 {gctu ;9. (c) Ngv vjg Kpeqog qh Rgvgt cpf Rcwn ctg 4z cpf 3z Ngv vjg Gzrgpugu qh Rgvgt cpf Rcwn ctg 3{ cpf 2{ Uq, Ceeqtfkpi vq swguvkqp 4z ˜ 3{ = 6000 ... (k) 3z ˜ 2{ = 6000 ... (kk) Pqy, Htqo gswcvkqp (k) cpf gswcvkqp (kk) 4z ˜ 3{ = 3z ˜ 2{ \ z = { Þ { = z Pqy, rwv vjg xcnwg qh { kp gswcvkqp (k), yg igv Þz = 6000 \ 4z = 24000 3z = 18000 Oqpvjn{ Kpeqogu qh Rgvgt cpf Rcwn ctg ` 24000 cpf ` 18000 tgurgevkxgn{. Uqn. ;: & ;;. E A C B/D F D/B 22 21 20 19 18 17 ;:. (d) H ku 18 {gctu qnf. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 58 ;;. (d) Vyq qtfgtu ku rquukdng kp kpetgcukpi cig. 100. (f) Ngv “i” dg vjg equv qh iqcvu. 4i < Eqy < 5i Pqy, Ikxgp c iqcv rtkeg = ` 600 2400 < Eqy < 3000 ... (k) Ikxgp, c iqcv rtkeg = ` 800 3200 < Eqy < 4000 ... (kk) Jgpeg, kv ecp dg uggp vjcv htqo cdqxg gswcvkqpu vjcv eqy equv ku dgvyggp ` 2400 cpf ` 4000. 101.(e) Ngv kpkvkcn rqrwncvkqp dg100 Ogp Yqogp ¯ 60% ¯ 40% 60 40 ¯ 70% ¯ 75% 42 30 ¯ 80% ¯ 70% 33 21 Kv ku engct vjcv oqtg ogp engctgf vjg gzcokpcvkqp vjcp yqogp. 104. (c) Ikxgp, ngpivj = z1o cpf dtgcfvj = z2o Cnuq, z1 + z2 = 40 yjgtg z1 cpf z2 ctg xctkcdngu Yg mpqy vjcv, qh cnn vjg tgevcpingu, c uswctg jcu vjg nctiguv ctgc. Hqt vjg ikxgp tgevcping vq dg c uswctg z1 = z2 Uq, z1 + z2 = 40 Þ z1 = z2 = 20 o \ Oczkowo ctgc qh vjg ikxgp tgevcping = z1 z2 = (20 Ù 20)o2 = 400 o2 105. (d) Ngv z1 , z2 , z3 , z4 cpf z5 dg vjg rtgugpv cigu qh vjg hcokn{ eqortkukpi qh 5 ogodgtu 3 {gctu ciq, (z1 + z2 + z3 + z4 + z5 ) ˜ 3 Ù 5 = 80 Þ (z1 + z2 + z3 + z4 + z5 ) ˜ 15 = 80 ...(k) Pqy, ngv vjg cig qh pgy dqtp dcd{ dg z6 . Ikxgp, Cxgtcig cig qh hcokn{ vqfc{ = Cxgtcig cig qh hcokn{ 3 {gctu ciq Þ 12345 (x x x x x ) 15 5 ++++ - 123456 xx xx xx 6 +++++ = Þ 6 80 15 80 x 5 6 + + = ]htqo (k)_ Þ z6 = 1 \ Dcd{”u cig = 1 {gct 106. (f) Ngv vjg dcuke rc{ qh vjg hktuv rgtuqp dg ` z cpf vjcv qh ugeqpf rgtuqp dg ` {. Ceeqtfkpi vq vjg swguvkqp, Goqnwogpv qh dqvj vjg rgtuqpu ctg ucog. Uq, z + 0.65z = { + 0.8{ Þ z(1 + 0.65) = {(1 + 0.8) Þ x 1.8 y 1.65 = Þ x 12 y 11 = qt 12 : 11 107. (d) C rgtuqp ku uvcpfkpi qp vjg hktuv uvgr htqo vjg dqvvqo qh c ncffgt. Pqy, jg jcu vq enkod 4 oqtg uvgru vq tgcej gzcevn{ vjg okffng uvgr, 9 8 7 6 5 4 3 2 1 Middle 4 more steps Step Uq, kv ku engct vjcv vjg ncffgt jcxg 9 uvgru. 108. (d) B A A 5m D C 12m Hki. Xgtvkecn Vtwpm Hki. Dtqmgp Vtwpm Ceeqtfkpi vq r{vjciqtcu vjgqtgo, EF2 = CF2 + CE2 Þ EF2 = 52 + 122 Þ EF2 = 25 144 + Þ EF = 169 = 13 o Pqy, CD = CE + EF (QEF ku vjg dtqmgp rctv qh vjg vtwpm CD vqwejkpi itqwpf cv F) Þ CD = (12 + 13) o = 25 o 109. (e) Ngv vjg yqtm fqpg d{ Tco cpf Uj{co dg T cpf U tgurgevkxgn{. Ikxgp, (T+U)¢u 4 fc{u yqtm = 60 100 qh yqtm Þ (T + U)¢u 1 fc{ yqtm = 60 1 100 4 ´ qh yqtm = 15 100 qh yqtm Chvgt Tco vcmgu ngcxg : U”u 8 fc{u yqtm = 60 1 100 æ ö ç ÷ - è ø qh yqtm = 40 100 qh yqtm Þ U¢u 1 fc{ yqtm 40 1 5 of work of work 100 8 100 ´ = Uq, Tco”u 1 fc{ yqtm = (T + U)¢u 1 fc{ yqtm ˜ U¢u 1 fc{ yqtm = 15 5 100 100 æ ö ç ÷ - è ø qh yqtm = 1 10 qh yqtm_ \ Tco yknn vcmg 10 fc{u vq eqorngvg vjg gpvktg lqd cnqpg. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Arithmetic F 59 10:. (d) D{ nqqmkpi cv cnn vjg qrvkqpu, yg qdugtxg vjcv qrvkqp (d) ku pqv pgeguuctkn{ vtwg. Yg mpqy vjcv, c pwodgt ku fkxkukdng d{ 10 khh kv jcu 0 cv vjg wpkv”u rnceg. (T + U) oc{ qt oc{ pqv jcxg 0 cv vjg wpkv”u rnceg. Vjgtghqtg, kv oc{ qt oc{ pqv dg fkxkukdng d{ 10. Vjwu, kv ku pqv pgeguuctkn{ vtwg. 10;. (c) Htqo 100 vq 199, vjgtg ctg 10 pwodgtu gpfkpi ykvj 2. Vjg{ ctg 102, 112, 122, 132, 142, 152, 162, 172, 182, 192. Cpf htqo 200 vq 300, vjgtg ctg 100 pwodgtu dgikppkpi ykvj 2. Vjg{ ctg 200, 201, 202...,299. \ Vjgtg ctg 110 pwodgtu dgvyggp 100 cpf 300 yjkej gkvjgt dgikp ykvj qt gpf ykvj 2. 110. (f) Y ecp fq 25% qh c yqtm kp 30 fc{u. Þ Y ecp fq 1 4 qh c yqtm kp 30 fc{u \ Y ecp fq vjg eqorngvg yqtm kp 120 fc{u. Z ecp fq 1 4 qh vjg yqtm kp 10 fc{u \ Z ecp fq vjg eqorngvg yqtm kp 40 fc{u. [ ecp fq 40% qh vjg yqtm kp 40 fc{u. Þ [ ecp fq 100% qh vjg yqtm kp 100 fc{u \ [ ecp fq vjg eqorngvg yqtm kp 100 fc{u. \ ecp fq 1 3 qh vjg yqtm kp 13 fc{u. \ \ ecp fq vjg eqorngvg yqtm kp 39 fc{u. Jgpeg, kv ku engct htqo cdqxg tguwnvu vjcv \ yknn eqorngvg vjg yqtm hktuv. 111. (c) Cxgtcig oqpvjn{ kpeqog qh c rgtuqp kp hcokn{ qh 5 = ` 10,000 \ Oqpvjn{ kpeqog qh hcokn{ = ` 10,000 Ù 5 = ` 50,000 Chvgt Kpetgcogpv Kpetgcug kp oqpvjn{ kpeqog qh qpg rgtuqp 1,20,000 10,000 12 = =` Pqy, vjg cxgtcig oqpvjn{ kpeqog qh c rgtuqp kp hcokn{ 50,000 10,000 5 + = = ` 12,000 114. (e) 5m 3m 3m 3m 3m 3m Fkuvcpegu eqxgtgf d{ vjg eqorgvkvqt vq eqnngev vjg crrngu kp vjg dwemgv ctg cu hqnnqyu: 1 uv crrng : 2(5) = 10 o 2 pf crrng : 2(5 + 3) = 16 o 3 tf crrng : 2(5 + 2 Ù 3) = 22 o 4 vj crrng : 2(5 + 3 Ù 3) = 28 o 5 vj crrng : 2(5 + 4 Ù 3) = 34 o 6 vj crrng : 2(5 + 5 Ù 3) = 40 o Vjgtghqtg, vqvcn fkuvcpeg eqxgtgf = 10 + 16 + 22 + 28 + 34 + 40 = 150 o 115. (e) R B Y W Yg mpqy vjcv, ctgc qh c ekteng = pt 2 Uq, Tgf dcpf ctgc = p(0.2)2 = 0.04p Cnn vjg qvjgt vjcp tgf ctg kp vjg hqto qh c tkpi. Uq, Dnwg dcpf ctgc = p((0.3)2 ˜ (0.2)2 ) = p((0.3 ˜ 0.2) (0.3 + 0.2)) = 0.05 p Ukoknctn{, {gnnqy dcpf ctgc = 0.07 p Cpf yjkvg dcpf ctgc = 0.09 p \ Tgswktgf rtqdcdknkv{ ( ) 0.04 0.04 0.05 0.07 0.09 p = +++ p = 0.16 Cnvgtpcvg Ogvjqf< Ctgc qh tgf ekteng = p(20)2 Tcfkwu qh Ctejt{ dqctf = 1 m .50m 2 = Ctgc qh Ctejt{ Dqctf = p(.50)2 R(Î) = 2 2 (.20) 0.400 0.16 .(50) 0.2500 p = = p 116. (e) Octmgf rtkeg (O.R.) qh vq{ = ` 770 Fkueqwpv = 10% qh OR 10 770 77 100 =´= ` Rtkeg chvgt fkueqwpv = ` (770 ˜ 77) = ` 693 Ngv equv rtkeg (E.R.) qh vq{ dg ` z. Ceeqtfkpi vq Swguvkqp, 10 693 – x of x 100 = Þ 693 ˜ z = 0.1 z Þ 1.1 z = 693 Þ z = 630 \ Equv rtkeg qh vjg vq{ = ` 630 OR = 770 UR chvgt fkueqwpv = 90 770 100 ´ ER igvvkpi 10% ickp = 100 90 770 110 100 ´ ´ = 630 117. (c) Encuu uvctv cv 11:00 co Encuu gpfu cv 02:27 ro Uq, fwtcvkqp qh encuu = 3j 27okp = 207 okp Vjgtg yknn dg 4 rgtkqfu. Chvgt gxgt{ rgtkqf, vjgtg yknn dg c 5 okp dtgcm. Jgtg, qpn{ 3 dtgcmu yknn dg vcmgp cu vjgtg ctg qpn{ 4 rgtkqfu cpf gpf qh 4vj rgtkqf ogcpu gpf qh vjg encuu. 4vj dtgcm ku pqv pggfgf vq dg eqpukfgtgf. Uq, fwtcvkqp qh vjg rgtkqfu = 207 ˜ 3Ù5 = 192 okp. \ Vkog cuukipgf vq gcej rgtkqf = 192 48min 4 = . Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 60 118. (f) Xguugn C : 30i uwict okzgf kp 180on ycvgt. Uq, vjg eqpegpvtcvkqp qh uwict kp xguugn C ku 30 g / ml 180 k.g., 1 g / ml 6 . Xguugn D : 40i uwict okzgf kp 280on ycvgt. Uq, vjg eqpegpvtcvkqp qh uwict kp xguugn D ku 40 g / ml 280 k.g., 1 g / ml 7 . Xguugn E : 20i uwict okzgf kp 100on ycvgt. Uq, vjg eqpegpvtcvkqp qh uwict kp xguugn E ku 20 g / ml 100 k.g. 1 g / ml 5 . Oqtg vjg eqpegpvtcvkqp qh uwict, oqtg yknn dg vjg uyggvpguu. Vjgtghqtg, kp vgtou qh uyggvpguu : E @ C @ D 119. (d) Ngv vjg pwodgt qh uvwfgpvu kp vjg encuu dg z. Vqvcn eqnngevkqp ykvjqwv eqpukfgtkpi vjg cffkvkqpcn eqpvtkdwvkqp d{ qpg uvwfgpv = 443 ˜ 2 = ` 441 Uq, z Ù z = 441 Þ z2 = 441 Þ x 441 21 = = 11:. (d) Swguvkqpu eqttgevn{ cpuygtgf d{ Cpkvc ctg cu hqnnqyu: Ctkvjogvke ˜ 70% qh 10 = 7 Cnigdtc ˜ 40% qh 30 = 12 Igqogvt{ ˜ 60% qh 30 = 18 \ Vqvcn swguvkqpu eqttgevn{ cpuygtgf = 7 + 12 + 18 = 37 Cpkvc jcf vq cvvgorv 60% qh 70 swguvkqpu k.g., 42 swguvkqpu eqttgevn{ vq rcuu vjg vguv. \ Pwodgt qh oqtg swguvkqpu tgswktgf vq dg cpuygtgf = 42 ˜ 37 = 5 11;. (d) Jgtg, 3 x 18 4 ´ = z = 24 Dq{u = 24 cpf 2 y 24 3 ´ = { = 36 Vqvcn uvwfgpvu = 36 Vjg pwodgt qh iktnu kp vjg encuu = 36 ˜ 24 =12. 140. (d) Ngv vjg pwodgt qh gornq{ggu kp vjg eqorcp{ dg 100 cpf vjg pwodgt qh ocng gornq{ggu kp vjg eqorcp{ dg z. Uq, vjg pwodgt qh hgocng gornq{ggu = 100 ˜ z. Ceeqtfkpi vq vjg swguvkqp, 5200x 4200(100 x) 5000 100 + - = Þ + -= 52x 42(100 x) 5000 Þ + -= 52x 4200 42x 5000 Þ = Þ= 10x 800 x 80 Uq, vjgtg ctg 80% ocng gornq{ggu kp vjg eqorcp{. 141. (d) Ngv vjg vjktf pwodgt \ = 100 Uq, Z = 80, [ = 72 \ Rgtegpvcig d{ yjkej [ ku nguu vjcp Z 80 72 100 10% 80 - = ´= 144. (f) Rqrwncvkqp qh vjg Eqoowpkv{ chvgt gxgt{ {gct = 2 3 qh vjg rtgxkqwu {gct. Jgpeg, vjg rqrwncvkqp qh vjg eqoowpkv{ chvgt 6 {gct = 6 2 3 æ ö ç ÷ è ø qh vjg qtkikpcn rqrwncvkqp qh vjg Eqoowpkv{. 6 2 64 th 3 729 æ ö = ç ÷ è ø rctv. 145. (d) C + D @ E + F .....(k) C + E = D + F .....(kk) C = B D 2 + Uq, B D C 2 + = qt, C = E ....(kkk) Htqo (k) cpf (kkk) D @ F ....(kx) Wukpi (k), (kk), (kkk) cpf (kx), D @ C = E @ F. Jgpeg, D”u kpeqog ku jkijguv. 146. (d) Fkuvcpeg vtcxgnngf d{ C kp qpg ejcpeg = (6 ˜1) eo = 5 eo Fkuvcpeg vtcxgnngf d{ D kp qpg ejcpeg = (7 ˜ 3) eo = 4 eo Fkuvcpeg vtcxgnngf d{ E kp qpg ejcpeg = (6.5 ˜ 2) eo = 4.5 eo. Jgpeg, Ngpivj qh rknnct C = 5 Ù 39 + 6 = 201 eo Ngpivj qh rknnct D = 4 Ù 39 +7 = 163 eo Ngpivj qh rknnct E = 4.5 Ù 39 + 6.5 = 182 eo Ngpivj qh ujqtvguv rknnct ® D. 163 eo. 147. (e) Tgockpkpi pcogu chvgt vjg tgoqxcn qh hckngf uvwfgpvu = 52 ˜ 15 = 37. Tcoguj”u rqukvkqp htqo vqr = 22. Jgpeg htqo dqvvqo Tcoguj ku (37 + 1 ˜ 22)vj = 16vj. 148. (e) Ngv vjg qtkikpcn rtkeg qh rjqpg = `100 UR qh Iqrcn 110 100 110 100 =´ =` UR qh Tco = 110 ˜ 10% qh 110 = `99 Vqvcn Rtqhkv qh iqrcn = `100 ˜ `99 = 1 Dwv rtqhkv ycu ocfg cu ER jgpeg, 1% rtqhkv 149. (e) Vjg ygkijv qh vjg 5vj rgtuqp = uwo qh hktuv 5 rgtuqp + Uwo qh ncuv hkxg rgtuqp˜ Uwo qh ygkijv qh 9 rgtuqpu. = 5 Ù 45 + 5 Ù 55 ˜ 9 Ù 50 mi = 50 mi Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Arithmetic F 61 14:. (f) Pqpg qh vjg cdqxg uvcvgogpv ku eqttgev. 14;. (d) 12% gctp nguu vjcp ` 30,000. 6% gctp oqtg vjcp ` 2,00,000. 22% gctp oqtg vjcp ` 1,00,000. Uq, dgvyggp b 30,000 ˜ ` 1, 00, 000 vjgtg ctg (100 ˜ 22 ˜ 12)% = 66% jqwugjqnf. 66% jqwugjqnf ku gswcn vq 990 Jgpeg, Pwodgt qh jqwugjqnf = 1500. Pwodgt qh jqwugjqnf dgvyggp 1,00,000 cpf 2,00,000 = 16 1500 240. 100 ´ = 150. (d) Cv 5 Q”enqem vjg enqem yknn uvtkmg 5 vkogu. Kv”u ikxgp vjcv kv vcmgu 12 ugeqpfu vq fq uq. Pqy, cv 10”Q enqem vjg enqem yknn uvtkmg 10 vkogu. Jgpeg, vjg vkog vcmgp d{ kv vq uvtkmg = 12 Ù 2 = 24. 151. (c) Ukpeg 39 ku vjg ogcp qh hktuv hkxg pwodgtu, hktuv hkxg pwodgtu ctg 35 , 37, 39, 41 cpf 43 cpf pgzv 8 pwodgtu ctg 45, 47, 49, 51, 53, 55, 57 cpf 59. Jgpeg, ogcp = (13 1) , 2 + 7vj pwodgt qt okffng pwodgt = 47. 154. (c) Ngv vjg qtkikpcn coqwpv dg 150 on. Ceeqtfkpi vq swguvkqp. 50 on qh okzvwtg + 50on qh rwtg oknm Þ 25 on qh Oknm + 25on qh ycvgt + 50 on qh rwtg oknm. Jgpeg, % qh ycvgt kp pgy okzvwtg = 25 100 25% 100 ´ = . 155. (e) Pwodgt qh uswctgu cpf tgevcpingu kp c 3 Ù 3 itkf = 13 + 23 +33 = 36. 156. (f) Tcpfjkt @ (Mwpcn + Fgdw) ------ ... (k) (Mwpcn + Ujcpmct) @ Tcpfjkt ----- ... (kk) Uqpcn @ Ujcpmct ------ ... (kkk) Pgjc @ Tcpfjkt ------ ... (kx) Htqo (k), (kk), (kkk) cpf (kx) yg ecp pqv eqpenwfg yjq qrvckpgf vjg jkijguv octm jgpeg, Fcvc ctg kpcfgswcvg. 157. (d) Ngv vjg pwodgtu ctg qh vjg hqto cde. Uq, Ceeqtfkpi vq swguvkqp, 100 c + 10d + e = 7M ....(k) 100e + 10d + c = 7o .....(kk) Htqo, (k) ˜ (kk) 99c ˜ 99e = 7 (m˜o) 99 (c ˜ e) = 7p c ˜ e = 7 c = 9, e = 2 c = 8, e = 1 Jgpeg, 4 pwodgtu, 259, 952, 168 cpf 861. 158. (e) ™ ™ 8 Vjgtg ctg 9 xcnwgu (1 vq 9) hqt jwpftgfu rnceg fkikv. Yjkng 10 xcnwgu (0 vq 10) hqt vgp”u rnceg fkikv. Jgpeg, 9 Ù 10 = 90 Pwodgtu. 159. (f) Umgygf vq vjg nghv. 15:. (d) Ot. z”u rtgugpv cig 26, dgecwug 25 ycu c rgthgev uswctg cpf vjg pgzv {gct yqwnf dg c rgthgev ewdg. Pgzv ewdg pwodgt ® 64 Jgpeg, okpkowo {gctu tgswktgf = 64 ˜ 26 = 38 {gctu. 15;. (c) Ngv vjg yqtm fqpg d{ S kp 1 fc{ = z wpkvu. Uq vjg yqtm fqpg d{ R kp 1 fc{ = 3z wpkvu Yqtm fqpg d{ T kp 1 fc{ = 3x x 4 + = z wpkvu Jgpeg, vjg tcvkq qh gctpkpiu = PQ R 3: : xx x = 3 : 1 : 1. 160. (f) 94 fkxkfgf d{ 49 ngcxgu vjg nctiguv tgockpfgt 45. 161. (d) Ngv vjg oqpvjn{ kpeqogu qh z cpf { dg 4z cpf 3z. Uq, 4x – 6000 3 3x – 6000 2 = Þ 8z ˜ 12000 = 9z ˜ 18000 \ z = ` 6,000 Vqvcn kpeqog qh z cpf { = (3 + 4)z = ` 6,000 Ù 7 = ` 42,000 164. (c) 9 = 22 2 (8) (1) (d) + + Þ 81 = 64 + 1 + (f)2 Þ (f)2 = 16 f = 4. 165. (f) Ngv vjg vyq fkikv pwodgtu ctg qh vjg hqto cd. Uq, 10c + d ˜ (10d + c) = 27 Þ 9c ˜ 9d = 27 Þ c ˜ d = 3 (c, d) Þ (9, 6), (8, 5), (7, 4) (6, 3) (4,1), (5, 2) Jgpeg, 96 , 85 , 74 , 63 , 41, 52 cpf 25, 14, 36, 47, 58, 69 ctg vjg tgswktgf pwodgtu. 166. (d) Pwodgt qh fkikvu wugf Hqt 1 ˜ 9 = 9 Ù 1 = 9 Pwodgt qh fkikvu wugf Hqt 10 ˜ 99 = 90 Ù 2 = 180 Pwodgt qh fkikvu wugf hqt 100 ˜ 150 = 51 Ù 3 = 153 Jgpeg, 153 + 180 + 9 = 342 fkikvu. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 62 1. Kp vjg Ectvgukcp rncpg hqwt rqkpvu R, S, T, U jcxg eqqtfkpcvgu (1, 1), (6, 4), (6, 6) cpf (1, 6) tgurgevkxgn{, Vjg ctgc qh vjg swcftkncvgtcn RSTU ku ]1;;7_ U(1, 6) T(6, 6) R(1, 1) S(6, 4) (c) ; (d) 9.7 (e) 6.7 (f) korquukdng vq hkpf wpnguu fkciqpcnu ctg mpqyp vjg ngpivju qh vjg 2. C tgevcpiwnct uwor qh fkogpukqp 8o Ù 7o Ù 6o ku vq dg dwknv d{ wukpi dtkemu vq ocmg vjg qwvgt fkogpukqp 8.4 o Ù 7.4 o Ù 6.4 o. Crrtqzkocvgn{ jqy ocp{ dtkemu qh uk|g 40 eo Ù 10 eo Ù 7 eo ctg tgswktgf vq dwknf vjg uwor hqt uvqtkpi ycvgtA ]1;;7_ (c) 1760: (d) 5000 (e) 17000 (f) 50000 3. Eqpukfgt vjg hkiwtg ikxgp dgnqy< U T R 1 S RSTU ku c uswctg qh ukfg 1 wpkv cpf S, U ctg vjg egpvtgu qh vjg vyq ektengu. Vjg ctgc qh vjg ujcfgf rqtvkqp ku ]1;;7_ (c) 4 p (d) 1 4 (e) 1 6 4 p - (f) 1 4 p - 4. Vjg hqnnqykpi hkiwtg eqpvckpu vjtgg uswctgu ykvj ctgcu qh 100, 18 cpf 6; us. wpkvu tgurgevkxgn{ nc{kpi ukfg d{ ukfg cu ujqyp. D{ jqy owej ujqwnf vjg ctgc qh vjg okffng uswctg dg tgfwegf kp qtfgt vjcv vjg vqvcn ngpivj RS qh vjg tguwnvkpi vjtgg uswctgu ku 1;A ]1;;8_ 100 6; 18 R S (c) 14 (d) 6 (e) 4 (f) 4 5. C tgevcping jcu rgtkogvgt qh 70 ogvtgu. Kh kvu ngpivj ku 15 ogvtgu oqtg vjcp kvu dtgcfvj, vjgp kvu ctgc ku< ]1;;8_ (c) 146 o4 (d) 166 o4 (e) 116 o4 (f) 106 o4 6. Eqpukfgt vjg hqnnqykpi hkiwtgu< ]1;;8_ 6 ; (k) 8 (kk) 8 : (kkk) ; Yjkej qpg qh vjg hqnnqykpi eqpenwukqpu ecp dg ftcyp htqo vjgug hkiwtguA (c) Vjg ctgcu qh vjg vjtgg hkiwtgu ctg cnn fkhhgtgpv (d) Vjg ctgcu qh cnn vjg vjtgg hkiwtgu ctg gswcn (e) Vjg rgtkogvgtu qh vjg vjtgg hkiwtgu ctg gswcn (f) Vjg rgtkogvgtu qh hkiwtgu K cpf KK ctg gswcn 7. Kp vjg hqnnqykpi hkiwtg ]1;;9_ Pqtvj S T R Q Gcuv R ku 500 mo gcuvyctf qh Q cpf S ku 600 mo pqtvj qh Q. T ku gzcevn{ kp vjg okffng qh S cpf R. Vjg fkuvcpeg dgvyggp S cpf T ku (c) 470 mo (d) 500 mo (e) 570 mo (f) 250 2 mo Chapter 3 Geometry
