गणित कक्षा ७

kf7 19 :yfgfGt/0f

(Transformation)

19.0 k'g/jnf]sg (Review)

tn lbOPsf lrqx¿sf] cjnfs] g u/L ;f]lwPsf kZ| gx¿nfO{ ;fyLx¿lar 5nkmn
u/L lgisif{ kQf nufpgx' f];\ .

lrq I lrq II

-s_ lrq I df s] dflg;sf] cg'xf/ / Pg] fdf bl] vPsf] cg'xf/ P]gfaf6 a/fa/
bl' /df 5g\ <

-v_ lrq I df, s] dflg;sf] cg'xf/ / Pg] fdf b]lvPsf] cgx' f/ p:t} / pq} 5g\ <
-u_ lrq II df s] lunf;nfO{ klxns] f] :yfgaf6 lglZrt lbzfdf ;fbf{ cfsf/df

kl/jtg{ cfPsf] 5 <

s'g} lglZrt lgoddf /xL s'g} j:ts' f] l:ylt (position) / gfkdf kl/jt{g
xg' 'nfO{ pSt j:t'sf] :yfgfGt/0f (Transformation) elgG5 .

19.1 k/fjt{g (Reflection)

lj|mofsnfk 1

;a} ljBfyLx{ ¿n] Ps Pscf]6f kk] / lnO{ tn lrqdf b]vfP h:t} u/L laraf6 bO' {
a/fa/ efu x'g] u/L k6\ofpgx' f];\ .

244 ul0ft, sIff &

ca sDkf;sf] rR' rf] jf sndn] k6o\ fOPsf] efusf lardf Pp6f Kjfn kfgx'{ f];\ .

To;kl5 lrqdf bv] fP h:t} u/L k6o\ fOPsf] efunfO{ vf]Ngx' f];\ M

sfuh k6\ofpFbf ags] f] /]vfb]lv bj' } Kjfn;Ddsf] b'/L gfkL ;fyLx¿;Fu 5nkmn
ug{'xf;] \ .

dflysf] 5nkmnaf6 lgDgfg';f/sf] lgisif{ kQf nufpg ;lsG5 .

● b'Oc{ f6] f Kjfnx¿dWo] s'g} Pp6f KjfnnfO{ cfsl[ tdfGbf csf]{ Kjfn To;sf]
kl| tlaDa xG' 5 .

● sfuh k6o\ fpbF f ags] f] /v] f k/fjt{gsf] cIf xf] .
● k/fjtg{ cIfaf6 cfs[lt / k|ltljDa a/fa/ b'/Ldf /x]sf] x'G5 .

lj|mofsnfk 2

lbOPsf lrq cjnfs] g ug'x{ f];\ / ;fyLx¿;Fu 5nkmn u/L ;fl] wPsf k|Zgx¿sf]

pQ/ vfH] gx' f];\ m

A A'

B B'

1 2 3 4 5 6 7 8 9 10 11 12

ul0ft, sIff & 245

-s_ lrqdf /v] f AB nfO{ k/fjt{g u/fpFbf ags] f] kl| tljDa (image) s'g xf] <
-v_ s] /]vf AB / /v] f A'B' p:t} / pq} 5g\ <
-u_ lrqdf k/fjtg{ sf] cIf s'g xf] <
-3_ s] k/fjt{gsf] cIfbl] v /v] f AB / /]vf A'B' ;Ddsf] b/' L a/fa/ 5 <
-ª_ s] jf:tljs cfs[lt -/v] f AB) / kl| tljDa -/v] f A'B') cg¿' k 5g\ <

● h'g /v] fsf cfwf/df k/fjtg{ u/LG5, To; /v] fnfO{ k/fjtg{ sf] cIf
(axis of reflection) elgG5 .

● jf:tljs j:t' k/fjt{g eO{ aGg] cfsl[ tnfO{ k|ltlaDa (Image) elgG5 .

● s'g} j:t' jf cfsl[ tnfO{ k/fjtg{ ubf{ cfs[lt / k|ltljDa k/fjt{gsf]
cIfaf6 a/fa/ b/' Ldf kb{5g\ .

● s'g} klg HoldtLo lrq jf cfs[ltnfO{ k/fjt{g ubf{ jf:tljs cfs[lt /
k|ltljDa cg'¿k x'G5g\ .

-s_ X – cIfdf k/fjtg{ (Reflection on X- axis)

;uF s} f] uf| kmdf b]vfP h:t} u/L Y
cfcfkmg\ f] uf| km sfkLdf X - cIf (XOX' ) A (4, 5)

/ Y- cIf (YOY') lvRg'xf];\ . ca u|fkmdf

s'g} laGb' A lnP/ XOX' af6 k/fjtg{

u/fpgx' f];\ / pSt laGb'nfO{ A' gfd

lbg'xf];\ . X- cIfaf6 A ;Ddsf] b'/L

/ X- cIfaf6 A' ;Ddsf] b/' L a/fa/ X' O X
x'g'kb5{ .

To;kl5 u|fkmdf laGb' A' sf] lgb{]zfªs\

ug/] n]Vgx' f;] \ . To;}u/L A sf] lgb{]zfªs\

slt xG' 5 < ;fyLx¿;Fu 5nkmn ug'x{ f;] \ . A' (4, –5)
Y'
oxfF uf| kmdf laGb' A sf] lgb{z] fª\s (4, 5)
/ A' sf] lgb]z{ fª\s (4, –5) 5 .

laGb' A(1, 2) / laGb' B(4, 3) nfO{ hf8] \bf aGg] /v] fv08nfO{ X- cIfdf k/fjt{g

ug'{xf];\ / aGg] k|ltljDanfO{ u|fkmdf bv] fO{ ;fyLx¿;Fu 5nkmn u/L sIffdf

kb| zg{ ug'{xf];\ .

246 ul0ft, sIff &

pbfx/0f 1

laGb' P(–3, 2) nfO{ uf| kmdf cª\sg u/L X- cIfaf6 P Y
k/fjt{g u/fO{ uf| kmdf b]vfpg'xf];\ . OX
Y'
;dfwfg
B' (3, 4)
oxfF p(x, y) = P (–3, 2) X

ca uf| kmdf P(–3, 2) nfO{ X' X
M'(4, –5)
X- cIfaf6 k/fjtg{ ubf{, P'
P(–3, 2) sf] kl| tljDa P'(–3, –2) eof]

t;y{ P(x', y') = P'(–3, –2)

-v_ Y- cIfdf k/fjt{g (Reflection on Y- axis) Y

;Fus} f] uf| kmdf bv] fP h:t} u/L cfcfkm\gf]

u|fkm sfkLdf sg' } laGb' B nfO{ YOY' B (–3, 4)
af6 k/fjt{g u/fpg'xf];\ o;sf] kl| tlaDa

YOY' /v] faf6 laGb' B sf] a/fa/ b'/Ldf
kb5{ . o;nfO{ B' gfd lbgx' f;] \ .

