Gujrrati Ganit 2nd

cpfs_y„ k„rh^p_

cpN 4 L$

_pNqfL$p¡_p d|mc|s L$s®ìep¡

A_yÃR>¡v$ 51 L$
d|mc|s L$s®ìe - cpfs_p âÐe¡L$ _pNqfL$_y„ A¡ L$s®ìe R>¡ L¡$ s¡Z¡ -
(L$) v$f¡L$ _pNqfL¡$ k„rh^p__y„ `pg_ L$fhy„. k„rh^p__p Apv$ip£, fpóV²$ÝhS> A_¡

fpóV²$Nus_p¡ Apv$f L$fhp¡.
(M) õhps„Ôe Qmhm_u â¡fZp Ap`_pfp Apv$ip£_y„ `pg_ L$fhy„.
(N) v¡$i_p kph®cp¥dÐh, A¡L$sp A_¡ AM„X$sp kyfrns fpMhp âeÐ_iug fl¡hy„.
(O) Ap`Zp v¡$i_y„ fnZ L$fhy„, v¡$i_u k¡hp L$fhu.
(P$) v$f¡L$ âL$pf_p c¡v$cph_¡ c|gu_¡ A¡L$sp A_¡ b„^yÐh_u cph_p rhL$kphhu.

÷uAp¡_p kÞdp__¡ W¡$k `lp¢QpX$_pfu â\pAp¡_p¡ ÐepN L$fhp¡.
(Q) Ap`Zu k„rdî k„õL©$rs_p hpfkp_y„ S>s_ L$fhy„.
(R>) _¥krN®L$ `ep®hfZ_y„ S>s_ L$fhy„. kÆh âpZuAp¡ âÐe¡ v$epcph fpMhp¡.
(S>) h¥opr_L$ ×[óV$, dp_hsphpv$ A_¡ rS>opkph©rÑ L¡$mhhu.
(T) kph®S>r_L$ dpgdÑp_y„ S>s_ L$fhy„. tlkp_p¡ ÐepN L$fhp¡.
(U) v¡$i_u DÑfp¡Ñf âNrs dpV¡$ ìe[¼sNs s¡dS> kpd|rlL$ L$pe®dp„ DÑdsp-

î¡óW$sp_y„ õsf Spmhu fpMhp_p¡ âeÐ_ L$fhp¡.
(V$) 6\u 14 he S|>\_p bpmL$p¡_¡ s¡d_p hpguA¡ rinZ_u sL$ `|fu `pX$hu.

ipk_ r_Ze® ¾$dpL„ $ : Aæepk - 2116/(â.¾$. 43/16) Ak¡ X$u-4 qv$_pL„ $ 25-4-2016 _p fpS¡ > õ\pr`s L$fpeg¡ kdÞhe krdrs_u
sp. 19-3-2019 _p fpS¡ > gh¡ peg¡ bW¡ $L$dp„ Ap `pWé`õy sL$ k_ 2019-20_p in¥ rZL$ hj\® u r_^pq® fs L$fhp_u dpÞesp Ap`hpdp„ Aphu R>.¡

NrZs

^p¡fZ-buSy>„

dlpfpóV²$ fpÄe ‘pWé‘yõsL$ r“rd®rs A“¡ Aæepk¾$d k„ip¡^“ d„X$m, ‘yZ¡ - 411 004
Ap`_p õdpV®$ap¡_dp„ DIKSHA App Üpfp `pWé`yõsL$_p `l¡gp `©óW$
`f_p Q.R. Code Üpfp qX$rS>V$g `pWé`yõsL$ A_¡ âÐe¡L$ `pW$dp„ Ap`¡gp
AÞe Q.R. Code Üpfp k„b„r^s AÝee_-AÝep`_ dpV¡$ D`ey¼s
×íe-îpìe kprlÐe D`gå^ \i¡.

â’dph©rÑ : 2019 © dlpfpô²$ fpÄe `pWé`õy sL$ r_rd®rs A_¡ Aæepk¾$d ki„ p^¡ _ dX„ $m,
`y_dy®ÖZ : 2021
`Zy ¡ 411 004.
dlpfpô²$ fpÄe `pWé`yõsL$ r_rd®rs A_¡ Aæepk¾$d k„ip¡^_ d„X$m

`pk¡ Ap `yõsL$_p b^p l½$ fl¡i¡. Ap `yõsL$_p¡ L$p¡C`Z cpN
k„QpgL$, dlpfpô²$ fpÄe `pWé`yõsL$ r_rd®rs A_¡ Aæepk¾$d

k„ip¡^_ d„X$m_u g¡rMs `fhp_Nu hNf R>p`u iL$pi¡ _rl.

NrZs rhjesÄo krdrs cpjp„sf : îu. ^uf¡_ v$p¡iu

X$p¸. d„Ngp _pfmuL$f (AÝen) cpjp„sf k„ep¡S>L$ : L¡$sL$u r_s¡i Å_u
rhi¡jpr^L$pfu,
X$p¸. ifv$ Np¡f¡ (kæe) NyS>fpsu rhcpN
îudsu âpS>[¼s Np¡Mg¡ (kæe) ‎`pWé`yõsL$ d„X$m, `yZ¡.‎
îu. âkpv$ Ly„$V¡$ (kæe)
îu. kyÆs tiv¡$ (kæe) dyM`©óW$ A_¡ kÅhV
îu. âëlpv$ rQà`gNË$u (kæe) îudsu L$õsyfu qv$hpL$f, rQÓL$pf, `yZ¡.

îu. k„v$u` `„QcpC (kæe) Anf N|„\Zu
kd\® N°pqa¼k, 522,_pfpeZ `¡W$,`yZ¡-30.
îu. fdpL$p„s kfp¡v¡$ (kæe)
îudsu `|Å Å^h (kæe)

îudsu DÄÄhgp Np¡X$bp¡g¡ (kæe, krQh)

NrZs rhje - fpÄe AæepkS|>\ kæep¡ r_rd®rs
îu. rh_peL$ Np¡X$bp¡g¡ îu. k[ÃQv$p_„v$ Apam¡
dy¿e r_rd®rs Ar^L$pfu
îudsu sê$b¡_ `p¡`V$
îu. kyr_g îuhpõsh îu. k„S>e L$p„bm¡
îu. Afthv$Ly$dpf rshpfu r_rd®rs Ar^L$pfu
îu. âL$pi L$p`k¡ îu. âip„s lfZ¡
îu. bkh¡ðf L$ëepZL$õsyf¡ klpeL$ r_rd®rs Ar^L$pfu
îudsu ^pfZp MmsL$f
îu. dr_j qv$O¡L$f L$pNm
îudsu kyhZp® `hpf 70 Æ.A¡k.A¡d. ¾$udìlp¡ìl
îu. Dd¡i f¡m¡
îu. rhipg i¡V¡$ dyÖZpv¡$i
îu. k„v$u` fpEs
dyÖL$

âdyM k„ep¡S>L : îudsu DÄÄhgp îuL$p„s Np¡X$bp¡g¡ âL$piL$
â. rhi¡jpr^L$pfu NrZs,
`pWé`yõsL$ d„X$m, `yZ¡. îu. rhh¡L$ DÑd Np¡kphu, r_e„ÓL$
`pWé`yõsL$ r_rd®rs d„X$m,
âcpv¡$hu, dy„bC - 25.