& Mensuration Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Geometry & Mensuration F 63 8. C tgevcpiwnct rnqv qh ncyp ujqyp kp vjg hkiwtg jcu fkogpukqpu 'z' cpf '{' cpf ku uwttqwpfgf d{ c itcxgn rcvjyc{ qh ykfvj 4 o. Yjcv ku vjg vqvcn ctgc qh vjg Itcxgn Rcvjyc{A ]1;;9_ ncyp Itcxgn Rcvjyc{ { z (c) 4z + 4{ + 6 (d) 4z + 4{ + : (e) 6z + 6{ + : (f) 6z + 6{ + 18 9. Kh vjg pwodgtu tgrtgugpvkpi xqnwog cpf uwthceg ctgc qh c ewdg ctg gswcn, vjgp vjg ngpivj qh vjg gfig qh vjg ewdg kp vgtou qh vjg wpkv qh ogcuwtgogpv yknn dg ]1;;9_ (c) 5 (d) 6 (e) 7 (f) 8 10. Vjg ngpivj, dtgcfvj cpf jgkijv qh c tqqo ctg l, d cpf j tgurgevkxgn{. Vjg rgtkogvgt qh vjg egknkpi gzrtguugf cu c rgtegpvcig qh vjg vqvcn ctgc qh vjg hqwt ycnnu, ku ]1;;9_ (c) 100 j % (d) 00 j 1 % (e) j % (f) 100 j % 11. NOPQR ku c ugokekteng ykvj egpvtg cv T cpf fkcogvtg NR. NUT cpf TSR ctg cnuq ugok ektengu ykvj egpvtgu cv V cpf W tgurgevkxgn{ cpf fkcogvgtu NT ? TR ? 1 4 NR. Vjg tcvkq qh rgtkogvgt qh NOPQR cpf NUTSR ku ]1;;:_ N V T W R S Q P O U (c) 0.97 < 1 (d) 1 < 1 (e) 1 < 0.97 (f) 1.47 < 1 12. C uswctg rqpf jcu 4 o ukfgu cpf ku 1o fggr. Kh kv ku vq dg gpnctigf, vjg fgrvj tgockpkpi vjg ucog, kpvq c ektewnct rqpf ykvj vjg fkciqpcn qh vjg uswctg cu fkcogvgt cu ujqyp kp vjg hkiwtg, vjgp yjcv yqwnf dg vjg xqnwog qh gctvj vq dg tgoqxgfA ]1;;:_ 4o 4o (c) (4p ˜ 6) o5 (d) (6p ˜ 6) o5 (e) (6p ˜ 4) o5 (f) (4p ˜ 4) o5 13. Vjg uwthceg ctgc qh urjgtkecn fqog-ujcrgf tqqh qh c e{nkpftkecn ycvgt vcpm ujqyp kp vjg hkiwtg ku ]1;;;_ 40 o E{nkpfgt Fkcogvgt 5 o Urjgtkecn Fqog (c) 80 p o4 (d) 10; p o4 (e) 140 p o4 (f) 500 p o4 14. C jgokurjgtkecn dqyn ku hknngf vq vjg dtko ykvj c dgxgtcig. Vjg eqpvgpvu qh vjg dqyn ctg vtcpuhgttgf kpvq c e{nkpftkecn xguugn yjqug tcfkwu ku 70% oqtg vjcp kvu jgkijv. Kh vjg fkcogvgt ku ucog hqt dqvj dqyn cpf e{nkpfgt, vjgp vjg xqnwog qh vjg dgxgtcig kp vjg e{nkpftkecn xguugn yknn dg ]1;;;_ (c) 4 88 % 5 (d) 9:.7% (e) 100% (f) Oqtg vjcp 100% (vjcv ku, uqog nkswkf yknn uvknn dg nghv kp vjg dqyn) 15. C ocp ku uvcpfkpi qp vjg 8o nqpi rqng yjqug ngpivj qh ujcfqy ku :o. Kh vjg ngpivj qh jku ujcfqy ku 4.6o, yjcv ku vjg jgkijv qh vjg ocp A ]1;;;_ (c) 1.6 o (d) 1.8 o (e) 1.: o (f) 4.0 o 16. Kh vjg cping qh vtkcping ctg kp vjg tcvkq qh 6 < 5 < 4, vjgp vjg vtkcping ]1;;;_ (c) ku qdvwug cpingf vtkcping (d) jcu qpg cping itgcvgt vjcp :0² (e) ku c tkijv vtkcping (f) ku cewvg cpingf vtkcping Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 64 17. Cv c ikxgp vkog, vyq rnc{gtu ctg uvcpfkpi qp c rnc{- hkgnf. Vjg ectvgukcp eqqtfkpcvgu qh vjgkt nqecvkqpu ctg (40, 80) cpf (˜60, ˜40) wpkvu. Yjcv ku vjg fkuvcpeg dgvyggp vjg rnc{gtuA ]1;;;_ (c) 80 wpkvu (d) :0 wpkvu (e) 100 wpkvu (f) 160 wpkvu 18. Vjg ctgc qh cp gnnkrug ku vykeg vjcv qh c ekteng. Vjg oclqt fkcogvgt qh vjg gnnkrug ku vykeg vjcv qh vjg okpqt fkcogvgt. Vjg tcfkwu qh vjg ekteng ku ]1;;;_ (c) 70% qh okpqt fkcogvgt qh vjg gnnkrug (d) 70% qh oclqt fkcogvgt qh vjg gnnkrug (e) okpqt fkcogvgt qh vjg gnnkrug (f) oclqt fkcogvgt qh vjg gnnkrug 19. R 50² 40² Q S T Kp vjg ikxgp hkiwtg Ð QSR ? 50 cpf Ð QTR?40., vjgp Ð SQT ku gswcn vq ]4000_ (c) 100² (d) 140² (e) 150² (f) 160² 20. Yjkej qpg qh vjg hqnnqykpi jcu c itgcvgt rgtkogvgt vjcp vjg tguvA ]4000_ (c) C uswctg ykvj cp ctgc qh 58 us.eo (d) Cp gswkncvgtcn vtkcping ykvj c ukfg qh ; eo (e) C tgevcping ykvj 10 eo cu ngpivj cpf 60 us eo cu ctgc (f) C ekteng ykvj c tcfkwu qh 6 eo 21. C iqcv ku vkgf vq vyq rqngu R cpf S ykvj tqrgu vjcv ctg 17 ogvgtu nqpi. R cpf S ctg 40 ogvtgu crctv cu ujqyp kp vjg ikxgp fkcitco< ]4000_ Iqcv Q 17 o 40 o 17 o R S Yjkej qpg qh vjg hqnnqykpi ujcfgf rqtvkqpu kpfkecvgu vjg vqvcn ctgc qxgt yjkej vjg iqcv ecp itc|gA (c) P Q (d) P Q (e) P Q (f) P Q 22. Yjcv ku vjg oczkowo pwodgt qh rkgegu qh 7 eo Ù 7 eo Ù 10 eo qh ecmg vjcv ecp dg ewv htqo c dki ecmg qh 7eo Ù 50 eo Ù 50 eo uk|gA ]4000_ (c) 10 (d) 17 (e) 1: (f) 50 23. C tgevcpiwnct ycvgt vcpm ogcuwtgu 17o Ù 8o cv vqr cpf ku 10o fggr. Kv ku hwnn qh ycvgt. Kh ycvgt ku ftcyp qwv nqygtkpi vjg ngxgn d{ 1 ogvgt, jqy owej qh ycvgt jcu dggp ftcyp qwvA ]4000_ (c) ;0000 nkvtgu (d) 67000 nkvtgu (e) 6700 nkvtgu (f) ;00 nkvtgu 24. Kp vjg ikxgp hkiwtg, cnn nkpg ugiogpvu qh vjg ujcfgf rqtvkqp ctg qh ucog ngpivj cpf cv tkijv cpingu vq gcej qvjgt. Vjg ucog ecp dg qwv qh c dqctf qh ukfg 10 eo. Yjcv ku vjg ctgc qh vjg ujcfgf rqtvkqpA ]4000_ 10 eo 10 eo (c) 58 eo4 (d) 6: eo4 (e) 74 eo4 (f) 86 eo4 25. C tgevcpiwnct rkgeg qh ktqp ujggv ogcuwtkpi 70 eo d{ 100 eo ku tqnngf kpvq e{nkpfgt qh jgkijv 70 eo. Kh vjg equv qh rckpvkpi vjg e{nkpfgt ku ` 70 rgt uswctg ogvtg, vjgp yjcv yknn dg vjg equv qh rckpvkpi vjg qwvgt uwthceg qh vjg e{nkpfgtA ]4000_ (c) ` 47.00 (d) ` 59.70 (e) ` 97.00 (f) ` :9.70 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Geometry & Mensuration F 65 26. 1 m C ekteng qh 1 o tcfkwu ku ftcyp kpukfg c uswctg cu ujqyp kp hkiwtg ikxgp cdqxg. Yjcv ku vjg ctgc qh vjg ujcfgf rqtvkqp (kp o4 ) A ]4001_ (c) (4 ) - p (d) 1 2 æ ö p ç ÷ - è ø (e) 1 4 4 æ ö p ç ÷ - è ø (f) 1 4 æ ö p ç ÷ - è ø 27. Kp vjg cdqxg hkiwtg, CDEF ku c e{enke swcftkncvgtcn, CD ? DE cpf ÐDCE ? 90², vjgp ÐCFE ku ]4001_ 90² F C D E (c) 60² (d) :0² (e) 110² (f) 160² 28. Vjg ngpivj qh vjg nqpiguv rqng vjcv ecp dg rncegf kp c tqqo 14 o nqpi, ; o ykfg cpf : o jkij, ku ]4004_ (c) 14 o (d) 16 o (e) 19 o (f) 41 o 29. Eqpukfgt vjg xqnwogu qh vjg hqnnqykpi< ]4004_ 1. C rctcnngnqrkrgf qh ngpivj 7 eo, dtgcfvj 5 eo cpf jgkijv 6 eo 4. C ewdg qh gcej ukfg 6 eo 5. C e{nkpfgt qh tcfkwu 5 eo cpf ngpivj 5 eo. 6. C urjgtg qh tcfkwu 5 eo. Vjg xqnwogu qh vjgug kp vjg fgetgcukpi qtfgt ku (c) 1, 5, 4, 6 (d) 6, 4, 5, 1 (e) 1, 4, 5, 6 (f) 6, 5, 4, 1 30. C dki tgevcpiwnct rnqv qh ctgc 6540 o4 ku fkxkfgf kpvq 5 uswctg ujcrgf uocnngt rnqvu d{ hgpekpi rctcnngn vq vjg uocnngt ukfg qh vjg rnqv. Jqygxgt uqog ctgc qh ncpf ycu uvknn nghv cu c uswctg eqwnf pqv dg hqtogf. Uq, 5 oqtg uswctg ujcrgf rnqvu ygtg hqtogf d{ hgpekpi rctcnngn vq vjg nqpigt ukfg qh vjg qtkikpcn rnqv uwej vjcv pq ctgc qh vjg rnqv ycu nghv uwtrnwu. Yjcv ctg vjg fkogpukqpu qh vjg qtkikpcn rnqvA ]4007_ (c) 180 o Ù 49 o (d) 460 o Ù 17 o (e) 140 o Ù 58 o (f) 157 o Ù 54 o 31. Vjg fkcogvgtu qh vyq ektewnct eqkpu ctg kp vjg tcvkq qh 1< 5. Vjg uocnngt eqkp ku, ocfg vq tqnn ctqwpf vjg dkiigt eqkp vknn kv tgvwtpu vq vjg rqukvkqp htqo yjgtg vjg, rtqeguu qh tqnnkpi uvctvgf. Jqy ocp{ vkogu vjg uocnngt eqkp tqnngf ctqwpf vjg dkiigt eqkpA ]4010_ (c) ; (d) 8 (e) 5 (f) 1.7 32. C xknncig jcxkpi c rqrwncvkqp qh 6000 tgswktgu 170 nkvtgu qh ycvgt rgt jgcf rgt fc{. Kv jcu c vcpm ogcuwtkpi 40 o Ù 17 o Ù 8 o. Vjg ycvgt qh vjku vcpm yknn ncuv hqt ]4011 - KK_ (c) 4 fc{u (d) 5 fc{u (e) 6 fc{u (f) 7 fc{u 33. Vyq incuugu qh gswcn xqnwog ctg tgurgevkxgn{ jcnh cpf vjtgg-hqwtvju hknngf ykvj oknm. Vjg{ ctg vjgp hknngf vq vjg dtko d{ cffkpi ycvgt. Vjgkt eqpvgpvu ctg vjgp rqwtgf kpvq cpqvjgt xguugn. Yjcv yknn dg vjg tcvkq qh oknm vq ycvgt kp vjku xguugnA ]4011 - KK_ (c) 1 < 5 (d) 4 < 5 (e) 5 < 4 (f) 7 < 5 34. C ictfgpgt kpetgcugf vjg ctgc qh jku tgevcpiwnct ictfgp d{ kpetgcukpi kvu ngpivj d{ 60% cpf fgetgcukpi kvu ykfvj d{ 40%. Vjg ctgc qh vjg pgy ictfgp ]4016 - KK_ (c) jcu kpetgcugf d{ 40%. (d) jcu kpetgcugf d{ 14%. (e) jcu kpetgcugf d{ :%. (f) ku gzcevn{ vjg ucog cu vjg qnf ctgc. 35. Kp c rncpg, nkpg Z ku rgtrgpfkewnct vq nkpg [ cpf rctcnngn vq nkpg \= nkpg W ku rgtrgpfkewnct vq dqvj nkpgu X cpf Y= nkpg Z ku rgtrgpfkewnct vq nkpg X. ]4017-K_ Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ku eqttgevA (c) \, W cpf Y ctg rctcnngn. (d) Z, X cpf [ ctg rctcnngn. (e) \, X cpf W ctg cnn rgtrgpfkewnct vq Y. (f) [, X cpf Y ctg rctcnngn. 36. C e{nkpftkecn qxgtjgcf vcpm qh tcfkwu 4 o cpf jgkijv 9 o ku vq dg hknngf htqo cp wpfgtitqwpf vcpm qh uk|g 7.7 o Ù 6 o Ù 8 o. Jqy owej rqtvkqp qh vjg wpfgtitqwpf vcpm ku uvknn hknngf ykvj ycvgt chvgt hknnkpi vjg qxgtjgcf vcpm eqorngvgn{A ]4018-KK_ (c) 1/5 (d) 1/4 (e) 1/6 (f) 1/8 37. C rkgeg qh vkp ku kp vjg hqto qh c tgevcping jcxkpi ngpivj 14 eo cpf ykfvj : eo. Vjku ku wugf vq eqpuvtwev c enqugf ewdg. Vjg ukfg qh vjg ewdg ku< (c) 4 eo (d) 5 eo ]4018-KK_ (e) 6 eo (f) 9 eo 38. Vjg qwvgt uwthceg qh c 6 eo Ù 6 eo Ù 6 eo ewdg ku rckpvgf eqorngvgn{ kp tgf. Kv ku unkegf rctcnngn vq vjg hcegu vq {kgnf ukzv{ hqwt 1eo Ù 1eo Ù 1eo uocnn ewdgu. Jqy ocp{ uocnn ewdgu fq not jcxg rckpvgf hceguA ]4019-KK_ (c) : (d) 18 (e) 46 (f) 58 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 66 1. (b) U(1, 6) T(6, 6) R(1, 1) P(1,4) S(6, 4) Ctgc qh vjg Swcftkncvgtcn ? Ctgc ( PSTU) + Ctgc ( RSP) Ctgc ( PSTU) ? PS Ù ST PS ? ( )( ) 4 4 61 44 - +- ? 5 ST ? ( )( ) 4 4 66 64 - +- ? 4 Ctgc ( PSTU) ? 5 Ù 4 ? 8 Ctgc ( RSP) ? 1 4 Ù PR Ù PS PR ? ( )4 4 (1 1) 4 1 - +- ? 1 PS ? ( )4 4 (6 1) 4 4 - +- ? 5 Ctgc ( RSP) ? 1 2 Ù 5 Ù 1? 1.7 \ Pgv ctgc ? 8 + 1.7 ? 9.7 2. (a) Ngv vjg pwodgt qh dtkemu dg p. Pqy, Xqnwog qh qwvgt fkogpukqp qh uwor ˜ xqnwog qh uwor ? xqnwog pggfgf vq dg dwknv d{ vjg dtkemu. ? (8.4 Ù 7.4 Ù 6.4 ˜ 8 Ù 7 Ù 6) ? 17.60: o5 . Xqnwog qh gcej dtkem ? 0.4 Ù 0.1 Ù 0.07 ? 10 Ù 10˜6o5 ? 1 Ù 10˜5o5 . \ (1 Ù 10˜5)p ? 17.60: p ? 5 17.60: 1 10- ´ ? 1760: 3. (d) Ngv wu vcmg vjg nqygt ekteng hktuv. Ctgc qh vjg cte RTS ? ( ) ;0 4 580 ° p ° t ? 1 4 (1) 6 p ? 6 p ctgc ( D RTS) ? 1 4 (1) (1) ? 1 4 \ Ctgc qh ujcfgf rqtvkqp qh vjg nqygt ekteng ? ctgc qh vjg cte RTS ˜ ctgc ( D RTS) ? 1 6 4 p - ? 4 6 p - Ukpeg, dqvj vjg ektengu ctg jcxkpi vjg ucog tcfkwu, uq vjg{ ctg u{oogvtkecn. \ Pgv ujcfgf Ctgc ? 4 4 6 æp- ö ç ÷ è ø ? 4 4 p - ? 1 4 p - 4. (a) Ngv vjg hkpcn ngpivj qh vjg ukfg qh vjg uocnngt uswctg dg c. Pqy, c + 10 + 9 ? 1; c ? 1; ˜ 19 ? 4 \ Ctgc qh vjg uocnngt uswctg ? (4)4 ? 6 \ Fgetgcug kp vjg ctgc qh vjg uocnngt uswctg ? 18 ˜ 6 ? 14 us. wpkvu. 5. (c) Ngv vjg dtgcfvj dg d. Vjgp, ngpivj ? d + 15 Rgtkogvgt ? 70 ? 4(n + d) 4(d + 15 + d) ? 70 d ? 8 o n ? 8 + 15 ? 1; o \ Ctgc ? ngpivj Ù dtgcfvj ? 1; (8) ? 116 o4 6. (b) Ctgc qh (tgevcping) ? ; Ù 6 ? 58 Ctgc qh (uswctg) ? 8 Ù 8 ? 58 Ctgc (vtkcping) ? 1 4 Ù ; Ù : ? 58 \ Ctgc qh cnn vjg vjtgg hkiwtgu ctg gswcn. 7. (a) SR ? ( )( ) 4 4 SQ QR + ? ( )( ) 4 4 600 500 + ? 700 \ ST ? 4 SR ? 470 mo. 8. (d) Ngpivj qh vjg ncyp kpenwfkpi Itcxgn rcvjyc{ ? z + 4 + 4 ? z + 6 Dtgcfvj qh vjg ncyp kpenwfkpi Itcxgn rcvjyc{ ? { + 4 + 4 ? { + 6 \ Ctgc qh vjg ncyp kpenwfkpi qh Itcxgn rcvjyc{ ? (z + 6) ({ + 6) \ Ctgc qh Itcxgn rcvjyc{ ? Ctgc qh vjg ncyp kpenwfkpi Itcxgn rcvjyc{ ˜ Ctgc qh vjg ncyp. ? (z + 6) ({ + 6) ˜ z{ ? 6z + 6{ + 18 9. (d) Ngv vjg ngpivj qh vjg gfig dg c Pqy, c 5 ? 8c 4 c ? 8 10. (b) Vqvcn ctgc qh hqwt ycnnu ? 4j(n+d) Rgtkogvgt qh vjg egknkpi ? 4n + 4d ? 4(n + d) Rgtkogvgt qh vjg egknkpi gzrtguugf kp rgtegpvcig qh vjg Vqvcn ctgc qh vjg hqwt ycnnu ? 4( ) 100 % 4( ) + ´ + n d jn d ? 100 % j HINTS & SOLUTIONS Explanations Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Geometry & Mensuration F 67 11. (b) Ngv NT ? T Rgtkogvgt qh NOPQR ? 4 4 p = p T T Rgtkogvgt qh NUTSR ? Rgtkogvgt qh NUT + Rgtkogvgt qh TSR ? 4 4 p p + =p T T T \ Rgtkogvgt 1<1 æ öp ç ÷ = = è ø p NOPQR T NUTSR T 12. (a) Fkciqpcn qh vjg uswctg ? () () 4 4 4 4 + ? 2 2 Tcfkwu qh vjg ekteng ? 2 2 2 ? 4 \ Xqnwog vq dg tgoqxgf ? (Xqnwog qh vjg ekteng ˜ Xqnwog qh vjg uswctg) ? ( ) ( ) 4 4 1 441 ì ü é ù í ý p ´ - ´´ ê ú î þ ë û ? 4 6 p13. (b) Ngv Tcfkwu qh vjg urjgtg ? to z ? { ? 10 o f ? 4t ˜ 5 \ z Ù { ? e Ù f Þ 10 Ù 10 ? 5(4t ˜ 5) Þ 8t ˜ ; ? 100, Þ 8t ? 10; \ t ? 10; 8 o 40 o e z q f c d { \ Uwthceg ctgc qh urjgtkecn fqog ? m 4 4 10; 6 5 8 10; 10; 4 8 æ ö p ´ ç ÷ è ø = p æ ö ç ÷ è ø 14. (c) Ngv vjg tcfkwu qh jgokurjgtkecn dqyn ? t \ Xqnwog qh jgokurjgtkecn dqyn ? 4 5 5 pt Ngv vjg jgkijv qh e{nkpftkecn xguugn ? j t ? 70 1 100 æ ö ç ÷ + è ø j j ? 4 5 t Xqnwog qh e{nkpftkecn xguugn ? 4 5 4 (4 / 5) 5 p =p tt t Jgpeg, xqnwog qh vjg dgxgtcig kp vjg e{nkpftkecn xguugn ? 5 5 (4 / 5) 100% (4 / 5) p ´ p t t ? 100% 15. (c) C D :o E F 8o 4.6o z G Kp DCDFcpf DGDE, = CD DG DF DE 8 8 10.6 : + = z z ? 1.: o. Yjgtg, z ? jgkijv qh vjg ocp. 16. (d) Ngv vjg cpingu dg 6z, 5z cpf 4 z. 6z + 5z + 4z ? 1:0² z ? 40² \ cpingu ctg :0², 80² cpf 60². 17. (c) C ? (40, 80) cpf D ? (˜60, ˜40) CD ? ( ) ( ) 4 4 é ùé ù 40 60 80 40 -- + -- ë ûë û ? 5800 8600 + ? 10000 ? 100 18. (a) Ngv vjg okpqt fkcogvgt qh gnnkrug ? 4d Oclqt fkcogvgt qh gnnkrug ? 4c ? 4(4d) 4c ? 6d c ? 4d Ngv vjg tcfkwu qh ekteng ? t Pqy, p cd ? 4 p t 4 qt p (4d)d ? 4 p t 4 \ t ? d \ Tcfkwu qh ekteng ? 1 4 Ù okpqt fkcogvgt qh gnnkrug ? 70% qh okpqt fkcogvgt qh cp gnnkrug 19. (a) R 50² 40² Q S T Kp DRQS , ÐRSQ ? ÐQRS ? 50²(Q QR ?QS ? tcfkwu) Kp DRQT , ÐQTR ? ÐTRQ ? 40² ÐTRS ? ÐQRS + ÐTRQ ? 50² + 40² ? 70² \ ÐSQT ? 4 ÐTRS ? 4(70²) ? 100² (Q Cping cv vjg egpvtg ? 4 Ù Cping qh vjg Rgtkogvgt) Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 68 20. (c) (c) Ukfg qh vjg uswctg ? 58 ? 8 eo Rgtkogvgt qh vjg uswctg ? 6(8) ? 46 eo (d) Rgtkogvgt qh vjg vtkcping ? ; + ; + ; ? 49 eo (e) Ctgc qh vjg tgevcping ? 60 nd ? 60 d ? 60 10 ? 6 Rgtkogvgt ? 4(n + d) ? 4(6 + 10) ? 4: eo (f) Rgtkogvgt qh vjg ekteng ? 4pt ? 4(5.16)(6) ? 47.14 eo Engctn{, Rgtkogvgt qh vjg tgevcping ku oczkowo. 21. (c) Yjgp vjg iqcv ku vkgf vq rqng R, vjgp kv yknn oqxg kp vjg hqto qh cp cte. Ukoknctn{, yjgp kv ku vkgf vq rqng S, cickp kv yknn vtcpxgtug cp cte. Qpn{ “e” ku ujqykpi vjg ecug. R S Iqcv 22. (c) Ngv vjg oczkowo pq qh uocnn rkgegu qh ecmg dg p. Pqy, p(7 Ù 7 Ù 10) ? 7 Ù 50 Ù 50 p ? 7 50 50 7 7 10 ´ ´ ´ ´ ? 1: 23. (a) Ycvgt ftcyp qwv ? Kpkvkcn xqnwog qh vjg vcpm ˜ Hkpcn xqnwog qh vjg vcpm ? ]17 Ù 8 Ù 10 ˜ 17 Ù 8 Ù (10 ˜ 1)_ ? 17 Ù 8 Ù (10 ˜ ;) ? ;0 o5 ? ;0000 l 24. (c) O P G H J I N K M L Q R C F D E 10 eo Jgpeg ctgc qh ujcfgf rqtvkqp ? 4 (Ctgc qh uswctg) + 4 (Ctgc qh tgevcping GHIJ KLMN) + Ctgc qh tgevcping CDEF ? 4 (6 + 8 Ù 4) + 10 Ù 4 ? 74 eo4 25. (a) Ngv t cpf j dg vjg tcfkwu cpf jgkijv qh e{nkpfgt tgurgevkxgn{. Ukpeg vjg e{nkpfgt ku ocfg d{ tqnnkpi 100 eo ukfg. \ j ? 70 eo ? 1 4 o cpf 4 100 p =t eo Þ 1 4 = p t o \ Ewtxgf uwthceg ctgc ? 4ptj ? 1 1 4 4 4 p´ ´ p ? 1 4 4 o Equv qh rckpvkpi ? ` 70 rgt o4 \ Vqvcn equv qh rckpvkpi ? 1 70 4 ´ ? ` 47 26. (d) Ukpeg tcfkwu qh ekteng ? 1 o \ Ukfg qh uswctg ? 4o Uq Ctgc qh ekteng ? 2 p(1) ? po4 cpf Ctgc qh uswctg ? 44 ? 6 o4 \ Ctgc qh ujcfgf tgikqp ? 1 6 (Ctgc qh uswctg ˜ Ctgc qh ekteng) ? 1 6 ( 6 - p )o4 ? 1 6 æ pö ç ÷ - è ø o4 27. (d) Kp D CDE, CD ? DE (kuquegngu vtkcping) \ ÐDCE ? ÐDEC ? 90² Pqy, ÐABC + ÐBAC + ÐBCA ? 1:0² ÐABC ? 1:0² ˜ (90² + 90²) ? 60² Cu, CDEF ku c e{enke swcftkncvgtcn cpf uwo qh qrrqukvg cping rcktu ku gswcn vq 1:0² Uq, ÐADC + ÐABC ? 1:0² ÐADC ? 1:0² ˜ 60² ? 160² 28. (c) Ngpivj qh vjg nqpiguv rqng yknn dg rncegf cnqpi vjg fkciqpcn qh vjg tqqo Ngpivj qh vjg fkciqpcn qt rqng ? ( )( )( ) 4 44 ngpivj dtgcfvj jgkijv + + ? ( ) () () 444 14 ; : + + ? 19 o. 29. (d) Xqnwog qh Rctcnngnqrkrgf ? n Ù d Ù j ? 7 Ù 5 Ù 6 ? 80 eo5 Xqnwog qh ewdg ? (ukfg)5 ? 65 ? 86 eo5 Xqnwog qh e{nkpfgt ? 2 pr h ? 5.16 Ù 54 Ù 5 ? :6.9: eo5 Xqnwog qh urjgtg ? 4 3 3 pr ? 6 Ù 5.16 Ù 54 ? 115.06 eo5 Vjgp vjg eqttgev fgetgcukpi qtfgt ku 6, 5, 4, 1. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Geometry & Mensuration F 69 30. (c) z z z z/5 z/5 z Tgswktgf ctgc ? 5(z)(z) + 5 3 æ ö x ç ÷ è ø 3 æ ö x ç ÷ è ø 5z 4 + 2 3 9 x ? 6540 z ? 58 o Qvjgt fkogpukqp ? 5z + 3 x ? 5(58) + 36 3 ? 140 o 31. (c) Rgtkogvgt qh dkiigt eqkp < Rgtkogvgt qh uocnngt eqkp ? 4p(5) < 4p(1) ? 5 < 1 Jgpeg, uocnngt eqkp yknn tqnn 5 vkogu ctqwpf vjg dkiigt eqkp. 32. (d) Xqnwog qh vcpm ? 40 ´ 17 ´ 8 o5 ? 40 ´ 17 ´ 8 ´ 1000 nkvtg \ Vjg ycvgt qh vjg vcpm yknn ncuv hqt 40 17 8 1000 170 6000 ´ ´´ ´ fc{u. k.g. Vjg ycvgt qh vjg vcpm yknn ncuv hqt 5 fc{u. 33. (d) Oknm kp 1uv Incuu ? 1 2 V Oknm kp 4pf Incuu ? 3 4 V Pqy vjg 1uv incuu ? 1 2 V Pqy vjg 4pf incuu ? 1 4 V Yjgp dqvj incuugu ctg okzgf vjgp vjg tcvkq qh oknm vq ycvgt 1 3 2 4 + < 1 1 2 4 + ? 2 321 : 4 4 + + ? 7 < 5 34. (b) Ngv kpkvkcn fkogpukqpu dg, l & d \ Hkpcn ngpivj ku 1.6 n Hkpcn dtgcfvj ku 0.: d \ Hkpcn ctgc ku ? 1.6 n Ù 0.: d ? 1.14 nd \ Ctgc ku kpetgcugf d{ 14%. Ujqtvewv Ogvjqf < + 60 ˜ 40 + 40 20 ( ) 100 ´ - ? 40 ˜ : ? 14% Vjgtghqtg, vjg ctgc qh vjg pgy ictfgp kpetgcugf d{ 14% 35. (d) Z \ Y [ X W W Htqo cdqxg fkcitco, kv ku engct vjcv [, X cpf Y ctg rctcnngn. 36. (a) Xqnwog qh e{nkpftkecn qxgtjgcf vcpm ? pt 4j ? 22 2 (2) 7 7 ´ ´ ? :: o5 Xqnwog qh wpfgtitqwpf vcpm ? (7.7 Ù 6 Ù 8)o5 ? 154o5 Rqtvkqp qh wpfgtitqwpf vcpm uvknn hknngf ykvj ycvgt chvgt hknnkpi vjg qxgtjgcf vcpm eqorngvgn{. Volumeof underground tank – Volumeof overhead tank Volumeof underground tank = 132 88 44 1 132 32 3 - = == 37. (c) Ctgc qh tgevcping ? 14 Ù : eo4 ? ;8 eo4 Tgevcping ku wugf vq eqpuvtwev c enqugf ewdg. Uwthceg ctgc qh ewdg hqtogf ? Ctgc qh ikxgp tgevcping. 8 (ukfg)4 ? ;8 eo4 Þ ukfg ? 16 Þ ukfg ? 6 eo. 38. (a) Pwodgt qh Eqnqwt nguu ewdgu ? (6 ˜ 4)5 ? :. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 70 1. C uvwfgpv jcu 80% ejcpeg qh rcuukpi kp Gpinkuj cpf 76% ejcpeg qh rcuukpi kp dqvj Gpinkuj cpf Ocvjgocvkeu. Yjcv ku vjg rgtegpvcig rtqdcdknkv{ vjcv jg yknn hckn kp OcvjgocvkeuA [1995] (c) 14 (d) 58 (e) 6 (f) 10 2. C vcdng jcu vjtgg ftcygtu. Kv ku mpqyp vjcv qpg qh vjg ftcygtu eqpvckpu vyq uknxgt eqkpu, cpqvjgt eqpvckpu vyq iqnf eqkpu cpf vjg vjktf qpg eqpvckpu c uknxgt eqkp cpf iqnf eqkp. Qpg qh vjg ftcygtu ku qrgpgf cv tcpfqo cpf c eqkp ku ftcyp. Kv ku hqwpf vq dg c uknxgt eqkp. Yjcv ku vjg rtqdcdknkv{ vjcv vjg qvjgt eqkp kp vjg ftcygt ku c iqnf eqkpA [1995] (c) 0.47 (d) 1.00 (e) 0.70 (f) 0.80 3. Z cpf [ ctg vyq xctkcdngu yjqug xcnwgu cv [ vkog ctg tgncvgf vq gcej qvjgt cu ujqyp kp Hki. (k). Z ku mpqyp vq xct{ rgtkqfkecnn{ ykvj tghgtgpeg vq vkog cu ujqyp kp Hki. (kk) Hkiwtg (k) Hkiwtg (kk) [ Z Q Z Q v Yjkej qh vjg hqnnqykpi ewtxgu fgrkevu eqttgevn{ vjg fgrgpfgpeg qh [ qp vkogA [1995] (c) [ Q v (d) [ Q v (e) [ Q v (f) [ Q v 4. Vyq rcemu qh ectfu ctg vjqtqwijn{ okzgf cpf ujwhhngf cpf vyq ectfu ctg ftcyp cv tcpfqo, qpg chvgt vjg qvjgt. Yjcv ku vjg rtqdcdknkv{ vjcv dqvj qh vjgo ctg lcemuA [1996] (c) 1/15 (d) 4/15 (e) 9/155; (f) 1/18; 5. Kp vjg ikxgp hkiwtg, kh STU ku cp gswkncvgtcn vtkcping cpf VSU ku cp kuquegngu vtkcping cpf x ? 69², vjgp vjg xcnwg qh y (kp fgitggu) yknn dg [1997] T V [ Z S U (c) 15² (d) 45² (e) 55² (f) 55² Chapter 4 Permutation, Combination