ca B / B' sf] lgb]{zfªs\ ug]/ slt slt X' O
x'G5 < ;fyLx¿;uF 5nkmn u/L n]Vg'xf;] \ . Y'

oxfF uf| kmdf laGb' B sf] lgbz]{ fªs\ (–3, 4)
/ B' sf] lgb{z] fªs\ (3, 4) 5 .

pbfx/0f 2

laGb' M(–4, –5) nfO{ uf| kmdf cªsg u/L X' Y
Y- cIfaf6 k/fjt{g u/fO{ uf| kmdf bv] fpgx' f];\ . M(–4, –5) O

;dfwfg Y'

oxfF M(x, y) = M (–4, –5)
ca u|fkm kk] /df M(–4, –5) nfO{ Y- cIfaf6
k/fjtg{ ubf{, M(–4, –5) sf] k|ltljDa M'(4, –5)
eof] t;y,{ M'(x', y') = M' (4, –5) xG' 5 .

ul0ft, sIff & 247

cEof; 19.1

1. lbOPsf HofldtLo cfsl[ tx¿nfO{ m cIf -X–cIf jf Y–cIf_ df k/fjt{g u/L
kl| tlaDa lrq lvRgx' f];\ .

-s_ -v_

m

m

-u_ -3_

mm

2. tnsf HofldtLo cfsl[ tx¿nfO{ k/fjtg{ sf] cIf XX' (X-cIf) df k/fjt{g ubf{ aGg]
k|ltlaDa nV] gx' f;] \ .

-s_ laGb' A -v_ laGb' M -u_ laGb' R
-3_ /]vf AC -ª_ /]vf PQ -r_ /v] f KL
-5_ RST -h_ UVW

A R TR M
S CK
X' X

P W
U
V
B L
Q

248 ul0ft, sIff &

3. lbOPsf HofldtLo lrqx¿nfO{ Y-cIfdf k/fjtg{ ug'{xf];\ / aGg] kl| tljDa kQf

nufpgx' f;] \ . YJ
F
-s_ laGb' F -v_ laGb' T
-u_ /]vf PQ -3_ /]vf MN Q L K
-ª_ ABC -r_ JKL T

P M
A

BC N

Y'

4. nv] flrqsf] k|of]u u/L lbOPsf lgb]z{ fªs\ x¿ nfO{ X- cIfdf k/fjtg{ u/L
kl| tlaDasf] lgb{]zfªs kQf nufpgx' f;] \ M

-s_ (1, 2) -v_ (3, 2) -u_ (–4, 4)

-3_ (–2, 6) -ª_ (8, –7) -r_ (9, –10)

-5_ (–6 –9) -h_ (–5, -8) -em_ (–9, 7)

5. k|Zg (4) sf laGb'x¿nfO{ Y-cIfaf6 k/fjtg{ u/L u|fkmkk] /df eg'{xf;] \ .

6. laGb' T' (3,-4) nfO{ X– cIfaf6 k/fjt{g ug'{xf];\ / T sf] lgbz{] fªs\ kQf
nufpg'xf];\ . /]vf TT' sf] b'/L kQf nufpgx' f];\ .

7. laGb' P(4, 5) nfO{ Y– cIfaf6 k/fjtg{ ug'x{ f];\ . P' sf] lgbz]{ fªs\ / /]vf PP'
sf] b'/L kQf nufpgx' f;] \ .

kl/of]hgf sfo{

cfˆgf] 3/, ljBfno, af6fdf x'g] u/]sf] k/fjt{gsf kfrF cf6] f cj:yfx¿sf]
vfh] L u/L l6kf6] ug{'xf];\ / sIffdf k:| tt' ug'{xf;] \ .

ul0ft, sIff & 249

pQ/

4. -s_ (1, –2) -v_ (3, –2) -u_ (–4, –4)

-3_ (–2, -6) -ª_ (8, 7) -r_ (9, 10)

-5_ (–6, 9) -h_ (–5, 8) -em_ (–9, –7)

5. -s_ (–1, 2) -v_ (–3, 2) -u_ (4, 4)

-3_ (2, 6) -ª_ (–8, –7) -r_ (–9, –10)

-5_ (6, –9) -h_ (5, –8) -em_ (9, 7)

6. T'(3, 4) 7. P' (–4,5)

19.2 lj:yfkg (Displacement)

lj|mofsnfk 1

;a} ljBfyL{n] cfcfkmg\ f sfkLdf Pp6f l;wf /]vf sf]gx{' f;] \ . lrqdf b]vfP h:t} u/L
Tof] /v] fsf] Ps 5]pdf O/]h/ /fVgx' f];\ / O/]h/sf] rf/cf6] } s'gfdf yfK] nf lbP/ gfd
ABCD /fVgx' f;] \ .

B B'

A C C'
D A'

D'

To;kl5 O/h] /nfO{ l3;f/]/ ToxL /v] fdf cufl8 ;fg'{xf];\ / O/]h/sf] rf/cf6] } sg' fdf
yfK] nf lbO{ A', B', C' / D' gfdfªs\ g ug{'xf];\ .

ca ;fyLx¿;uF 5nkmn u/L tnsf k|Zgx¿sf] pQ/ vfH] gx' f];\

-s_ AA', BB', CC' / DD' sf] ;DaGw s] xf]nf <
-v_ s] O/h] /sf] :yfg lglZrt lbzfdf kl/jt{g eof] <
-u_ s] cfs[lt / kl| tlaDa cg¿' k 5g\ <

ca dflysf ljm| ofsnfksf cfwf/df lj:yfkgsf] kl/efiff nv] L cfkm"n] n]v]sf]
kl/efiffnfO{ ;fyLn] n]v]sf] kl/efiff;Fu tn' gf u/L x]gx'{ f];\ .

250 ul0ft, sIff &

● s'g} klg j:t'nfO{ lglZrt lbzf / b/' Ldf ;fg'{ jf :yfgfGt/0f ug{n' fO{
lj:yfkg elgG5 .

● lj:yfkgsf nflu lj:yfkgsf] kl/df0f jf gfk / lbzf pNn]v ug'{kb5{ .
● lj:yfkgdf cfsl[ t / kl| tlaDa cg'¿k xG' 5g\ .
● sg' } klg laGbn' fO{ lj:yfkg ubf{ lbOPsf] kl/df0f / lbzfdf ;dfgfGt/ /v] f

lvRgk' 5{ .

pbfx/0f 1

;uF s} f] /]vfv08 PQ nfO{ ls/0f /]vf ON sf] kl/df0f / P O

lbzfdf lj:yflkt ug'{xf];\ . N

;dfwfg O Q

-s_ laGb' P af6 ON sf] lbzf / kl/df0f ;uF a/fa/ N Q
Q'
/ ;dfgfGt/ xg' ] u/L PP' lvRg'xf];\ . P

-v_ laGb' Q af6 ON sf] lbzf / kl/df0f;uF a/fa/

/ ;dfgfGt/ xg' ] u/L QQ' lvRg'xf];\ .