âõsph_p

bpmrdÓp¡,
buÅ ^p¡fZdp„ sdpfy„ õhpNs R>¡!
sd¡ `l¡gp ^p¡fZ_p¡ Aæepk L$fu_¡, `yõsL$p¡ hp„Qu_¡ buÅ ^p¡fZdp„ Apìep R>p¡ _¡...?
ApNm_p¡ Aæepk `Z Ap_„v$ krls L$fhp_p¡ R>¡. sdpfu kp\¡ sdpfu S> Jdf_p ei
A_¡ fdp `Z R>¡. hÃQ¡ hÃQ¡ fdsp„ fdsp„ Aæepk L$fhp_p¡ R>¡.
sd_¡ hõsy_u NZsfu L$fsp„ AphX¡$ R>¡. lh¡ _p_p kfhpmp A_¡ `R>u bpv$bpL$u
iuMhp_u R>¡. L©$rs A\hp fus bfpbf kdÆ gp¡. `R>u s¡_p¡ Ap_„v$ dpZu iL$ip¡.
ipmpdp„ rinL$p¡_u dv$v$ dmi¡. s¡ S> fus¡ Of¡ dpsp, r`sp, bl¡_, cpC A\hp L$p¡C_u
`Z dv$v$ sd¡ gC iL$p¡ R>p¡.
f¡Mp_p¡ A_¡ rhrh^ ApL$pfp¡_p¡ Aæepk L$fsu hMs¡ sdpf¡ rQÓp¡ v$p¡fhp_p R>¡. rQÓp¡
v$p¡fhp A_¡ f„N `|fhp sd_¡ Nd¡ R>¡ _¡? s¡_u `Z sL$ dmi¡. _p_u k„¿ep_p kfhpmp
A_¡ bpv$bpL$u iuMhp dpV¡$ Ap_„v$âv$ fdsp¡_p¡ D`ep¡N \i¡. _p_u k„¿ep_p kfhpmp A_¡
bpv$bpL$u L$fsp„ bfpbf AphX$i¡, sp¡ ApNm_p ^p¡fZ_y„ NrZs kfm \i¡.
NrZs_p Sy>v$p Sy>v$p âL$pf Ap`Zp„ L$pdp¡ kfm L$fhp dpV¡$ dv$v$ê$` \pe R>¡. A¡L$ S>
k„¿ep_p¡ afu afu kfhpmp¡ L$fhp_y„ L„$V$pmpS>_L$ L$pd OqX$ep_u dv$v$\u L¡$hu fus¡ aV$paV$
\C Åe R>¡ s¡ A_ychp¡. A¡L$buÅ_¡ OqX$ep_p NyZpL$pf `|R>hp_u fds fdu iL$pe.
hv$uhpmp kfhpmp kpfu fus¡ kdS>hp dpV¡$ v$k ê$r`ep_u _p¡V$ A_¡ A¡L$ ê$r`ep_p¡
rk½$p¡ hp`fp¡. s¡ dpV¡$ sd¡ S> L$pNm_u _p¡V$ A_¡ `|W$p_p rk½$p b_phu iL$p¡ R>p¡. kpQp
ê$r`ep gC_¡ fdhp_u S>ê$f _\u.
v$f¡L$ `pW$_p A„s¡ ¼e|. Apf. L$p¡X$ Ap`hpdp„ Apìep¡ R>¡. L$p¡X$ Üpfp Ap`hpdp„ Aph¡gu
dprlsu `Z sd_¡ M|b D`ep¡Nu \i¡.
buÅ ^p¡fZ_y„ NrZs kl¡gy„ S> R>¡. fdsp„ fdsp„ iuMp¡ A_¡ b^p¡ Aæepk
Ap_„v$ krls L$fp¡.

`yZ¡‎ (‎ X$p¸. kyr_g dNf)‎
sp. : 7 d¡, 2019. Anes©rsep k„QpgL$‎
cpfsue kp¥f qv$_p„L$ : 17 h¥ipM, 1941.
dlpfpô²$ fpÄe `pWé`yõsL$ r_rd®rs
A_¡ Aæepk¾$d k„ip¡^_ d„X$m, `yZ¡.‎

^p¡fZ buSy>„ - NrZs AÝee_ r_ó`rÑ

AÝee_ dpV¡$ k|Qh¡gu i¥nrZL$ âq¾$ep AÝee_ r_ó`rÑ

rhÛp\}_¡ ìe[¼sNs/kd|ldp„/Å¡X$udp„ _uQ¡_u L©$rs L$fhp rhÛp\} -

âp¡Ðkprls L$fhp. 02.71.01. b¡ A„L$u k„¿ep k„b„r^s L©$rs L$f¡ R>¡.
_ 99 ky^u_u k„¿ep_y„ hp„Q_ A_¡ g¡M_ L$f¡ R>¡.
• k„¿ep hp„Q_ A_¡ A„L$g¡M__u `Ùrs Ap¡mM¡ A_¡ 99 _ v¥$r_L$ Æh__u hõsyAp¡_p Ap^pf¡ 2, 3, 4, 5

ky^u_u k„¿epAp¡ gM¡ A_¡ hp„Q¡.

• k„¿epdp„_p A„L$p¡_p S|>\ s¥epf L$fsu hMs¡ A_¡ Ap¡mMsu A_¡ 10_p OqX$ep s¥epf L$f¡ R>¡ A_¡ s¡_p¡

hMs¡ õ\pr_L$ qL„$ds_u kdS|>su_p¡ D`ep¡N L$f¡ R>¡. D`ep¡N L$f¡ R>¡.
• 9 ky^u_u k„¿ep_p kfhpmp_p sÕep¡_p¡ D`ep¡N L$fu_¡ 99 _ b¡ A„L$u k„¿ep_y„ g¡M_ A_¡ kfMpdZu L$fsu

ky^u_u b¡ A„L$u k„¿ep_p kfhpmp L$f¡. hMs¡ õ\pr_L$ qL„$ds_p¡ D`ep¡N L$f¡ R>¡.
• k„¿ep_p kfhpmp A_¡ bpv$bpL$u dpV¡$ `ep®eu `Ùrs _ dp¡V$pdp„ dp¡V$u A_¡ _p_pdp„ _p_u b¡ A„L$u k„¿ep

rhL$kph¡ A_¡ s¡_p¡ D`ep¡N L$f¡. s¥epf L$f¡ R>¡. (Ap`¡g A„L$p¡_¡ afu\u hp`fu_¡/

• k„¿ep_p kfhpmp A_¡ bpv$bpL$u L$fhp_u S>ê$fs `X¡$ s¡hu hp`ep® hNf)
`qf[õ\rsAp¡ s¥epf L$f¡. S>¡dL¡$- b¡ S|>\p¡_¡ A¡L$rÓs L$fhp/ _ b¡ A„L$u k„¿ep_p kfhpmp `f Ap^pqfs kfm

A¡L$ S|>\dp„ h^y hõsyAp¡ Dd¡fu_¡ s¡_p¡ rhõspf L$fhp¡. fp¡tS>v$p âñp¡/kdõep DL¡$g¡ R>¡.
• rhÛp\} `p¡sp_p A_ych_p Ap^pf¡ kfhpmp A_¡ bpv$bpL$u _ b¡ A„L$u k„¿ep_u bpv$bpL$u `f Ap^pqfs kfm

`f Ap^pqfs Dv$plfZp¡/âñp¡ `p¡sp_u fus¡ s¥epf L$f¡. fp¡tS>v$p âñp¡/kdõep DL¡$g¡ R>¡.
• k„¿ep_¡ afu afu_¡ Dd¡fhu `X¡$ A¡hp k„v$c®/[õ\rs r_dp®Z _ fds dpV¡$_p kfMu/Sy>v$u qL„$ds_p rhrh^ _p¡V$

L$f¡. A_¡ rk½$p_p¡ D`ep¡N L$fu_¡ 100 ê$r`ep ky^u_u

• rÓ`qfdpZue hõsy_p Sy>v$p Sy>v$p `pkpAp¡ L$pNm `f v$p¡f¡ fL$d s¥epf L$f¡ R>¡.

A_¡ qÜ`qfdpZue hõsy_p k„v$c®dp„ s¡_p _pd L$l¡. 02.71.02. qÜ`qfdpZue A_¡ rÓ`qfdpZue ApL$pfp¡_y„

• rhrh^ ApL$pfp¡ L$p`u_¡ s¥epf L$f¡gu ApL©$rs Üpfp/`¡`f s¡d_u Ahgp¡L$_nd gpnrZL$sp_¡ Ap^pf¡

hpmu_¡ s¡d_p cp¥rsL$ NyZ^dp£_¡ Ap^pf¡ hN}L$fZ L$f¡. hZ®_ L$f¡ R>¡.
• ApL$pfp¡ A_¡ s¡_p cp¥rsL$ NyZ^dp£_y„ hZ®_ L$fhp dpV¡$ _ O_, _mpL$pf, i„Ly$-ApL$pf, Np¡mp¡ S>¡hp d|mc|s

Ahgp¡L$_/õ`i® k„h¡v$_p_p¡ D`ep¡N L$f¡. rÓ`qfdpZue ApL$pfp¡_¡ _pd\u Ap¡mM¡ R>¡.
• Sy>v$u Sy>v$u qL„$ds_p fds dpV¡$_p _pZp„_p¡ D`ep¡N L$fu_¡ _ rÓrdrse hõsyAp¡_u qÜrdrse ApL©$rs v$p¡f¡ R>¡.
_ qÜrdrse ApL$pfp¡ Ap¡mM¡ R>¡. (Qp¡fk,
100 ê$r`ep ky^u_u fL$d s¥epf L$f¡.

• rhÛp\} Sy>v$p„ Sy>v$p„ hS>_ ^fphsu hõsyAp¡_p kdsp¡g__p g„bQp¡fk, rÓL$p¡Z, hsy®m).