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Permutation, Combination & Probability F 71 8. Yjgp vjtgg eqkpu ctg vquugf vqigvjgt, vjg rtqdcdknkv{ vjcv cnn eqkpu jcxg vjg ucog hceg wr, ku ]1;;9_ (c) 1 5 (d) 1 8 (e) 1 : (f) 1 14 9. Kp c hcevqt{ swcnkv{ cuuwtcpeg vguv ku eqpfwevgf qp xctkqwu ucorngu hqt c urgekhke ejctcevgtkuvke xcnwg qh vjg rtqfwev. Vjg xcnwgu cpf vjg pwodgt qh ucorngu ctg cu ikxgp kp vjg hqnnqykpi vcdng< ]1;;;_ Ejctcevgtkuvke xcnwg, Z Pq. qh Ucorngu 10 5 11 9 14 10 15 17 16 4: 17 55 18 46 19 11 1: 10 1; 8 40 5 Eqpukfgt vjg hqnnqykpi uvcvgogpvu dcugf qp vjg vcdng< 1. Vjg rtqdcdknkv{ vjcv Z £ 17 ku 0.86 4. Vjg rtqdcdknkv{ vjcv 15 19 < £ Z ku itgcvgt vjcp 0.86 5. Vjg rtqdcdknkv{ vjcv Z ? 17 ku nguu vjcp 0.44 Yjkej qh vjg cdqxg uvcvgogpvu ku/ctg pqv vtwgA (c) 1 cnqpg (d) 1 cpf 4 (e) 4 cpf 5 ( f) 1, 4 cpf 5 :. C dci eqpvckpu 40 dcnnu, : dcnnu ctg itggp, 9 ctg yjkvg cpf 7 ctg tgf. Yjcv ku okpkowo pwodgt qh dcnnu vjcv owuv dg rkemgf wr htqo vjg dci dnkpf-hqnfgf (ykvjqwv tgrncekpi cp{ qh kv) vq dg cuuwtgf qh rkemkpi cvngcuv qpg dcnn qh gcej eqnqwtA ]4000_ (c) 6 (d) 9 (e) 11 (f) 18 ;. C eqorngvg e{eng qh c vtchhke nkijv vcmgu 80 ugeqpfu. Fwtkpi gcej e{eng vjg nkijv ku itggp hqt 47 ugeqpfu, {gnnqy hqt 7 ugeqpfu cpf tgf hqt 50 ugeqpfu. Cv c tcpfqon{ ejqugp vkog, vjg rtqdcdknkv{ vjcv vjg nkijv yknn pqv dg itggp, ku ]4004_ (c) 1/5 (d) 1/6 (e) 7/14 (f) 9/14 10. Vjtgg hnciu, gcej qh fkhhgtgpv eqnqwt, ctg cxckncdng hqt c oknkvct{ gzgtekug. Wukpi vjgug hnciu, fkhhgtgpv eqfgu ecp dg igpgtcvgf d{ ycxkpi ]4005_ (k) ukping hnci qh fkhhgtgpv eqnqwtu qt (kk) cp{ vyq hnciu kp c fkhhgtgpv ugswgpeg qh eqnqwt Qt (kkk) vjtgg hnciu kp c fkhhgtgpv ugswgpeg qh eqnqwtu. Vjg oczkowo pwodgt qh eqfgu vjcv ecp dg igpgtcvgf, ku (c) 8 (d) ; (e) 17 (f) 1: 11. C vyq ogodgt eqookvvgg eqortkukpi qh qpg ocng cpf qpg hgocng ogodgt ku vq dg eqpuvkvwvgf qwv qh hkxg ocngu cpf vjtgg hgocngu. Coqpiuv vjg hgocngu, Otu. C tghwugf vq dg c ogodgt qh vjg eqookvvgg kp yjkej Ot. D ku vcmgp cu vjg ogodgt. Kp jqy ocp{ fkhhgtgpv yc{u ecp vjg eqookvvgg dg eqpuvkvwvgfA ]4005_ (c) 11 (d) 14 (e) 15 (f) 16 14. Kp c swguvkqp qh c vguv rcrgt, vjgtg ctg hkxg kvgou gcej wpfgt Nkuv-C cpf Nkuv-D. Vjg gzcokpggu ctg tgswktgf vq ocvej gcej kvgo wpfgt Nkuv-C ykvj kvu eqttgurqpfkpi eqttgev kvgo wpfgt Nkuv-D. Hwtvjgt, kv ku ikxgp vjcv (k) pq gzcokpgg jcu ikxgp vjg eqttgev cpuygt. (kk) cpuygtu qh pq vyq gzcokpggu ctg kfgpvkecn Yjkej ku vjg oczkowo pwodgt qh gzcokpggu yjq vqqm vjku vguvA ]4006_ (c) 46 (d) 48 (e) 11; (f) 14; 15. Pkpg fkhhgtgpv ngvvgtu ctg vq dg ftqrrgf kp vjtgg fkhhgtgpv ngvvgt dqzgu. Kp jqy ocp{ fkhhgtgpv yc{u ecp vjku dg fqpgA ]4006_ (c) 49 (d) 5; (e) ;4 (f) 5; ˜5 16. Kp jqy ocp{ fkhhgtgpv yc{u ecp ukz rnc{gtu dg cttcpigf kp c nkpg uwej vjcv vyq qh vjgo, Clkv cpf Owmjgtlgg, ctg pgxgt vqigvjgtA ]4006_ (c) 140 (d) 460 (e) 580 (f) 6:0 17. Vjtgg uvwfgpvu ctg rkemgf cv tcpfqo htqo c uejqqn jcxkpi c vqvcn qh 1000 uvwfgpvu. Vjg rtqdcdknkv{ vjcv vjgug vjtgg uvwfgpvu yknn jcxg kfgpvkecn fcvg cpf oqpvj qh vjgkt dktvj, ku ]4006_ (c) 5 1000 (d) 5 587 (e) 4 1 (587) (f) Pqpg qh vjgug 18. Qp c tcknyc{ tqwvg dgvyggp vyq rncegu C cpf D, vjgtg ctg 40 uvcvkqpu qp vjg yc{. Kh 6 pgy uvcvkqpu ctg vq dg cffgf, jqy ocp{ v{rgu qh pgy vkemgvu yknn dg tgswktgf kh gcej vkemgv ku kuuwgf hqt c qpg yc{ lqwtpg{A ]4007_ (c) 16 (d) 6: (e) ;8 (f) 10: 19. 4 ogp cpf 1 yqogp dqctf c dwu kp yjkej 7 ugcvu ctg xcecpv. Qpg qh vjgug hkxg ugcvu ku tgugtxgf hqt ncfkgu. C yqogp oc{ qt oc{ pqv ukv qp vjg ugcv tgugtxgf hqt ncfkgu dwv c ocp ecp pqv ukv qp vjg ugcv tgugtxgf hqt ncfkgu. Kp jqy ocp{ fkhhgtgpv yc{u ecp vjg hkxg ugcvu qeewrkgf d{ vjgug rcuugpigtuA ]4007_ (c) 17 (d) 58 (e) 6: (f) 80 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 72 1:. C uswctg ku fkxkfgf kpvq ; kfgpvkecn uocnngt uswctgu. Ukz kfgpvkecn dcnnu ctg vq dg rncegf kp vjgug uocnngt uswctg uwej vjcv gcej qh vjg vjtgg tqyu igvu cv ngcuv qpg dcnn (qpg dcnn kp qpg uswctg qpn{). Kp jqy ocp{ fkhhgtgpv yc{u ecp vjku dg fqpgA ]4007_ (c) 49 (d) 58 (e) 76 (f) :1 1;. Vjgtg ctg 10 kfgpvkecn eqkpu cpf gcej qpg qh vjgo jcu “J” gpitcxgf qp kvu qpg hceg cpf “V” gpitcxgf qp kvu qvjgt hceg. Vjgug 10 eqkpu ctg n{kpi qp c vcdng cpf gcej qpg qh vjgo jcu “J” hceg cu vjg wrrgt hceg. Kp qpg cvvgorv, gzcevn{ hqwt (pgkvjgt oqtg pqt nguu) eqkpu ecp dg vwtpgf wrukfg fqyp. Yjcv ku vjg okpkowo vqvcn pwodgt qh cvvgorvu kp yjkej vjg “V” hcegu qh cnn vjg 10 eqkpu ecp dg dtqwijv vq dg vjg wrrgt hceguA ]4007_ (c) 6 (d) 9 (e) : (f) Pqv rquukdng 40. Vgp kfgpvkecn rctvkengu ctg oqxkpi tcpfqon{ kpukfg c enqugf dqz. Yjcv ku vjg rtqdcdknkv{ vjcv cv cp{ ikxgp rqkpv qh vkog cnn vjg vgp rctvkengu yknn dg n{kpi kp vjg ucog jcnh qh vjg dqzA ]4007_ (c) 1 4 (d) 1 7 (e) ; 1 4 (f) 4 11 41. Gcej qh vyq yqogp cpf vjtgg ogp ku vq qeewr{ qpg ejckt qwv qh gkijv ejcktu, gcej qh yjkej pwodgtgf htqo 1 vq :. Hktuv, yqogp ctg vq qeewr{ cp{ vyq ejcktu htqo vjqug pwodgtgf 1 vq 6= cpf vjgp vjg vjtgg ogp yqwnf qeewr{ cp{, vjtgg ejcktu qwv qh vjg tgockpkpi ukz ejcktu. Yjcv ku vjg oczkowo pwodgt qh fkhhgtgpv yc{u kp yjkej vjku ecp dg fqpgA ]4008_ (c) 60 (d) 154 (e) 1660 (f) 5880 44. Kp c vqwtpcogpv, gcej qh vjg rctvkekrcpvu ycu vq rnc{ qpg ocvej cickpuv gcej qh vjg qvjgt rctvkekrcpvu. Vjtgg rnc{gtu hgnn knn chvgt gcej qh vjgo jcf rnc{gf vjtgg ocvejgu cpf jcf vq ngcxg vjg vqwtpcogpv. Yjcv ycu vjg vqvcn pwodgt qh rctvkekrcpvu cv vjg dgikppkpi, kh vjg vqvcn pwodgt qh ocvejgu rnc{gf ycu 97A ]4008_ (c) 0: (d) 10 (e) 14 (f) 17 45. Vjgtg ctg vjtgg rctcnngn uvtckijv nkpgu. Vyq rqkpvu, 'C' cpf 'D', ctg octmgf qp vjg hktuv nkpg, rqkpvu, 'E' cpf 'F' ctg octmgf qp vjg ugeqpf nkpg= cpf rqkpvu, 'G' cpf 'H', ctg octmgf qp vjg vjktf nkpg. Gcej qh vjgug 8 rqkpvu ecp oqxg vq cp{ rqukvkqp qp kvu tgurgevkxg uvtckijv nkpg. ]4008_ Eqpukfgt vjg hqnnqykpi uvcvgogpvu< 1. Vjg oczkowo pwodgt qh vtkcpingu vjcv ecp dg ftcyp d{ lqkpkpi vjgug rqkpvu ku 1:. 4. Vjg okpkowo pwodgt qh vtkcpingu vjcv ecp dg ftcyp d{ lqkpkpi vjgug rqkpvu ku |gtq. Yjkej qh vjg uvcvgogpv(u) ikxgp cdqxg ku/ctg eqttgevA (c) 1 qpn{ (d) 4 qpn{ (e) Dqvj 1 cpf 4 (f) Pgkvjgt 1 pqt 4 46. C okzgf fqwdngu vgppku icog ku vq dg rnc{gf dgvyggp vyq vgcou (gcej vgco eqpukuvu qh qpg ocng cpf qpg hgocng.) Vjgtg ctg hqwt octtkgf eqwrngu. Pq vgco ku vq eqpukuv qh c jwudcpf cpf jku ykhg. Yjcv ku vjg oczkowo pwodgt qh icogu vjcv ecp dg rnc{gfA ]4008_ (c) 14 (d) 41 (e) 58 (f) 64 47. 5 fkikvu ctg ejqugp cv tcpfqo htqo 1,4,5,6,7,8,9,: cpf ; ykvjqwv tgrgcvkpi cp{ fkikv. Yjcv ku vjg rtqdcdknkv{ vjcv vjgkt rtqfwev ku qffA ]4008_ (c) 4/5 (d) 7/10: (e) 7/64 (f) :/64 48. Kp c swguvkqp rcrgt, vjgtg ctg hqwt ownvkrng ejqkeg v{rg swguvkqpu. Gcej swguvkqp jcu hkxg ejqkegu ykvj qpn{ qpg ejqkeg hqt kvu eqttgev cpuygt. Yjcv ku vjg vqvcn pwodgt qh yc{u kp yjkej c ecpfkfcvg yknn pqv igv cnn vjg hqwt cpuygtu eqttgevA ]4008_ (c) 1; (d) 140 (e) 846 (f) 1046 49. Gcej qh gkijv kfgpvkecn dcnnu ku vq dg rncegf kp vjg uswctgu ujqyp kp vjg hkiwtgu ikxgp dgnqy kp c jqtk|qpvcn fktgevkqp uwej vjcv qpg jqtk|qpvcn tqy eqpvckpu ukz dcnnu cpf vjg qvjgt jqtk|qpvcn tqy eqpvckpu vyq dcnnu. Kp jqy ocp{ oczkowo fkhhgtgpv yc{u ecp vjku dg fqpgA ]4008_ (c) 5: (d) 4: (e) 18 (f) 16 4:. Gcej qh vjg 5 rgtuqpu ku vq dg ikxgp uqog kfgpvkecn kvgou uwej vjcv rtqfwev qh vjg pwodgtu qh kvgou tgegkxgf d{ gcej qh vjg vjtgg rgtuqpu ku gswcn vq 50. Kp jqy ocp{ oczkowo fkhhgtgpv yc{u ecp vjku fkuvtkdwvkqp dg fqpgA ]4009_ (c) 41 (d) 46 (e) 49 (f) 55 4;. Kp vjg hkiwtg ujqyp dgnqy, yjcv ku vjg oczkowo pwodgt qh fkhhgtgpv yc{u kp yjkej : kfgpvkecn dcnnu ecp dg rncegf kp vjg uocnn vtkcpingu 1, 4, 5 cpf 6 uwej vjcv gcej vtkcping eqpvckpu cv ngcuv qpg dcnnA ]4009_ 4 5 6 1 (c) 54 (d) 57 (e) 66 (f) 78 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Permutation, Combination & Probability F 73 50. Cokv jcu hkxg htkgpfu< 5 iktnu cpf 4 dq{u. Cokv”u ykhg cnuq jcu 7 htkgpfu< 5 dq{u cpf 4 iktnu. Kp jqy ocp{ oczkowo pwodgt qh fkhhgtgpv yc{u ecp vjg{ kpxkvg 4 dq{u cpf 4 iktnu uwej vjcv vyq qh vjgo ctg Cokv”u htkgpfu cpf vyq ctg jku ykhg”uA ]4009_ (c) 46 (d) 5: (e) 68 (f) 7: 51. Hkxg dcnnu qh fkhhgtgpv eqnqwtu ctg vq dg rncegf kp vjtgg fkhhgtgpv dqzgu uwej vjcv cp{ dqz eqpvckpu cv ngcuv qpg dcnn. Yjcv ku vjg oczkowo pwodgt qh fkhhgtgpv yc{u kp yjkej vjku ecp dg fqpgA ]4009_ (c) ;0 (d) 140 (e) 170 (f) 1:0 54. Cnn vjg ukz ngvvgtu qh vjg pcog UCEJKP ctg cttcpigf vq hqto fkhhgtgpv yqtfu ykvjqwv tgrgcvkpi cp{ ngvvgt kp cp{ qpg yqtf. Vjg yqtfu uq hqtogf ctg vjgp cttcpigf cu kp c fkevkqpct{. Yjcv yknn dg vjg rqukvkqp qh vjg yqtf UCEJKP kp vjcv ugswgpegA ]4009_ (c) 658 (d) 7;0 (e) 801 (f) 971 55. Vjtgg fkeg (gcej jcxkpi ukz hcegu ykvj gcej hceg jcxkpi qpg pwodgt htqo 1 vq 8) ctg tqnngf. Yjcv ku vjg pwodgt qh rquukdng qwveqogu uwej vjcv cv ngcuv qpg fkeg ujqyu vjg pwodgt 4A ]4009_ (c) 58 (d) :1 (e) ;1 (f) 118 56. Kp jqy ocp{ oczkowo fkhhgtgpv yc{u ecp 5 kfgpvkecn dcnnu dg rncegf kp vjg 14 uswctgu (gcej dcnn vq dg rncegf kp vjg gzcev egpvtg qh vjg uswctgu cpf qpn{ qpg dcnn ku vq dg rncegf kp qpg uswctg) ujqyp kp vjg hkiwtg ikxgp dgnqy uwej vjcv vjg{ fq pqv nkg cnqpi vjg ucog uvtckijv nkpgA ]4009_ (c) 166 (d) 400 (e) 406 (f) 418 57. Itqwru gcej eqpvckpkpi 5 dq{u ctg vq dg hqtogf qwv qh 7 dq{u - C, D,E, F cpf G uwej vjcv pq qpg itqwr eqpvckpu dqvj E cpf F vqigvjgt. Yjcv ku vjg oczkowo pwodgt qh uwej fkhhgtgpv itqwruA ]4009_ (c) 7 (d) 8 (e) 9 (f) : 58. Kp jqy ocp{ fkhhgtgpv yc{u ecp hqwt dqqmu C, D, E cpf F dg cttcpigf qpg cdqxg cpqvjgt kp c xgtvkecn qtfgt uwej vjcv vjg dqqmu C cpf D ctg pgxgt kp eqpvkpwqwu rqukvkqpA ]400:_ (c) ; (d) 14 (e) 16 (f) 1: 59. C uejqqnvgcejgt jcu vq ugngev vjg oczkowo rquukdng pwodgt qh fkhhgtgpv itqwru qh 5 uvwfgpvu qwv qh c vqvcn qh 8 uvwfgpvu. Kp jqy ocp{ itqwru cp{ rctvkewnct uvwfgpv yknn dg kpenwfgfA ]400:_ (c) 8 (d) : (e) 10 (f) 14 5:. Kp jqy ocp{ fkhhgtgpv yc{u ecp cnn qh 7 kfgpvkecn dcnnu dg rncegf kp vjg egnnu ujqyp dgnqy uwej vjcv gcej tqy eqpvckpu cv ngcuv 1 dcnnA ]400:_ (c) 86 (d) :1 (e) :6 (f) 10: 5;. Vjgtg ctg 8 fkhhgtgpv ngvvgtu cpf 8 eqttgurqpfkpin{ cfftguugf gpxgnqrgu. Kh vjg ngvvgtu ctg tcpfqon{ rwv kp vjg gpxgnqrgu, yjcv ku vjg rtqdcdknkv{ vjcv gzcevn{ 7 ngvvgtu iq kpvq vjg eqttgevn{ cfftguugf gpxgnqrguA ]400:_ (c) \gtq (d) 1/8 (e) 1 2 (f) 7/8 60. Vjgtg ctg vyq kfgpvkecn tgf, vyq kfgpvkecn dncem cpf vyq kfgpvkecn yjkvg dcnnu. Kp jqy ocp{ fkhhgtgpv yc{u ecp vjg dcnnu dg rncegf kp vjg egnnu (gcej egnn vq eqpvckp qpg dcnn) ujqyp dgnqy uwej vjcv dcnnu qh vjg ucog eqnqwt fq pqv qeewr{ cp{ vyq eqpugewvkxg egnnuA ]400:_ (c) 17 (d) 1: (e) 46 (f) 50 61. C rgtuqp jcu 6 eqkpu gcej qh fkhhgtgpv fgpqokpcvkqp. Yjcv ku vjg pwodgt qh fkhhgtgpv uwou qh oqpg{ vjg rgtuqp ecp hqto (wukpi qpg qt oqtg eqkpu cv c vkog)A ]400;_ (c) 18 (d) 17 (e) 14 (f) 11 64. Jqy ocp{ pwodgtu nkg dgvyggp 500 cpf 700 kp yjkej 6 eqogu qpn{ qpg vkogA ]400;_ (c) ;; (d) 100 (e) 110 (f) 140 65. Jqy ocp{ vjtgg-fkikv pwodgtu ecp dg igpgtcvgf htqo 1, 4, 5, 6, 7, 8, 9, :, ; uwej vjcv vjg fkikvu ctg kp cuegpfkpi qtfgtA ]400;_ (c) :0 (d) :1 (e) :5 (f) :6 66. Kp c ecttqo dqctf icog eqorgvkvkqp, o dq{u cpf p iktnu (o @ p @ 1) qh c uejqqn rctvkekrcvg kp yjkej gxgt{ uvwfgpv jcu vq rnc{ gzcevn{ qpg icog ykvj gxgt{ qvjgt uvwfgpv. Qwv qh vjg vqvcn icogu rnc{gf, kv ycu hqwpf vjcv kp 441 icogu qpg rnc{gt ycu c dq{ cpf vjg qvjgt rnc{gt ycu c iktn. ]400;_ Eqpukfgt vjg hqnnqykpi uvcvgogpvu< 1. Vjg vqvcn pwodgt qh uvwfgpvu vjcv rctvkekrcvgf kp vjg eqorgvkvkqp ku 50. 4. Vjg pwodgt qh icogu kp yjkej dqvj rnc{gtu ygtg iktnu ku 9:. Yjkej qh vjg uvcvgogpvu ikxgp cdqxg ku/ctg eqttgevA (c) 1 qpn{ (d) 4 qpn{ (e) Dqvj 1 cpf 4 (f) Pgkvjgt 1 pqt 4 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 74 67. C swguvkqp rcrgt jcf vgp swguvkqpu. Gcej swguvkqp eqwnf qpn{ dg cpuygtgf cu Vtwg (V) qt Hcnug (H). Gcej ecpfkfcvg cpuygtgf cnn vjg swguvkqpu. [gv, pq vyq ecpfkfcvgu ytqvg vjg cpuygtu kp cp kfgpvkecn ugswgpeg. Jqy ocp{ fkhhgtgpv ugswgpegu qh cpuygtu ctg rquukdngA ]4010_ (c) 40 (d) 60 (e) 714 (f) 1046 68. Yjgp vgp rgtuqpu ujcmg jcpfu ykvj qpg cpqvjgt, kp jqy ocp{ yc{u ku kv rquukdngA ]4010_ (c) 40 (d) 47 (e) 60 (f) 67 69. Kp jqy ocp{ yc{u ecp hqwt ejknftgp dg ocfg vq uvcpf kp c nkpg uwej vjcv vyq qh vjgo, C cpf D ctg cnyc{u vqigvjgtA ]4010_ (c) 8 (d) 14 (e) 1: (f) 46 6:. C itqwr qh 850 ejknftgp ku ugcvgf kp tqyu hqt c itqwr rjqvq uguukqp. Gcej tqy eqpvckpu vjtgg nguu ejknftgp vjcp vjg tqy kp htqpv qh kv.Yjkej qpg qh vjg hqnnqykpi pwodgt qh tqyu ku pqv rquukdng A ]4016 - KK_ (c) 5 (d) 6 (e) 7 (f) 8 6;. Vygnxg rgqrng hqto c enwd. D{ rkemkpi nqvu, qpg qh vjgo yknn jquv c fkppgt hqt cnn qpeg kp c oqpvj. Vjg pwodgt qh fkppgtu c rctvkewnct ogodgt jcu vq jquv kp qpg {gct ku ]4017-KK_ (c) Qpg (d) \gtq (e) Vjtgg (f) Ecppqv dg rtgfkevgf 70. Vjgtg ctg 7 vcumu cpf 7 rgtuqpu. Vcum-n ecppqv dg cuukipgf vq gkvjgt rgtuqp-n qt rgtuqp-4. Vcum-4 owuv dg cuukipgf vq gkvjgt rgtuqp-5 qt rgtuqp-6. Gxgt{ rgtuqp ku vq dg cuukipgf qpg vcum. Kp jqy ocp{ yc{u ecp vjg cuukipogpv dg fqpgA ]4017-KK_ (c) 8 (d) 14 (e) 46 (f) 166 71. Kp c uqekgv{ kv ku ewuvqoct{ hqt htkgpfu qh vjg ucog ugz vq jwi cpf hqt htkgpfu qh qrrqukvg ugz vq ujcmg jcpfu yjgp vjg{ oggv. C itqwr qh htkgpfu ogv kp c rctv{ cpf vjgtg ygtg 46 jcpfujcmgu. Yjkej qpg coqpi vjg hqnnqykpi pwodgtu kpfkecvgu vjg rquukdng pwodgt qh jwiuA ]4017-KK_ (c) 5; (d) 50 (e) 41 (f) 40 74. Kp c dqz qh octdngu, vjgtg ctg vjtgg nguu yjkvg octdngu vjcp vjg tgf qpgu cpf hkxg oqtg yjkvg octdngu vjcp vjg itggp qpgu. Kh vjgtg ctg c vqvcn qh 10 yjkvg octdngu, jqy ocp{ octdngu ctg vjgtg kp vjg dqzA ]4017-KK_ (c) 48 (d) 4: (e) 54 (f) 58 75. C ugngevkqp ku vq dg ocfg hqt qpg rquv qh Rtkpekrcn cpf vyq rquvu qh Xkeg-Rtkpekrcn. Coqpiuv vjg ukz ecpfkfcvgu ecnngf hqt vjg kpvgtxkgy, qpn{ vyq ctg gnkikdng hqt vjg rquv qh Rtkpekrcn yjkng vjg{ cnn ctg gnkikdng hqt vjg rquv qh Xkeg-Rtkpekrcn. Vjg pwodgt qh rquukdng eqodkpcvkqpu qh ugngevggu ku ]4017-KK_ (c) 6 (d) 14 (e) 1: (f) Pqpg qh vjg cdqxg 76. C uvwfgpv jcu vq qrv hqt 4 uwdlgevu qwv qh 7 uwdlgevu hqt c eqwtug, pcogn{, Eqoogteg, Geqpqokeu, Uvcvkuvkeu, Ocvjgocvkeu K cpf Ocvjgocvkeu KK. Ocvjgocvkeu KK ecp dg qhhgtgf qpn{ kh Ocvjgocvkeu K ku cnuq qrvgf. Vjg pwodgt qh fkhhgtgpv eqodkpcvkqpu qh vyq uwdlgevu yjkej ecp dg qrvgf ku ]4017-KK_ (c) 7 (d) 8 (e) 9 (f) : 77. C rgtuqp qtfgtgf 7 rcktu qh dncem uqemu cpf uqog rcktu qh dtqyp uqemu. Vjg rtkeg qh c dncem rckt ycu vjtkeg vjcv qh c dtqyp rckt. Yjkng rtgrctkpi vjg dknn, vjg dknn engtm kpvgtejcpigf vjg pwodgt qh dncem cpf dtqyp rcktu d{ okuvcmg yjkej kpetgcugf vjg dknn d{ 100%. Yjcv ycu vjg pwodgt qh rcktu qh dtqyp uqemu kp vjg qtkikpcn qtfgtA ]4017-KK_ (c) 10 (d) 17 (e) 40 (f) 47 78. Vjg pwodgt qh rgtuqpu yjq tgcf ocic|kpg Z qpn{ ku vjtkeg vjg pwodgt qh rgtuqpu yjq tgcf ocic|kpg [. Vjg pwodgt qh rgtuqpu yjq tgcf ocic|kpg [ qpn{ ku vjtkeg vjg pwodgt qh rgtuqpu yjq tgcf ocic|kpg Z. Vjgp, yjkej qh vjg hqnnqykpi eqpenwukqpu ecp dg ftcypA ]4017-KK_ 1. Vjg pwodgt qh rgtuqpu yjq tgcf dqvj vjg ocic|kpgu ku vykeg vjg pwodgt qh rgtuqpu yjq tgcf qpn{ ocic|kpg Z. 4. Vjg vqvcn pwodgt qh rgtuqpu yjq tgcf gkvjgt qpg ocic|kpg qt dqvj vjg ocic|kpgu ku vykeg vjg pwodgt qh rgtuqpu yjq tgcf dqvj vjg ocic|kpgu. Ugngev vjg eqttgev cpuygt wukpi vjg eqfg ikxgp dgnqy< (c) 1 qpn{ (d) 4 qpn{ (e) Dqvj 1 cpf 4 (f) Pgkvjgt 1 pqt 4 79. Hqwt-fkikv pwodgtu ctg vq dg hqtogf wukpi vjg fkikvu 1, 4, 5 cpf 6= cpf pqpg qh vjgug hqwt fkikvu ctg tgrgcvgf kp cp{ ocppgt. Hwtvjgt, ]4018-KK_ 1. 