-u_ P' / Q' nfO{ hf]8\gx' f;] \ . o;/L P'Q' g} /]vfv08 PQ sf] P'
cfjZos k|ltlaDa xf] .

cEof; 19.2

1. tn lbOPsf laGb' tyf /v] fv08x¿nfO{ lbOPsf lbzf / kl/df0fdf lj:yfkg
ug{'xf];\ .

-s_ A -v_ B -u_ -3_ X 10 cm

5 cm 7 cm P 10 cm

-ª_ P -r_ -5_ X

8 cm 3.5 cm 6.5 cm Y
Q MN

ul0ft, sIff & 251

2. /]vf XY nfO{ OK sf] gfk / lbzfdf lj:yfkg ug{'xf;] \ .

K

XO Y

3. /]vf PQ nfO{ OM sf] gfk / lbzfdf lj:yfkg ug{'xf];\ .

P

OM

Q

4. tnsf k|Tos] HofldtLo cfsl[ tsx¿nfO{ lbOPsf] lbzf / kl/df0fdf lj:yfkg ubf{
aGg] k|ltlaDa lvRg'xf;] \ .

-s_ A -v_ L -u_ Q Z

BC M XY
N

5. Pp6f aRrf lrKn6] L vN] bf lrKn/] 4m tn cfof] eg] s] of] lj:yfkg xf,] sf/0f
lbgx' f;] \ .

6. eO' dF f Pp6f dfq 6K' kf] ;dft]/ 1 ld6/ cfkml" t/ tfGbf afsF L ;a} 6K' kfx¿ pxL
lbzf / kl/df0fdf :yfgfGt/0f xf]nfg\ <

7. Pp6f k:' tsnfO{ Go'hlkG| 6 jf 8«Oª kk] / dfly /fv/] 10 cm cufl8 ;fbf{ s]
k':tssf afsF L ;a} s'gfx¿ pxL lbzf / kl/df0fdf :yfgfGt/0f xf]nfg < s]

of] lj:yfkg xf] <

kl/of]hgf sfo{

Pp6f sfuhdf Pp6f l;wf /]vf sf]g{x' f;] \ . pSt /v] fsf] dfly Pp6f sg' } laGb'
A lng'xf];\ . ca To; laGbn' fO{ t];f| ] /v] fdf bfoflF t/ 15cm sf] kl/df0fdf
lj:yfkg u/L k|ltlaDa kQf nufpg'xf];\ . pSt cfs[ltnfO{ sIffdf k:| tt'
ug{'xf];\ .

pQ/
lzIfsnfO{ bv] fpgx' f;] \ .

252 ul0ft, sIff &

lbzf l:ylt / :s]n 8O« ª

kf7 20 (Bearing and Scale Drawing )

20.0 kg' /jnf]sg (Review)

;Fus} f] sDkf;sf] lrqsf] cjnf]sg u/L tnsf k|Zgx¿df 5nkmn ugx{' f;] \ M

-s_ pSt pks/0f s] sfdsf nflu k|of]u u/LG5 <
-v_ pks/0fdf ePsf] N, S, E, W n] s] s] hgfp5F <
-u_ pks/0fdf l;of] sg' lbzflt/ kms{]sf] 5 <
-3_ pSt pks/0fdf s'g lbzfnfO{ cfwf/ lbzf dflgPsf] x'G5 <
-ª_ pks/0fdf ePsf] NE, SE, SW, NW n] s] s] hgfp5F <

N ⇒ pQ/ (North) NE ⇒ pQ/ kj" { (North East)
S ⇒ blIf0f (South) SE ⇒ blIf0f kj" { (South East)
E ⇒k"j{ (East) SW ⇒ blIf0f klZrd (South West)
W ⇒ klZrd (West) NW ⇒ pQ/ klZrd (North West)

20.1 lbzf l:ylt (Bearing)

lj|mofsnfk 1

cfˆgf] a]Grdf a;s] f ;fyLx¿sf] Pp6f ;d"x agfpg'xf;] \ .
k|Tos] ;dx" n] Pp6f Pp6f sfuhsf kfgf lng'xf];\ / lrqdf bv] fP h:t} u/L
kfgfnfO{ l7s laraf6 bO' { k6s k6\ofpg\xf];\ .

ul0ft, sIff & 253

kml] / s'gfaf6 pSt kfgfnfO{ b'O{ k6s k6\ofpgx' f;] \ .

To;kl5 k6o\ fPsf] efunfO{ vfN] gx' f];\ pQ/ klZrd pQ/ (N) k"j{ (NE)
/ lrqdf b]vfP h:t} u/L k6\ofOPsf (NW)
7fpdF f ags] f /]vfsf 5]pdf gfdfª\sg pQ/
u/L ;fyLx¿;uF 5nkmn u/L tnsf
kZ| gx¿sf] pQ/ vf]Hg'xf];\ M 045°

klZrd kj" { (E)
(W)

-s_ cfkmn' ] agfPsf] gd'gf -lrq_df blIf0f klZrd blIf0f k"j{ (SE)
sltcf6] f lbzfx¿ 5g\ < ltgLx¿
s] s] x'g\ < (SW) blIf0f (S)

-v_ pQ/ kj" { lbzf bv] fpg] /v] fn] slt l8uL| sf] sf]0f agfPsf] 5 <

-u_ pQ/ / pQ/ k"j{ lbzf b]vfpg] /v] flar slt l8uL| sf] sf]0f 5, gfKg'xf];\ .

-3_ s] pQ/ / klZrd, klZrd / blIf0f tyf blIf0f / kj" { bv] fpg] /v] fx¿lar
klg 90° sf sf0] f ag]sf 5g\ <

-ª_ s] pQ/ / pQ/ klZrd, klZrd / blIf0f klZrd tyf blIf0f kj" { bv] fpg]
;a} /]vfx¿n] cfk;df 45°/45° sf sf0] f agfPsf 5g\ <

s'g} Pp6f :yfgdf pQ/ lbzf hgfpg] /v] fnfO{ cfwf/ dfg/] 38Lsf] ;'O{sf]
lbzfdf s'g} b'O{ :yfglarsf] b'/LnfO{ tLg cª\sdf sf0] fsf ¿kdf k|:tt' ug{]
tl/sfnfO{ lbzf l:ylt (Bearing) elgG5 .

254 ul0ft, sIff &

20.1.1 gS;f k9fO (Map reading) a;kfs{ dlGb/
ljBfno
ljm| ofsnfk 2
c:ktfn gu/kflnsf ejg
;Fu}sf] lrqdf sg' } gu/kflnsfsf s]xL
:yfgx¿ b]vfOPsf] 5 . pSt lrqnfO{ rft} f/f
sfkLdf 6]«; ug'{xf;] \ . gu/kflnsf
ejgnfO{ cfwf/ dfgL ;fyLx¿;Fu k|x/L sfofn{ o
5nkmn u//] lgDglnlvt :yfgx¿sf]
lbzfl:ylt kQf nufpg'xf];\ / sIffdf kfgL 6\ofªs\ L
k:| t't ugx'{ f;] \ .