A_ych_u QQp® L$f¡. 02.71.03. kfm A_¡ h¾$ f¡Mp hÃQ¡ saphs L$f¡ R>¡.

• s¡d_u ApSy>bpSy>_u Sy>v$u Sy>v$u hõsyAp¡_y„ hS>_ L$fhp dpV¡$ 02.71.04. rhrh^ k„õL$fZp¡dp„ (Ecu/ApX$u/Óp„ku) ku^u

A_¡ syg_p L$fhp dpV¡$ `p¡sp_p¡ kpv$p¡ hS>_ L$p„V$p¡ s¥epf L$f¡ f¡Mp v$p¡f¡/fS|> L$f¡ R>¡.

R>¡. 02.71.05. hõsy_y„ (O_pL©$rs_y„) s¡_p cp¥rsL$ NyZ^dp®_ykpf

• `p¡sp_p¡ kpv$p¡ hS>_ L$p„V$p¡ A_¡ hS>_ s¥epf L$fu_¡ rhrh^ `p¡sp_p iåv$p¡dp„ hZ®_ L$f¡ R>¡. v$p.s. v$X$p¡ NbX¡$

hõsyAp¡_p hS>__u syg_p L$fhu. R>¡, bp¸¼k gkf¡ R>¡, hN¡f¡.

• Ap„Nmp, lp\_u g„bpC, `Ngp S>¡hp AâdprZs A¡L$d_u 02.71.06. lp\, lp\_p¡ `„Å¡, `Ngp„ hN¡f¡ S>¡hp kdp_

dv$v$\u `qfkf_u Ap¡R>u g„bpC lp¡e s¡hu hõsy dp`¡ R>¡. rb_âdpZc|s A¡L$dp¡_p¡ D`ep¡N L$fu_¡ g„bpC

• Sy>v$u Sy>v$u O_pL©$rs/ApL$pf_y„ hN}L$fZ L$fsu hMs¡ dp`¡ R>¡ A_¡ A„v$pS> L$f¡ R>¡.

A`_ph¡gp dp`v„$X$ A\hp NyZ^d® L$l¡sp AphX¡$.

AÝee_ dpV¡$ k|Qh¡gu i¥nrZL$ âq¾$ep AÝee_ r_ó`rÑ

• A¡L$pv$ Mpk qv$hk/AW$hpqX$ep_p¡ Qp¡½$k qv$hk Äepf¡ 02.71.07. kpv$p hS>_L$p„V$p_p D`ep¡N Üpfp hõsy_u lgL$u/

rhÛp\} s¡d_p Ly$Vy„$b_p kæep¡ kp\¡ OfNÕ\y L$pe® L$f¡ A_¡ cpf¡ A¡hu syg_p L$f¡ R>¡.

kde Npm¡ s¡ rhi¡ QQp® L$f¡. 02.71.08. AW$hpqX$ep_p qv$hkp¡_p _pdp¡ A_¡ hj®_p

• `¡V$_®(`Ùrs)dp„ `y_fphrs®s \sp A¡L$dp¡_u dp¥rML$ drl_p_p _pdp¡ Ap¡mM¡ R>¡.

fS|>Aps L$f¡ s¡_p rhõspf rhi¡_u L$ë`_p fS|> L$f¡ A_¡ s¡ 02.71.09. c¡Nu L$f¡gu dprlsu `f\u A_ydp_ L$f¡ R>¡. S>¡d L¡$

L$ë`_p_¡ iåv$p¡dp„ gM¡. L©$`p L$fsp Aprij_p Ofdp„ h`fpsp hpl_p¡_u

• rhrh^ ApL$pfp¡, Ap„Nmp_u R>p`, `p„v$X$p_u R>p`, k„¿ep k„¿ep h^y R>¡.

hN¡f¡_p D`ep¡N\u s¥epf L$f¡g `¡V$_®(`Ùrs)_p¡ rhõspf 02.71.10. 100 ê$r`ep ky^u_u _p¡V$ A_¡ rk½$p_u qL„$ds

L$f¡. Ap¡mM¡ R>¡ A_¡ s¡_p kfhpmp s\p bpv$bpL$u L$f¡

• Apk`pk_u ìe[¼sAp¡ `pk¡\u dprlsu A¡L$rÓs L$f¡, s¡_u R>¡.

_p¢^ fpM¡ A_¡ s¡_p `f\u r_óL$j® L$pY¡$ R>¡.

rinL$p¡ dpV¡$ k|Q_p

buÅ ^p¡fZ_p NrZs_p `yõsL$dp„ 21\u 99 k„¿ep_p `pf„`qfL$ _pdp¡_u kp\¡ _hp _pdp¡ `Z
Å¡hp dmi¡. A¡ _pdp¡ Ap`hp_p¡ l¡sy bpmL$p¡ kfmsp\u k„¿epop_ iuM¡ s¡ R>¡. v$p.s. 28 dpV¡$
AÌ$phuk_u kp\¡ huk ApW$ b„_¡ _pd Ap`hpdp„ Apìep R>¡. AÌ$phuk_p¡ DÃQpf L$fsu hMs¡ `l¡gp
ApW$_p¡ DÃQpf A_¡ `R>u b¡ dpV¡$ huk Aph¡ R>¡. Äepf¡ huk ApW$ A¡hp¡ DÃQpf L$fuA¡ sp¡ DÃQpf
A_¡ g¡M__p¡ ¾$d A¡L$ S> fl¡ R>¡. S>¡\u rhÛp\}_¡ kfmsp fl¡ R>¡. bpmL$p¡ k„¿ep_¡ iåv$dp„
gM¡ Ðepf¡ Ap b„_¡dp„\u L$p¡C `Z fus¡ gM¡ sp¡ s¡_¡ õhuL$pe® dp_hy„. Ap `Ý^rs\u s¡d_y„
k„¿epop_ `pLy„$ \C S>i¡. ^p¡fZ ÓuÅ\u `yõsL$dp„ dpÓ `pf„`qfL$ _pdp¡ Ap`hpdp„ Apìep R>¡.

rhÛp\}Ap¡ `pk¡ dpÓ 1\u 50 ky^u_u k„¿ep_y„ g¡M_ A`¡rns R>¡, s¡ Ýep_dp„ fpMhy„.

NrZs_u kdS>Z `l¡gp_u S>¡d S> R>¡. hv$uey¼s kfhpmp-bpv$bpL$u `|fsp¡ kde A_¡ dlphfp¡
Ap`u iuMhhp. rhÛp\}Ap¡_¡ 10 A¡L$d_p¡ A¡L$ v$iL$ s¥epf L$fhp¡ A_¡ A¡L$ v$iL$_p R|>V$p v$k A¡L$d
d¡mhhp Ap q¾$ep kdÅhu Å¡CA¡. s¡ dpV¡$ dZL$p A_¡ v$iL$ v$p„X$uAp¡ rkhpe 10 ê$r`ep_u _p¡V$p¡
A_¡ 1 ê$r`ep_p rk½$p D`ep¡Nu \i¡. rhÛp\}Ap¡_p klcpN\u g„bQp¡fkpL$pf L$pNm_p Vy$L$X$p gC
10 ê$r`ep_u _p¡V$p¡ A_¡ L$X$L$ `|W$p_p 1 ê$r`ep_p rk½$p s¥epf L$fhp. s¡d_p¡ D`ep¡N L$fu hv$uey¼s
kfhpmp A_¡ bpv$bpL$u L$fhp âp¡Ðkprls L$fhp. 2, 3, 4, 5_p OqX$ep rhÛp\}Ap¡ `pk¡ s¥epf
L$fphhp. Sy>v$u Sy>v$u L©$rsAp¡ Üpfp _p_p Dv$plfZp¡_p¡ cf`|f dlphfp¡ Ap`hp¡.