4 cpf 5 ctg pqv vq koogfkcvgn{ hqnnqy gcej qvjgt 4. 1 ku pqv vq dg koogfkcvgn{ hqnnqygf d{ 5 5. 6 ku pqv vq crrgct cv vjg ncuv rnceg 6. 1 ku pqv vq crrgct cv vjg hktuv rnceg Jqy ocp{ fkhhgtgpv pwodgtu ecp dg hqtogfA (c) 8 (d) : (e) ; (f) Pqpg qh vjg cdqxg 7:. C dci eqpvckpu 40 dcnnu. : dcnnu ctg itggp, 9 ctg yjkvg cpf 7 ctg tgf. Yjcv ku vjg okpkowo pwodgt qh dcnnu vjcv owuv dg rkemgf wr htqo vjg dci dnkpfhqnfgf (ykvjqwv tgrncekpi cp{ qh kv) vq dg cuuwtgf qh rkemkpi cv ngcuv qpg dcnn qh gcej eqnqwtA ]4019-KK_ (c) 19 (d) 18 (e) 15 (f) 11 7;. Kh 4 dq{u cpf 4 iktnu ctg vq dg cttcpigf kp c tqy uq vjcv vjg iktnu ctg pqv pgzv vq gcej qvjgt, jqy ocp{ rquukdng cttcpigogpvu ctg vjgtgA ]4019-KK_ (c) 5 (d) 8 (e) 14 (f) 46 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Permutation, Combination & Probability F 75 1. (f) R(G) ? Rtqdcdknkv{ qh rcuukpi kp Gpinkuj ? 0.8 R(G Ç O) ? Rtqdcdknkv{ qh rcuukpi kp Ocvju cpf Gpinkuj ? 0.76 R(O) ? Rtqdcdknkv{ qh rcuukpi kp Ocvju Ukpeg, R(O) cpf R(G), dqvj ctg kpfgrgpfgpv gxgpvu. Uq, R(G Ç O) ? R(G) Ù R(O) R(O) ? R(G Ç O)/ R(G) ? 0.54 0.6 ? 0.; \ Rtqdcdknkv{ qh hcknkpi kp Ocvju ? 1 ˜ 0.; ? 0.1 ? 10% 4. (e) Hqt hkpfkpi vjg uknxgt eqkp, qpn{ ftcygt 1 cpf 5 tgockpu kp eqpukfgtcvkqp, dgecwug vjg qrgp ftcygt kp cp{ ecug ecppqv dg vjg ftcygt vjcv jcxg qpn{ iqnf eqkpu. Pqy vjg rtqdcdknkv{ qh pgzv eqkp dgkpi c iqnf eqkp ? 1/4. 5. (e) Ngv vjg tcfkwu qh vjg ekteng dg wpkv{ Gswcvkqp qh vjg ekteng, z 4 + {4 ? 1 { ? - 2 1 x .....(k) cpf, z ? ukp v .... (kk) Htqo (k) cpf (kk), { ? 4 1 ukp - v ? equ v Pqy, qrvkqp (e) ku vjg itcrj qh { ? equ v. 6. (e) Vqvcn pwodgt qh ectfu ? 106 ? 4 Ù 74 cpf vqvcn pwodgt qh lcemu ? : ? 4 Ù 6 \ Rtqdcdknkv{ hqt vjg lcem kp hktuv ftcy ? : 106 cpf rtqdcdknkv{ hqt vjg lcem kp ugeqpf ftcy ? 9 105 Ukpeg dqvj vjg gxgpvu ctg kpfgrgpfgpv gxgpvu. Jgpeg vjg rtqdcdknkv{ vjcv dqvj qh vjgo ctg lcemu. ? :9 9 106 105 155; ´ = 7. (c) Cu D VSU ku cp kuquegngu vtkcping. \ Ð VUS ? Ð VSU ? 69² Pqy, kp gswkncvgtcn vtkcping D STU, Ð TSU ? Ð TUS ? Ð STU ? 80² Pqy, Ð TSU ? Ð TSV + Ð VSU ? 80² Ð TSV ? [ ? 80² ˜ 69² ? 15² 8. (e) Rtqdcdknkv{ qh Jgcf qt Vckn qp vjg wrrgt ukfg hqt c eqkp ? 1 4 \ Rtqdcdknkv{ qh ucog ukfg qp vjg wrrgt ukfg hqt vjg vjtgg eqkpu ? 1 4 Ù 1 4 Ù 1 4 ? 5 1 4 æ ö ç ÷ è ø ? 1 : 9. (e) Pwodgt qh ucorngu ? 170 Uq rtqdcdknkv{ (R) ? Pwodgt qh ucorngu hqt ( ) Vqvcn pwodgt qh ucorngu (170) X Yjgp yg eqpukfgt vjg ikxgp uvcvgogpvu (1) R Z( 17) £ ? 5 9 10 17 4: 55 170 ++ + + + ? ;8 170 ? 0.86 (4) R Z (15 19) < £ ? 4: 55 46 11 170 +++ ? ;8 170 ? 0.86 (5) R(Z ? 17) ? 55 170 ? 0.44 :. (f) Ukpeg, : Itggp dcnnu + 9 Yjkvg dcnnu ? 17 dcnnu 9 Yjkvg dcnnu + 7 Tgf dcnnu ? 14 dcnnu cpf : Itggp dcnnu + 7 Tgf dcnnu ? 15 dcnnu Pqy, kh yg rkem 17 dcnnu, vjg{ oc{ dg yjkvg, itggp qt tgf dwv kh yg rkem 18 dcnnu, vjgp kvu egtvckp vjcv vjgtg yknn dg cvngcuv qpg dcnn qh gcej eqnqwt. ;. (f) Rtqdcdknkv{ vjcv vjg nkijv ku pqv itggp ? vkog hqt yjkej nkijv ku pqv itggp vkog vcmgp hqt vjg gpvktg e{eng ? (7 50) 80 + ? 57 80 ? 9 14 10. (e) (k) Pwodgt qh yc{u qh cttcpikpi vjtgg eqnqwtu vcmgp 1 cv c vkog ? 5 1 R ? 5 4! 4! ´ ? 5 (kk) Pwodgt qh yc{u qh cttcpikpi vjtgg eqnqwtu vcmgp 4 cv c vkog ? 5 4 R ? 5 ! 1! ?8 (kkk) Pwodgt qh yc{u qh cttcpikpi vjtgg eqnqwtu vcmgp 5 cv c vkog ? 5 5 R ? 8 Jgpeg, Oczkowo pq. qh eqfgu ? Pq. qh yc{u qh cttcpikpi vjgug hnciu ? 5 + 8 + 8 ? 17 11. (f) Hqt gcej eqodkpcvkqp, ngv wu pcog vjg hgocngu cpf ocngu Hgocng (5) Ocng (7) C D E F G H I J Ukpeg C ecp”v iq ykvj D, kv yknn ocmg vgco ykvj hqwt ocngu kp hqwt yc{u CF, CH, CI, CJ. Ukpeg vjgtg ku pq tguvtkevkqp ykvj hgocng E cpf G, vjg{ oc{ eqodkpg ykvj 7 ocngu kp 7 fkhhgtgpv yc{u gcej. Vqvcn pwodgt qh yc{u ? 6 + 7 + 7 ? 16 14. (e) Ukpeg, cpuygtu qh pq. vyq gzcokpggu ctg kfgpvkecn, uq hktuv kvgo kp Nkuv-C ecp dg ocvejgf ykvj cp{ qh vjg 7 kvgou kp Nkuv-D. Kv ecp dg fqpg kp 7 yc{u. Ukoknctn{, 4pf kvgo kp Nkuv-C ecp dg ocvejgf ykvj cp{ qh vjg tgockpkpi 6 kvgou kp Nkuv-D. Kv ecp dg fqpg kp 6 yc{u. Eqpvkpwkpi kp vjg ucog yc{, Pq qh yc{u qh cttcpikpi vjg kvgou ? 7 Ù 6 Ù 5 Ù 4 Ù 1?140 Pqy, kp vjku cttcpigogpv vjgtg ku qpg uwej cttcpigogpv, yjkej ku vjg eqttgev cpuygt. \ Oczkowo pwodgt qh gzcokpggu ? pq. qh yc{u qh cttcpigogpv qh kvgou ? 140 ˜ 1 ? 11; HINTS & SOLUTIONS Explanations Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 76 15. (d) Hktuv ngvvgt ecp dg ftqrrgf kpvq cp{ qh vjg 5 dqzgu. Kv ecp dg fqpg kp 5 yc{u. Ukoknctn{ ugeqpf ngvvgt ecp cnuq dg ftqrrgf kpvq cp{ qh vjg 5 dqzgu kp 5 yc{u cpf uq qp. Jgpeg, vqvcn pq qh yc{u ? 5Ù5Ù5Ù.........wrvq ; vkogu ? 5; 16. (f) Vqvcn pq qh yc{u qh cttcpigogpv hqt ukz rnc{gtu ? 8! Ngv wu vcmg Clkv cpf Owmgtlgg cu qpg gpvkv{. Uq pqy vjgtg ctg (8 ˜ 4 + 1) ? 7 rnc{gtu Vjgug 7 rnc{gtu ecp dg cttcpigf kp 7! yc{u cpf Clkv cpf Owmgtlgg ecp dg cttcpigf coqpi vjgougnxgu kp 4! yc{u. Vjwu, pq qh yc{u, yjgp Clkv cpf Owmgtlgg ctg cnyc{u vqigvjgt ? 7 ! Ù 4! Jgpeg, pq qh yc{u yjgp vjg{ ctg pgxgt vqigvjgt ? Vqvcn pq qh yc{u ˜ pq qh yc{u yjgp vjg{ ctg cnyc{u vqigvjgt ? 8 ! ˜ (7 ! Ù 4 !) ? 8 Ù 7 ! ˜ (7 ! Ù 4 !) ? 7 ! (8 ˜ 4) ? 6:0 17. (e) Hqt 1uv uvwfgpv, Rtqdcdknkv{ qh ugngevkpi cp{ qpg fc{ cu jku dktvjfc{ ? 587 587 ? 1 Pqy, vjg tgockpkpi vyq uvwfgpvu vq dg ugngevgf owuv jcxg ucog fc{ cu vjgkt dktvjfc{ cu hqt vjg 1uv uvwfgpv. Rtqdcdknkv{ qh tguv vyq uvwfgpvu, jcxkpi vjg ucog dktvjfc{ cu vjcv qh vjg 1uv uvwfgpv ? 1 587 Ù 1 587 Jgpeg, tgswktgf rtqdcdknkv{ ? ( )4 1 1 587 ´ ? ( )4 1 587 18. (f) Hqt (10 + C + D) ? 14 uvcvkqpu, pq qh vkemgvu tgswktgf, yjgp 6 pgy uvcvkqpu ctg cffgf hqt qpg yc{ lqwtpg{ ? 14 Ù 6 ? 6: Cnuq, gcej 6 pgy uvcvkqpu tgswktg (18 ˜ 1) ? 17 pgy vkemgvu hqt qpg yc{ lqwtpg{. \ Pq. qh vkemgvu hqt 6 pgy uvcvkqpu ? 17 Ù 6 ? 80 Jgpeg, vqvcn pgy vkemgvu ? 80 + 6: ? 10: 19. (d) Vjgtg ecp dg vyq ecugu < (k) Ncf{ qeewrkgu vjg tgugtxgf ugcv (kk) Ncf{ fqgu pqv qeewr{ vjg tgugtxgf ugcv. (k) Ncf{ Hkzkpi qpg ugcv hqt vjg ncf{, 1uv ocp ecp qeewr{ cp{ qh vjg tgockpkpi 6 ugcvu kp hqwt yc{u cpf vjg 4pf ocp qeewr{ cp{ qh vjg tgockpkpi 5 ugcvu kp vjtgg yc{u. Jgpeg, pq qh yc{u ? 1 Ù 6 Ù 5 ? 14 (kk) Ngcxkpi vjg tgugtxgf ugcv, 1uv ocp ecp qeewr{ cp{ qh vjg 6 ugcvu kp hqwt yc{u. 4pf ocp ecp qeewr{ cp{ qh vjg tgockpkpi 5 ugcvu kp vjtgg yc{u. Ncf{ ecp qeewr{ cp{ qh vjg tgockpkpi 4 ugcvu kp vyq yc{u. Jgpeg, pq qh yc{u ? 6 Ù 5 Ù 4 ? 46 Vjwu, Vqvcn pq qh yc{u ? 14 + 46 ? 58 1:. (f) Vqvcn pwodgt qh yc{u kp yjkej ; dcnnu qeewr{ cp{ qh vjg 8 uswctgu ? ;E8 ? :6 Pwodgt qh yc{u kp yjkej qpg tqy ku pqv hknngf ? 5 \ Pwodgt qh yc{u kp yjkej cv ngcuv qpg dcnn qeewrkgu gcej tqy ? :6 ˜ 5 ? :1 1;. (c) Qp vjg hktuv cvvgorv hqwt eqkpu ctg qxgtvwtpgf. Pqy, ukz eqkpu ctg nghv. Kp vjg pgzv vwtp, hqwt oqtg ctg qxgtvwtpgf. Pqy qpn{ vyq yqwnf dg nghv. Yg vcmg qpg oqtg htqo vjg nghv qxgt vyq eqkpu cpf cp{ vjtgg htqo vjg rtgxkqwun{ vwtpgf qpgu. Hkpcnn{, vjg nghvqxgt eqkp cpf vjg vjtgg eqkpu htqo vjg rtgukfkpi uvgr yjkej jcxg cntgcf{ dggp vwtpgf vykeg ecp dg qxgtvwtpgf. Vjwu, kp hqwt cvvgorvu, qpg ecp eqorngvg vjg rtqeguu. 40. (e) Rtqdcdknkv{ qh c rctvkeng n{kpi kp cp{ rctvkewnct jcnh ? 1 4 \ Rtqdcdknkv{ qh cnn 10 rctvkengu n{kpi kp gkvjgt 1uv jcnh qt 4pf jcnh ? 10 10 1 1 4 4 æö æö ç÷ ç÷ + èø èø ? 10 1 4 4 æ ö ç ÷ è ø ? ; 1 4 41. (e) 4 Yqogp ecp qeewr{ 4 ejcktu qwv qh vjg hktuv hqwt ejcktu kp 6R4 yc{u. 5 ogp ecp dg cttcpigf kp vjg tgockpkpi 8 ejcktu kp 8R5 yc{u. Jgpeg, vqvcn pq. qh yc{u ? 6R4 Ù 8R5 ? 1660 44. (f) Ngv vjg vqvcn pq. qh rctvkekrcpvu dg 'p' cv vjg dgikppkpi. Rnc{gtu tgockpkpi chvgt uqogvkog ? p ˜ 5 Pqy, p˜5E4 + (5 Ù 5) ? 97 ( ˜ 5)! ; 97 4!( ˜ 7)! + = p p p 4 ˜ 9p ˜ 140 ? 0 (p + :) (p ˜ 17) ? 0 pgingevkpi p ? ˜ :, p ? 17 45. (d) Oczkowo pwodgt qh vtkcpingu ecp dg hqtogf d{ ugngevkpi 5, 6 qt 7 rqkpvu qwv qh 8 cv c vkog. Uq, oczkowo pq. qh vtkcpingu ? 8E5 + 8E6 + 8E7 yjkej ku engctn{ oqtg vjcp 1:. Pqy, vtkcpingu hqtogf yknn dg okpkowo k.g., |gtq, yjgp vjg rqkpvu yknn qxgtncr qp vjg ucog nkpg cpf cnn vjg rqkpvu ctg cnqpi vjg ucog xgtvkecn nkpg. 46. (f) Octtkgf eqwrngu< OH OH OH OH c , e , g , i df hj Rquukdng vgcou< cf ed gd id ch eh gf if cj ej gj ih Pqy, vgco cf ecp rnc{ qpn{ ykvj< ed, ei, ej, gd, gj, id, ih, k.g. 9 Vjg ucog yknn crrn{ ykvj cnn vgcou. Uq pq. qh vqvcn ocvej ? 14 Ù 9 ? :6 Ukpeg gxgt{ ocvej kpenwfgu 4 vgcou, uq vjg Pq. qh ocvejgu ? :6/4 ? 64 47. (e) Ngv G dg vjg gxgpv qh ugngevkpi vjg vjtgg pwodgtu uwej vjcv vjgkt rtqfwev ku qff cpf U dg vjg ucorng urceg. Hqt vjg rtqfwev vq dg qff, 5 pwodgtu ejqqugp owuv dg qff. \ p (G) ? 7E5 p (U) ? ;E5 \R (G) ? 7 5 ; 5 () 7 ( ) 64 = = p G E p U E Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Permutation, Combination & Probability F 77 48. (e) Ukpeg, gxgt{ swguvkqp jcu hkxg qrvkqpu, uq pq. qh ejqkegu hqt gcej swguvkqp ? 7 \ vqvcn pq. qh ejqkegu ? 7 Ù 7 Ù 7 Ù 7 ? 847 Pqy, pq. qh ejqkegu qh cnn eqttgev cpuygt ? 1 Jgpeg, pq qh ejqkegu hqt cnn vjg hqwt cpuygtu pqv eqttgev ? vqvcn pq. qh ejqkegu ˜ pq. qh ejqkegu qh cnn eqttgev cpuygt ? 847 ˜ 1 ? 846 49. (c) x y Vjgtg ecp dg vyq ecugu< Ecug (K) < Yjgp z tqy eqpvckpu 8 dcnnu< Vjgp vjg 4 dcnnu ecp dg cttcpigf kp { tqy kp 8R4 yc{u ? 17 qt vjg 4 dcnnu ecp dg cttcpigf kp cp{ qh vjg 6 vyq dqz tqy kp 6 yc{u. Uq, pq qh yc{u, yjgp z eqpvckpu 8 dcnnu ? 17 + 6 ? 1;. Ecug (KK) < Ukoknctn{, pq. qh yc{u, yjgp { tqy eqpvckpu 8 dcnnu ? 1; Cu, gkvjgt qh ecug (K) qt ecug (KK) ku rquukdng, Jgpeg, vqvcn pq. qh yc{u ? 1; + 1; ? 5: 4:. (e) Uwrrqug vjtgg rgqrng jcxg dggp ikxgp c, d cpf e pwodgt qh kvgou. Vjgp, c Ù d Ù e ? 50 Pqy, Vjgtg ecp dg 7 ecugu < Ecug K < Yjgp qpg qh vjgo ku ikxgp 50 kvgou cpf tguv vyq 1 kvgo gcej. Uq, pwodgt qh yc{u hqt (50 Ù 1 Ù 1) ? 5! 5 4! = (Cu vyq qh vjgo jcxg ucog pwodgt qh kvgou) Ecug KK < Ukoknctn{, pwodgt qh yc{u hqt (10 Ù 5 Ù 1) ? 5! ? 8 Ecug KKK < Pwodgt qh yc{u hqt (17 Ù 4 Ù 1) ? 5! ? 8 Ecug KX < Pwodgt qh yc{u hqt (8 Ù 7 Ù 1) ? 5! ? 8 Ecug X < Pwodgt qh yc{u hqt (7 Ù 5 Ù 4) ? 5! ? 8 Jgtg, gkvjgt qh vjgug 7 ecugu ctg rquukdng. Jgpeg, vqvcn pwodgt qh yc{u ? 5 + 8 + 8 + 8 + 8 ? 49 4;. (d) Vjgtg ecp dg hkxg ecugu < Ecug K < Hktuv vtkcping ecp jcxg 7 dcnnu cpf tguv vjtgg 1 gcej. Uq, pwodgt qh yc{u hqt (7, 1, 1, 1) ? 6! 5! ? 6 (Q Vjtgg vtkcpingu ctg jcxkpi ucog pwodgt qh dcnnu) Ecug KK < Pwodgt qh yc{u hqt (6, 4, 1, 1) ? 6! 4! ? 14 (Q Vyq vtkcpingu ctg jcxkpi ucog pwodgt qh dcnnu) Ecug KKK < Ukoknctn{, pwodgt qh yc{u hqt (4, 4, 4, 4) ? 6! 6! ?1 Ecug KX < Pwodgt qh yc{u hqt (5, 5, 1, 1) ? 6! 4! 4! ´ ? 8 Ecug X < Pwodgt qh yc{u hqt (5, 4, 4, 1) ? 6! 14 4! = Cu, gkvjgt qh vjgug hkxg ecugu ctg rquukdng, Jgpeg vqvcn pwodgt qh yc{u ? 6 + 14 + 1 + 8 + 14 ? 57 50. (e) Vjgtg ecp dg vjtgg ecugu < Cokv Ykhg (K) 1 Dq{ cpf 1 Iktn 1 Dq{ cpf 1 Iktn (KK) 4 Iktnu 4 Dq{u (KKK) 4 Dq{u 4 Iktnu Ecug K < pwodgt qh yc{u ? 4E1 Ù 5E1 Ù 5E1 Ù 4E1 ? 58 Ecug KK < pwodgt qh yc{u ? 5E4 Ù 5E4 ? ; Ecug KKK < pwodgt qh yc{u ? 4E4 Ù 4E4 ? 1 Jgpeg, vqvcn pwodgt qh yc{u ? 58 + ; + 1 ? 68 51. (e) Vjgug ecp dg vyq ecugu < Ecug K - Qpg dqz eqpvckp 5 dcnnu cpf tguv vyq Eqpvckpu 1 dcnn gcej. Ecug KK - Qpg dqz eqpvckp 1 dcnn cpf tguv vyq Eqpvckpu 4 dcnnu gcej. Ecug 1 < Pwodgt qh yc{u ? 7E5 Ù 4E1 Ù 1E1 ? 40 Pqy, vjgug 5 dqzgu ecp dg cttcpigf kp 5! 4! coqpi vjgougnxgu, cu vyq qh vjgo eqpvckpu ukoknct pwodgt qh dcnnu. Uq, pwodgt qh yc{u ? 5! 40 80 4! ´ = Ecug KK < Pwodgt qh yc{u ? 7E1 Ù 6E4 Ù 4E4 ? 50 Cnuq, vjgug 5 dqzgu ecp dg cttcpigf coqpi vjgougnxgu kp 5! 4! , cu vyq qh vjgo eqpvckpu ukoknct pwodgt qh dcnnu. Vjwu, pwodgt qh yc{u ? 5! 50 ;0 4! ´ = Pqy, gkvjgt qh ecug (K) qt ecug (KK) ku rquukdng, Jgpeg, vqvcn pwodgt qh yc{u ? 80 + ;0 ? 170 54. (e) Qwv qh vjg ikxgp ngvvgtu kp vjg yqtf UCEJKP, U ku vjg ncuv ngvvgt kp vjg cnrjcdgvkecn qtfgt vq uvctv c yqtf. Kh vjg yqtf uvctvu ykvj C, vjgp C ecp dg mgrv hkzgf cpf vjg tgockpkpi ngvvgtu ecp dg cttcpigf kp 7! yc{u. Ukoknctn{, pwodgt qh yqtfu uvctvkpi ykvj E ? 7! Pwodgt qh yqtfu uvctvkpi ykvj J ? 7! Pwodgt qh yqtfu uvctvkpi ykvj K ? 7! Pwodgt qh yqtfu uvctvkpi ykvj P ? 7! Pqy, yjgp vjg yqtf uvctvu ykvj U, vjgp UCEJKP ku vjg hktuv yqtf kp vjg cnrjcdgvkecn qtfgt vq hqnnqy wr. Uq, Rqukvkqp qh vjg yqtf UCEJKP ? 7 (7!) + 1 ? 801 55. (e) Vjgtg ecp dg 5 ecugu < K. Yjgp qpg fkeg ujqyu 4. KK. Yjgp vyq fkeg ujqyu 4. KKK. Yjgp vjtgg fkegu ujqyu 4. Ecug K < Vjg fkeg yjkej ujqyu 4 ecp dg ugngevgf qwv qh vjg 5 fkegu kp 5E1 yc{u. Tgockpkpi 4 fkegu ecp jcxg cp{ 7 pwodgtu gzegrv 4. Uq pwodgt qh yc{u hqt vjgo ? 7E1 gcej, uq pq qh yc{u yjgp qpg fkeg ujqyu 4 ? 5E1 Ù 7E1 Ù 7E1 . Ecug KK < Vyq fkegu, ujqykpi 4 ecp dg ugngevgf qwv qh vjg 5 fkegu kp 5E4 yc{u cpf vjg tguv qpg ecp jcxg cp{ 7 pwodgtu gzegrv 4, uq pwodgt qh yc{u hqt vjg tgockpkpi 1 fkeg ? 7. Uq, pwodgt qh yc{u, yjgp vyq fkegu ujqy 4 ? 5E4 Ù 7 Ecug KKK < Yjgp vjtgg fkegu ujqy 4 vjgp vjgug ecp dg ugngevgf kp 5E5 yc{u. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 78 Uq, pwodgt qh yc{u, yjgp vjtgg fkegu ujqy 4 ? 5E5 ? 1 Cu, gkvjgt qh vjgug vjtgg ecugu ctg rquukdng. Jgpeg, vqvcn pwodgt qh yc{u ? (5 Ù 7 Ù 7) + (5 Ù 7) + 1 ? ;1 56. (d) 5 dcnnu ecp dg rncegf dg kp cp{ qh vjg 14 uswctgu kp 14E5 yc{u. Vqvcn pwodgt qh cttcpigogpvu ? 14E5 ? 440 Pqy, cuuwog vjcv dcnnu nkg cnqpi vjg uqog nkpg. Vjgtg ecp dg 5 ecugu < Ecug K< Yjgp dcnnu nkg cnqpi vjg uvtckijv jqtk|qpvcn nkpg. 5 dcnnu ecp dg rwv kp cp{ qh vjg 6 dqzgu cnqpi vjg jqtk|qpvcn tqy kp 6E5 yc{u. Pqy, ukpeg vjgtg ctg 5 tqyu, uq pwodgt qh yc{u hqt ecug K ? 6E5 Ù 5 ? 14 Ecug KK < Yjgp dcnnu nkg cnqpi vjg xgtvkecn uvtckijv nkpg 5 dcnnu ecp dg rwv kp cp{ qh vjg 5 dqzgu cnqpi vjg xgtvkecn tqy kp 5E5 yc{u. Pqy, cu vjgtg ctg 6 xgtvkecn tqyu, uq pwodgt qh yc{u hqt Ecug KK ? 5E5 Ù 6 ? 6 Ecug KKK < Dcnnu nkg cnqpi vjg 4 fkciqpcn nkpgu vqyctfu vjg nghv cpf 4 fkciqpcn nkpgu vqyctfu vjg tkijv. Pwodgt qh yc{u ? 4 + 4 ? 6 Pwodgt qh yc{u, yjgp dcnnu nkg cnqpi vjg nkpg ? 14 + 6 + 6 ? 40 Pwodgt qh yc{u yjgp dcnnu fqp'v nkg cnqpi vjg nkpg ? Vqvcn pwodgt qh yc{u ˜ pwodgt qh yc{u yjgp dcnnu nkg cnqpi vjg nkpg. ? 440 ˜ 40 ? 400. 57. (e) Vqvcn pwodgt qh cttcpigogpvu, yjgp cp{ 5 dq{u ctg ugngevgf qwv qh 7 ? 7E5 . Pqy, yjgp itqwru eqpvckpu dqvj E cpf F, vjgp vjgkt ugngevkqp ku hkzgf cpf vjg tgockpkpi 1 dq{ ecp dg ugngevgf qwv qh vjg tgockpkpi 5 dq{u. Kv ecp dg fqpg kp 5E1 yc{u. Uq, pwodgt qh itqwru, yjgp pqpg eqpvckpu dqvj E cpf F ? vqvcn pwodgt qh cttcpigogpvu-pwodgt qh cttcpigogpvu yjgp itqwr eqpvckpu dqvj E cpf F ? 7E5 ˜ 5E1 ? 10 ˜ 5 ? 9 58. (d) Ngv wu vcmg dqqmu C cpf D cu qpg k.g., vjg{ ctg cnyc{u eqpvkpwqwu. Pqy, pwodgt qh dqqmu ? 6 ˜ 4 + 1 ? 5 Vjgug vjtgg dqqmu ecp dg cttcpigf kp 5! yc{u cpf cnuq C cpf D ecp dg cttcpigf kp 4 yc{u coqpi vjgougnxgu. Uq, pwodgt qh yc{u yjgp dqqmu C cpf D ctg cnyc{u eqpvkpwqwu ? 4 Ù 5! Vqvcn pwodgt qh yc{u qh cttcpigogpv qh C, D, E cpf F ? 6! Jgpeg, pwodgt qh yc{u yjgp C cpf D ctg pgxgt eqpvkpwqwu ? Vqvcn pwodgt qh yc{u ˜ pwodgt qh yc{u yjgp C cpf D cnyc{u eqpvkpwqwu ? 6! ˜ 4 Ù 5! ? 14 59. (e) Uwrrqug cp{ rctvkewnct uvwfgpv ku cnyc{u ugngevgf. Pqy, tgockpkpi 4 uvwfgpvu ctg vq dg ugngevgf qwv qh vjg tgockpkpi 7 uvwfgpvu. Kv ecp dg fqpg kp 7E4 yc{u. ? 7! 10 4! 5! = ´ 5:. (f) Vjgtg ecp dg vyq ecugu < Ecug K < Yjgp 1 tqy eqpvckpu 5 dcnnu cpf tguv vyq eqpvckpu 1 dcnn gcej. Pqy, vjg tqy yjkej eqpvckpu 5 dcnnu ecp dg ugngevgf qwv qh vjg 5 tqyu kp 5E1 yc{u cpf kp vjku tqy pwodgt qh yc{u qh cttcpigogpv ? 