-s_ ljBfno -v_ dlGb/

-u_ a;kfs { -3_ k|x/L sfof{no

-ª_ c:ktfn -r_ kfgL 6o\ fªs\ L

20.2 :sn] 8«Oª (Scale Drawing)

lj|mofsnfk 3

;a} ljBfyLx{ ¿ pko'St ;dx" df a:gx' f;] \ . lbOPsf] cj:yfsf] cWoog u/L tnsf
k|Zgx¿af/] ;d"xdf 5nkmn ugx'{ f;] \ / sIffdf k|:tt' ug'x{ f];\ .

elnan sf]6{

9 cm

4.5 cm

|kxf/ ]/vf
dWo ]/vf
|kxf/ ]/vf
aflx/L lsgf/f

3 cm 1.5 cm 1.5 cm 3 cm

:s]n 1:200 (1 cm = 200 cm)

ul0ft, sIff & 255

jm| =;= /v] fsf] gfd gS;fsf] jf:tljs jf:tljs sf]6{ lgisif{
/v] fsf] gfk sf6] {sf] gfk / gS;fsf]
1 sf]6s{ f] nDafO
2 . sf]6s{ f] rf8} fO gfksf] cgk' ft
3 . dWo /v] fb]lv
9 cm 18 m 1:200
kx| f/ /v] f–
;Ddsf] b'/L

● jf:tljs sf]6s{ f] rf}8fO / gS;fsf] rf}8fOsf] cgk' ft slt 5 <
● jf:tljs sf6] s{ f] nDafO / gS;fsf] nDafOsf] cgk' ft slt 5 <
● gS;fsf] dWo /]vfbl] v kx| f/ /v] f;Ddsf] b/' L 6 cm 5 eg] jf:tljs b/' L

slt xfn] f <

● dflysf] elnan sf]6n{ fO{ :s]n 1 cm = 1 OGr lnP/ 8«Oª kk] /df gS;f
tof/ ug'{xf];\ .

● dflysf] 5nkmnsf cfwf/df s] lgisif{ lgsfNg ;lsG5 <

1. lglZrt :sn] sf] k|ofu] u/L Hofb} 7'nf / Hofb} j:t'nfO{ /]vfªs\ g ug{
;lsG5 .

2. :s]ndf jf:tljs j:t' / lrq -gS;f_ lvr/] cfjZostfcg';f/ 7'nf] jf
;fgf] gfk lnP/ lglZrt cg'kft agfOG5 .

3. lglZrt :s]nsf] ko| f]u u/L gS;faf6 j:ts' f] jf:tljs gfk lgsfNg
;lsG5 .

pbfx/0f 1

1 cm = 500 m sf] :sn] ko| fu] u/L Pp6f gS;f tof/ ubf{ bO' { :yfglarsf] gS;fsf]
b/' L 9cm eP pSt b'O{ :yfgx¿larsf] jf:tljs b'/L slt xfn] f <

;dfwfg
oxfF :sn] 1 cm = 500 m jf:tljs b/' L
:sn] 9cm = (9 × 500) m = 4500 m
t;y,{ bO' 7{ fpF larsf] jf:tljs b/' L= 4500m

256 ul0ft, sIff &

cEof; 20

1. sIffsf ljBfyLx{ ¿ lrqdf b]vfP h:t} u/L rp/df plePsf 5g\ eg] tnsf

kZ| gx¿sf] pQ/ lbgx' f];\ . C A

-s_ bfh] ]{ plePsf] :yfgsf] lbzfl:ylt s'g xf] < F
-v_ hfls/ plePsf] lbzfl:ylt sg' xf] <

-u_ s] ;s' d' fof / rdn] L plePsf] lbzfl:ylt O E
ldN5 < B

2. tn lbOPsf] lrqsf cfwf/df ;fl] wPsf kZ| gx¿sf] D
hjfkm n]Vgx' f;] \ M

-s_ :yfg O af6 laGb' A sf] lbzfl:ylt kd| fb]
kQf nufpgx' f;] \ . kD] af bf]h]{

-v_ :yfg O af6 laGb' C sf] lbzf l:ylt
kQf nufpgx' f];\ .
hfls/ k|ltef

-u_ :yfg O af6 laGb' F sf] lbzf l:ylt rd]nL lht'
kQf nufpg'xf;] \ . ;s' 'dfof

-3_ :yfg O af6 laGb' B sf] lbzf l:ylt
kQf nufpg'xf;] \

3. g]kfnsf] jf:tljs gS;f cjnf]sg u/L tn ;f]lwPsf k|Zgx¿sf] pQ/ n]Vg'xf;] \ M

-s_ kfv] /faf6 gk] fnuGhsf] lbzfl:ylt nV] gx' f;] \ .

-v_ sf7df8f}Faf6 dgfª\sf] lbzfl:ylt nV] g'xf];\ .

-u_ hgsk'/af6 tfKnh] 'ªsf] lbzfl:ylt n]Vgx' f;] \ .

4. tnsf kZ| gx¿df b'O{ :yfg larsf] jf:tljs b/' L kQf nufpgx' f;] \ M

-s_ bO' { :yfglarsf] gS;fsf] b'/L = 9 cm [:sn] 1 cm = 200m]
-v_ bO' { :yfglarsf] gS;fsf] b'/L = 3.5 cm, [:sn] 1 cm = 500 ft]
-u_ 306f3/ / 38Lcjf{ kfv] /Llarsf] gS;fsf] b/' L = 5.3 cm,

[ :sn] 1 cm = 1000 m]

5. Pp6f rp/sf] jf:tljs nDafO 125 m / 75 m 5 . 1 cm : 10 cm sf]

cgk' ft lnP/ rp/sf] /]vfª\sg ug{x' f];\ .

6. 1cm n] jf:tljs 2 lkm6 hgfpg] u/L 20 ft nDafO / 18 ft rf8} fO ePsf]
sIffsf]7fsf] lrq agfP/ b]vfpg'xf];\ .

ul0ft, sIff & 257

7. lrqdf lbOPsf] lah'nLsf] vDaf 1:100 cm sf] :s]ndf agfOPsf]
5 . ?n/n] gfk]/ vDafsf] jf:tljs prfO kQf nufpgx' f;] \ .