A_y¾$drZL$p

rhcpN `l¡gp¡ rhcpN buÅ¡

 Qpgp¡ Sy>v$p Sy>v$p ApL$pfp¡ ip¡^uA¡........ 1  k„¿ep_y„ _p_pdp¡V$p`Ï„.................. 36
 Qpgp¡ cp¥rdrsL$ ApL$pf QL$pkuA¡....... 2  k„¿ep_p `pX$p¡iu, sfs `l¡gp„_u A_¡
 f¡Mp_u Nçds .......................... 6 `R>u_u k„¿ep........................... 38
 Qpgp¡ cp¥rdrsL$ ApL©$rsAp¡
Ap¡mMuA¡............................... 8  k„¿ep_p¡ QY$sp¡ A_¡ Dsfsp¡ ¾$d........ 39
 Qpgp¡, k„¿ep s¥epf L$fuA¡ .............. 41
 k„¿ep_y„ rhð............................ 9  k„¿ephpQL$ (d|ëehpQL$)
 k„¿ep hp„QuA¡ - gMuA¡................ 10 ¾$dhpQL$ iåv$........................... 43
 S|>\ L$fu_¡ NZsfu...................... 12
 rQÓdp„ v$ip®h¡gu k„¿ep.................. 13  rQÓ `f\u dprlsu d¡mhuA¡............ 46
 õ\pr_L$ qL„$ds A¡V$g¡ iy„................. 15  Mpk kfhpmp, hØuhpmp............... 48
 k„¿ep_y„ rhõspfus ê$` .................. 17  hpsp®dp„ kfhpmp - 2................... 51
 V$à`¡ k„¿ep NZuA¡...................... 19  bpv$bpL$u dpV¡$ v$iL$ R|>V$p L$fuA¡......... 53
 kfhpmp_u Nçds....................... 20  rk½$p-_p¡V$p¡ Ap¡mMuA¡................. 56
 kfhpmp¡ - ApNm NZu_¡.............. 21  g„bpC dp`uA¡........................... 58
 kfhpmp - hØu hNf_p................. 23  hS>_ L$fuA¡............................. 60
 i|Þe_p kfhpmp A_¡ bpv$bpL$u......... 25  ^pfL$sp dp`uA¡......................... 62
 hpsp®dp„ kfhpmp - 1................... 26  dprlsu_y„ ìehõ\p`_................... 64
 bpv$bpL$u hX¡$ Ap¡R>p L$fuA¡.............. 27  ApL©$rsb„^.............................. 66
 kfhpmp - bpv$bpL$u_u Å¡X$u............ 30  NyZpL$pf `|h®s¥epfu...................... 69
 hpsp®dp„ bpv$bpL$u....................... 32  OqX$ep s¥epf L$fuA¡...................... 71
 hj®_p bpf drl_p....................... 33  hpsp®dp„ NyZpL$pf........................ 76

rhcpN `l¡gp¡

Qpgp¡ Sy>v$p Sy>v$p
ApL$pfp¡ ip¡^uA¡

frhhpf¡ b^p M¡sfdp„ Nep afhp,
L$üy„ L¡$ afsp„ afsp„ ipL$cpÆ c¡Np„ L$fhp.

ky„hpmu dpV$u Mp¡v$u_¡ dp¡su gpìep¡ NpS>f,
^pf s¡_u i„Ly$ S>¡hu, gugp„ `p_ D`f.

ei gpìep¡ f]NZp„ _¡ V$d¡V$p„ gpg MpV$p„,
V$d¡V$p„ ky„v$f Np¡m, `Z f]NZp„ S>fp gp„bp.

h¡gu D`f\u fdp sp¡ sp¡X$u gphu L$pL$X$u,
L¡$V$guL$ _mpL$pf, `Z L¡$V$guL$ L$df\u hp„L$u.

N„`y sp¡X$u gpìep¡ Apdgu, TpX$ D`f QX$u,
Myi \C_¡ `pR>p afsp„, gkZ gphu dZu.

`à`pA¡ b_pìey„ ipL$, dçduA¡ b_phu cpMfu,
TpX$ _uQ¡ S>dsp„ S>dsp„ kp¥A¡ dÅ L$fu.

1

Qpgp¡ cp¥rdrsL$ ApL$pf
QL$pkuA¡

c¡Ny„ L$fuA¡ : dpQuk_u `¡V$u, V|$\`¡õV$_y„ Mp¡My„, duW$pC_y„ Mp¡My„, `pZu_u bpV$guAp¡,
rhrh^ L$v$_p v$X$p, L$pX®$`¡`fdp„\u b_ph¡gu rhv|$jL$_u V$p¡`u, L$pX®$`¡`f_p¡ _mpL$pf
krmep¡.

V¡$bg `f fl¡g kdp_ ApL$pf_u hõsyAp¡_p S|>\ s¥epf L$f.
g„bO_ :
duW$pC_y„ Mp¡My„ lp\dp„ gC QL$pk. Aphp ApL$pf_¡ g„bO_ L$l¡hpe R>¡.

^pf s¡ IV$ Å¡C li¡. IV$ S>¡hp ApL$pf_¡ g„bO_ L$l¡ R>¡.

M|Zp

Ap g„bO__¡ L¡$V$gu ^pf R>¡, L¡$V$gp M|Zp R>¡ s¡ Å¡CA¡.

g„bO__u ^pf - M|Zp -

lh¡ g„bO__p `©óW$cpN Å¡CA¡ ....
s¡_u bpSy> k`pV$ R>¡ s¡ Sy>Ap¡. s¡_¡ Ly$g R> `©óW$ R>¡. Ap gb„O__p `©óW$cpN k`pV$
lp¡hp\u s¡_¡ gkf`Ë$u `f d|L$uA¡ sp¡ s¡ gkfu_¡ _uQ¡ Aph¡ R>¡.

ip¡^
V¡$bg `f_u g„bO_ ApL$pf_u hõsy

2

i„Ly$ :
lh¡ s¡ b_ph¡gu rhv|$jL$_u V$p¡`u Å¡CA¡. Ap V$p¡`u i„Ly$
ApL$pf_u R>¡.

ApCk¾$ud_p¡ L$p¡_ A\hp d¢v$u_p¡ L$p¡_, rhv|$jL$_u V$p¡`u
S>¡hp ApL$pf_¡ i„Ly$ L$l¡hpe R>¡.

i„Ly$_¡ A¡L$ ^pf A_¡ A¡L$ M|Zp¡ lp¡e R>¡.
i„Ly$_y„ k`pV$ srmey„ hsy®mpL$pf R>¡. Ecp¡ sufR>p¡ (Óp„kp¡) `©óW$cpN L¡$hu fus¡ hmsp¡
Åe R>¡ s¡ Å¡. Ap hm_pfp¡ `©óW$cpN A¡V$g¡ h¾$`©óW$cpN.
_mpL$pf :
lh¡ Ap `pZu_u bpV$gu Å¡CA¡.
Ap `pZu_u bpV$gu_p ApL$pf_¡ _mpL$pf L$l¡ R>¡.

hsy®mpL$pf srmey„ ^fphsp X$bp S>¡hp ApL$pf_¡ _mpL$pf L$l¡hpe
R>¡.

Ap _mpL$pf_¡ b¡ ^pf R>¡ A_¡ AL¡ $ `Z D`f_p¡ k`pV$ `©óW$cpN
MZ| p¡ _\u. _mpL$pf_p¡ srmep_p¡ A_¡ h¾$ `©óW$cpN
D`f_p¡ `ó© W$cpN kdp_ A_¡ srmep_p¡ k`pV$ `©óW$cpN
hs®ympL$pf R>¡ s\p hQgp¡ hmg¡ p¡
`ó© W$cpN h¾$`ó© W$cpN R>¡.

L$fu Å¡
gkf`Ë$u `f _mpL$pf d|L$uA¡ sp¡ s¡ gkf¡ R>¡ L¡$ NbX¡$ R>¡.
gkf`Ë$u `f hõsy_p k`pV$ `©óW$cpN d|L$uA¡ sp¡ s¡ hõsy gkf¡ R>¡ A_¡ h¾$`©óW$cpN
d|L$uA¡ sp¡ s¡ hõsy NbX¡$ R>¡. A¡ hps _mpL$pf_u dv$v$\u kfk fus¡ kdÅe R>¡.

3

Np¡m :
v$X$p¡ Np¡m lp¡e R>¡ s¡ sd_¡ Mbf R>¡.

v$X$p S>¡hp ApL$pf_¡ Np¡mp¡ L$l¡hpe R>¡.

Ap Np¡mp_¡ ^pf `Z _\u A_¡ M|Zp¡ `Z _\u.

Np¡mp_p¡ `©óW$cpN ¼ep„e k`pV$ _\u. s¡ kss hmsp¡ Åe R>¡ dpV¡$ Np¡mp_¡ a¼s h¾$
`©óW$cpN R>¡.

L$fu Å¡
gkf`Ë$u `f Np¡mp¡ d|L$uA¡ sp¡ s¡ gkfi¡ L¡$ NbX$i¡.

* Å¡X$L$p Å¡X$. ApL$pf_p _pd
   ApL$pf

 1) A) _mpL$pf

 2) b) g„bO_

 3) L$) i„Ly$

 4) X$) Np¡m

* _uQ¡_pdp„\u L$C hõsy gkfi¡ A_¡ L$C hõsy NbX$i¡ s¡ L$l¡.