5E5 . Kp qvjgt vyq tqyu, pwodgt qh yc{u qh cttcpigogpv kp gcej ? 5E1 . Vjwu, pwodgt qh yc{u hqt ecug K ? 5E1 Ù 5E5 Ù 5E1 Ù 5E1 ? 5 Ù 1 Ù 5 Ù 5 ? 49 Ecug KK < Yjgp 1 tqy eqpvckpu 1 dcnn cpf tguv vyq tqyu eqpvckp 4 dcnnu gcej. Vjku tqy, eqpvckpkpi 1 dcnn ecp dg ugngevgf kp 5E1 yc{u cpf pwodgt qh yc{u qh cttcpigogpv kp vjku tqy ? 5E1 . Kp qvjgt vyq tqyu, eqpvckpkpi 4 dcnnu gcej, pwodgt qh yc{u qh cttcpigogpv kp gcej ? 5E4 . Vjwu, pwodgt qh yc{u hqt ecug KK ? 5E1 Ù 5E1 Ù 5E4 Ù 5E4 ? 5 Ù 5 Ù 5 Ù 5 ? :1 Cu, gkvjgt qh vjgug vyq ecugu ctg rquukdng, jgpeg vqvcn pwodgt qh yc{u ? ecug K qt ecug KK ? 49 + :1 ? 10:. 5;. (c) Cu vjgtg ctg 8 ngvvgtu cpf gpxgnqrgu, uq kh gzcevn{ 7 ctg kpvq eqttgevn{ cfftguugf gpxgnqrgu, vjgp vjg tgockpkpi 1 yknn cwvqocvkecnn{ dg rncegf kp vjg eqttgevn{ cfftguugf gpxgnqrg. Vjwu, vjg rtqdcdknkv{ vjcv gzcevn{ 7 iq kpvq vjg eqttgevn{ cfftguugf gpxgnqrg ku |gtq. 60. (e) Ngv wu uvctv ykvj Tgf eqnqwt Yjgtg, T ? Tgf, D ? Dncem, Y ? Yjkvg T D TY TYT D TDTD TYTY T DYT T Y D T TDDT T YY T Vjgtg ctg gkijv uwej cttcpigogpvu, kh yg uvctv ykvj Tgf dcnn. Ukoknctn{, vjgtg ctg : cttcpigogpvu, kh yg uvctv ykvj dncem qt yjkvg dcnn. Jgpeg, Pq. qh cttcpigogpvu ? : + : + : ? 46 61. (d) Pq. qh fkhhgtgpv uwou qh oqpg{ ? cp{ 1 eqkp cv c vkog + cp{ 4 eqkpu + cp{ 5 eqkpu kv cnn 6 eqkpu ? 6E1 + 6E4 + 6E5 + 6E6 ? 6 + 8 + 6 + 1 ? 17 64. (c) Ecug K < Yjgp 6 ku cv vjg jwpftgfvj rnceg. Tgockpkpi vyq rncegu ecp dg hknngf vjtqwij cp{ qh vjg pwodgtu 0 vq ; gzegrv 6 kp ; yc{u. Uq, pq qh yc{u ? 1 Ù ; Ù ; ? :1 Ecug KK < Yjgp 6 ku cv vjg wpkvu qt vgpu rnceg cpf 5 ku cv vjg jwpftgfvj rnceg. Jgtg, 6 ku cv vjg wpkvu rnceg, vjgp vgpu rnceg ecp dg hknngf vjtqwij cp{ qh vjg pwodgtu 0 vq ; gzegrv 6 kp ; yc{u qt gnug kh 6 ku cv vjg vgpu rnceg, vjgp wpkvu rnceg ecp dg hknngf kp ; yc{u. Uq, pq qh yc{u ? 1 Ù (; + ;) ? 1 Ù 1: ? 1: Jgtg, gkvjgt ecug K qt ecug KK ku rquukdng. Jgpeg, vqvcn pq. qh yc{u ? :1 + 1: ? ;; 65. (f) Cp{ 5 pwodgtu qwv qh ; ecp dg ugngevgf kp ;E5 yc{u. Pqy, vjgug vjtgg pwodgtu ecp dg cttcpigf coqpi vjgougnxgu kp cuegpfkpi qtfgt kp qpn{ 1 yc{. Jgpeg, vqvcn pq. qh yc{u ? ;E5 Ù 1 ? :6 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Permutation, Combination & Probability F 79 66. (e) Ukpeg kp 441 icogu gcej dq{ rnc{u gzcevn{ qpg icog ykvj gcej iktn, Uq, op ? 441 (1) cu, o @ p @ 1, uq qpn{ o ? 19 cpf p ? 15 ucvkuhkgu (1) \ Vqvcn pq qh uvwfgpvu ? o + p ? 19 + 15 ? 50 Pwodgt qh icogu kp yjkej dqvj rnc{gtu ctg iktnu ? 15E4 ? 9: 67. (f) Gcej swguvkqp ecp dg cpuygtgf kp 4 yc{u. Jgpeg, vqvcn pq. qh ugswgpegu ? 4 Ù 4 Ù ........ 10 vkogu ? 410 ? 1046 68. (f) Hktuv rgtuqp ecp ujcmg jcpf ykvj vjg qvjgt ; k.g, kp ; yc{u. Ugeqpf rgtuqp ecp ujcmg jcpf ykvj vjg tgockpkpi : rgtuqpu cpf uq qp. \ vqvcn pq. qh jcpfu ujcmgf ? ; + : + ....... + 4 + 1 ? ;(; 1) 67 4 + = 69. (d) Vcmg, C cpf D vq dg cnyc{u vqigvjgt cu c ukping gpvkv{. Pqy, vqvcn pq. qh ejknftgp ? 6 ˜ 4 + 1 ? 5 Vjgug ecp dg cttcpigf kp 5! yc{u cpf C, D ecp dg cttcpigf coqpi vjgougnxgu kp 4! yc{u. Jgpeg, pq. qh cttcpigogpvu uwej vjcv C cpf D ctg cnyc{u vqigvjgt ? 5! Ù 4! ? 5 Ù 4 Ù 4 ? 14 6:. (f) Ngv pq. qh eqnwop ? z, pq. qh tqyu ? { \ z{ ? 850 ˜ ]5 Ù 1 + 5 Ù 4 + ......... + 5 Ù ({ ˜ 1)_ ? 850 ˜ 5 ]1 + 4 + ........ + ({ ˜ 1)_ z{ ? 850 ˜ 5{ 1{ ( ) 4 - (c) Kh { ? 5, vjgp 5z ? 850 ˜ ; Þ 841 z 5 = ? 409 (d) Kh { ? 6, vjgp 6z ? 850 ˜ 1: Þ 814 z 6 = ? 175 (e) Kh { ? 7, vjgp 7z ? 850 ˜ 50 Þ 800 z 7 = ? 140 6;. (f) Yg ecppqv rtgfkev vjg pwodgt qh fkppgtu hqt c rctvkewnct ogodgt htqo vjg ikxgp fcvc. Kv oc{ dg rquukdng vjcv d{ ejqqukpi ogodgtu htqo rkemkpi nqvu, qpg oc{ jcxg vq jquv c fkppgt oqtg vjcp qpg vkogu. 70. (e) Jgtg ctg hkxg rgtuqpu, cpf 7 vcumu Uq, Yjgp V4 vcum ku hkzgf hqt rgtuqp 5 Vcum V4 1 4 5 6 7 Hqt Vcum 1 pq. qh yc{u ? 4 Vcum 4 pq. qh yc{u ? 1 Vcum 5 pq. qh yc{u ? 5 Vcum 6 pq. qh yc{u ? 5 Vcum 7 pq. qh yc{u ? 5 Vqvcn pq. qh yc{u hqt eqpfkvkqp ? 5 + 5 + 5 + 4 + 1 ? 14 Eqpfkvkqp KK Yjgp vcum V4 ku ikxgp vq dg rgtuqp 6 Vcum 1 4 5 6 7 V4 Pq. qh yc{u hqt Vcum V1 ? 4 Pq. qh yc{u hqt Vcum V4 ? 1 Pq. qh yc{u hqt Vcum V5 ? 5 Pq. qh yc{u hqt Vcum V6 ? 5 Pq. qh yc{u hqt Vcum V7 ? 5 Vqvcn pwodgt qh yc{u hqt eqpfkvkqp KK ? 5 + 5 + 5 + 4 +1 ? 14 Vqvcn pwodgt qh yc{u hqt eqpfkvkqp K cpf KK ? 14 + 14 ? 46 71. (e) Ngv z dg vjg pwodgt qh yqogp. Ngv { dg vjg pwodgt qh ogp. Vqvcn pwodgt qh jcpf ujcmgu ? z{ ? 46 Vjgp, vjg rquukdng hcevqtu qh z cpf { ctg z ? 8 qt 6, { ? 6 qt 8 Pwodgt qh jwiu z { E E 4 4 = + ? 8 6 E E 4 4 + ? 87 65 41 4 ´ ´ + ´ ? 17 + 8 ? 41 74. (d) Yjkvg Octdngu Tgf Octdngu 10 15 Yjkvg Octdngu Itggp Octdngu 10 . 0 7 Pqy, vqvcn pwodgt qh Octdngu ? 7 + 10 + 15 ? 4: 75. (f) Pwodgt qh yc{u vq ugngev Rtkpekrcn ? 4E1 Pwodgt qh yc{u vq ugngev Xkeg Rtkpekrcn ? 7E4 Vqvcn pwodgt qh yc{u ? 4E1 + 7E4 ? 7 6 4 4 1 ´ + ´ ? 4 + 10 ? 14 Pwodgt qh rquukdng eqodkpcvkqpu qh ugngevtgu ? 4 Ù 10 ? 40 76. (e) Kv ocvjgocvkeu K ku pqv qrvgf, vjgp vyq uwdlgevu qwv qh hqwt uwdlgevu jcxg vq dg qrvgf hqt. \ Pwodgt qh yc{u kp yjkej vyq uwdlgevu ecp dg qrvgf hqt 6 5 8 4 ´ = Kh ocvjgocvkeu KK ku qrvgf, vjgp kv ecp dg qhhgtgf qpn{ kh ocvjgocvkeu K ku cnuq qrvgf hqt Pwodgt qh yc{u kp yjkej vyq uwdlgevu ecp dg qrvgf hqt ? 8 +1 ? 9. 77. (f) Ngv pwodgt qh c rcktu qh dtqyp uqemu ? { Rtkeg qh dtqyp uqemu ? z Rtkeg qh dncem uqemu ? 5z Ceeqtfkpi vq swguvkqp Þ 7 ´ 5z + {z ? 100 ... (k) Pqy, engtm jcu kpvgtejcpigf uqemu rcktu vjgp rtkeg ku kpetgcugf d{ 100% 5z{ + 7z ? (17z {z) 100 (17 z {z) 100 + ´ + + Þ 5z{ + 7z ? 50z + 4z{ ... (kk) Þ 50z + 4{z ? 5z{ + 7z Þ 47z ? z{ { ? 47 \ Uq, pwodgt qh dtqyp uqemu ? 47 78. (*) Fcvc Kpeqpukuvgpv. 79. (c) 7:. (d) Eqpukfgtkpi vjg yqtuv ecug Hktuv 17 rkemgf dcnnu ctg tgf cpf yjkvg. Jgpeg kp 18vj vkog kv ku cuuwtgf vjcv 5 fkhhgtgpv eqnqwt dcnnu gzkuv. 7;. (e) —B —B — 1 2 4 dq{u ecp vcmg vjgkt ugcvu kp 4! yc{u cpf 5 iktnu ecp vcmg vjg tgockpkpi 5 ugcvu kp C2 3 2! ´ yc{u. Jgpeg, C2 2! 3 2! ´ ´ ? 14 yc{u. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 80 1. C rgtuqp vtcxgnngf htqo qpg rnceg vq cpqvjgt cv cp cxgtcig urggf qh 60 mknqogvtgu/jqwt cpf dcem vq vjg qtkikpcn rnceg cv cp cxgtcig urggf qh 70 mknqogvtgu/ jqwt. Yjcv ku jku cxgtcig urggf (kp mknqogvtgu/jqwt) fwtkpi vjg gpvktg tqwpf-vtkrA [1995] (c) 67 (d) 40 7 (e) 600 / ; (f) korquukdng vq hkpf qwv wpnguu vjg fkuvcpeg dgvyggp vjg vyq rncegu ku mpqyp 2. Fkuvcpeg vkog itcrj kp tgurgev qh c tceg coqpi hqwt rgtuqpu ku ujqyp kp vjg ikxgp hkiwtg. Eqpukfgt vjg hqnnqykpi uvcvgogpvu kp vjku tgictf< [1996] F C D E Vkog Fkuvcpeg 1. 'C' uvqqf hktuv kp vjg tceg 4. 'E' ngf cnn vjg yc{ 5. 'F' tcp hcuvgt vjcp qvjgtu kp vjg ncvgt rctv qh vjg tceg Qh vjgug uvcvgogpvu (c) 1 cpf 5 ctg hcnug cpf 4 ku vtwg (d) 1 cpf 4 ctg hcnug cpf 5 ku vtwg (e) 1 cpf 5 ctg vtwg cpf 4 ku hcnug (f) 1 ku vtwg cpf 4 cpf 5 ctg hcnug 3. C dqcv yjkej jcu c urggf qh 7 mo/jt kp uvknn ycvgt etquugu c tkxgt qh ykfvj 1 mo cnqpi vjg ujqtvguv rquukdng rcvj kp 17 okpwvgu. Vjg xgnqekv{ qh vjg tkxgt ycvgt (kp mo/jt) ku [1997] (c) 1 (d) 5 (e) 6 (f) 41 4. Qpg nqecn cpf cpqvjgt gzrtguu vtckp ygtg rtqeggfkpi kp vjg ucog fktgevkqp qp rctcnngn vtcemu cv 4; mo/jqwt cpf 87 mo/jqwt tgurgevkxgn{. Vjg ftkxgt qh vjg hqtogt pqvkegf vjcv kv vqqm gzcevn{ 18 ugeqpfu hqt vjg hcuvgt vtckp vq rcuu d{ jko. Yjcv ku vjg ngpivj qh vjg hcuvgt vtckpA [1998] (c) 80 o (d) 140 o (e) 180 o (f) 460 o 5. Vjg cxgtcig urggf qh c vtckp kp vjg qpyctf lqwtpg{ ku 47% oqtg vjcp vjcv qh vjg tgvwtp lqwtpg{. Vjg vtckp jcnvu hqt qpg jqwt qp tgcejkpi vjg fguvkpcvkqp. Vjg vqvcn vkog vcmgp hqt vjg eqorngvg vq cpf htq lqwtpg{ ku 19 jqwtu eqxgtkpi c fkuvcpeg qh :00 mo. Vjg urggf qh vjg vtckp kp vjg qpyctf lqwtpg{ ku [1999] (c) 67 mo rgt jqwt (d) 69.08 rgt jqwt (e) 70.00 mo rgt jqwt (f) 78.47 mo rgt jqwt 6. C rgtuqp uvctvu htqo c rqkpv C cpf vtcxgnu 5 mo gcuvyctfu vq D cpf vjgp vwtpu nghv cpf vtcxgnu vjtkeg vjcv fkuvcpeg vq tgcej E. Jg cickp vwtpu nghv cpf vtcxgnu hkxg vkogu vjg fkuvcpeg jg eqxgtgf dgvyggp C cpf D cpf tgcejgu jku fguvkpcvkqp F. Vjg ujqtvguv fkuvcpeg dgvyggp vjg uvctvkpi rqkpv cpf fguvkpcvkqp ku [2000] (c) 1: mo (d) 18 mo (e) 17 mo (f) 14 mo 7. C rgtuqp vtcxgnu htqo X vq Y cv c urggf qh 60 morj cpf tgvwtpu d{ kpetgcukpi jku urggf 70%. Yjcv ku jku cxgtcig urggf hqt dqvj vjg vtkruA [2001] (c) 58 morj (d) 67 morj (e) 6: morj (f) 70 morj 8. C yqtmgt tgcejgu jku hcevqt{ 5 okpwvgu ncvg kh jku urggf htqo jku jqwug vq vjg hcevqt{ ku 7 mo/jt Kh jg ycnmu cv c urggf qh 8 mo/jt, vjgp jg tgcejgu vjg hcevqt{ 9 okpwvgu gctn{. Vjg fkuvcpeg qh vjg hcevqt{ htqo jku jqwug ku [2001] (c) 6 mo (d) 7 mo (e) 8 mo (f) 9 mo Chapter 5 Time
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Time and Distance F 81 ;. C eqpxg{gt dgnv fgnkxgtu dciicig cv vjg tcvg qh 5 vqppu kp 7 okpwvgu cpf c ugeqpf eqpxg{gt dgnv fgnkxgtu dciicig cv vjg tcvg qh 1 vqppu kp 4 okpwvgu. Jqy owej vkog yknn kv vcmg vq igv 55 vqppu qh dciicig fgnkxgtgf wukpi dqvj vjg eqpxg{gt dgnvuA ]4001_ (c) 47 okpwvgu cpf 50 ugeqpfu (d) 50 okpwvgu (e) 57 okpwvgu (f) 60 okpwvgu cpf 67 ugeqpfu 10. Vyq ncfkgu ukownvcpgqwun{ ngcxg ekvkgu C cpf D eqppgevgf d{ c uvtckijv tqcf cpf vtcxgn vqyctfu gcej qvjgt. Vjg hktuv ncf{ vtcxgnu 4 mo/jt hcuvgt vjcp vjg ugeqpf ncf{ cpf tgcejgu D qpg jqwt dghqtg vjg ugeqpf ncf{ tgcejgu C. Vjg vyq ekvkgu C cpf D ctg 46 mo. crctv. Jqy ocp{ mknqogvgtu fqgu gcej ncf{ vtcxgn kp qpg jqwtA ]4004_ (c) 7 mo, 5 mo (d) 9 mo, 7 mo (e) : mo, 8 mo (f) 18 mo, 16 mo 11. C dwu ku oqxkpi cv c urggf qh 50 mo/jt cjgcf qh c ect ykvj urggf qh 70 mo/jt. Jqy ocp{ mknqogvtgu crctv ctg vjg{ kh kv vcmgu 17 okpwvgu hqt vjg ect vq ecvej wr vjg dwuA ]4004_ (c) 7 mo (d) 9.7 mo (e) 14.7 mo (f) 17 mo 14. C vtckp qh ngpivj 170 ogvtgu, oqxkpi cv c urggf qh ;0 mo/jt ecp etquu c 400 ogvtgu dtkfig kp ]4004_ (c) : ugeqpfu (d) 16 ugeqpfu (e) 8 ugeqpfu (f) 17 ugeqpfu 15. C ect vtcxgnu vjg hktuv qpg-vjktf qh c egtvckp fkuvcpeg ykvj c urggf qh 10 mo/jtu. Vjg pgzv qpg-vjktf qh fkuvcpeg ykvj c urggf qh 40 mo/jtu. cpf vjg ncuv qpgvjktf fkuvcpeg ykvj c urggf qh 80 mo/jtu. Vjg cxgtcig urggf qh vjg ect hqt vjg yjqng lqwtpg{ ku < ]4005_ (c) 1: mo/jtu (d) 46 mo/jtu (e) 50 mo/jtu (f) 58 mo/jtu 16. Vqvcn vkog vcmgp d{ c rgtuqp kp iqkpi vq c rnceg d{ ycnmkpi cpf tgvwtpkpi qp e{eng ku 7 jqwtu 67 okpwvgu. Jg yqwnf jcxg ickpgf 4 jqwtu d{ e{enkpi dqvj yc{u. Vjg vkog vcmgp d{ jko vq ycnm dqvj yc{u, ku ]4005_ (c) 8 jqwtu 67 okpwvgu (d) 9 jqwtu 67 okpwvgu (e) : jqwtu 17 okpwvgu (f) : jqwtu 50 okpwvgu, 17. Vyq ectu Z cpf [ uvctvu htqo vyq rncegu C cpf D tgurgevkxgn{ yjkej ctg 900 mo crctv cv ; c.o. Dqvj vjg ectu twp cv cp cxgtcig urggf qh 80 mo/jt. Ect Z uvqru cv 10 c.o. cpf cickp uvctvu cv 11 c.o., yjkng vjg qvjgt ect [ eqpvkpwgu vq twp ykvjqwv uvqrrkpi. Yjgp fq vjg vyq ectu etquu gcej qvjgtA ]4006_ (c) 4<60 r.o. (d) 5.40 r.o. (e) 6<10 r.o. (f) 6< 40 r.o. 18. C cpf D uvctv hqto vjg ucog rqkpv cpf kp vjg ucog fktgevkqp cv 9 c.o. vq ycnm ctqwpf c tgevcpiwnct hkgnf 600 o Ù 500 o. C cpf D ycnm cv vjg tcvg qh 5 mo/jt cpf 4.7 mo/jt tgurgevkxgn{. Jqy ocp{ vkogu ujcnn vjg{ etquu gcej qvjgt, kh vjg{ eqpvkpwg vq ycnm vknn 14<50 r.o.A ]4006_ (c) Pqv gxgp qpeg (d) Qpeg (e) Vykeg (f) Vjtkeg 19. 70 ogp qt :0 yqogp ecp hkpkuj c lqd kp 70 fc{u. C eqpvtcevqt gornq{u 60 ogp cpf 6: yqogp hqt vjku yqtm, dwv chvgt gxgt{ fwtcvkqp qh 10 fc{u, 7 eqorngvgf. Vjg yqtm ku eqorngvgf kp ]4006_ (c) 67 fc{u (d) 70 fc{u (e) 76 fc{u (f) 84 fc{u 1:. Ct{cp twpu cv c urggf qh 60 ogvtgu/okpwvg. Tcjwn hqnnqyu jko chvgt cp kpvgtxcn qh 7 okpwvgu cpf twpu cv c urggf qh 70 ogvtgu/okpwvg. Tcjwn'u fqi twpu cv c urggf qh 80 ogvtgu/okpwvg cpf uvctvu cnqpi ykvj Tcjwn. Vjg fqi tgcejgu Ct{cp cpf vjgp eqogu dcem vq Tcjwn, cpf eqpvkpwgu vq fq uq vknn Tcjwn tgcejgu Ct{cp. Yjcv ku vjg vqvcn fkuvcpeg eqxgtgf d{ vjg fqiA ]4007_ (c) 800 ogvtgu (d) 970 ogvtgu (e) ;:0 ogvtgu (f) 1400 ogvtgu 1;. Vjgtg ctg gkijv gswkfkuvcpv rqkpvu 'C', 'D', 'E', 'F', 'G', 'H', 'I', cpf 'J' kp vjg enqemykug fktgevkqp qp vjg rgtkrjgt{ qh c ekteng. Kp c vkog kpvgtxcn v, c rgtuqp tgcejgu htqo' C' vq 'E' ykvj wpkhqto oqvkqp yjkng cpqvjgt rgtuqp tgcejgu vjg rqkpv 'G' htqo vjg rqkpv 'D' fwtkpi vjg ucog vkog kpvgtxcn ykvj wpkhqto oqvkqp. Dqvj vjg rgtuqpu oqxg kp vjg ucog fktgevkqp cnqpi vjg ektewohgtgpeg qh vjg ekteng cpf uvctv cv vjg ucog kpuvcpv. Jqy owej vkog chvgt vjg uvctv, yknn vjg vyq rgtuqpu oggv gcej qvjgtA ]4008_ (c) 6v (d) 9v (e) ;v (f) Pgxgt 40. Cokv uvctvu htqo c rqkpv C cpf ycnmu vq cpqvjgt rqkpv D, cpf vjgp tgvwtpu htqo D vq C d{ jku ect cpf vjwu vcmgu c vqvcn vkog qh 8 jqwtu cpf 67 okpwvgu. Kh jg jcf ftkxgp dqvj yc{u kp jku ect, jg yqwnf jcxg vcmgp 4 jqwtu nguu. Jqy nqpi yqwnf kv vcmg hqt jko vq ycnm dqvj yc{uA ]4009_ (c) 9 jqwtu 67 okpwvgu (d) : jqwtu 17 okpwvgu (e) : jqwtu 50 okpwvgu (f) : jqwtu 67 okpwvgu 41. C cpf D ecp eqorngvg yqtm vqigvjgt kp 7 fc{u. Kh C yqtmu cv vykeg jku urggf cpf D cv jcnh qh jku urggf, vjku yqtm ecp dg hkpkujgf kp 6 fc{u. Jqy ocp{ fc{u yqwnf kv vcmg hqt C cnqpg vq eqorngvg vjg lqdA ]4009_ (c) 10 (d) 14 (e) 17 (f) 1: Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 82 44. C vtckp eqorngvgu c lqwtpg{ ykvj c hgy uvqrrcigu kp dgvyggp cv cp cxgtcig urggf qh 60 mo rgt jqwt. Kh vjg vtckp jcf pqv uvqrrgf cp{yjgtg, kv yqwnf jcxg eqorngvgf vjg lqwtpg{ cv cp cxgtcig urggf qh 80 mo rgt jqwt. Qp cp cxgtcig, jqy ocp{ okpwvgu rgt jqwt fqgu vjg vtckp uvqr fwtkpi vjg lqwtpg{A ]4009_ (c) 40 okpwvgu rgt jqwt (d) 1: okpwvgu rgt jqwt (e) 17 okpwvgu rgt jqwt (f) 10 okpwvgu rgt jqwt 45. Ectrgpvgt C ecp ocmg c ejckt kp 8 jqwtu, ectrgpvgt D kp 9 jqwtu cpf ectrgpvgt E kp : jqwtu. Kh gcej ectrgpvgt yqtmu hqt : jqwtu rgt fc{, jqy ocp{ ejcktu yknn dg ocfg kp 41 fc{uA ]400:_ (c) 81 (d) 89 (e) 95 (f) 9; 46. Vyq vtckpu ngcxg Pgy Fgnjk cv vjg ucog vkog. Qpg vtcxgnu pqtvj cv 80 morj cpf vjg qvjgt vtcxgnu uqwvj cv 60 morj. Chvgt jqy ocp{ jqwtu yknn vjg vtckpu, dg 170 mo crctv A ]4010_ (c) 5 4 (d) 6 5 (e) 5 6 (f) 17 4 47. Twppkpi cv c urggf qh 80 mo rgt jqwt, c vtckp rcuugf vjtqwij c 1.7 mo nqpi vwppgn kp vyq okpwvgu. Yjcv ku vjg ngpivj qh vjg vtckpA ]4010_ (c) 470 o (d) 700 o (e) 1000 o (f) 1700 o 48. C rgtuqp vtcxgnngf c fkuvcpeg qh 70 mo kp : jqwtu. Jg eqxgtgf c rctv qh vjg fkuvcpeg, qp hqqv cv vjg tcvg qh 6 mo rgt jqwt cpf c rctv qp c dke{eng cv vjg tcvg qh 10 mo rgt jqwt. Jqy owej fkuvcpeg fkf jg vtcxgn qp hqqvA ]4010_ (c) 10 mo (d) 40 mo (e) 50 mo (f) 60 mo 49. Vjtgg ogp uvctv vqigvjgt vq vtcxgn vjg ucog yc{ ctqwpf c ektewnct vtcem qh 11 mo. Vjgkt urggfu ctg 6, 7.7 cpf : morj tgurgevkxgn{. Yjgp yknn vjg{ oggv cv vjg uvctvkpi rqkpv hqt vjg hktuv vkogA ]4010_ (c) Chvgt 11 jqwtu (d) Chvgt 41 jqwtu (e) Chvgt 44 jqwtu (f) Chvgt 55 jqwtu 4:. Kh c dwu vtcxgnu 180 mo kp 6 jqwtu cpf c vtckp vtcxgnu 540 mo kp 7 jqwtu cv wpkhqto urggfu, vjgp yjcv ku vjg tcvkq qh vjg fkuvcpegu vtcxgnngf d{ vjgo kp qpg jqwt A ]4011 - KK_ (c) : < 7 (d) 7 < : (e) 6 < 7 (f) 1 < 4 4;. Ot. Mwoct ftkxgu vq yqtm cv cp cxgtcig urggf qh 6: mo rgt jqwt. Vjg vkog vcmgp vq eqxgt vjg hktuv 80% qh vjg fkuvcpeg ku 10 okpwvgu oqtg vjcp vjg vkog vcmgp vq eqxgt vjg tgockpkpi fkuvcpeg. Jqy hct ku jku qhhkegA ]4014 - KK_ (c) 50 mo (d) 60 mo (e) 67 mo (f) 6: mo 50. C rgtuqp ecp ycnm c egtvckp fkuvcpeg cpf ftkxg dcem kp ukz jqwtu. Jg ecp cnuq ycnm dqvj yc{u kp 10 jqwtu. Jqy owej vkog yknn jg vcmg vq ftkxg dqvj yc{uA ]4015 - KK_ (c) Vyq jqwtu (d) Vyq cpf c jcnh jqwtu (e) Hkxg cpf c jcnh jqwtu (f) Hqwt jqwtu 51. Hqwt ectu ctg jktgf cv vjg tcvg qh ` 8 rgt mo rnwu vjg equv qh fkgugn cv ` 60 c nkvtg. Kp vjku eqpvgzv, eqpukfgt vjg fgvcknu ikxgp kp vjg hqnnqykpi vcdng< ]4015 - KK_ Okngcig Vqvcn Ect Jqwtu (mo / ) Rc{ogpv( ) C : 40 4140 D 10 47 1;70 E ; 46 4086 F 11 44 1:14 l ` Yjkej ect ockpvckpgf vjg oczkowo cxgtcig urggfA (c) Ect C (d) Ect D (e) Ect E (f) Ect F 54. C vjkgh twppkpi cv : mo/jt ku ejcugf d{ c rqnkegocp yjqug urggf ku 10 mo/jt. Kh vjg vjkgh ku 100 o cjgcf qh vjg rqnkegocp, vjgp vjg vkog tgswktgf hqt vjg rqnkegocp vq ecvej vjg vjkgh yknn dg ]4015 - KK_ (c) 4 okp (d) 5 okp (e) 6 okp (f) 8 okp 55. C vtckp vtcxgnu cv c egtvckp cxgtcig urggf hqt c fkuvcpeg qh 85 mo cpf vjgp vtcxgnu c fkuvcpeg qh 94 mo cv cp cxgtcig urggf qh 8 mo/jt oqtg vjcp kvu qtkikpcn urggf. Kh kv vcmgu 5 jqwtu vq eqorngvg vjg vqvcn lqwtpg{, yjcv ku vjg qtkikpcn urggf qh vjg vtckp kp mo/jtA ]4015 - KK_ (c) 46 (d) 55 (e) 64 (f) 88 56. Nqecvkqp qh D ku pqtvj qh C cpf nqecvkqp qh E ku gcuv qh C. Vjg fkuvcpegu CD cpf CE ctg 7 mo cpf 14 mo tgurgevkxgn{. Vjg ujqtvguv fkuvcpeg (kp mo) dgvyggp vjg nqecvkqpu D cpf E ku ]4016 - KK_ (c) 80 (d) 15 (e) 19 (f) 9 57. Vyq ectu uvctv vqyctfu gcej qvjgt, htqo vyq rncegu C cpf D yjkej ctg cv c fkuvcpeg qh 180 mo. Vjg{ uvctv cv vjg ucog vkog 0: <10 CO. Kh vjg urggfu qh vjg ectu ctg 70 mo cpf 50 mo rgt jqwt tgurgevkxgn{, vjg{ yknn oggv gcej qvjgt cv ]4016 - KK_ (c) 10 <10 CO (d) 10 <50 CO (e) 11<10 CO (f) 11<40 CO Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Time and Distance F 83 58. C uvtckijv nkpg ugiogpv ku 58 eo nqpi. Rqkpvu ctg vq dg octmgf qp vjg nkpg htqo dqvj vjg gpf rqkpvu. Htqo gcej gpf, vjg hktuv rqkpv ku cv c fkuvcpeg qh 1eo htqo vjg gpf, vjg ugeqpf rqkpv ku cv c fkuvcpeg qh 4 eo htqo vjg hktuv rqkpv cpf vjg vjktf rqkpv ku cv c fkuvcpeg qh 5 eo htqo vjg ugeqpf rqkpv cpf uq qp. Kh vjg rqkpvu qp vjg gpfu ctg pqv eqwpvgf cpf vjg eqooqp rqkpvu ctg eqwpvgf cu qpg, yjcv ku vjg pwodgt qh rqkpvu A ]4016 - KK_ (c) 10 (d) 14 (e) 16 (f) 18 59. C cpf D fgekfg vq vtcxgn htqo rnceg Z vq rnceg [ d{ dwu. C jcu ` 10 ykvj jko cpf jg hkpfu vjcv kv ku :0% qh vjg dwu hctg hqt vyq rgtuqpu. D hkpfu vjcv jg jcu ` 5 ykvj jko cpf jcpfu kv qxgt vq C. Kp vjku eqpvgzv, yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ku eqttgev A ]4016 - KK_ (c) Pqy vjg oqpg{ C jcu ku lwuv gpqwij vq dw{ vyq vkemgvu. (d) C uvknnpggfu ` 4 hqt dw{kpi vjg vkemgvu. (e) Chvgt dw{kpi vjg vyq vkemgvu C yknn dg nghv ykvj 70 rckug. (f) Vjg oqpg{ C pqy jcu ku uvknn pqv uwhhkekgpv vq dw{ vyq vkemgvu. 