8. ljBfnosf] rp/df uP/ k|Zg g= ! sf] lrqdf b]vfP h:t} u/L
kT| os] lbzfdf Ps Ps hgf ;fyLx¿ pleP/ lbzf l:ylt kQf
nufpgx' f;] \ . kT| os] ;fyLnfO{ lbzfl:yltsf] gfdn] afn] fpgx' f;] \ .

kl/of]hgf sfo{

gk] fnsf] gS;f lnP/ sg' } kb| ]zsf] ;b/d'sfdnfO{ s]Gb| dfgL cf7cf]6f
lbzf (N, S, E, W, SE, SW, NW, NE) df kg{] Ps Pscf]6f :yfgsf] gfd
nV] g'xf;] \ .

pQ/

lzIfsnfO{ b]vfpg'xf;] \ .

ldl>t cEof;

1. cf;Gg sf]0f (Adjacent angles) sf] kl/efiff n]Vg'xf;] \ .
2. sDkf;sf] k|of]u u/]/ tn lbOPsf sf]0fx¿ lvRgx' f;] \ M

-s_ 1050 -v_ 1350 -u_ 1500
3. lbOPsf lrqsf cfwf/df x / y sf] dfg kQf nufpg'xf;] \ M

-s_ -v_

xo 60° 85°
yo

xo

258 ul0ft, sIff &

4. tnsf lrqx¿dWo] s'g s'g cfs[ltx¿ cg¿' k 5g\, 56' \ofpgx' f;] \ M

-s_ -v_ -u_

35 43 44

45 5

5. tkfOsf 3/ ;d'bfodf kfOg] sg' } kfFrcf6] f cg'¿k cfs[ltx¿sf gfd nV] gx' f];\ .

6. tnsf k|To]s laGb'x¿nfO{ nv] flrq agfO{ cªs\ g ug'x{ f;] \ . k|To]s laGb'nfO{ j|mdzM
hf]8\b} hfg'xf;] \ . o;/L aGg] cfs[ltsf] gfd klg nV] g'xf;] \ .

A(-4,2), B(4, 3), C(2, -5)

7. Pp6f lqeh' PQR sf] /rgf ug{x' f]; h;df PQ = PR = 4 cm / QR = 5 cm
5.

8. olb Pp6f cfotsf] nDafO 3 cm / rf}8fO 4 cm 5 eg] pSt cfotsf]
ljs0fs{ f] nDafO slt xfn] f <

9. 1 cm n] jf:tljs 10 m hgfpg] u/L 90 m nDafO / 45 m rf8} fO ePsf]
km'6an d}bfgsf] lrq agfpg'xf;] \ .

10. tnsf cª\sx¿dWo] s'g s'g cªs\ x¿df /v] Lo ;dldlt 5g\ / lsg, kQf
nufpgx' f];\ .

11. /v] Lo ;dldlt x'g] cªu\ |]hL cIf/x¿dWo] V df Pscf]6f / H df b'O{cf]6f /v] f
;dldltsf cIf x'G5g\ . o:t} c¿ /]vLo ;dldlt xg' ] cª\uh]| L cIf/x¿ kQf
nufO{ ;r" L tof/ kfgx'{ f;] \ .

12. tnsf egfOx¿ l7s 5g\ jf 5}gg,\ 56' o\ fpgx' f];\ M

-s_ jus{ f ;a} u0' fx¿ cfotdf klg xG' 5g\ .
-v_ ju{sf b'a} ljs0fx{ ¿ cfk;df a/fa/ xG' 5g\ .
-u_ cfotsf ;a} u'0fx¿ ;dfgfGt/ rt'e{'hdf xG' 5g\ .
-3_ ;dafx' rte' h{' sf ;a} u0' fx¿ cfotsf u0' f;uF ldN5 .

ul0ft, sIff & 259

13. tn lbOPsf laGbx' ¿sf] lgb]{zfªs\ x¿ n]Vgx' f;] \ M

Y C
D
A
B X

E
F

GH

O

14. tnsf k|Tos] lrqdf /]vLo ;dldltsf] cIfx¿ lvRgx' f;] \ / /v] Lo ;dldltsf
cIfx¿sf] ;ªV\ of klg n]Vgx' f;] \ M

-s_ -v_ -u_ -3_

-ª_ -r_ -5_

15. Pp6f uf8L T :yfgaf6 200 km kj" {sf] :yfg S df k'u]sf] 5 . uf8Ln] S af6
csf]{ klZrddf kg{] :yfg U df 300 km sf] ofqf u/]5 . of] hfgsf/LnfO{
:s]n 8«Oª u/L lgDglnlvt s'/f kQf nufpg'xf;] \ MM
-s_ T af6 U ;Ddsf] b'/L -v_ U af6 T ;Ddsf] lbzfl:ylt

16. ;Fu}sf] lrqdf s]xL :yfgx¿ b]vfOPsf] 5 . lrqnfO cEof; k'l:tsfdf 6;«]
u/L / sf7df8f}nF fO{ cfwf/ dfgL lgDglnlvt :yfgx¿sf] lbzfl:ylt kQf
nufpg'xf];\ .

260 ul0ft, sIff &

uf];fOs0' 8

b]j3f6 tftf]kfgL

sf7df8fF} bfn] vf
kgft} L
knfGrf]s
eujtL

hgsk/'

-s_ uf;] fOs0' 8

-v_ tftf]kfgL

-u_ b]j3f6

-3_ bf]nvf

-ª_ knfGrfs] eujtL

-r_ kgf}tL

-5_ hgsk/'

17. lrqdf Pp6f ufpFsf] d'Vo xf6ahf/ dlGb/
7fpxF ¿ bv] fOPsf] 5 . olb
:jf:Yo
:sn] 1 cm = 100 m eP ?n/ rf}sL x'nfs
sfofn{ o
k|of]u u/L :j:Yo rf}sLaf6 ljBfno
261
lgDglnlvt 7fpxF ¿sf] jf:tljs

b/' L kQf nufpgx' f];\ M

-s_ dlGb/ kfgLsf]
-v_ kfgLsf] d'xfg dx' fg

-u_ ljBfno -3_ xf6ahf/

-ª_ xn' fs sfof{no

pQ/
lzIfsnfO{ b]vfpg'xf;] \ .

ul0ft, sIff &

kf7 21 tYofª\ssf] k|:tt' Ls/0f

(Presentation of Data)

21.0 kg' /jnf]sg (Review)

Pp6f k:' ts k;ndf Ps dlxgfdf kT| os] lbg lajm| L ePsf k:' tssf] ;ª\VofTds
ljj/0f o;k|sf/ 5 M

13, 14, 13, 16, 18, 20
13, 25, 10, 18, 12, 10
28, 25, 12, 15, 17, 15
25, 24, 20, 10, 25, 18

20, 22, 18, 15, 13, 20

dflysf] hfgsf/LnfO{ tnsf] h:t} tflnsf agfP/ e/L tflnsf k/" f ugx'{ f];\ .

k':tssf] ldnfg lrxg\ af/Daf/tf ;l~rt af/Daf/tf
;ªV\ of
4 4
13 .... 1 4+1=5

14

dflysf] tflnsfnfO{ s:tf] tflnsf elgG5, ;fyLx¿lar 5nkmn u/L lgisif{ lgsfNgx' f;] \ .