4

* _uQ¡ Ap`¡gu hõsyAp¡_p¡ Aæepk L$f. v$f¡L$ hõsy_¡ L¡$V$gu ^pf A_¡ L¡$V$gp M|Zp
R>¡ s¡ Å¡ A_¡ gM.

^pf - ^pf - ^pf - ^pf -
M|Zp - M|Zp - M|Zp - M|Zp -

* rQÓdp„_u L$C hõsy gkfi¡ A_¡ L$C hõsy NbX$i¡ s¡ L$l¡.

O_pL©$rs ApL$pf_u A_¡L$ hõsy rhÛp\}Ap¡ kpd¡ d|L$u s¡d_¡ cp¥rdrsL$ ApL$pf_p„ _pdp¡
Ap¡mMhp L$l¡hy„. s¡ hõsyAp¡_p ^pf A_¡ M|Zp dp`hp L$l¡hp.

ICT Tools

"`¢V$- b°i'dp„ S>C_¡ `¡_rkg_u dv$v$\u Sy>v$p
Sy>v$p cp¥rdrsL$ ApL$pfp¡ v$p¡f A_¡ s¡dp„ f„N `|f.

5

f¡Mp_u Nçds

* Ap`Z¡ b¡ lp\¡\u v$p¡fp¡ `L$X$u_¡ M¢QuA¡, sp¡ ku^u f¡Mp(f¡M) dm¡ R>¡ A_¡ v$p¡fp¡
Y$ugp¡ R>p¡X$uA¡ sp¡ h¾$f¡Mp dm¡ R>¡. (v$p¡fu_p A¡L$ R>¡X¡$ `Õ\f bp„^u_¡ _uQ¡ R>p¡X$uA¡,
sp¡ ku^u f¡Mp dm¡ R>¡ s¡ L$fu Å¡.)

Ap`Z¡ `yõsL$dp„ ku^u f¡Mp_p¡ S> Aæepk L$fhp_p R>uA¡.
dpV¡$ f¡Mp A\hp f¡M A¡V$g¡ ku^u f¡Mp A¡d kdÆiy„.
_¡lpA¡ Ecu f¡Mp v$p¡fu A_^pA¡ ApX$u f¡Mp v$p¡fu lrdv$pA¡ Óp„ku f¡Mp v$p¡fu

* L©$rs : L$pNm_u OX$u hpmu_¡ Ecu, ApX$u, Óp„ku f¡Mp bsph.

* _uQ¡ f¡Mp v$p¡fu_¡ bsphu R>¡. s¡ âdpZ¡ f¡Mp v$p¡f.

66

* lz„ `yõsL$_u dv$v$\u f¡Mp v$p¡fy„ Ry>„. * lz„ Mp¡Mp_u ^pf_u dv$v$\u f¡Mp
v$p¡fy„ Ry>„.

* d¢ awV$`Ë$u_p¡ D`ep¡N L$fu_¡ * d¢ L$p¡B`Z kp^__p¡ D`ep¡N
f¡Mp v$p¡fu. L$ep® hNf lp\¡\u S> f¡Mp v$p¡fu.

ApL$pf Ap¡mM A_¡ f„N `|f.

bpSy>_p rQÓdp„ ,,
Ap¡mM.

dp„ gpg, dp„ _ugp¡ A_¡ dp„
`ump¡ f„N `|f.

rhÛp\}Ap¡ `pk¡ D`f_u L©$rs _p¡V$dp„ L$fphhu.

7

Qpgp¡ cp¥rdrsL$ ApL©$rsAp¡
Ap¡mMuA¡

* rQÓdp„ v$ip®ìep âdpZ¡ v$f¡L$ hõsy_u ^pf afs¡ `¡_rkg a¡fhu_¡ ApL©$rs v$p¡f A_¡
ApL©$rs_u bpSy>_y„ r_funZ L$f. s¥epf \e¡gu ApL©$rs_y„ _pd L$l¡.

Ap g„bQp¡fk R>¡. Ap hsy®m R>¡. Ap rÓL$p¡Z R>¡. Ap Qp¡fk R>¡.
g„bQp¡fk_u hsy®m_¡ A¡L$ S> rÓL$p¡Z_u bpSy>_u Qp¡fk_u bpSy>_u

bpSy>_u k„¿ep 4 h¾$^pf R>¡. A¡L$ `Z k„¿ep 3 k„¿ep 4

ku^u bpSy> _\u.

_uQ¡ s_¡ Nd¡ s¡hu L¡$V$guL$ L©$rsAp¡ Ap`u R>¡. s¡ L$fu Å¡.

* L©$rs 1 : L$pNm_u A¡L$ lp¡X$u s¥epf L$f. s¡_¡ Mp¡gu _pMsp„ L¡$V$gp rÓL$p¡Z A_¡
Qp¡fk s¥epf \ep, s¡ NZ. s¡dp„\u L$p¡C`Z b¡ rÓL$p¡Z A_¡ b¡ Qp¡fkdp„
f„N `|f.

* L©$rs 2 : v$uhpkmu A\hp _p_u gpL$X$u_u `Ë$uAp¡_u dv$v$\u rÓL$p¡Z, Qp¡fk
s¥epf L$f.

* L©$rs 3 : fdsNds_p L$ep L$ep kp^_p¡dp„ rÓL$p¡Z, Qp¡fk, hsy®m S>¡hp ApL$pfp¡
v¡$Mpe R>¡, s¡ ip¡^.

* L©$rs 4 : Qp¡fk, rÓL$p¡Z A_¡ hsy®m S>¡hp ApL$pfp¡ hX¡$ kfk

rQÓ v$p¡fu s¡dp„ f„N `|f.

ìehlpfdp„ h`fpsu rhrh^ hõsyAp¡ hp`fu_¡ ApL©$rs v$p¡fhp_p¡
dlphfp¡ L$fphhp¡. rhÛp\}Ap¡_¡ dy¼slõs ApL©$rsAp¡ v$p¡fhp_p¡
Aæepk L$fhp L$l¡hy„.

88

k„¿ep_y„ rhð

* Qpgp¡ 1\u 100 ky^u_u k„¿ep_y„ L$p¡óV$L$ `|Z® L$f.

1 4 6 8 10 `s„rNep_u `p„M `f_u

12 13 15 17 19 Sy>v$u Sy>v$u k„¿ep hp„Q.

21 24 26 28 30

32 35 37 39 1 26 82 36
75 69 77 51
41 43 44 48 50

52 54 56 59

63 65 68 70 19 64 99 43
72 76 79 56 83 30 12

81 84 87 90

92 95 98 100

bpSy>dp„ A¡L$ k„¿ep_u dpmp Ap`u R>¡. 18
dpmp_u D`f Ap`¡g k„¿ep Å¡. s¡ b^u 33
k„¿ep ¾$d\u A¡V$g¡ L¡$ gpC_kf L$l¡.

_uQ¡_u dpmp_y„ r_funZ L$f A_¡ s¡dp„_u hÃQ¡_u k„¿ep L$l¡. 86
59

98
77

1\u 100 ky^u_u L$p¡C`Z k„¿ep gM¡gy„ L$pX®$ bsphu k„¿ep hp„Q_ L$fphhy„.