5:. Kp c 700 ogvtgu tceg, D uvctvu 67 ogvtgu cjgcf qh C, dwv C ykpu vjg tceg yjkng D ku uvknn 57 ogvtgu dgjkpf. Yjcv ku vjg tcvkq qh vjg urggfu qh C vq D cuuwokpi vjcv dqvj uvctv cv vjg ucog vkogA ]4017-KK_ (c) 47< 41 (d) 47< 40 (e) 7<5 (f) 7<9 5;. Vyq ekvkgu C cpf D ctg 580 mo crctv. C ect iqgu htqo C vq D ykvj c urggf qh 60 mo/jt cpf tgvwtpu vq C ykvj c urggf qh 80 mo/jt. Yjcv ku vjg cxgtcig urggf qh vjg ectA ]4017-KK_ (c) 67 mo/jt (d) 6: mo/jt (e) 70 mo/jt (f) 77 mo/jt 60. Vyq rkrgu C cpf D ecp kpfgrgpfgpvn{ hknn c vcpm eqorngvgn{ kp 40 cpf 50 okpwvgu tgurgevkxgn{. Kh dqvj vjg rkrgu ctg qrgpgf ukownvcpgqwun{, jqy owej vkog yknn vjg{ vcmg vq hknn vjg vcpm eqorngvgn{A ]4017-KK_ (c) 10 okpwvgu (d) 14 okpwvgu (e) 17 okpwvgu (f) 47 okpwvgu 61. C cpf D ycnm ctqwpf c ektewnct rctm. Vjg{ uvctv cv : c.o. htqo vjg ucog rqkpv kp vjg qrrqukvg fktgevkqpu. C cpf D ycnm cv c urggf qh 4 tqwpfu rgt jqwt cpf 5 tqwpfu rgt jqwt tgurgevkxgn{. Jqy ocp{ vkogu ujcnn vjg{ etquu gcej qvjgt chvgt :¹00 c.o. cpf dghqtg ;.50. c.o.A ]4018-KK_ (c) 9 (d) 8 (e) 7 (f) : 64. Hqwt htkgpfu C, D, E cpf F pggf vq etquu c dtkfig. C oczkowo qh vyq rgtuqpu ecp etquu kv cv c vkog. Kv ku pkijv cpf vjg{ lwuv jcxg qpg ncor. Rgtuqpu vjcv etquu vjg dtkfig owuv ectt{ vjg ncor vq hkpf vjg yc{. C rckt owuv ycnm vqigvjgt cv vjg urggf qh unqygt rgtuqp. Chvgt etquukpi vjg dtkfig, vjg rgtuqp jcxkpi hcuvgt urggf kp vjg rckt yknn tgvwtp ykvj vjg ncor gcej vkog vq ceeqorcp{ cpqvjgt rgtuqp kp vjg itqwr. Hkpcnn{, vjg ncor jcu vq dg tgvwtpgf cv vjg qtkikpcn rnceg cpf vjg rgtuqp yjq tgvwtpu vjg ncor jcu vq etquu vjg dtkfig cickp ykvjqwv ncor. Vq etquu vjg dtkfig, vjg vkog vcmgp d{ vjgo ku cu hqnnqyu < C < 1 okpwvg, D < 4 okpwvgu, E < 9 okpwvgu cpf F < 10 okpwvgu. Yjcv ku vjg vqvcn okpkowo vkog tgswktgf d{ cnn vjg htkgpfu vq etquu vjg dtkfigA ]4018-KK_ (c) 45 okpwvgu (d) 44 okpwvgu (e) 41 okpwvgu (f) 40 okpwvgu 65. C fckn{ vtckp ku vq dg kpvtqfwegf dgvyggp uvcvkqp C cpf uvcvkqp D uvctvkpi htqo gcej cv 8 CO cpf vjg lqwtpg{ ku vq dg eqorngvgf kp 64 jqwtu. Yjcv ku vjg pwodgt qh vtckpu pggfgf kp qtfgt vq ockpvckp vjg Ujwvvng UgtxkegA ]4018-KK_ (c) 4 (d) 5 (e) 6 (f) 9 66. C htgkijv vtckp nghv Fgnjk hqt Owodck cv cp cxgtcig urggf qh 60 mo/jt. Vyq jqwtu ncvgt, cp gzrtguu vtckp nghv Fgnjk hqt Owodck, hqnnqykpi vjg htgkijv vtckp qp c rctcnngn vtcem cv cp cxgtcig urggf qh 80 mo/jt. Jqy hct htqo Fgnjk yqwnf vjg gzrtguu vtckp oggv vjg htgkijv vtckpA ]4019-KK_ (c) 6:0 mo (d) 480 mo (e) 460 mo (f) 140 mo Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 84 1. (e) Ngv vjg fkuvcpeg eqxgtgf d{ vjg rgtuqp dg z mo kp gcej ncr. Vqvcn vkog vcmgp ? 60 70 + z z ? ; 400 z Vqvcn fkuvcpeg eqxgtgf ? z + z ? 4z mo \ Cxgtcig urggf ? Vqvcn fkuvcpeg eqxgtgf Vqvcn vkog vcmgp ? 4 (; / 400) z z ? 600 ; mo/j. 4. (d) “C” pgxgt uvqqf 1uv kp vjg tceg, kv ycu “F” yjq uvqqf 1 uv. Htqo vjg itcrj, kv ecp dg uggp vjcv “E” fq pqv ngcf cnn vjg yc{. Yjkng “F” chvgt uvctvkpi unqygt, tcp hcuvgt vjcp qvjgtu kp vjg ncvgt rctv qh vjg tceg. 5. (d) Vjg urggf qh vjg dqcv cnqpi vjg ujqtvguv rquukdng rcvj 1 17 80 CD = ? 6 mo/j A C v 1 km B 5 km/h Pqy vjg xgnqekv{ qh vjg tkxgtycvgt 4 4 x = - 7 6 = - 47 18 x = ; x ? 5 mo/j 6. (e) Tgncvkxg urggf qh hcuvgt vtckp ykvj tgurgev vq vjg unqygt vtckp ? (87 4; 1000 ) 5800 - ´ ? 10 o/u \ Ngpivj qh vjg hcuvgt vtckp ? Tgncvkxg urggf Ù vkog vcmgp ? 10 Ù 18 ? 180 o 7. (f) Fkuvcpeg eqxgtgf fwtkpi qpyctf lqwtpg{ ? Fkuvcpeg eqxgtgf fwtkpi tgvwtp lqwtpg{ ? :00 4 ? 600 mo Ngv vjg vkog vcmgp fwtkpi qpyctf lqwtpg{ dg v jt. Ukpeg 1 jqwt ku vjg jcnv vkog, uq vkog vcmgp fwtkpi vjg tgvwtp lqwtpg{ ? (19 ˜ 1 ˜ v) ? 18 ˜ v jt. Ngv vjg cxgtcig urggf fwtkpi vjg tgvwtp lqwtpg{ dg x mo/jt \ Cxgtcig urggf fwtkpi vjg qpyctf lqwtpg{ ? x 1 1 6 æ ö ç ÷ + è ø ? 7 6 x mo/jt Pqy, 600 ? 7 6 æ ö ç ÷´ è ø x v v ? 540 x .....(k) Cnuq, 600 ? x(18 ˜ v) .....(kk) Rwvvkpi xcnwg qh (k) kp (kk), 540 18 æ ö ç ÷ - è ø x x ? 600 x ? 67 mo/jt \ Urggf fwtkpi qpyctf lqwtpg{ ? 7 (67) 6 ? 78.47 mo/jt. 8. (e) 17 mo P U Y G F E C S 5 mo ; mo D EP ? CD ? 5 mo PF ? EF ˜ EP ? 17 ˜ 5 ? 14 mo CP ? DE ? ; mo CF ku vjg tgswktgf ujqtvguv fkuvcpeg. D{ rc{vjcitqwu vjgqtgo, CF ? ( )( ) 4 4 CP PF + ? () ( ) 4 4 ; 14 + ?17 mo 9. (e) Ngv vjg fkuvcpeg htqo Z vq [ ? z mo Urggf vqyctfu hqto Z vq [ ? 60 mo/jt. Vkog vcmgp ? 60 z Tgvwtpkpi urggf htqo [ vq Z ? 60 + (70% qh 60) ? 60 + 40 ? 80 mo/jt \ Vkog vcmgp kp lqwtpg{ ? 80 z HINTS & SOLUTIONS Explanations Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Time and Distance F 85 Pqy, cxgtcig urggf hqt yjqng lqwtpg{ ? Vqvcn Fkuvcpeg Vqvcn vkog ? 4z 6:00 z z 100 60 80 = + ? 6: mo. :. (d) Ngv vjg fkuvcpeg dg z mo Cu rgt swguvkqp, z5 z9 7 80 8 80 - =+ z z 10 1 7 8 80 8 -= = z 1 50 8 = z ? 7 mo ;. (d) Hqt 1uv dgnv, dciicig fgnkxgtgf kp 1 okp ? 5 7 vqppu Hqt 4pf dgnv, dciicig fgnkxgtgf kp 1 okp ? 1 4 vqppu Vqvcn dciicig fgnkxgtgf kp 1 okp ? 5 1 7 4 + ? 11 10 vqppu Pqy, Vkog vcmgp vq fgnkxgt 11 10 vqppu dciicig ? 1 okp. Vkog vcmgp vq fgnkxgt 1 vqppu ? 10 11 okp Jgpeg, vkog vcmgp vq fgnkxgt 55 vqppu ? 10 11 Ù55 ? 50 okp 10. (e) Ngv vjg urggf qh vjg ugeqpf ncf{ dg x. Vjgp, vjg urggf qh vjg 1uv ncf{ ? x + 4 Cnuq, ngv vjg vkog vcmgp d{ vjg 4pf ncf{ vq tgcej C ? v. Vjgp, vjg vkog vcmgp d{ vjg 1uv ncf{ vq tgcej D ? (v ˜1) Pqy, 46 ? (x + 4)(v ˜1) ? xv .....(k) xv ? 46 x ? 46 v ....(kk) Rwvvkpi xcnwg qh x htqo gswcvkqp (kk) kp gswcvkqp (k), (x + 4)(v ˜ 1) ? 46 46 4 æ ö ç ÷ + è ø v (v ˜ 1) ? 46 v 4 ˜ v ˜ 14 ? 0 v 4 ˜ 6v + 5v ˜ 14 ? 0 v(v ˜ 6) + 5(v˜ 6) ? 0 v ˜ 6 ? 0= v + 5 ? 0 v ? ˜5 cpf v ? 6 pgingevkpi v ? ˜5 \ v ? 6 \ x ? 46 6 ? 8 mo. Jgpeg, Fkuvcpeg vtcxgnngf d{ vjg 1uv ncf{ kp qpg jqwt ? (x + 4) Ù 1 ? : mo Fkuvcpeg vtcxgnngf d{ vjg 4pf ncf{ kp qpg jqwt ? x Ù 1 ? 8 mo 11. (c) Ceeqtfkpi vq swguvkqp tgncvkxg urggf qh vjg ect ykvj tgurgev vq vjg dwu ? 70 ˜ 50 ? 40 mo/jt. Pqy, Fkuvcpeg dgvyggp vjg ect cpf vjg dwu, yjgp vjg ect ecvejgu vjg dwu ? Fkuvcpeg vtcxgnngf d{ vjg ect kp 17 okp ? 17 40 80 ´ ? 7 mo. 14. (d) Ngpivj qh vtckp ? 170 o Urggf qh vtckp ? ;0 mo/j ? 7 ;0 1: ´ ? 47 o/u Ngpivj qh dtkfig ? 400 o Vq etquu vjg dtkfig, vjg vtckp jcu vq vtcxgn c fkuvcpeg gswcn vq uwo qh vjg ngpivj qh dtkfig cpf vjg ngpivj qh vtckp. Vqvcn fkuvcpeg vq dg eqxgtgf ? 170 + 400 ? 570 o Vkog vcmgp ? Fkuvcpeg Urggf ? 570 47 ? 16 ugeqpfu. 15. (c) Ngv vjg vqvcn fkuvcpeg dg “f” Hktuv 1/5tf fkuvcpeg k.g. f/5 mo ku eqxgtgf cv urggf qh 10 mo/jtu. \ Vkog vcmgp ? / 5 10 f jtu. Ugeqpf 1/5tf fkuvcpeg k.g., f/5 mo ku eqxgtgf cv urggf qh 40 mo/jtu. \ Vkog vcmgp ? / 5 40 f jtu. Ncuv 1/5tf fkuvcpeg k.g. f/5 mo ku eqxgtgf cv urggf qh 80 mo/jtu. \ Cxgtcig urggf ? Vqvcn eqxgtgf fkuvcpeg Vqvcn vcmgp vkog ? /5 /5 /5 /5 /5 /5 10 40 80 + + + + fff fff ? 1:0 851 + + Uq Cxgtcig urggf ? 1: mo/jtu. 16. (d) Ycnmkpi vkog + e{enkpi vkog ? 7 Jqwtu 67 okpwvgu ? 567 okp. ...(k) kh jg jcf e{engf dqvj yc{ jg yqwnf jcxg ickp 4 jtu (140 okp.) 4 Ù e{enkpi vkog ? 567 ˜ 140 ? 447 okp ...(kk) e{enkpi vkog ? 447 4 ? 114.7 Ycnmkpi vkog ? 567 ˜ 114.7 ? 454.7 \ Vkog vcmgp d{ jko vq ycnm dqvj yc{u ? 4(454.7) ? 687 okp ? 9 jt 67 okp Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 86 17. (d) Fkuvcpeg vtcxgnngf d{ Z wrvq 11 c.o. ? Fkuvcpeg vtcxgnngf d{ Z wrvq 10 c.o. ? 80 Ù 1 ? 80 mo. Fkuvcpeg vtcxgnngf d{ [ wrvq 11 c.o. ? 4 Ù 80 ? 140 Pqy, cv 11 c.o., fkuvcpeg dgvyggp Z cpf [ ? 900 ˜ (140 + 80) ? 740 mo.jt. Tgncvkxg urggf qh Z ykvj tgurgev vq [ ? 80 ˜ (˜80) ? 140 mo/jt. Pqy, vjg{ yknn etquu gcej qvjgt, yjgp vjg{ eqxgt c fkuvcpeg qh 740 mo ykvj c tgncvkxg urggf qh 140 mo/jt chvgt 11 c.o. Vkog vcmgp chvgt 11 c.o. ? 740 140 ? 15 80 5 ´ okp ? 480 okp ? 6 jt. 40 okp. \ Vkog ? 11 + 6 jt. 40 okp ? 5<40 r.o. 18. (d) Vqvcn vkog hqt yjkej C cpf D vtcxgn ? 7 jt 50 okp ? 1 7 4 jtu (htqo 9 c.o. ˜ 14<50 r.o.) Fkuvcpeg vtcxgnngf d{ C kp 1 7 4 jqwtu ? 5 Ù 11/4 ? 18.7 mo Fkuvcpeg vtcxgngf d{ D kp 1 7 4 jqwtu? 4.7Ù 11/4 ? 15.97mo Vjgtghqtg kp 1 7 4 jqwtu, fkhhgtgpeg kp fkuvcpeg vtcxgnngf d{ C cpf D ku (18.7 ˜ 15.97) mo, k.g. 4.97 mo. Vjg vqvcn gzvtc fkuvcpeg pggf vq dg vtcxgnngf d{ qpg kp qtfgt vq etquu vjg qvjgt d{ cv ngcuv qpeg. Ngpivj qh rcvj ctqwpf vjg hkgnf ? rgtkogvgt qh tgevcping ? 4(n + d) ? 4(600 + 500) ? 1600 o ? 1.6 mo C okijv etquu D oqtg vjcp qpeg, hqt vjcv vjg{ oc{ pggf cv ngcuv 1.6 Ù 4 ? 4.: mo fkhhgtgpeg dgvyggp vjgougnxgu, dwv vjg fkhhgtgpeg ku 4.97 mo. Jgpeg, vjg{ yknn etquu gcej qvjgt qpn{ qpeg. 19. (d) Vqvcn pwodgt qh yqtmkpi fc{ ? 70 Ù 70 ? 4700 fc{u hqt ogp Hqt yqogp kv ku gswcn vq 6000 fc{u Hqt 1uv 10 fc{ ogcpu 60 ogp Ù 10 ? 600 fc{, 6: yqogp Ù 10 ? 6:0 fc{u 4pf chvgt 10 fc{u ogcpu 57 ogp Ù 10 ? 570 fc{, 60 yqogp Ù 10 ? 600 fc{u 5tf 10 fc{ 50 ogp Ù 10 ? 500 fc{u, 54 yqogp Ù 10 ? 540 fc{u 6vj 10 fc{ 47 ogp Ù 10 ? 470 fc{u, 46 yqogp Ù 10 ? 460 fc{u 7vj 10 fc{ 40 ogp Ù 10 ? 400 fc{u, 18 yqogp Ù 10 ? 180 fc{u Ogp ? 1700 fc{u, Yqogp ? 1800 fc{u 1 ocp ? 1.8 yqogp 1800 fc{u qh yqogp ? 1000 fc{ qh ogp Uq, 4700 fc{u pggf vq eqorngvg yqtm ogcp chvgt 70 fc{ k.g., Ocp qh 1800 yqtmkpi fc{u + yqocp qh 1800 fc{u k.g., 70 fc{u. 1:. (f) Ngv vjg{ oggv cv c fkuvcpeg qh “z” htqo uvctv, chvgt vkog “v” ukpeg Tcjwn uvctvu. 60 Ù (7 + v) ? 70 v Þ 400 + 60 v ? 70 v Þ v ? 400 10 ? 40 okp. \ z ? 70 Ù v ? 70 Ù 40 ? 1000 ogvtgu Htqo vjg ikxgp qrvkqpu kv ku engct vjcv cnn qrvkqpu gzegrv 1400 ogvtgu ctg uocnngt vjcp 1000 o cpf fqi kp cp{ ecug jcu vq oqxg oqtg vjcp 1000 o. 1;. (d) G H I J C D E F Ngv fkuvcpeg dgvyggp gcej rqkpv dg z. Cnuq, ngv urggf qh rgtuqpu htqo rqkpv C cpf D dg w cpf x tgurgevkxgn{. Fkuvcpeg dgvyggp C vq E ? 4z ? wv w ? 4z v Fkuvcpeg dgvyggp D vq G ? 5z ? xv x ? 5z v Tgncvkxg urggf qh rgtuqp htqo D ykvj tgurgev vqC ? 5 4 ˜ = z zz vvv Fkuvcpeg dgvyggp C cpf D ? 9z \ Rgtuqpu yknn oggv chvgt vkog 9 9 ( /) = = z v z v 40. (f) Ect Ycnm D Ngv vjg vkog vcmgp d{ ect ? E cpf vjg vkog vcmgp d{ ycnmkpi ? Y E + Y ? 8 jtu 67 okpwvgu ? 5 49 8 qt jtu 6 6 E + E ? 8 jtu 67 okpwvgu ˜ 4 jtu ? 6 jt 67 okpwvgu qt ? 5 5 8 4jt 6 jtu 6 6 - = Y + Y ? 49 5 4 6 jtu 6 6 ´ - ? 76 1; 57 5 jtu : jtu 66 6 6 -= = ? : jtu 67 okpwvgu Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Time and Distance F 87 41. (c) Ngv cnqpg vkog hqt C cpf D dg z cpf { tgurgevkxgn{. Pqy, 111 7 + = z { ...(k) Cnuq, 411 4 6 + = z { ...(kk) Uqnxkpi (k) cpf (kk), yg igv, z ? 10 cpf { ? 10 44. (c) Ykvjqwv uvqrrcig, fkuvcpeg vtcxgnngf rgt jqwt ? 80 mo Ykvj uvqrrcig, fkuvcpeg vtcxgnngf rgt jqwt ? 60 mo. \ Uvqrrcig fkuvcpeg rgt jqwt ? 80 ˜ 60 ? 40 mo Ukpeg, urggf ku 80 mo rgt jqwt, k.g., kp 80 okp.(1 mo ˜ 1 okp.) Jgpeg, uvqrrcig vkog rgt jqwt ? 40 okp. 45. (e) Kp 8 jqwtu, pwodgt qh ejcktu ocfg d{ ectrgpvgt C ? 1 \ Kp (41 Ù :) jqwtu, pwodgt qh ejcktu d{ C ? 41 : 4: 8 ´ = Ukoknctn{ kp (41 Ù :) jqwtu, pwodgt qh ejcktu d{ D ? 41 : 46 9 ´ = cpf pwodgt qh ejcktu d{ E kp (41 Ù :) jqwtu ? 41 : 41 : ´ = Jgpeg, vqvcn pwodgt qh ejcktu kp 41 fc{u ? 4: + 46 + 41 ? 95 46. (c) Ukpeg, dqvj vtckpu ctg oqxkpi kp qrrqukvg fktgevkqpu, uq tgncvkxg urggf qh qpg vtckp ykvj tgurgev vq vjg qvjgt ? 80 ˜ (˜ 60) ? 100 mo/jt \ Vkog ? 170 5 100 4 = jt. 47. (d) Ngv ngpivj qh vjg vtckp dg z. Vjgp, 1.7 + z ? 80 4 80 æ ö ç ÷ è ø z ? 4 ˜ 1.7 ? 0.7 mo ? 0.7 Ù 1000 ? 700 o. 48. (d) Ngv vjg vkog vcmgp vq vtcxgn qp hqqv cpf dke{eng dg v 1 cpf v 4 tgurgevkxgn{ Cnuq, ngv fkuvcpeg vtcxgnngf qp hqqv dg z. Pqy, v 1 + v 4 ? : 70 ˜ : 6 10 + = z z 7 100 ˜ 4 := 40 + = z z 5z ? 180 ˜ 10 z ? 80 5 z ? 40 mo. 49. (e) Ngv vjg okpkowo vkog dg v, yjgp vjg{ oggv cv vjg uvctvkpi rqkpv hqt vjg hktuv vkog. Uq, vjg pgv fkuvcpeg eqxgtgf owuv dg c ownvkrng qh 11. Pqy, (6 + 7.7 + :) v ? 11 (p) yjgtg, p ku cp kpvgigt. v ? 11( ) 19.7 p okpkwo xcnwg qh p ku 57, uq vjcv yg ecp igv cp crrtqrtkcvg xcnwg qh vkog. \ v ? 11 57 44 jt. 19.7 ´ = 4:. (d) Fkuvcpeg eqxgtgf d{ c dwu kp 6 jqwtu ? 180 mo. \ Fkuvcpeg eqxgtgf d{ c dwu kp 1 jqwt 180 60mo 6 = = Hwtvjgt, Fkuvcpeg eqxgtgf d{ c vtckp kp 7 jqwtu ? 540 mo \ Fkuvcpeg eqxgtgf d{ c vtckp kp 1 jqwt 540 86 mo 7 = = Tgswktgf tcvkq 60 7 7<: 86 : = == 4;. (d) 0.6 0.4 10 – = 48 48 60 d d 0.4 f ? 1 × 48 60 0 \ f ? 60 mo 50. (c) 4-yc{ ycnm ? 10 jtu \ 1-yc{ ycnm ? 7 jtu 1-yc{ ycnm + 1 yc{ ftkxg ? 8 jtu \ 1 yc{ ftkxg ? 8 ˜ 7 ? 1 jt Jgpeg, vyq yc{ ftkxg vcmg 4 jtu. 51. (c) Ngv vjg fkuvcpegu vtcxgnngf d{ ectu C, D, E cpf F dg c, d, e cpf f tgurgevkxgn{. Vjgp, vjg vqvcn rc{ogpv hqt ect C ? 8 60 : ´+ ´ c c ? 11c Þ 11c ? 4140 c ? 4140 11 Jgpeg, cxgtcig urggf qh “C” ? 40 c ? 4140 ;.85 11 40 = ´ Hqt D, vqvcn rc{ogpv hqt ect D ? 6 40 10 ´+ ´ b b Þ 10d ? 1;70 \ d ? 1;7 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 88 Jgpeg, cxgtcig urggf qh “D” ? 47 d \ 1;7 47 ? 9.: Hqt E, vqvcn rc{ogpv hqt ect E ? 8 60 ; ´+ ´ e e Þ e ? ; 1054 69 ´ Jgpeg cxgtig urggf d{ “E” ? 46 e ? ; 1054 :.45 69 46 ´ = ´ Hqt F, vqvcn rc{ogpv hqt ect F ? 8 60 11 ´+ ´ f f ? 1:14 f ? 11 ;08 75 ´ Jgpeg, vjg cxgtcig urggf qh F ? 675 :.7 44 75 = = f Cnn urggfu gzegrv C ctg nguu vjcp ;. Jgpeg kv”u itgcvguv xcnwg. 54. (d) Kh yg eqpukfgt vjg fkhhgtgpeg qh urggfu, rqnkegocp ku 4 mo/jt ngcfkpi urggf cpf jg ecp ecvej vjg vjkgh cv 100 o cjgcf d{ 100 o 100 80 4 morj 1000 4 æ ö ç ÷ = ´ ´ è ø ? 5 okp. 55. (e) Ngv vjg qtkikpcn urggf ? z Vqvcn vkog vcmgp ? 5 jt Þ 85 94 5 8 = + z z + Þ (z) (z + 8) ? 41(z + 8) + 46(z) Þ z 4 ˜ 5;z ˜ 148 ? 0 Þ z 4 ˜ 64z + 5z ? 148 ? 0 Þ (z ˜ 64) (z + 5) ? 0 z ? 64, z ? ˜ 5 z ? ˜ 5 ku tglgevgf. Jgpeg, qtkikpcn urggf ycu 64 mo/jt. 56. (d) Ujqtvguv Fkuvcpeg, DE ? 7 + 14 ? 15 mo 4 4 C D E 7 14 57. (c) C D 180 mo 70 morj 50 morj E Uwrrqug vjg ectu oggv cv rqkpv E chvgt “v” jtu. \ CE ? 70 v cpf DE ? 50 v \ 70 v + 50 v ? 180 180 v :0 = ? 4 jtu. Uq, vjg ectu yknn oggv cv 10 < 10 CO 58. (e) 58 eo 1 4 5 .......... p \ 1 + 4 + 5 + ........ p ? 58 pp 1 ( ) 58 4 + = p(p + 1) ? 94 Þ p ? : \ Ngcxkpi vjg gpf rqkpvu vjg pq. qh rqkpvu uvctvkpi htqo C ku 9. Ukoknctn{ uvctvkpi htqo D, vjg pq. qh rqkpvu yknn dg 9. Cpf cnuq pq. qh vjg rqkpvu dgvyggp C & D yknn eqkpekfg. \ Vqvcn pq. qh rqkpvu ? 9 + 9 ? 16 59. (e) Ngv equv qh 1 vkemgv ku ` z. \ hqt C, 10 ? :0 4z 100 ´ Þ 70 47 z 8.47 : 6 === ` Pqy D ikxgu ` 5 vq C. Uq, C jcu 15 `. Equv qh 4 vkemgvu ? ` 14.70, yjkej ku oqtg vjcp gpqwij vq dw{ 4 vkemgvu. \ (c) Twngu qwv (d) ku engctn{ twngf qwv (e) ku vtwg, dgecwug chvgt dw{kpi 4 vkemgvu. C ku nghv ykvj ` 15 ˜ 14.70 ? 70 rckug Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Time and Distance F 89 5:. (c) Vqvcn fkuvcpeg ? 700o Fkuvcpeg eqxgtgf d{ C ? 700o Fkuvcpeg eqxgtgf d{ D ? 700 ˜ 67 ˜ 57 ? 700 ˜ :0 ? 640 urggfqh C urggfqh D ? fkuvcpeg qh C vkog fkuvcpegqh D vkog ? 700 vkog vkog 640 ´ ? 700 640 ? 47 41 ? 47 < 41 5;. (d) Cxgtcig urggf qh vyq ectu cv c urggf X1 cpf X4 mo/jt ? 1 4 1 4 4X X X X+ ? 4 60 80 80 60 ´ ´ + ? 4 60 80 100 ´ ´ ? 6: mo/jt 60. (d) Vkog vcmgp d{ dqvj vcpmu ? 50 40 50 40 ´ + ? 50 40 70 ´ ? 14 okp 61. (c) Jgtg, C cpf D ctg oqxkpi kp qrrqukvg fktgevkqpu. Uq, Tgncvkxg urggf ? 4 + 5 ? 7 tqwpfu/jqwt Uq, vjg{ etquu gcej qvjgt 7 vkogu kp cp jqwt cpf 4 vkogu kp jcnh cp jqwt. Jgpeg, vjg{ etquu gcej qvjgt 9 vkogu dghqtg ; < 50 c.o. 64. (c) Jgtg, C vcmgu vjg ujqtvguv vkog vq etquu vjg dtkfig k.g. 1 okp. Cpf, F vcmgu 10 okp, E vcmgu 9 okp cpf D vcmgu 4 okp vq etquu vjg dtkfig. Uq, 6 htkgpfu ecp etquu vjg dtkfig kp okpkowo vkog kp vjg hqnnqykpi yc{u. 1. C + D etquukpi cpf C tgvwtpkpi < (4 + 1) okp 4. C + E etquukpi cpf C tgvwtpkpi < (9 + 1) okp 5. C + F etquukpi cpf C tgvwtpkpi < (10 + 1) okp 6. C etquukpi vjg dtkfig hqt vjg ncuv vkog < 1 okp. Jgpeg, vqvcn okpkowo vkog ? 5 + : + 11 + 1 ? 45 okp. 65. (e) A B Fig. 1 day st 6 am 6 am A B Fig. 2 day nd 6 am 6 am Train 2 Train 1 Cdqxg ikxgp hkiwtgu ujqy vjcv vtckp 1 ngcxgu uvcvkqp C qp 1uv fc{ cpf vtckp 4 ngcxgu uvcvkqp D qp 1uv fc{. Dqvj vjg vtckpu fqp”v tgcej vjgkt fguvkpcvkqp gxgp qp vjg 4pf fc{ chvgt 46 jqwtu cu vjg lqwtpg{ eqorngvgu kp 64 jqwtu. \ Vyq oqtg vtckpu pggf vq dg kpvtqfwegf cv dqvj vjg uvcvkqpu k.g., uvcvkqp C cpf D. Uq, 6 vtckpu ctg pggfgf kp qtfgt vq ockpvckp vjg ujwvvng ugtxkeg. 66. (e) Fkuvcpeg vtcxgnngf d{ htgkijv vtckp kp 4 jqwt ? 4 Ù 60 ? :0 mo. Tgncvkxg urggf ? 80 mo/jt ˜ 60 mo/jt ? 40 mo/jt Jgpeg, vkog vcmgp d{ gzrtguu vtckp vq oggv Htgkijv vtckp ? 80 km 4 hr. 20 km / hr = Uq, Fkuvcpeg vtcxgnngf ? 6 Ù 80 qt 8 Ù 60 ? 460 mo. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 90 1. Eqpukfgt vjg fkcitco ikxgp dgnqy< [1995] Q T Ec H F C S V < Vtcpurqtv Ge < Gfwecvkqp cpf ejknftgp J < Jqwukpi E < Enqvjkpi H < Hqqf U < Ucxkpiu Q < Qvjgtu Htqo vjg fkcitco ujqyp kv yqwnf dg tkijv vq eqpenwfg vjcv (c) vjg hcokn{ urgpv oqtg vjcp jcnh qh kpeqog qp hqqf cpf enqvjkpi (d) vjg coqwpv ucxgf d{ vjg hcokn{ ycu vqq nkvvng (e) vjg hcokn{ jcf pq jgcnvj rtqdngou (f) vjg hcokn{ ocpcigf vq oggv cnn vjg guugpvkcn gzrgpugu qwv qh vjg kpeqog gctpgf 4. Eqpukfgt vjg vcdng ikxgp dgnqy rtqxkfkpi fgvcknu qh vtchhke xqnwog rgt jqwt hqt hqwt nqecvkqpu< [1995] Nqecvkqp Vqvcn % qh Cxgtcig Pqkug Vtchhke Jgcx{ Pqkug Rqnnwvkqp Xgjkengu Ngxgn Ngxgn K 599 46.60 95.70 :6.00 KK 5:0 14.70 94.80 :5.00 KKK 599 50.00 95.70 :8.70 KX 447 14.70 94.;: :0.;0 Yjgp vjg vqvcn vtchhke xqnwog ku vjg ucog, tgurgevkxgn{ vjg hcevqt(u) yjkej chhgev(u) vjg pqkug rqnnwvkqp ngxgn ku/ctg (c) rgtegpvcig qh jgcx{ xgjkengu (d) pqkug rqnnwvkqp ngxgn cpf cxgtcig pqkug ngxgn (e) cxgtcig pqkug ngxgn cpf % qh jgcx{ xgjkengu (f) kpfgvgtokpcdng qp vjg dcuku qh fgvcknu ikxgp 5. Vjg xctkcvkqpu kp vgorgtcvwtgu hqto 0²E vq 100²E ykvj tgurgev vq vkog qh vyq nkswkfu R, S ctg ujqyp kp vjg itcrj ikxgp dgnqy< [1995] Vgo rgtcvwtg 100²E S R (0, 0) Vkog Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ku eqttgevA (c) Fwtkpi jgcvkpi, nkswkf R tgockpgf jqvvgt vjcp nkswkf S vjtqwijqwv (d) Cv pq rqkpv qh vkog fwtkpi jgcvkpi fkf vjg vyq nkswkfu jcxg vjg ucog vgorgtcvwtg (e) R cvvckpgf vjg vgorgtcvwtg qh 100²E-hcuvgt vjcp S (f) S cvvckpgf vjg vgorgtcvwtg qh 100²E hcuvgt vjcp R 6. Vjg rtkeg hnwevwcvkqpu qh 6 uetkru kp c uvqem octmgv kp vjg hqwt swctvgtu qh c {gct ctg ujqyp kp vjg vcdng dgnqy. Hqwt fkhhgtgpv kpxguvqtu jcf vjg hqnnqykpi rqtvhqnkqu qh kpxguvogpv kp vjg hqwt eqorcpkgu vjtqwijqwv vjg {gct. Rqtvhqnkqu Kpxguvqt 1<10 qh C, 40 qh D, 50 qh E, cpf 60 qh F Kpxguvqt 4 < 60 qh C, 10 qh D, 40 qh E, cpf 50 qh F Kpxguvqt 5 < 50 qh C, 60 qh D, 10 qh E, cpf 40 qh F Kpxguvqt 6 < 40 qh C, 50 qh D, 60 qh E, cpf n0 qh F Uvqem Octmgv Rgthqtocpeg K KK KKK KX Swctvgt Swctvgt Swctvgt Swctvgt Uektr C Wr 10% Fqyp 17% WR 10% Fqyp 10% Uetkr D WR 4% WR 1% WR 4% WR 4% Uetkr E WR 1% WR 1% Fqyp 7% Fqyp 1% Uetkr F WR 40% Fqyp 17% WR 50% Fqyp 10% Kp vjg nkijv qh vjg cdqxg yjkej qpg qh vjg hqnnqykpi uvcvgogpv ku eqttgevA [1995] (c) Kpxguvqt 4 jcu ocfg vjg dguv kpxguvogpv (d) Kpxguvqt 1 jcu ocfg vjg dguv kpxguvogpv (e) Kpxguvqt 4 uwhhgtgf c pgv nquu fwtkpi vjg {gct (f) Kpxguvqt 5 uwhhgtgf c pgv nquu fwtkpi vjg {gct Chapter 6 Data
Interpretation Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Data Interpretation F 91 7. Vjg hqnnqykpi vcdng ujqyu vjg rgtegpvcig fkuvtkdwvkqp qh tgxgpwg gzrgpfkvwtg qh Iqxgtpogpv qh Kpfkc kp 1;:;-;0 cpf 1;;6-;7 < Gzrgpfkvwtg Jgcf (rgtegpv vq vqvcn) [gctu Fghgpeg Kpvgtguv Uwdukfkgu Itcpvu vq Rc{ogpvu Uvcvgu/Wvu Qvjgt 1;:;-;0 17.1 49.9 18.5 15.8 49.6 1;;6-;7 15.8 5:.9 :.0 18.9 45.0 Dcugf qp vjku vcdng, kv ecp dg uckf vjcv vjg Kpfkcp geqpqo{ ku kp rqqt ujcrg dgecwug vjg Egpvtcn iqxgtpogpv eqpvkpwgu vq dg wpfgt rtguuwtg vq < ]1;;8_ (c) tgfweg gzrgpfkvwtg qp fghgpeg (d) urgpf oqtg cpf oqtg qp kpvgtguv rc{ogpvu (e) tgfweg gzrgpfkvwtg qp uwdukfkgu (f) urgpf oqtg cpf oqtg cu itcpvu-kp-ckf vq Uvcvg iqxgtpogpv/Wpkqp Vgttkvqtkgu 8. Vjg hqnnqykpi hkiwtg tgrtgugpvu ucngu (kp vjqwucpfu). qxgt vjg rgtkqf 1;9: vq 1;:5. ]1;;8_ Vjg ucngu kp 1;:1 gzeggfgf vjcv kp 1;9; d{ [gctu Ucngu kp V j q wucp fu 500 560 5:0 640 680 9: 9; :0 :1 :4 :5 (a) ` Qpg jwpftgf (b) ` Vgp vjqwucpf (c) ` Qpg ncmj (d) ` Vgp ncmj 9. Vjg ikxgp rkg ejctvu ujqy vjg rtqrqtvkqp qh nkvgtcvgu cpf knnkvgtcvgu kp c eqwpvt{, kp vjg {gct 1;90 cpf 1;;0, KNNKVGTCVGU NKVGTCVGU H O KNNKVGTCVGU H O NKVGTCVGU cpf cnuq vjg rtqrqtvkqp qh ocngu (O) cpf hgocngu (H) coqpi vjg nkvgtcvgu. Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ecp dg uckf vq dg vtwg dg{qpf cp{ fqwdvA ]1;;8_ (c) Kp 1;90 jcnh qh vjg knnkvgtcvgu ygtg yqogp (hgocngu) (d) Vjg rtqrqtvkqp qh nkvgtcvg ocngu vq vjg vqvcn rqrwncvkqp qh ocngu tgockpgf vjg ucog qxgt vjg {gctu (e) Ocng nkvgtce{ fkf pqv kortqxg qxgt vjku rgtkqf (f) Vjg tcvkq qh hgocng nkvgtcvgu vq ocng nkvgtcvgu kortqxgf ukipkhkecpvn{ qxgt vjku rgtkqf :. Vjg pwodgt qh uvwfgpvu kp vyq ugevkqpu, C cpf D jcxkpi fkhhgtgpv jgkijvu ku ujqyp kp vjg hqnnqykpi Vcdng. ]1;;9_ Jgkijv Pwodgt qh uvwfgpvu (kp ogvtgu) kp ugevkqp C kp ugevkqp D 1.77 5 4 1.80 9 8 1.84 14 16 1.87 17 16 1.8: : ; 1.91 8 7 1.97 5 6 Vjg tcvkq qh vjg pwodgt qh uvwfgpvu qh c rctvkewnct jgkijv kp ugevkqp C vq vjcv kp ugevkqp D ku vjg oczkowo hqt vjg jgkijv qh (c) 1.77 o (d) 1.80 o (e) 1.87 o (f) 1.91 o ;. Vjg hqnnqykpi vcdng ujqyu vjg rgtegpv ejcpig kp vjg coqwpv qh ucngu (kp twrggu) cv fkhhgtgpv tgvckn uvqtgu kp c ikxgp pgkijdqwtjqqf octmgv kp vjg rgtkqf 1;;5 vq 1;;7 ]1;;9_ Tgvckn uvqtg Rgtegpv ejcpig 1;;5 vq 1;;6 1;;6 vq 1;;7 Cpujw + 10 ˜ 10 Dqtpc ˜ 40 + ; Ecnrq + 7 + 14 Fknkr ˜ 9 ˜ 17 Gngicpv + 19 ˜ : Kh vjg ucngu cv Cpujw uvqtg coqwpvgf vq ` 8 ncmj kp 1;;5, vjgp vjg coqwpv qh ucngu (kp ncmj twrggu) cv vjcv uvqtg kp 1;;7 ycu (c) 9.;4 (d) :.00 (e) :.:0 (f) ;.8: 10. Vjg okugt{ kpfgz ku vjg uwo qh c eqwpvt{'u wpgornq{ogpv cpf kphncvkqp tcvg. Vjg jkijgt vjg kpfgz, vjg oqtg okugtcdng ku vjg eqwpvt{ vq nkxg kp. Vjg hkiwtg ikxgp dgnqy ku vjg okugt{ kpfgz hqt xctkqwu eqwpvtkgu kp Gwtqrg. ]1;;:_ 7 10 17 40 47 50 % cig U rckp Dgnikwo Kvcn{ Htcpeg Igtocp{ Dtkvckp Wpgornq{ogpv Tcvg Kphncvkqp Tcvg Okugt{ Kpfgz Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 92 Yjkej qh vjg hqnnqykpi eqpenwukqpu ecp dg ftcyp htqo vjg okugt{ kpfgz ikxgp cdqxgA 1. Dtkvckp ku vjg oquv okugtcdng eqwpvt{ vq nkxg Kp 4. Vjg kphncvkqp tcvg kp Urckp ku nguu vjcp vjcv kp Dgnikwo cpf Dtkvckp 5. Kvcn{ cpf Htcpeg uggo vq jcxg cnoquv kfgpvkecn wpgornq{ogpv 6. Vjg jkijgt vjg okugt{ kpfgz, vjg jkijgt vjg kphncvkqp tcvg Ugngev vjg eqttgev cpuygt wukpi vjg eqfgu ikxgp dgnqy< Eqfgu< (c) 1 cnqpg (d) 4 cpf 5 (e) 1, 4, 5 cpf 6 (f) Pqpg qh vjgug 11. Rtqfwevkqp qh Tkeg cpf Yjgcv (Kp “oknnkqp qh Vqppgu”) ]1;;:_ [gct Tkeg Yjgcv Rgtegpvcig qh Yjgcv vq Tkeg 1;70 ˜71 40.7: 8.68 51.6 1;80 ˜81 56.7: 11.00 51.: 1;90˜91 64.44 45.:5 78.6 1;:0˜:1 7:.85 58.51 89.9 1;;0˜;1 96.4; 77.16 96.4 1;;6˜;7 :1.:1 87.99 :0.6 1;;7˜;8 9;.84 84.84 9:.8 Vjg cdqxg vcdng kpfkecvgu vjg rgthqtocpeg qh Kpfkc kp tkeg cpf yjgcv rtqfwevkqp htqo 1;70-71 vq 1;;7-;8. Yjkej qh vjg hqnnqykpi eqpenwukqpu cttkxgf cv htqo vjg cdqxg vcdng yqwnf dg xcnkfA 1. Tgeqtf rtqfwevkqp qh tkeg cu ygnn cu yjgcv jcu dggp kp 1;;6-;7 4. Vjg tcvkq qh yjgcv vq tkeg rtqfwevkqp uggou vq jcxg uvgcfkn{ kpetgcugf qxgt 18 {gctu 5 Yjgcv jcu pqv dggp rqrwnct coqpi vjg Kpfkcp rqrwncvkqp dghqtg 1;:0 6. Kpfkc dgecog ugnh-uwhhkekgpv kp tkeg cpf yjgcv qpn{ chvgt 1;;0 Ugngev vjg eqttgev cpuygt wukpi vjg eqfgu ikxgp dgnqy< Eqfgu< (c) 1 cpf 4 (d) 1, 4, 5 cpf 6 (e) 5 cpf 6 (f) Pqpg qh vjgug 14. Vjg {kgnf xgtuwu hgtvknk|gt kprwv ku ujqyp kp vjg itcrj. ]1;;;_ {kgnf 70 D (Oczkowo Rqkpv) E (Ucffng Rqkpv) F 1 7 10 17 0 : 40 Hgtvknk|gt kprwv C Eqpukfgt vjg hqnnqykpi uvcvgogpvu dcugf qp vjku itcrj< 1. [kgnf tcvg ku |gtq cv D cpf E 4. Vjgtg ku pq {kgnf ykvj pq hgtvknk|gt kprwv 5. Vjg {kgnf ku okpkowo cv F 6. Vjg {kgnf ku pgkvjgt okpkowo pqt oczkowo cv E Yjkej qh vjg cdqxg uvcvgogpvu ctg eqttgevA (c) 1, 4 cpf 6 (d) 5 cpf 6 (e) 4 cpf 5 (f) 1, 5 cpf 6 15. C eqorcp{ ocpwhcevwtkpi ckt-eqpfkvkqpgtu ugv c oqpvjn{ vctigv. Vjg vctigv cpf tgcnkugf xcnwgu ctg ujqyp kp vjg dct ejctv. ]1;;;_ Ucngu 4: 0 10 40 50 60 70 80 90 :0 ;0 100 1 4 5 6 7 8 9 : Pq qh Wpkvu Vctigv Cevwcn 4; 60 70 87 97 :7 ;7 60 77 87 :0 60 70 40 10 Eqpukfgt vjg hqnnqykpi uvcvgogpvu dcugf qp vjg ejctv 1. Vjg vctigvgf ucngu qp c oqpvjn{ dcuku jcxg dggp cejkgxgf 4. Vjg qxgtcnn vctigv xcnwg jcu dggp gzeggfgf d{ 9.7% 5. Vjg Ucngu Fgrctvogpv fgugtxgu c rcv qp vjg dcem Yjkej qh vjg cdqxg uvcvgogpvu ku/ctg eqttgevA (c) 1 cnqpg (d) 4 cnqpg (e) 1 cpf 4 (f) 4 cpf 5 16. Vjg fkuvtkdwvkqp qh 1,00,000 vqwtkuvu yjq xkukvgf Kpfkc fwtkpi c rctvkewnct {gct ku ujqyp kp vjg ikxgp ejctvu. Dcugf qp vjku, vjg pwodgt qh Lcrcpgug vqwtkuvu dgnqy vjg cig qh 5; yjq xkukvgf Kpfkc kp vjg {gct eqpegtpgf ku ]4000_ WUC 80% W.M. 10% 10% Qvjgtu Lcrcp 40% 970 [gctu 80% 10% 4 { ; gctu 10% 50-5; {gctu 40% 60-6; {gctu (c) 10,000 (d) :,000 (e) 8,000 (f) 6,000 Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Data Interpretation F 93 17. Vjg hqnnqykpi vcdng ujqyu vjg rgtegpvcig ejcpig kp vjg eqpuworvkqp qh gngevtkekv{ d{ hkxg vqypu R, S, T, U, V htqo 1;:8 vq 1;:: < ]4001_ Rgtegpv ejcpig Vqyp Htqo Htqo 1;:8 vq 1;:9 1;:9 vq 1;:: R + : ˜ 1: S ˜ 17 + 11 T + 8 + ; U ˜ 9 ˜ 7 V + 15 ˜ 8 Kh vqyp V eqpuwogf 700,000 wpkvu kp 1;:8, jqy owej fkf kv eqpuwog kp 1;::A (c) 591,000 wpkvu (d) 751, 100 wpkvu (e) 771,100 wpkvu (f) 791, 100 wpkvu 18. Eqpukfgt vjg hqwt cig r{tcokfu ikxgp dgnqy pcogn{ C, D, E cpf F tgrtgugpvkpi hqwt fkhhgtgpv eqwpvtkgu. ]4011 - KK_ Rgtegpv kp cig encuu C D E F A ge Yjkej qpg qh vjgo kpfkecvgu vjg fgenkpkpi rqrwncvkqp A (c) C (d) D (e) E (f) F 19. Vjg hqnnqykpi hkiwtg jcu hqwt ewtxgu pcogn{ C, D, E cpf F. Uvwf{ vjg hkiwtg cpf cpuygt vjg kvgo vjcv hqnnqyu. ]4011 - KK_ CF 400 600 800 :00 1000 1400 1600 1800 [gct F E D C 1:00 4000 8 7 6 5 4 1 0 Pop ulation (billions) Yjkej ewtxg kpfkecvgu vjg gzrqpgpvkcn itqyvj A (c) C (d) D (e) E (f) F Fktgevkqpu hqt vjg hqnnqykpi 4 (vyq) kvgou< Vjg hqnnqykpi rkg ejctvu ujqy vjg dtgcm wr qh fkugcug ecvgiqtkgu tgeqtfgf kp vjg rcvkgpvu htqo vyq vqypu, Vqyp C cpf Vqyp D. Rkg ejctvu rnqv vjg fkugcug ecvgiqtkgu cu rgtegpvcig qh vjg vqvcn pwodgt qh rcvkgpvu. Dcugf qp vjgug cpuygt vjg vyq kvgou vjcv hqnnqy vjg ejctvu. ]4011 - KK_ Fkuvtkdwvkqp qh fkugcugu kp Vqyp - C Jgctv Fkugcug 44% Fkcdgvgu 1:% Jkij DR 15% Qvjgtu 15% Qdgukv{ 56% Fkuvtkdwvkqp qh fkugcugu kp Vqyp - D Jgctv Fkugcug 50% Fkcdgvgu 46% Jkij DR 1;% Qvjgtu 40% Qdgukv{ 4:% 1:. Yjkej qh vjg vyq vqypu jcu c jkijgt pwodgt qh rgtuqpu ykvj Fkcdgvgu A (c) Vqyp C (d) Vqyp D (e) Ucog kp Vqyp C cpf Vqyp D (f) Pq kphgtgpeg ecp dg ftcyp 1;. Yjcv ecp yg uc{ cdqwv rgtuqpu ykvj oqtg vjcp qpg fkugcug htqo vjgug itcrju A (c) Vjgtg ctg nkmgn{ vq dg rgtuqpu ykvj oqtg vjcp qpg fkugcug kp Vqyp C. (d) Vjgtg ctg nkmgn{ vq dg rgtuqpu ykvj oqtg vjcp qpg fkugcug kp Vqyp D. (e) Vjgtg ctg nkmgn{ vq dg rgtuqpu ykvj oqtg vjcp qpg fkugcug kp dqvj Vqypu C cpf D. (f) Pq kphgtgpeg ecp dg ftcyp. 40. Eqpukfgt vjg hqnnqykpi Xgnqekv{ ˜ Vkog itcrj. Kv ujqyu vyq vtckpu uvctvkpi ukownvcpgqwun{ qp rctcnngn vtcemu. Vtckp D Vtckp C Vkog Xgnqekv{ 0 v0 Ykvj tghgtgpeg vq vjg cdqxg itcrj, yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ku pqv eqttgev A ]4011 - KK_ (c) Vtckp D jcu cp kpkvkcn ceegngtcvkqp itgcvgt vjcp vjcv qh Vtckp C. (d) Vtckp D ku hcuvgt vjcp Vtckp C cv cnn vkogu. (e) Dqvj vtckpu jcxg vjg ucog xgnqekv{ cv vkog v0 . (f) Dqvj vtckpu vtcxgn vjg ucog fkuvcpeg kp vkog v0 wpkvu. Fktgevkqpu hqt vjg hqnnqykpi 5 (vjtgg) kvgou < Tgcf vjg rcuucig ikxgp dgnqy, uvwf{ vjg itcrj vjcv hqnnqyu cpf cpuygt vjg vjtgg kvgou ikxgp dgnqy vjg hkiwtg. Fwtkpi c rctv{, c rgtuqp ycu gzrqugf vq eqpvcokpcvgf ycvgt. C hgy fc{u ncvgt, jg fgxgnqrgf hgxgt cpf nqqug oqvkqpu. Jg uwhhgtgf hqt uqog fc{u dghqtg iqkpi vq c fqevqt hqt vtgcvogpv. Qp uvctvkpi vjg vtgcvogpv, jg uqqp dgecog dgvvgt cpf tgeqxgtgf eqorngvgn{ c hgy fc{u ncvgt. Vjg hqnnqykpi itcrj ujqyu fkhhgtgpv rjcugu qh vjg rgtuqp'u fkugcug eqpfkvkqp cu tgikqpu C, D, E, F cpf G qh vjg ewtxg. ]4011 - KK_ Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 94 C D E F G Vkog Pw odgt qh Dcevgtkc 0 0 41. Yjkej tgikqp/tgikqpu qh vjg ewtxg eqttgurqpf/ eqttgurqpfu vq kpewdcvkqp rjcug qh vjg kphgevkqpA (c) C qpn{ (d) D qpn{ (e) D cpf E (f) Pq rctv qh vjg ewtxg kpfkecvgu vjg kpewdcvkqp rjcug 44. Yjkej tgikqp qh vjg ewtxg kpfkecvgu vjcv vjg rgtuqp dgicp ujqykpi vjg u{orvqou qh kphgevkqp A (c) C (d) D (e) E (f) F 45. Yjkej tgikqp qh vjg ewtxg kpfkecvgu vjcv vjg vtgcvogpv {kgnfgf ghhgevkxg tgnkgh A (c) E (d) F (e) G (f) Vjg ewtxg fqgu pqv kpfkecvg vjg vtgcvogpv 46. Eqpukfgt vjg hqnnqykpi fkuvcpeg - vkog itcrj. Vjg itcrj ujqyu vjtgg cvjngvgu C, D cpf E twppkpi ukfg d{ ukfg hqt c 50 mo tceg. 7 10 17 40 47 50 57 E D C E D C Vkog kp okp 7 10 17 40 47 50 57 60 67 Fkuvcpeg kp mo 0 Ykvj tghgtgpeg vq vjg cdqxg itcrj, eqpukfgt vjg hqnnqykpi uvcvgogpvu < ]4011 - KK_ 1. Vjg tceg ycu yqp d{ C. 4. D ycu cjgcf octm qh C wr vq 47 mo octm 5. E tcp xgt{ unqyn{ htqo vjg dgikppkpi. Yjkej qh vjg uvcvgogpvu ikxgp cdqxg ku/ctg eqttgev A (c) 1 qpn{ (d) 1 cpf 4 qpn{ (e) 4 cpf 5 qpn{ (f) 1, 4 cpf 5 47. Eqpukfgt vjg hqnnqykpi kphqtocvkqp tgictfkpi vjg rgthqtocpeg qh c encuu qh 1000 uvwfgpvu kp hqwt fkhhgtgpv vguvu< Vguvu K KK KKK KX Cxgtcig octmu 80 80 90 :0 Tcpig qh octmu 50 67 40 0 vq vq vq vq ;0 97 100 100 Kh c uvwfgpv ueqtgu 96 octmu kp gcej qh vjg hqwt vguvu, kp yjkej qpg qh vjg hqnnqykpi vguvu ku jgt rgthqtocpeg vjg dguv eqorctcvkxgn{A ]4014 - KK_ (c) Vguv K (d) Vguv KK (e) Vguv KKK (f) Vguv KX 48. Eqpukfgt vjg hqnnqykpi fkcitcou< ]4015 - KK_ z ogp, yqtmkpi cv eqpuvcpv urggf, fq c egtvckp lqd kp { fc{u. Yjkej qpg qh vjgug fkcitcou ujqyu vjg tgncvkqp dgvyggp z cpf {A Ogp 0 z { fkcitco K Days Ogp 0 z { fkcitco KK Days Ogp 0 z { fkcitco