262 ul0ft, sIff &

ul0ft 'k:tss ]f ; \ªVof21.1 /]vflrq (Line Graph)

ljm| ofsnfk 1
Pp6f k:' ts laj|m]tfn] Ps xKtfdf laj|mL u/s] f ul0ft ljifosf] kf7\ok':tsx¿sf]
;ªV\ ofnfO{ 8f]Ndfn] lgDg /v] flrqdf k|:tt' u/Lg\ . lbOPsf] /v] flrqsf] cWoog u/L
lgDglnlvt k|Zgx¿sf af/]df 5nkmn ug{x' f;] \ M

Y

45
40
35
30
25
20
15
10
5
O cfOtaf/ ;fd] af/ dªu\ naf/ aw' af/ laxLaf/ zj' m| af/ zlgaf/ X

af/x¿

-s_ ;fd] af/ sltcf]6f ul0ft k:' ts lajm| L eP5 <
-v_ zj' m| af/ sltcf6] f ul0ft k:' ts laj|mL eP5 <
-u_ sg' s'g af/ a/fa/ ;ª\Vofdf ul0ft k':ts laj|mL eP5 <
-3_ sg' af/ ;a}eGbf a9L ul0ft k':ts laj|mL eP5 <

lbOPsf r/ d"No / To;sf] af/Daf/tfnfO{ uf| kmdf cª\lst u/L j|mdzM l;wf
/]vfx¿n] hf8] \bf aGg] lrqnfO{ /]vflrq (Line Graph) elgG5 .
/]vflrq agfpbF f ckgfpgk' g]{ r/0fx¿
1. lbOPsf] tYofª\snfO{ tflnsfdf /fVg'k5{ .
2. af/Daf/tfnfO{ Y – cIfdf / r/ dN" o -kl/df0f_ nfO{ X – cIfdf /fVg'k5{ .
3. pkoS' t :s]nsf] 5gf]6 ug'{k5{ .
4. laGbx' ¿nfO{ uf| kmdf k:| t't u/L k|Tos] laGbn' fO{ /v] fv08n] hf8] \gk' 5{ .

ul0ft, sIff & 263

la |jmL ; \ªVofpbfx/0f 1

Pp6f df]afOn k;ndf 5 dlxgfdf laj|mL ePsf] dfa] fOnsf] ljj/0f tnsf] /v] flrqdfc; ]fh
bv] fOPsf] 5 . pSt /v] flrqsf] cWoog u/L lgDglnlvt kZ| gx¿sf] pQ/ lbgx' f];\ .sfl {ts
+dl;/
dfa] fOnsf] laj|mL ljj/0f
'kif
Ydf3
35kmfN 'u0f
30
25
20
15
10
5

OX

-s_ sg' dlxgfdf ;ae} Gbf a9L df]afOn lajm| L ePsf] 5 <
-v_ s\'g dlxgfdf ;a}eGbf sd dfa] fOn lajm| L ePsf] 5 <
-u_ c;f]h dlxgfdf slcf]6f df]afOn lajm| L ePsf] /x5] <
-3_ k:| tt' /v] flrqnfO{ af/Daf/tf tflnsfdf b]vfpg'xf];\ .

;dfwfg
oxf,F
lbOPsf] /]vflrqsf cfwf/df dfly lbOPsf kZ| gx¿sf pQ/ o;k|sf/ 5g\ <
-s_ kmfNu'0f dlxgfdf ;a}eGbf a9L (35 cf6] f_ df]afOn laj|mL ePsf] 5 .
-v_ k'; dlxgfdf ;a}eGbf sd 10 cf]6f dfa] fOn laj|mL ePsf] 5 .
-u_ c;f]h dlxgfdf 20 cf6] f df]afOn laj|mL ePsf] 5 .

dlxgf c;f]h sflt{s dªl\ ;/ k;' df3 kmfNu0' f
df]afOn ;ªV\ of 20 30 15 10 20 35

264 ul0ft, sIff &

pbfx/0f 2

jiffo{ fddf s'g} 7fpdF f nuftf/ 5 lbg;Dd k/s] f] jiffs{ f] dfkg o;k|sf/ 5 M

lbg cfOtaf/ ;fd] af/ dª\unaf/ a'waf/ laxLaf/ zj' m| af/
jiff{ 20 mm 15 mm 25 mm 10 mm 28 mm 30 mm
dflysf] tYofª\snfO{ /v] flrqdf k|:tt' ug'{xf];\ .
;dfwfg
oxfF ;donfO{ X – cIfdf / jiffn{ fO{ Y – cIfdf /fvL /v] flrq lvRbf,

^ lbgsf] jiff{ ljj/0f

jif {f -mm df_ Y
35
30 X
25
20
15
10
5

O

lbgx¿
zj' |maf/
laxLaf/
a'waf/
dª\unaf/
;f]daf/
cfOtaf/

ul0ft, sIff & 265

cEof; 21.1

1. lbOPsf /v] flrqdf sf7df8f}sF f] ^ Ytfk |jmd (°C)
lbgsf] tfkjm| d ljj/0f b]vfOPsf]
30 cfOtaf/
5 . o;sf] cWoog u/L 25 ; ]faf/
20
lgDglnlvt kZ| gx¿sf] pQ/ 15 d \ªunaf/
'awaf/
n]Vgx' f;] \ .
laxLaf/
-s_ s'g af/ ;aeGbf a9L tfkjm| d 10 X
/x5] < 'z |jmaf/5

-v_ sg' af/ ;aeGbf sd tfkjm| d O

/x5] ] <

-u_ a'waf/sf] tfkj|md slt /x]5 < af/x¿
-3_ lbOPsf] /]vflrqnfO{ af/Daf/tf

tflnsfdf b]vfpgx' f];\ .

2. zf/bf cfwf/et" ljBfnosf] sIff 7 df ljut 6 jifs{ f] egfb{ / o;k|sf/ 5 M

jif{ 2074 2075 2076 2077 2078
egfb{ / 20 26 18 14 12

lbOPsf] cfFs8fnfO{ /]vflrqdf k:| t't ug{'xf];\ .

3. sIff 7 sf ljBfyLn{ fO{ sfl] e8–19 af6 aRg sg' sg' ;'/Iffsf ;fwgx¿ ko| fu]
ug{k' 5 egL ;f]lwPsf] k|Zgdf kl| tlj|mof o;ks| f/ kfOof] M

;fwg df:s ;l] g6fOh/ km];l;N8 kGhf ;fag'
ljBfyL{ ;ª\Vof 30 22 18 8 25

dflysf] hfgsf/LnfO{ /v] flrqdf k:| tt' ugx{' f];\ .