9

k¿„ ep hpQ„ uA¡ - gMuA¡

AL¡ $huk\u kp¡ ( 21\u 100 k^y u_u k¿„ ep_„y iåv$dp„ gM¡ _)

21 huk AL¡ $ - AL¡ $huk 31 Óuk AL¡ $ - AL¡ $Óuk 41 Qpguk AL¡ $ - AL¡ $spguk

22 huk b¡ - bphuk 32 Óuk b¡ - bÓuk 42 Qpguk b¡ - bs¡ pguk
23 huk ÓZ - Óh¡ uk 33 Óuk ÓZ - sÓ¡ uk 43 Qpguk ÓZ - ss¡ pguk
24 huk Qpf - Qph¡ uk 34 Óuk Qpf - QpÓ¡ uk 44 Qpguk Qpf - Q„ydpguk

25 huk `pQ„ - `Quk 35 Óuk `pQ„ - `pÓ„ uk 45 Qpguk `pQ„ - r`õspguk

26 huk R> - R>ìhuk 36 Óuk R> - R>Óuk 46 Qpguk R> - R>s¡ pguk

27 huk kps - kÑphuk 37 Óuk kps - kpX$Óuk 47 Qpguk kps - kXy $spguk

28 huk ApW$ - AÌ$phuk 38 Óuk ApW$ - ApX$Óuk 48 Qpguk ApW$ - AX$spguk

29 huk _h - ApN¡ ZÓuk 39 Óuk _h-ApN¡ ZQpguk 49 Qpguk _h - ApN¡ Z`Qpk

30 Óuk 40 Qpguk 50 `Qpk

rhij¡ kQ| _p : 50 k^y u_u k¿„ ep_„y ip[åv$L$ gM¡ _ A_¡ 100 k^y u_u k¿„ ep_„y hpQ„ _ A`r¡ ns R>.¡

51 `Qpk AL¡ $ - AL¡ $ph_ 61 kpW$ AL¡ $ - AL¡ $kW$ 71 rkÑf¡ AL¡ $ - AL¡ $ps¡ f¡

52 `Qpk b¡ - bph_ 62 kpW$ b¡ - bpkW$ 72 rkÑf¡ b¡ - bps¡ f¡

53 `Qpk ÓZ - Ó`¡ _ 63 kpW$ ÓZ - Ók¡ W$ 73 rkÑf¡ ÓZ - sps¡ f¡
54 `Qpk Qpf - Qp`¡ _ 64 kpW$ Qpf - Qpk¡ W$ 74 rkÑf¡ Qpf - Qd„y ps¡ f¡
55 `Qpk `pQ„ - `Q„ ph_ 65 kpW$ `pQ„ - `pk„ W$ 75 rkÑf¡ `pQ„ - `Q„ ps¡ f¡

56 `Qpk R> - R>à`_ 66 kpW$ R> - R>pkW$ 76 rkÑf¡ R> - R>ps¢ f¡

57 `Qpk kps - kÑph_ 67 kpW kps - kX$kW$ 77 rkÑf¡ kps - rkÐeps¡ f¡

58 `Qpk ApW$ - AÌ$ph_ 68 kpW$ ApW$ - AX$kW$ 78 rkÑf¡ ApW$ - AÌéps¡ f¡

59 `Qpk _h - ApN¡ ZkpW$ 69 kpW$ _h-ApN¡ Zpr¡ kÑf¡ 79 rkÑ¡f _h-Ap¡NÎepA¢ku

60 kpW$ 70 rkÑ¡f 80 A¢ku

81 A¢ku A¡L$ - A¡¼epku 88 A¢ku ApW$ - AWépku 95 _¡hy `p„Q - `„QpÏ
82 A¢ku b¡ - åepku
83 A¢ku ÓZ - Ôep„ku 89 A¢ku _h - _¡ìepku 96 _¡hy R> - R>Þ_y
84 A¢ku Qpf - Qp¡fpku
85 A¢ku `p„Q - `„Qpku 90 _¡hy 97 _¡hy kps - kÑpÏ
86 A¢ku R> - R>epku
87 A¢ku kps - kÐepku 91 _¡hy A¡L$ - A¡L$pÏ 98 _¡hy ApW$ - AÌ$pÏ

92 _¡hy b¡ - bpÏ 99 _¡hy _h - _ìhpÏ

93 _¡hy ÓZ - ÓpÏ 100 kp¡

94 _¡hy Qpf - Qp¡fpÏ

1100

* _uQ¡_u L©$rs `|Z® L$f.

21 `Qpk ÓZ kpW$
Ó¡`_ 48
Óuk ÓZ 18
s¡Óuk huk R> 37 Qpguk R>
R>ìhuk R>¡spguk
40

kpW$ `p„Q 29 rkÑ¡f b¡
`p„kW$ bp¡s¡f

44 A¢ku R> 32
R>epku

k„¿ep iåv$dp„ gMsu hMs¡ rhÛp\}Ap¡ `pk¡\u L$p¡C`Z A¡L$ âL$pf
A`¡rns R>¡.
Dv$plfZ sfuL¡$ 47 dpV¡$ Qpguk kps A\hp kyX$spguk.$

11

S|>\ L$fu_¡ NZsfu

NZu_¡ gM

Ap v$uhpkmuAp¡ ei A_¡ fdp_¡ NZhp Ap`u. s¡ b„_¡A¡ Sy>v$u Sy>v$u fus¡ NZu.

1, 2, 3, 4, ...35 Ap fus¡ NZu. 3 v$iL$ 5 A¡L$d

v$iL$_y„ S|>\ L$fu_¡ NZhy„ kl¡gy„ R>¡.

Aldv$_p rdÓp¡ `pk¡ v$uhpkmu R>¡. v$iL$_y„ S|>\ L$fu_¡ s¡ NZu R>¡.

kgdp `pk¡ 24 v$uhpkmu  ifv$ `pk¡ 45 v$uhpkmu

2 v$+ 4 A¡= 24 v$+ A¡=

Qpgp¡ Ðepf¡ Ap`Z¡ `Z A¡ fus¡ _uQ¡_u hõsyAp¡ NZuA¡.

v$iL$ + A¡L$d= v$iL$ + A¡L$d= v$iL$ + A¡L$d=

1122

rQÓdp„ v$ip®h¡gu k„¿ep

rQÓdp„ v$ip®h¡gu k„¿ep Qp¡fkdp„ L¡$hu fus¡ gMu R>¡, s¡ Å¡.

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d

12 28 47
bpf huk ApW$ Qpguk kps

rQÓp¡dp„ v$ip®h¡gu k„¿ep A„L$dp„ A_¡ iåv$dp„ gM. v$iL$ A¡L$d

v$iL$ A¡L$d v$iL$ A¡L$d

Mpgu S>Áepdp„ ep¡Áe k„¿ep iåv$dp„ gM.

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d

huk R>

1133

rhQpf L$f :
* hõsy `f\u k„¿ep NZ A_¡ _uQ¡_p hsy®mdp„ gM.

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d

34

* k„¿ep hp„Q A_¡ s¡V$gu hõsy bsph. (v$iL$v$p„X$u - R|>V$p, v$uhpkmu_p S|>\ - R|>V$p)
39 41 22

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d

k„¿ep_p A„L$p¡_u õ\pr_L$ qL„$ds

Óuk kps b¡ A„L$u k„¿ep kdS>su hMs¡ Ap`Z¡ v$iL$_p Ofdp„
v$k_p L¡$V$gp S|>\ A_¡ L¡$V$gp A¡L$d R>¡ s¡ Å¡ey„.

37 Dv$plfZ sfuL¡$ : 37dp„ v$iL$_p Ofdp„ 3 S|>\ A_¡ A¡L$d_p
37 Ofdp„ 7 R>¡.

14

õ\pr_L$ qL„$ds
A¡V$g¡ iy„

35 50

ÓZ v$iL$ `p„Q A¡L$d `p„Q v$iL$ i|Þe A¡L$d

Óuk `pQ/ `p„Óuk `Qpk

35dp„ 3 v$iL$ õ\p_¡ R>¡. 3 v$iL$ 50dp„ v$iL$ õ\p_¡ 5 R>¡. 5 v$iL$ S|>\
S|>\_p R|>V$p L$fuA¡ sp¡ 30 A¡L$d dm¡ R|>V$p L$fuA¡ sp¡ 50 A¡L$d dm¡ R>¡.
R>¡. A¡V$g¡ 35dp„ 3_u õ\pr_L$ qL„$ds A¡V$g¡ 50 k„¿epdp„ 5_u õ\pr_L$
30 R>¡. A¡L$d õ\p_¡ 5 R>¡. dpV¡$ 5_u qL„$ds 50 R>¡. A¡L$d õ\p_¡ 0 R>¡.
õ\pr_L$ qL„$ds 5 S> R>¡. i|Þe_u õ\pr_L$ qL„$ds i|Þe R>¡.

_uQ¡_u k„¿ep Å¡C_¡ v$f¡L$ A„L$_u õ\pr_L$ qL„$ds Ap¡mM.

A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d

6 26
6 20 6

15

v$f¡L$ A^p¡f¡rMs A„L$p¡_u õ\pr_L$ qL„$ds Ap¡mM.

18 1_u õ\pr_L$ qL„$ds 10 L$pfZL¡$ v$iL$_p Ofdp„ 1 R>¡.

23 3_u õ\pr_L$ qL„$ds 3 L$pfZL¡$ A¡L$d_p Ofdp„ 3 R>¡.

65 5_u õ\pr_L$ qL„$ds 5 L$pfZL¡$ A¡L$d_p Ofdp„ 5 R>¡.

72 7_u õ\pr_L$ qL„$ds 70 L$pfZL¡$ v$iL$_p Ofdp„ 7 R>¡.