KKK Days fkcitco KX F c{u Ogp 0 z { (c) Fkcitco K (d) Fkcitco KK (e) Fkcitco KKK (f) Fkcitco KX Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Data Interpretation F 95 Fktgevkqpu hqt vjg hqnnyqkpi 7 (hkxg) kvgou < Uvwf{ vjg vyq hkiwtgu ikxgp dgnqy cpf cpuygt vjg swguvkqpu vjcv hqnnqy< 54 4: 46 40 18 14 : 6 0 Rj{ukeu Ocvjgocvkeu Ejgokuvt{ Jkuvqt{ Ru{ejqnqi{ Geqpqokeu Ocng Hgocng Hki 1 < Pwodgt qh Rtqhguuqtu kp ugngevgf fkuekrnkpgu kp c Wpkxgtukv{ d{ ugz 60% 40% 10% 50% 57 ˜ 66 47 ˜ 56 80 ˜ 87 67 ˜ 7; Hki. 4 < Cig qh Rj{ukeu Rtqhguuqtu 49. Jqy ocp{ Rj{ukeu rtqhguuqtu dgnqpi vq vjg cig itqwr 57 ˜ 66A ]4015 - KK_ (c) 1: (d) 18 (e) 16 (f) 14 4:. Yjkej qpg qh vjg hqnnqykpi fkuekrnkpgu jcu vjg jkijguv tcvkq qh ocngu vq hgocnguA ]4015 - KK_ (c) Rj{ukeu (d) Ocvjgocvkeu (e) Ejgokuvt{ (f) Geqpqokeu 4;. Yjcv rgtegpvcig qh cnn Ru{ejqnqi{ rtqhguuqtu ctg hgocnguA ]4015 - KK_ (c) 60% (d) 70% (e) 80% (f) 90% 50. Kh vjg pwodgt qh hgocng Rj{ukeu rtqhguuqtu kp vjg cig itqwr 47 ˜ 56 gswcnu 47% qh cnn vjg Rj{ukeu rtqhguuqtu kp vjcv cig itqwr, vjgp yjcv ku vjg pwodgt qh ocng Rj{ukeu rtqhguuqtu kp vjg cig itqwr 47 ˜ 56A ]4015 - KK_ (c) ; (d) 8 (e) 5 (f) 4 51. Kh vjg Ru{ejqnqi{ rtqhguuqtu kp vjg Wpkxgtukv{ eqpuvkvwvg 4% qh cnn vjg rtqhguuqtu kp vjg Wpkxgtukv{, vjgp yjcv ku vjg pwodgt qh rtqhguuqtu kp vjg Wpkxgtukv{A ]4015 - KK_ (c) 600 (d) 700 (e) 800 (f) 900 Fktgevkqpu hqt vjg hqnnqykpi 6 (hqwt) kvgou < Vjg hqnnqykpi itcrj ujqyu vjg cxgtcig rtqhkv qh vyq htwkv-ugnngtu C cpf D kp vjqwucpfu (`) rgt {gct htqo vjg {gct 1;;7 vq 4000. Eqpukfgt vjg itcrj cpf cpuygt vjg 6 (hqwt) kvgou vjcv hqnnqy : 1;;7 1;;8 1;;9 1;;: 1;;; 4000 Z 8 7 6 5 4 1 0 [ [gct C D 54. Kp yjkej {gct ku vjg cxgtcig rtqhkv qh C cpf D ucog A ]4016 - KK_ (c) 1;;7 (d) 1;;8 (e) 1;;9 (f) 1;;: 55. Yjcv ku vjg fkhhgtgpeg dgvyggp vjg cxgtcig rtqhkv qh D cpf C kp vjg {gct 1;;: A ]4016 - KK_ (c) ˜ ` 100 (b) – `1,000 (e) + ` 800 (f) ˜ ` 500 56. Jqy owej oqtg cxgtcig rtqhkv fkf C ocmg kp vjg {gct 4000 vjcp kp vjg {gct 1;;; A ]4016 - KK_ (c) ` 400 (d) ` 1,000 (e) ` 1,700 (f) ` 4,000 57. Yjcv ku vjg vtgpf qh vjg cxgtcig rtqhkv qh D htqo vjg {gct 1;;9 vq vjg {gct 4000 A ]4016 - KK_ Eqpukfgt vjg hqnnqykpi ocvtkz < (c) Pqp-kpetgcukpi (d) Pqp-fgetgcukpi (e) Uvgcf{ (f) Hnwevwcvkpi 58. Vjg hqnnqykpi vcdng ujqyu vjg octmu qdvckpgf d{ vyq uvwfgpvu kp fkhhgtgpv uwdlgevu < ]4016 - KK_ Student A Maximum Marks Student B Maximum Marks English 60 100 80 150 Paychology 70 100 70 100 History 50 100 60 100 Sanskrit 30 50 15 25 Vjg fkhhgtgpeg kp vjg ogcp ciitgicvg rgtegpvcig octmu qh vjg uvwfgpvu ku (c) 4.7 % (d) 15.97% (e) 1.47% (f) \gtq Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 96 59. Vjg hqnnqykpi vcdng ikxgu rqrwncvkqp cpf vqvcn kpeqog qh c ekv{ hqt hqwt {gctu < ]4016 - KK_ [gct 1;;4 1;;5 1;;6 1;;7 Rqrwncvkqp kp ncmju 40 41 44 45 Kpeqog kp etqtgu (`) 1010 1111 1447 1567 Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu ku eqttgev kptgurgev qh vjg cdqxg fcvc A (c) Rqrwncvkqp kpetgcugf d{ 7% qt oqtg gxgt{ {gct. (d) Kpeqog kpetgcugf d{ 10% qt oqtg gxgt{ {gct. (e) Rgt ecrkvc kpeqog ycu cnyc{u cdqxg ` 7,000. (f) Rgt ecrkvc kpeqog ycu jkijguv kp 1;;6. 5:. Cp cwvqoqdkngu qypgt tgfwegf jku oqpvjn{ rgvtqn eqpuworvkqp yjgp vjg rtkegu ygpv wr. Vjg rtkegeqpuworvkqp tgncvkqpujkr ku cu hqnnqyu< ]4017 - KK_ Rtkeg (kp ` Rgt nkvtg) 60 70 80 97 Oqpvjn{ eqpuworvkqp (kp nkvtgu) 80 6: 60 50 Kh vjg rtkeg iqgu wr vq ` :0 rgt nkvtg, jku gzrgevgf eqpuworvkqp (kp nkvtgu) yknn dg (c) 50 (d) 4: (e) 48 (f) 46 5;. Vjg itcrj dgnqy fgrkevu vjg gctpkpiu qh C cpf D qxgt vjg rgtkqf 4000 vq 4010< ]4017 - KK_ A B 2007 2010 Years 2000 Earnin gs Htqo vjg itcrj, yjkej qpg qh vjg hqnnqykpi ecp dg eqpenwfgfA (c) Qp vjg cxgtcig C gctpgf oqtg vjcp D fwtkpi vjku rgtkqf. (d) Qp vjg cxgtcig D gctpgf oqtg vjcp C fwtkpi vjku rgtkqf. (e) Vjg gctpkpiu qh C cpf D ygtg gswcn fwtkpi vjku rgtkqf. (f) Vjg gctpkpiu qh C ygtg nguu cu eqorctgf vq D fwtkpi vjku rgtkqf. 60. [gct-ykug xctkcvkqp qh vjg rtkeg qh c egtvckp eqooqfkv{ ku ujqyp kp vjg hqnnqykpi itcrj< ]4017 - KK_ Vjg rtkeg qh vjg eqooqfkv{ kp vjg {gct 1;;0 (c) owuv jcxg dggp ` 10/- (d) owuv jcxg dggp ` 14/- (e) owuv jcxg dggp cp{ yjgtg dgvyggp ` 10/- cpf ` 40/- (f) ku jkijgt vjcp vjcv kp vjg {gct 1;;1 61. Vjg rtqrqtvkqp qh gzrgpfkvwtg qp xctkqwu kvgou d{ vyq hcoknkgu C cpf D ctg tgrtgugpvgf kp vjg hqnnqykpi Dct Ejctvu< ]4017 - KK_ Htqo vjgug ejctvu, yg ecp eqpenwfg vjcv (c) Hcokn{ C urgpv oqtg oqpg{ qp hqqf vjcp Hcokn{ D. (d) Hcokn{ D urgpv oqtg oqpg{ qp hqqf vjcp Hcokn{ C. (e) Hcokn{ C cpf Hcokn{ D urgpv vjg ucog coqwpv qp hqqf. (f) Vjg gzrgpfkvwtg qp hqqf d{ Hcokn{ C cpf Hcokn{ D ecppqv dg eqorctgf. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Data Interpretation F 97 1. (f) Htqo vjg fkcitco, hcokn{ fq pqv urgpf oqtg vjcp jcnh qh kpeqog qp hqqf cpf enqvjkpi. Coqwpv ucxgf d{ vjg hcokn{ ku pqv vqq nkvvng. Jgcnvj rtqdngou oc{ eqog wpfgt vjg qvjgtu ecvgiqt{. Jgtg, hcokn{ engctn{ ocpcigu vq oggv cnn vjg gzrgpugu qwv qh vjg kpeqog. 4. (c) Hqt K cpf KKK, vtchhke xqnwog ku ucog. Ukpeg, Cxgtcig Pqkug ngxgn ku ucog hqt K cpf KKK cpf % qh Jgcx{ xgjkengu fkhhgtu hqt K cpf KKK, uq engctn{ % qh Jgcx{ xgjkengu chhgevu vjg pqkug rqnnwvkqp ngxgn. 5. (f) Cu ikxgp kp vjg Itcrj, engctn{ S cvvckpu 100² E vgorgtcvwtg hcuvgt vjcp R. 6. (d) 7. (d) Ceeqtfkpi vq vjg fcvc ujqykpi tgxgpwgu gzrgpfkvwtg qh Kpfkcp Iqxgtpogpv, kv ecp dg uckf vjcv vjg Kpfkcp geqpqo{ ku kp rqqt ujcrg fwg vq kv”u kpetgcukpi fgdv rc{ogpvu. Fwg vq vjg dwtfgp qh fgdv rc{ogpvu vjgtg tgockpu nkvvng ueqrg vq wvknk|g vjku oqpg{ hqt cp{ qvjgt rwtrqug. 8. (e) Ucngu kp {gct 1;9; ? 540, 000 Ucngu kp {gct 1;:1 ? 640,000 Vjwu vjg tgswktgf fkhhgtgpeg ? 640,000 ˜ 540,000 ? ` 100,000 9. (f) Kv ecp dg engctn{ uggp htqo vjg ejctv vjcv vjg tcvkq qh hgocng nkvgtcvgu vq ocng nkvgtcvgu jcu kortqxgf. :. (c) Tcvkq qh uvwfgpvu qh ugevkqp C vq D ku oczkowo hqt 1.77 ecvgiqt{ jgkijv, kv ku 5 4 ? 1.7 ;. (c) Kh vjgtg ctg vyq ejcpigu qh z % cpf { %, vjgp pgv ejcpig ? z + { + 100 z{ Pgv ejcpig? 10 ˜ 10 + (10)( 10) 100 - ? ˜1% \ Coqwpv qh ucngu kp 1;;7 ? 1 : 1 100 æ ö ç ÷ - è ø ? 9.;4 10. (d) Kphncvkqp tcvg, k.g., ujcfgf rqtvkqp kp vjg itcrj ku nguu hqt Urckp vjcp Dgnikwo cpf Dtkvckp. Htqo vjg itcrj, Kvcn{ cpf Htcpeg jcxg kfgpvkecn wpgornq{ogpv tcvg. 11. (c) 14. (d) Htqo vjg itcrj, kv ecp dg uggp vjcv {kgnf tcvg ku pqv |gtq cv D cpf E. Ykvj pq hgtvknk|gt kprwv, {kgnf ku 40. [kgnf ku engctn{ okpkowo cv F, k.g., :. Cv E, {kgnf ku 40 cpf kv ku pgkvjgt oczkowo pqt okpkowo. Uq engctn{ qrvkqp 5 cpf 6 ctg eqttgev. 15. (d) 16. (f) Vqwtkuvu htqo Lcrcp ? 40 (100000) 100 ? 40000 % dgnqy 5; {gctu ? 10 + 10 ? 40% \ % qh Vqwtkuvu htqo Lcrcp dgnqy 5; {gctu ? 40 (40000) 100 ? 6000 17. (d) Kh vjgtg ctg vyq rgtegpvcig ejcpigu qh z% cpf {%, vjgp pgv % ejcpig ? 100 + + z{ z { Pgv % ejcpig hqt V htqo 1;:8 vq 1;::, 15 ˜ 8 ˜ (15)(8) 100 ? 8.44 \ Eqpuworvkqp qh gngevtkekv{ d{ V kp 1;:: ? 8.44 700000 1 100 æ ö ç ÷ + è ø ? 751100 18. (e) Fgenkpkpi rqrwncvkqp ogcpu itgcvgt pwodgt qh fgcvj tcvg k.g. pcttqygt wrrgt rctv cpf nqygt pwodgt qh dktvj tcvg k.g. pcttqygt dcug. Vjgug eqpfkvkqpu ctg ucvkuhkgf d{ “r{tcokfu E”. 19. (f) Gzrqpgpvkcn itqyvj ogcpu kpetgcug gzrqpgpvkcnn{. Qpn{ itcrj F ujqyu vjg gzrqpgpvkcn itqyvj qh rqrwncvkqp fwtkpi {gct 1:00 - 4000. 1:. (f) Rqrwncvkqpu qh dqvj vqypu C cpf D ctg pqv ikxgp, jgpeg, pq kphgtgpeg ecp dg ftcyp. 1;. (d) Vjg uwo qh rgtegpvcig qh rcvkgpvu kp vqyp C ku 100, jgpeg vjgtg ku pq cp{ rcvkgpv ykvj oqtg vjcp qpg fkugcug. 40. (f) Fkuvcpeg ? vkog ´ urggf, jgtg vtckp D ku hcuvgt vjcp vtckp C, jgpeg Vtckp D yknn eqxgt oqtg fkuvcpeg vjcp vtckp C. 41. (c) Kpewdcvkqp rjcug ogcpu vjg vkog dgvyggp uqogdqf{ dgkpi kphgevgf ykvj c fkugcugu kp itcrj rctv C ujqyu vjcv rjcug. 44. (d) Tgikqp D engctn{ ujqyu vjg u{orvqou qh kphgevkqp. 45. (e) Vjqwij tgnkgh dgicp htqo tgikqp E dwv qpn{ tgikqp G kpfkecvgu ghhgevkxg tgnkgh. 46. (d) Ukpeg z czku ujqyu vjg fkuvcpeg cpf { czku ujqyu vjg vkog, jgpeg nqygt itcrj yknn ujqy hcuvgt cvjngvg cpf jkijgt itcrj yknn ujqy unqygt cvjngvg. Jgkijv qh C'u itcrj ku vjg nqyguv, jgpeg, vjg tceg ycu yqp d{ C. Jgkijv qh D'u itcrj ku nqygt vjcp C'u itcrj wr vq 47 mo, jgpeg D ycu twppkpi hcuvgt vjcp C wr vq 47 mo. Vjg jgkijv qh E'u itcrj ku vjg nqyguv htqo vjg dgikppkpi, jgpeg jg twp xgt{ hcuvn{ htqo vjg dgikppkpi, Jgpeg uvcvgogpv 5 ku pqv eqttgev. HINTS & SOLUTIONS Explanations Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 98 47. (d) Vguvu K KK KKK KX Cxgtcig octmu 80 80 90 :0 Tcpig qh octmu 50 vq ;0 67 vq 97 40 vq 100 0 vq 100 ;0 ˜ 50 ? 97, 97 ˜ 67 ? 50 100 ˜ 40 ? :0 110 ˜ 0 ? 110 Kh c uvwfgpv ueqtgu 96 octmu kp gcej qh vjg hqwt vguvu, jku rgthqtocpeg yqwnf dg vjg dguv eqorctcvkxgn{ kp vguv KK dgecwug vjgtg yqwnf dg nguu pwodgtu qh vjg uvwfgpvu kp vjku tcpig kp vguv KK qpn{. 48. (f) Vkog vcmgp vq hkpkuj c yqtm ku kpxgtugn{ rtqrqtvkqpcn vq vjg pwodgt qh rgtuqpu yqtmkpi cv kv. \ Oqtg rgtuqpu vjgp nguu ku vjg vkog vcmgp vq hkpkuj c lqd. Jgpeg, fkcitco KX tgrtgugpvu vjg tgncvkqp dgvyggp z cpf {. O X Y Ogcp Fc{u 49. (d) Pwodgt qh rtqhguuqtu kp rj{ukeu ? 60 Rgtegpvcig qh rtqhguuqtu kp cig itqwr 57 ˜ 66 ? 60% \ Rj{ukeu rtqhguuqtu dgnqpi vq cig itqwr 57 ˜ 66 ? 60% qh 60 ? 18 4:. (c) D{ nqqmkpi vq itcrj K. Yg ecp fgfweg vjcv rj{ukeu fkuekrnkpg jcu vjg jkijguv tcvkq qh ocngu vq hgocngu. 4;. (e) Pq. qh hgocngu ru{ejqnqi{ rtqhguuqt ? 8 Pq. qh ocngu ru{ejqnqi{ rtqhguuqt ? 6 Tgswktgf rgtegpvcig ? Pq. qh hgocngu 100 Ocngu + Hgocngu ´ ? 8 100 80% 10 ´ = 50. (c) Pwodgt qh cnn rj{ukeu rtqhguuqtu kp cig itqwr 47 ˜ 56 ? 50% qh 60 ? 50 60 14 100 ´ = Pwodgt qh hgocng rj{ukeu rtqhguuqtu kp vjg cig itqwr 47 ˜ 56 ? 47% qh 14 ? 47 14 5 100 ´ = \ Pwodgt qh ocng rj{ukeu rtqhguuqtu kp vjg cig itqwr 47 ˜ 56 ? 14 ˜ 5 ? ; 51. (d) Ngv vjg pwodgt qh rtqhguuqtu kp vjg wpkxgtukv{ ? z Ceeqtfkpi vq swguvkqp 4% qh z ? 10 Þ z ? 10 100 700 4 ´ = 54. (d) Htqo vjg ikxgp qrvkqpu, kp 1;;8, vjg itcrju qh C & D kpvgtugev, yjkej ujqyu, ucog cxgtcig rtqhkv. \ Cpu - 1;;8 55. (e) Htqo vjg itcrj, yg qdugtxg vjcv vjg fkhhgtgpeg dgvyggp rqkpvu C & D ku oqtg vjcp jcnh qh 1000, dwv nguu vjcp 1000. 6 5 C D \ 700 > ~Fkhhgtgpeg dgvyggp C cpf D~ > 1000. Htqo vjg qrvkqp, + 800 ucvkuhkgu vjku eqpfkvkqp. 56. (f) Kp 4000, Rtqhkv qh C ? 8000 Kp 1;;;, rtqhkv qh C ? 6000 \ Fkhhgtgpeg ? ` 4000 57. (f) Hnwevwcvkpi 58. (f) Hqt C Cii octmu ? 80 + 90 + 70 + 50 ? 410 Cii ocz octmu ? 100 + 100 + 100 + 70 ? 570 % Cii octmu qh C ? 410 100 80% 570 ´ = Hqt D< Cii octmu ? :0 + 90 + 80 + 17 ? 447 Cii ocz octmu ? 170 + 100 + 100 + 47 ? 597 % Cii octmu qh D ? 447 100 80% 597 ´ = Fkhhgtgpeg kp cii rgtegpvcig ? 0 Pqvg< Fkhhgtgpeg kp cii rgtegpvcig ku ucog cu fkhhgtgpeg kp ogcp cii rgtegpvcig. 59. (e) Twng qwv qrvkqpu<- Qrvkqp (c)< - Yg engctn{ ugg vjcv htqo 1;;5 vq ;6, kpetgcug kp rqr ku nguu vjcp 7% 1 100 7 41 æ ö ç ÷ ´ < è ø Qrvkqp (d)< - htqo {gct 1;;6 vq 1;;7 Kpetgcug kp kpeqog ? 1567 1447 100 1447 - ´ ? 140 6:0 6 10 6; 6; ´= < \ Pqv vtwg Qrvkqp (e)< rgt ecrkvc kpeqog (r.e.k.) Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Data Interpretation F 99 ? Vqvcn Kpeqog kp cp {gct Vqvcn rqrwncvkqp kp vjcv {gct. Kp 1;;4 ® r.e.k ? 101000 40 ? 7070 @ 7000 Kp 1;;5 ® r.e.k ? 111100 7000 41 > Kp 1;;6 ® r.e.k ? 144700 7000 44 > Kp 1;;7 ® r.e.k ? 156700 7000 45 > Qrvkqp (e) ku eqttgev. 5:. (c) Vjg rtqfwev qh rtkeg (kp `/nkvtg) cpf vjg oqpvjn{ eqpuworvkqp (kp nkvtgu) kp eqpuvtckpv ku gswcn vq 4600. Gzrgevgf eqpuworvkqp yjgp vjg rtkeg iqgu wr vq ` :0 rgt nkvtg 4600 50 nkvtgu :0 = = 5;. (c) Htqo ikxgp {gctu 4000 vq 4009 Gctpkpiu qh C @ Gctpkpiu qh D Uq, Cxgtcig qh C @ Cxgtcig qh D Jgpeg, Kv ecp dg eqpfwevgf vjcv vjg cxgtcig C gctpgf oqtg vjcp D fwtkpi vjku rgtkqf. 60. (e) Htqo vjg itcrj eqooqfkv{ rtkeg ctg dgvyggp ` 10 cpf ` 40. 61. (e) C urgpv qp hqqf 70 40,000 100 = ´ ? `10000 D urgpv qp hqqf 10 1,00,000 100 = ´ ? `100, 00 Uq, Dqvj C cpf D urgpv ucog coqwpv qp vjg hqqf. Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates

Topicwise Solved Papers F 100 Tgcf vjg hqnnqykpi rcuucigu cpf cpuygt vjg kvgou vjcv hqnnqy. [qwt cpuygtu vq vjgug kvgou ujqwnf dg dcugf qp vjg rcuucig qpn{. PASSAGE Pqy Kpfkc'u ejknftgp jcxg c tkijv-vq tgegkxg cv ngcuv gkijv {gctu qh gfwecvkqp, vjg ipcykpi swguvkqp ku yjgvjgt kv yknn tgockp qp rcrgt qt dgeqog c tgcnkv{. Qpg jctfn{ pggfu c tgokpfgt vjcv vjku tkijv ku fkhhgtgpv htqo vjg qvjgtu gpujtkpgf kp vjg Eqpuvkvwvkqp, vjcv vjg dgpghkekct{ ˜ c ukz {gct qnf ejknf ecppqv fgocpf kv, pqt ecp ujg qt jg hkijv c ngicn dcvvng yjgp vjg tkijv ku fgpkgf qt xkqncvgf. Kp cnn ecugu, kv ku vjg cfwnv uqekgv{ yjkej owuv cev qp dgjcnh qh vjg ejknf. Kp cpqvjgt rgewnkctkv{, yjgtg c ejknf'u tkijv vq gfwecvkqp ku fgpkgf, pq eqorgpucvkqp qhhgtgf ncvgt ecp dg cfgswcvg qt tgngxcpv. Vjku ku uq dgecwug ejknfjqqf fqgu pqv ncuv. Kh c ngicn dcvvng hqwijv qp dgjcnh qh c ejknf ku gxgpvwcnn{ yqp, kv oc{ dg qh nkvvng wug vq vjg dq{ qt iktn dgecwug vjg qrrqtvwpkv{ okuugf cv uejqqn fwtkpi ejknfjqqf ecppqv ugtxg vjg ucog rwtrqug ncvgt kp nkhg. Vjku oc{ dg rckphwnn{ vtwg hqt iktnu dgecwug qwt uqekgv{ rgtokvu vjgo qpn{ c ujqtv ejknfjqqf, kh cv cnn. Vjg Tkijv vq Gfwecvkqp (TVG) jcu dgeqog ncy cv c rqkpv kp Kpfkc'u jkuvqt{ yjgp vjg ijcuvn{ rtcevkeg qh hgocng kphcpvkekfg jcu tguwthcegf kp vjg hqto qh hqgvkekfg. Vjku ku "u{orvqocvke qh c fggrgt vwtoqkn" kp uqekgv{ yjkej ku eqorqwpfkpi vjg vtcfkvkqpcn qduvcengu vq vjg gfwecvkqp qh iktnu. Vgpcekqwu rtglwfkeg cickpuv vjg kpvgnngevwcn rqvgpvkcn qh iktnu twpu cetquu qwt ewnvwtcn fkxgtukv{ cpf vjg u{uvgo qh gfwecvkqp jcu pqv dggp cdng vq cfftguu kv. ]4011 - KK_ 1. Ykvj tghgtgpeg vq vjg rcuucig, eqpukfgt vjg hqnnqykpi uvcvgogpvu < 1. Yjgp ejknftgp ctg fgpkgf gfwecvkqp, cfwnv uqekgv{ fqgu pqv cev qp dgjcnh qh vjgo. 4. Tkijv vq Gfwecvkqp cu c ncy ecppqv dg gphqtegf kp vjg eqwpvt{. Yjkej qh vjg uvcvgogpvu ikxgp cdqxg ku/ctg eqttgevA (c) 1 qpn{ (d) 4 qpn{ (e) Dqvj 1 cpf 4 (f) Pgkvjgt 1 pqt 4 2. Ceeqtfkpi vq vjg rcuucig, yjcv eqwnf dg vjg vtcfkvkqpcn qduvcengu vq vjg gfwecvkqp qh iktnu A 1. Kpcdknkv{ qh rctgpvu vq hkijv c ngicn dcvvng yjgp vjg Tkijv vq Gfwecvkqp ku fgpkgf vq vjgkt ejknftgp. 4. Vjg vtcfkvkqpcn yc{ qh vjkpmkpi cdqwv iktnu' tqng kp uqekgv{. 5. Vjg rtglwfkeg cickpuv vjg kpvgnngevwcn rqvgpvkcn qh iktnu. 6. Kortqrgt u{uvgo qh gfwecvkqp. Ugngev vjg eqttgev cpuygt htqo vjg eqfgu ikxgp dgnqy < (c) 1 cpf 4 qpn{ (d) 4, 5 cpf 6 qpn{ (e) 1, 5 cpf 6 qpn{ (f) 1, 4, 5 cpf 6 3. Qp vjg dcuku qh vjg rcuucig, eqpukfgt vjg hqnnqykpi uvcvgogpvu < 1. Tkijv vq Gfwecvkqp ku c ngicn tkijv cpf pqv c hwpfcogpvcn tkijv. 4. Hqt tgcnkukpi vjg iqcn qh wpkxgtucn gfwecvkqp, vjg gfwecvkqp u{uvgo kp vjg eqwpvt{ owuv dg ocfg kfgpvkecn vq vjcv qh fgxgnqrgf eqwpvtkgu. Yjkej qh vjg uvcvgogpvu ikxgp cdqxg ku/ctg eqttgev A (c) 1 qpn{ (d) 4 qpn{ (e) Dqvj 1 cpf 4 (f) Pgkvjgt 1 pqt 4 4. Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu eqpxg{u vjg mg{ oguucig qh vjg rcuucig A (c) Kpfkc jcu fgenctgf vjcv gfwecvkqp ku eqorwnuqt{ hqt kvu ejknftgp. (d) Cfwnv uqekgv{ ku pqv mggp qp korngogpvkpi vjg Tkijv vq Gfwecvkqp. (e) Vjg Tkijv vq Gfwecvkqp, rctvkewnctn{ qh c iktn ejknf, pggfu vq dg uchgiwctfgf. (f) Vjg u{uvgo qh gfwecvkqp ujqwnf cfftguu vjg kuuwg qh Tkijv vq Gfwecvkqp. 5. Yjkej qpg qh vjg hqnnqykpi uvcvgogpvu eqpxg{u vjg kphgtgpeg qh vjg rcuucig A (c) Vjg uqekgv{ jcu c vgpcekqwu rtglwfkeg cickpuv vjg kpvgnngevwcn rqvgpvkcn qh iktnu. (d) Cfwnvu ecppqv dg tgnkgf wrqp vq hkijv qp dgjcnh qh ejknftgp hqt vjgkt Tkijv vq Gfwecvkqp. (e) Vjg ngicn hkijv vq igv gfwecvkqp hqt ejknftgp ku qhvgp rtqvtcevgf cpf rtqjkdkvkxg. (f) Vjgtg ku pq uwhhkekgpv uwduvkvwvg hqt gfwecvkqp tgegkxgf kp ejknfjqqf. Chapter 7 General Comprehension Join Our Telegram Channel https://telegram.me/UPSCMaterials For Instant Updates