4. tnsf af/Daf/tf tflnsfx¿nfO{ /v] flrqdf k|:tt' ug{'xf;] \ M

-s_ sIff 1234567

ljBfyL{ ;ªV\ of 26 24 28 40 35 45 50

266 ul0ft, sIff &

-v_ kl/df0f (kg) 2 4 6 9 12
d"No (?=) 500 1000 1500 2250 3000

5. ljBfnodf Ps lbg laxfg !)M)) ahb] ]lv $M)) ah;] Dd 2/2 306fsf]
km/sdf ydf{]ld6/n] tfkjm| d gfk/] /v] flrq agfO{ sIffdf k:| tt' ug{'xf;] \ .

kl/ofh] gf sfo{

/l] 8of], 6l] nlehg jf kqkqLsfnufotsf cGo ljleGg dfWodx¿af6
Ps xKtf;Ddsf tfkj|mdsf] l6kf6] ug{x' f];\ / To;nfO{ /v] flrqdf bv] fO{
sIffsf7] fdf k:| t't ugx'{ f;] \ .

pQ/

lzIfsnfO{ bv] fpg'xf;] \ .

21.2 ax':tDe lrq (Multiple Bar Diagram)

sIffsf ljBfyL{x¿nfO{ s'g vn] a9L dg k/fpg'x'G5 egL ;f]lwPsf kZ| gdf k|fKt
kl| tlj|mofcg;' f/ tof/ u/LPsf] :tDe lrq lbOPsf] 5 . pSt :tDe lrqsf] cWoog
u/L lgDglnlvt kZ| gx¿sf af/]df 5nkmn ug{x' f];\ M

ljBfyL{x¿n] dg k/fPsf] v]n

Y

50
40
30
20
10

OX
ljBfy {L ; \ªVof
'km6an
elnan
l |jm ]s6
Aof8ldG6g
]6an ]6lg;

vn] x¿

ul0ft, sIff & 267

-s_ lbOPsf] :tDe lrq s:tf] :tDe lrq xf] <
-v_ ;ae} Gbf a9L ljBfyL{n] dg k/fPsf] v]n s'g xf] <
-u_ ;a}eGbf yf]/} ljBfyL{n] dg k/fPsf] vn] sg' xf] <
-3_ slt hgf ljBfyL{n] lj|ms6] vn] dg k/fpFbf /x]5g\ <

lj|mofsnfk 1

;/:jtL dfWolds ljBfnosf sIff 6 bl] v 10 ;Ddsf ljBfyLx{ ¿sf] 5fq / 5fqf
;ªV\ ofnfO{ tnsf] :tDe lrqdf k:| tt' u/LPsf] 5 . ;fyL;uF 5nkmn u/L ;fl] wPsf
kZ| gx¿sf] pQ/ vfH] gx' f;] \ M

>L ;/:jtL df= lj=sf ljBfyL{ ljj/0f

ljBfy {L ; \ªVof Y ;ªs\ t]
70 5fq
60 6 78 5fqf
50
40 sIffx¿ 9 10 X
30
20
10

O

-s_ ;aeGbf a9L / ;aeGbf sd ljBfyL{x¿ sg' sg' sIffdf /x5] g\ <
-v_ sg' sg' sIffdf 5fqeGbf 5fqf a9L /x]5g\ <
-u_ s'g s'g sIffdf 5fqfeGbf 5fq a9L /x]5g\ <
-3_ s'g sg' sIffdf 5fq / 5fqf a/fa/ /x]5g\ <
-ª_ of] s:tf] :tDe lrq xf] <

● PseGbf a9L cfk;df ;DalGwt ;r" gf tyf tYofª\sx¿nfO{ k:| t't u/LPsf]
:tDe lrqnfO{ ax':tDe lrq (Multiple Bar Diagram) elgG5 .

● ax:' tDe lrqsf] lgdf{0f ubf{ ;fwf/0f :tDe lrqdf h:t} k|To]s :tDesf]
rf8} fO a/fa/ xg' k' 5{ .

● ax':tDe lrqsf] prfOn] ;ªV\ of hgfp5F .

268 ul0ft, sIff &

pbfx/0f 1

gu/ ;'wf/ ;ldltsf] cfofh] gfdf ;~rfng ePsf] cfvF f, sfg, 3f6F L / bfFt k/LIf0f
lzlj/df btf{ eO{ :jf:Yo k/LIf0f u/fpg] JolStx¿sf] tYofª\s o;k|sf/ kfOof] .

:jf:Yo k/LIf0f cfvF f sfg 3f6F L bGt
;]jf
dlxnf k?' if dlxnf k'?if dlxnf k?' if dlxnf k'?if
k/LIf0f 15 20 17 22 65 73 32 40

;ª\Vof

pSt tYofª\ssf] ax':tDe lrqnfO{ u|fkmdf b]vfpgx' f;] \ .
;dfwfg
oxfF ;fgf] sf]7f a/fa/ Ps hgf JolSt dfg/] ax:' tDe lrq agfpFbf,

la/fdL ; \ªVof :jf:Yo lzlj/ btf{ tYofªs\ ;ªs\ t]
dlxnf
Y k?' if
80
70 X
60
50
40
30
20
10

O cfvF f sfg 3f6F L bftF

:jf:Yo k/LIf0f ;j] f

pbfx/0f 2

Pp6f ljBfnosf] sIff 6 b]lv 8 ;Ddsf] jflifs{ k/LIffsf] glthf tnsf] ax':tDe
lrqdf k:| t't u/LPsf] 5 . pSt :tDe lrqsf cfwf/df tnsf k|Zgsf] pQ/
n]Vg'xf;] \ .

ul0ft, sIff & 269

ljBfy {L ; \ªVof Y jflif{s k/LIffsf] glthf ;ªs\ t]
A u8]|
40 B u8]|
35 C u8]|
30
25 X
20
15
10
5

O6 7 8

sIffx¿

-s_ sIff 8 df slt hgfn] u8|] A NofPsf /x]5g\ <

-v_ sIff 6 b]lv 8 ;Dd slt hgfn] u]8| B /x]5g\ <

-u_ s'g sIffdf ;a} eGbf a9L ljBfyLn{ ] u|]8 A /x5] g\ <

-3_ s'g sIffdf ;a} eGbf sd ljBfyLn{ ] u|]8 C /x]5g\ <

;dfwfg

oxfF lbOPsf] ax:' tDe lrqsf cfwf/df dfly lbOPsf kZ| gsf] pQ/ o; ks| f/ 5 M
-s_ sIff 8 df 10 hgfn] u]|8 A NofPsf /x5] g\ .

-v_ sIff 6 b]lv 8 ;Dd u8]| B Nofpg] ljBfyL{sf] ;ªV\ of = 25 + 30 + 35 = 90
hgf

-u_ sIff 7 df ;ae} Gbf a9L ljBfyL{n] u]8| A NofPsf /x]5g\ .

-3_ sIffdf 6 df ;a}eGbf sd ljBfyLn{ ] u8]| C NofPsf /x5] g\ .