50 0_u õ\pr_L$ qL„$ds ......................................

40 4_u õ\pr_L$ qL„$ds ......................................

88 8_u õ\pr_L$ qL„$ds ......................................

88 8_u õ\pr_L$ qL„$ds ......................................

61 6_u õ\pr_L$ qL„$ds ......................................

lh¡ _uQ¡ Ap`g¡ u k¿„ ep_p v$fL¡ $ AL„ $p_¡ u õ\pr_L$ qL$„ds gM !

22 38 41 60 95
20 2

16

k„¿ep_y„ rhõspfus ê$`

35dp„ 3_u õ\pr_L$ qL„$ds 30 R>¡. 5_u õ\pr_L$ qL„$ds 5 R>¡. A¡V$g¡ L¡$ 35 k„¿ep
A¡V$g¡ 30 + 5.
30 + 5 _¡ 35_y„ rhõspfus ê$` L$l¡ R>¡.
94_y„ rhõspfus ê$` 90 + 4 R>¡.
60_y„ rhõspfus ê$` 60 + 0 R>¡.

35 24 73 49

30 5 20 4 70 3 40 9

Óuk A_¡ `p„Q huk A_¡ Qpf rkÑ¡f A_¡ ÓZ Qpguk A_¡ _h

30 + 5 20 + 4 70 + 3 40 + 9

Ap `f\u Ap`Zp Ýep_dp„ Apìey„ L¡$ -
35_y„ rhõspfus ê$` → 30 + 5   24_y„ rhõspfus ê$` → 20 + 4
73_y„ rhõspfus ê$` → 70 + 3   49_y„ rhõspfus ê$` → 40 + 9

_uQ¡_u k„¿ep_p rhõspfus ê$` gM.

k„¿ep Anf ê$` rhõspfus ê$`

32 Óuk A_¡ b¡ 30 + 2

10 .......... A_¡ ..........
64 .......... A_¡ ..........
17 .......... A_¡ ..........

17

\p¡X$u Nçds :
`p_p _„. 9 `f s¡ `|Z® L$f¡g L$p¡óV$L$ Å¡C_¡ L$l¡.
• 10\u 100 ky^u_u k„¿epdp„...
→ v$iL$ õ\p_¡ 5 A„L$ L¡$V$gu hpf Aph¡ R>¡ ?

→ s¡ k„¿ep _p¡V$dp„ gM.

• 10\u 99 ky^u_u k„¿epdp„...

→ A¡L$d õ\p_¡ 0 L¡$V$gu hpf Aph¡ R>¡ ?

→ s¡ k„¿ep _p¡V$dp„ gM.

Aæepk :

• A^p¡f¡rMs A„L$p¡_u õ\pr_L$ qL„$ds gM.
........ ........
16 = 77 =

48 ........ 82 ........
= =

54 ........ 91 ........
= =

• rhõspfus ê$` `f\u k„¿ep gM.
70 + 8 = 90 + 7 =

60 + 1 = 80 + 0 =

• Mpgu S>Áep cf.

52 98
8
10 1 50
87
76 4 v$iL$ 0 A¡L$d 7 A¡L$d
7 v$iL$

18

V$à`¡ k„¿ep
NZuA¡

• kkgpA¡ dpf¡gp L|$v$L$p Å¡.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

kkgpA¡ S>¡ Qp¡fk D`f\u L|$v$L$p¡ dpep£ R>¡ Ðep„_u k„¿ep Å¡. 15
3 6 9 12

3_u ApNm 3 k„¿ep NZhp\u 6 dm¡ R>¡. 6_u ApNm 3 k„¿ep NZhp\u
9 dm¡ R>¡. s¡hu fus¡ v$f¡L$ hMs¡ 3 k„¿ep NZhp\u Al] ApNm_u k„¿ep dm¡ R>¡.

3_u ApNm 3, 6, 9, 12, 15 Ap 3_p V$à`¡ Aphsu k„¿ep R>¡.

• lfZ¡ dpf¡gp L|$v$L$p Å¡.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

lfZ¡ Äep„\u L|$v$L$p dpep® R>¡ Ðep„_u k„¿ep gM.

4_u ApNm 9, 14, 19, 24 Ap 5_p V$à`¡ Aphsu k„¿ep R>¡.

f„Nu_ Qp¡fkdp„_u k„¿ep Å¡. Ap k„¿ep ¼ep V$à`¡ Aph¡gu R>¡ s¡ ip¡^.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

S>du_ D`f Qp¡fk v$p¡fu s¡dp„ k„¿ep ¾$d\u gMu_¡, k„¿ep_p¡ L$p¡C`Z
A¡L$ V$à`p¡ L$l¡hp¡, Ap V$à`p A_ykpf Aphsu k„¿ep D`f L|$v$L$p dpfhp
L$l¡hy„, Aphu L©$rs L$fphhu.

19

kfhpmp_u Nçds

  5 + 2 = 7

  2 + 5 = 7

5 A_¡ 2 dmu_¡ 7 \pe A¡V$g¡ ¾$d bv$guA¡
s¡ S> fus¡ 2 A_¡ 5 sp¡ kfhpmp¡ bv$gpsp¡
dmu_¡ `Z 7 \pe. R>¡ _\u !
_¡ Nçds !

bfpbf ! A¡ QL$pkhp dpV¡$ Ap`¡gp
kfhpmp L$fu Å¡.

4+1= 1 + 4 =
5+9= 9 + 5 =
3+7= 7 + 3 =
8+3= 3 + 8 =
8+4= 4 + 8 =
5+6= 6 + 5 =
0+3= 3 + 0 =



2200

kfhpmp¡ - ApNm NZu_¡

rinL$ : kgdp, Ap b¡ fp¡` g¡, spfp Ap„NZpdp„ hph.
kgdp : Qp¡½$k, dpfp Of¡ `l¡g¡\uS> 5 fp¡` hph¡gp R>¡.
rinL$ : M|b kfk ! bpmL$p¡ lh¡ kgdp_p Ap„NZpdp„ L¡$V$gp fp¡` \i¡ ?

 fdp_u NZsfu ei_u NZsfu
    2 Ap„N mu + 5 A p„Nm u 5 Ap„Nmu + 2 Ap„Nmu

   kps kps

(fdpA¡ 1, 2, 3, ... A¡d 7 ky^u Ap„NmuAp¡ NZu, Äepf¡ ei¡ 5 `R>u 6-7 A¡d b¡
Ap„Nmu NZu.)

rinL$ : b„_¡_p¡ kfhpmp¡ kdp_ A_¡ kpQp¡ S> R>¡, `f„sy L$p¡_p¡ kfhpmp¡ TV$`V$
\ep¡ ?

ei : dpfp¡.

rinL$ : ^pfp¡ L¡$ 9 v$uhpkmu A_¡ 3 v$uhpkmu_¡ kfhpmp¡ L$fhp dpV¡$ c¡Nu L$fu A_¡
NZu, sp¡ S>hpb iy„ Aphi¡ ?

fdp : S>hpb R>¡ 12 v$uhpkmu ! d¢ 1\u 12 ky^u NZu.

+

rinL$ : `Z 9\u ApNm 10, 11, 12 A¡d NZuA¡ sp¡ S>hpb 12 Aph¡ R>¡. Al]
Ap`Zu `pk¡ 9 v$uhpkmu R>¡. A¡d dp_u_¡ a¼s _hu dm_pfu v$uhpkmu_¡
gpC_\u ApNm NZu.

ei : Ap`Zu `pk¡ 3 v$uhpkmu R>¡, 9 v$uhpkmu _hu dmu sp¡ 3 `R>u ApNm 9
NZuA¡ sp¡ `Z S>hpb 12 Aph¡ ! `Z 3 `R>u 9 NZhp L$fsp„ 9 `R>u
ApNm 3 NZhp kl¡gp„ \C `X¡$.

ApNm NZu_¡ kfhpmp¡ L$f.

25 + 3, 5 + 38, 5 + 19, 4 + 23.

21

bpSy>dp„ Ap`¡g Qp¡fkdp„ 1\u 50 k„¿ep ¾$d\u gM.

lh¡ spfu `p¡sp_u NZhp_u V¡$` s¥epf R>¡. s¡_p¡ D`ep¡N kfhpmp¡ L$fhp dpV¡$

L$f. 8 A_¡ 9_p¡ kfhpmp¡ L$fhp dpV¡$ "8' A„L$ 52 Ap„Nmu d|L$. s¡_p\u

ApNm_p 9 Mp_p NZ. "17' k„¿ep `f `lp¢Ãep¡ _¡ ? A¡V$g¡ L¡$ 8 A_¡ 9_p¡

kfhpmp¡ 17 \ep¡.