270 ul0ft, sIff &

cEof; 21.2

1. tnsf] tYofªs\ nfO{ ax':tDe lrqdf bv] fpgx' f;] \ M

-s_ lbgx¿ cfOtaf/ ;f]daf/ dª\unaf/ aw' af/ ljxLaf/ z'j|maf/

laj|mL kl/df0f df5f df;' df5f df;' df5f df;' df5f df;' df5f df;' df5f df;'
-lsnfu] |fddf 10 18 15 12 17 20 19 22 20 25 27 20

-v_ ljBfno A B C D E

ljBfyL{x¿ 5fq 5fqf 5fq 5fqf 5fq 5fqf 5fq 5fqf 5fq 5fqf

250 210 125 175 310 350 425 400 520 550

2. sg' } ljBfnodf ljBfyL{x¿ hfFbf ;jf/L ;fwg ko| f]u u/L tyf lxF8/] cfpg]
u/]sf] ljj/0f o; ks| f/ 5 M

ljBfno cfpg] ;fwg lx8F ]/ a; df6] /;fOsn ;fOsn

ljBfyL{ ;ª\Vof 5fq 5fqf 5fq 5fqf 5fq 5fqf 5fq 5fqf

25 30 40 45 20 15 55 60

dflysf] tYofªs\ nfO{ ax:' tDe lrqdf bv] fpg'xf];\ .

3. lbOPsf] ax:' tDe lrqdf gk] fnsf] kfFrcf6] f k|b]zdf pTkfbg xg' ] wfg / uxs'F f]
kl/df0f -xhf/ dl] 6«s6gdf_ lbOPsf] 5 . pSt ax':tDe lrqsf] cjnf]sg u/L
tnsf k|Zgx¿sf] pQ/ nV] g'xf;] \ M

kfrF cf6] f kb| z] df pTkflbt wfg / uxsF' f] kl/df0f ;ªs\ t]
wfg
90 Y uxF'
80
70 X
60
50
40
30
20
10

O
pTkflbt kl/df0f
|k ]bz g=!
|k ]bz g=@

afUdtL
u08sL
'nlDagL

kb| z] x¿

ul0ft, sIff & 271

-s_ s'g k|bz] df ;ae} Gbf a9L wfgsf] pTkfbg kl/0ffddf ePsf] /x]5 <
-v_ sg' k|b]zdf ;ae} Gbf a9L ux'Fsf] pTkfbg ePsf] /x]5 <
-u_ sg' k|b]zdf a/fa/ k/L0ffdf wfg / ux'sF f] pTkfbg ePsf] /x5] <
-3_ sg' sg' k|bz] df ;aeGbf sd wfgsf] pTkfbg ePsf] /x5] <

4. Pp6f ljBfnosf] tLg jifs{ f] P;=O=O sf] glthf tnsf] ax':tDe lrqdf
k:| tt' u/LPsf] 5 . pSt :tDe lrqsf cfwf/df tnsf k|Zgx¿sf] pQ/

nV] gx' f];\ M

ljBfy {L ; \ªVof 18 Y SEE sf] glthf ;ªs\ t]

16 A+
14 A
12

10 B

8

6

4

2

O 2075 2076 2077 X

;fn -lj=;=_df

-s_ lj= ;= 2075 df slt hgf ljBfyL{x¿n] u8|] A+ NofPsf /x5] g\ <

-v_ lj= ;= 2076 df slt hgf ljBfyL{x¿n] u]|8 A NofPsf /x]5g\ <

-u_ s'g ;fndf ;a}eGbf a9L ljBfyL{x¿n] u8]| A+ NofPsf /x5] g\ <

-3_ sg' ;fndf ;ae} Gbf sd ljBfyLx{ ¿n] u|]8 B NofPsf /x5] g\ <

kl/of]hgf sfo{

tkfO{sF f] ljBfnodf ePsf hDdf ljBfyL{ ;ª\Vof, 5fq ;ª\Vof / 5fqf
;ª\Vof ;ª\sng u/L ax:' tDe lrq agfpg'xf];\ / sIffdf k:| tt' ugx{' f];\ .

pQ/
lzIfsnfO{ b]vfpg'xf];\ .

272 ul0ft, sIff &

ldl>t cEof; jfli {fs Aofhb/

1. sg' } ;x/sf] j}zfv dlxgfsf] Ps xKtfsf] clwstd tfkjm| d lgDglnlvt tflnsfdf
lbOPsf] 5 . pSt tYofª\ssf cfwf/df :tDelrq agfpgx' f];\ .

ut] clwstd tfkj|md (°Cdf_

16 35.5
17 37
18 36
19 32
20 30
21 33
22 34.5

2. sg' } a}ª\sn] d4' lt vftfdf /sd hDdf ug]{ vftfjfnfnfO{ lbPsf] Aofhb/nfO{
tnsf] /v] flrqdf bv] fOPsf] 5 . pSt /v] flrqsf cfwf/df lgDglnlvt k|Zgx¿sf]
pQ/ nV] gx' f];\ .

vftfjfnfnfO{ lbPsf] jflif{s Aofhb/sf] ljj/0f

Y

16
14
12
10
8
6
4
2

O 2074 2075 2076 2077 2078 X

;fn -lj=;=df_

-s_ s'g jifs{ f] Aofhb/ ;aeGbf a9L 5 <

-v_ sg' jif{sf] Aofb/ ;aeGbf sd 5 <

-u_ s'g sg' jif{sf] Aofhb/ a/fa/ 5g\ <

ul0ft, sIff & 273

3. sg' } ufpFsf] kfFr jif{sf] dlxnf / k?' ifsf] hg;ª\Vof lgDgfg;' f/ /x]sf] 5 M

;fn -lj=;_ 2073 2074 2075 2076 2077

hg;ªV\ of dlxnf k?' if dlxnf k'?if dlxnf k'?if dlxnf k'?if dlxnf k?' if

12 11 13 14 14 15 17 13 17 11

pSt tYofª\ssnfO{ ax':tDe lrqdf b]vfpgx' f];\ .

4. Pp6f t/sf/L k;ndf rf/ xKtfdf laj|mL ePsf] cfn' / sfpnLsf] ljj/0fnfO{ lgDg
ax:' tDe lrqdf b]vfOPsf] 5 . pSt ax:' tDe lrqsf cfwf/df tnsf kZ| gx¿sf]
pQ/ n]Vgx' f];\ .

cfn' / sfpnLsf] lajm| L ljj/0f ;ªs\ t]
cfn'
Y sfpnL
16
14 X
12
10
8
6
4
2

O
t/sf/Ls ]f kl/df0f -kg df_
klxn ]f xKtf
b ]f |; ]f xKtf

]t |; ]f xKtf
r }fy ]f xKtf

;do -xKtfdf_
-s_ klxnf] xKtfdf slt lsnfu] |fd cfn' lajm| L ePsf] /x5] <
-v_ s'g xKtfdf cfn' / sfpnL a/fa/ kl/df0fdf lajm| L ePsf] /x]5 <
-u_ ;aeGbf a9L sg' xKtfdf laj|mL ePsf] /x]5 <
-3_ ;aeGbf sd cfn' sg' xKtfdf ljj|mL ePsf] /x]5 <
-ª_ rfy} f] xKtfdf slt slt cfn' / sfpnL lajm| L ePsf] /x]5 <

274 ul0ft, sIff &