• ApNm NZu_¡ kfhpmp¡ L$f.

• fdp `pk¡ 18 L$Q|L$p A_¡ ei `pk¡ 7 L$Q|L$p R>¡. sp¡ b„_¡_p dmu_¡ Ly$g L¡$V$gp

L$Q|L$p R>¡ ?

iy„ Apàey„ R>¡ ? fdp `pk¡ A_ ¡

`|R>ey„ R>¡ ? ei `pk¡ f lg¡ p L$QL| $ p + fdp `pk¡ fl¡g L$Q|L$p
iy„ L$yg L$QL| $p ei `pk¡ fl¡g L$Q|L$p

iy„ L$fuiy„ ? kfhpmp¡ Ly$g L$Q|L$p

• Ap_„v$ `pk¡ 27 [õV$L$k® R>¡. s¡Z¡ buÅ 5 [õV$L$k® h¡Qpsp gu^p. lh¡ s¡_u `pk¡

L¡$V$gp [õV$L$k® \ep ?

iy„ Apàey„ R>¡ ?
iy„ `|R>ey„ R>¡ ? +

iy„ L$fuiy„ ?

• ApNm NZu_¡ kfhpmp¡ L$f.

12 15 62 54 41
+ 5+ 4+ 3+ 8+ 9

  27 + 8 = 8 + = 14  67 + 3 =

  + 9 = 16 54 + 9 =  49 + 2 =

22

kfhpmp - hØuhNf_p

`y_fphs®_ : A¡L$ A„L$u k„¿ep_p kfhpmp. 4 A¡L$d R>¡, dpV¡$ s¡ A¡L$d_p Ofdp„

A¡L$d A¡L$d g¿ep.

4 2 `Z A¡L$d R>¡ dpV¡$ s¡ `Z A¡L$d_p

+ 2 Ofdp„ g¿ep.

kfhpmp¡ L$fsp„ 6 dm¡ R>¡ s¡ `Z A¡L$d
6 R>¡, dpV¡$ A¡L$d_p Ofdp„ g¿ep.

5+3 6+2 5+4 4+4 3+6
A¡L$d A¡L$d
A¡L$d A¡L$d A¡L$d

b¡ A„L$u k„¿ep_p¡ kfhpmp¡ :

23 + 12 = ?

v$iL$ A¡L$d v$iL$ A¡L$d 2 v$iL$ 3 A¡L$d
+ 1 v$iL$ 2 A¡L$d
23
3 v$iL$ 5 A¡L$d
+ +
12

35

+ +  v$iL$ A¡L$d
v$iL$ A¡L$d

  v$iL$ A¡L$d

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d
+4 7
+ 2 3 +2 4 + 31 2
3 2 3 6 41
88
55 27 48

23

• _uQ¡_p kfhpmp L$f.

v$ A¡ v$ A¡ v$ A¡ v$ A¡ v$ A¡
12 15 24 16 37
+1 3 +1 2 +5 +2 3 +2

• v$iL$ dpV¡$ "v$' A_¡ A¡L$d dpV¡$ "A¡' gM A_¡ kfhpmp L$f.

v$ A¡

+ 1  5 + 1 2 + 1 7 + 31 3 + 31   7
2  1 3 5 2 2 6 2

+ 2  3 +5 2 +1 8 +4 4 +6 1
3  6 2 0 30 1 4 24

• kfhpmp_p Dv$plfZp¡ s¥epf L$f A_¡ NZ.

+  + + + +
 

24

i|Þe_p kfhpmp A_¡
bpv$bpL$u

i|Þe Dd¡fhy„ A_¡ i|Þe bpv$ L$fhy„ :
A¡L$ fL$pbudp„ ÓZ kafS>_ R>¡. A¡L$ fL$pbu Mpgu R>¡. Ly$g kafS>_ ÓZ S> R>¡.

  3 + 0 = 3

fdp `pk¡ 2 kafS>_ R>¡. s¡_u _p_u bl¡__¡ kafS>_ M|b cph¡ R>¡. dpV¡$ s¡Z¡ b„_¡
kafS>_ bl¡_ dpV¡$ fp¿ep. A¡L$ `Z Mp^„y _l].  

  2 − 0 = 2

L$p¡C`Z k„¿epdp„ i|Þe Dd¡fsp„ s¡ S> k„¿ep dm¡ R>¡. i|Þe
bpv$ L$fuA¡ sp¡ `Z s¡dS> \pe R>¡.

Qp¡fkdp„ ep¡Áe k„¿ep gM :

2 + 0 = 4 + 0 = 7 + 0 =

19 + 0 = 27 + 0 = 65 + 0 =

78 + 0 = 0 + 0 = 6 + =6

3 − 0 = 5 − 0 = 8 − 0 =

11 − 0 = 19 − 0 = 23 − 0 =
55 − 0 = 82 − = 82 − 0 = 17

2255

hpsp®dp„ kfhpmp - 1

• d_Äep¡s¡ bv$pd_p 14 TpX$ A_¡ `¡fy_p 21 TpX$ hpìep, sp¡ s¡Z¡ Ly$g L¡$V$gp TpX$

hpìep ? v$ A¡

iy„ Apàey„ R>¡ ? bv$pd_p TpX$, `¡fy_p TpX$ 1 4 bv$pd_p TpX$
iy„ `|Rey„ R>¡ ? Ly$g TpX$ + 2 1 `¡fy_p TpX$

iy„ L$fuiy„ ? kfhpmp¡ 3 5 Ly$g TpX$

• frh `pk¡ 15 azÁNp R>¡. _usp `pk¡ 21 azÁNp R>¡. b„_¡_p dmu_¡ Ly$g L¡$V$gp azÁNp
\i¡ ?

iy„ Apàey„ R>¡ ? +  
iy„ `|Rey„ R>¡ ?  

iy„ L$fuiy„ ?  

NZ :

• cpC `pk¡ 15 ê$r`ep lsp. dpkuA¡ s¡_¡ buÅ 20 ê$r`ep Apàep, lh¡ cpB `pk¡
L¡$V$gp ê$r`ep \ep ?

• L$bpV$dp„ 24 `yõsL$p¡ lsp, s¡dp„ buÅ 12 `yõsL$p¡ d|¼ep„, sp¡ L$bpV$dp„ Ly$g L¡$V$gp
`yõsL$p¡ \ep„ ?

• Ofdp„ 18 X$bp lsp, dçdu bÅfdp„\u buÅ 11 X$bp gpìep, lh¡ Ofdp„ Ly$g
L¡$V$gp X$bp R>¡ ?

• kpÆv$ `pk¡ 24 IX$p„ R>¡ A_¡ ibp_p `pk¡ 32 IX$p„ R>¡, sp¡ b„_¡_p dmu_¡ Ly$g L¡$V$gp
IX$p„ \i¡ ?

• dpqfep `pk¡ 30 rk½$p R>¡, rdrlf `pk¡ 24 rk½$p R>¡,

b„_¡_p dmu_¡ Ly$g L¡$V$gp rk½$p \i¡ ?

2266

bpv$bpL$u hX¡$ Ap¡R>p
L$fuA¡

5 − 3 =  

rnrsS> `pk¡ 5 L$` lsp. s¡Z¡ Ap„Qg_¡ 3 L$` Apàep. lh¡ rnrsS> `pk¡ L¡$V$gp L$`

hÝep ? A¡L$d

−5 rnrsS> `pk¡_p L$`
3 Ap„Qg_¡ Ap`¡gp L$`

rnrsS> `pk¡ h^¡gp L$`

Å¡X$L$p Å¡X$u_¡ bpv$bpL$u
• 8 L„$v$ug A_¡ 4 v$uhp R>¡. sp¡ v$uhp L$fsp„ L¡$V$gp„ L„$v$ug h^pf¡ R>¡ ?

−8
4
4

v$uhp L$fsp„ 4 L„$v$ug h^pf¡ R>¡.
• 6 `pV$u A_¡ 11 `yõsL$p¡ R>¡, `yõsL$p¡ L$fsp `pV$u L¡$V$gu Ap¡R>u R>¡ ?

−

  `yõsL$ L$fsp„ `pV$u Ap¡R>u R>¡.

• 8 õV²$p¡b¡fu A_¡ 6 v$pX$d R>¡. õV²$p¡b¡fu L¡$V$gu h^pf¡ R>¡ s¡ k„¿ep_u bpv$bpL$u L$fu_¡
_½$u L$fuA¡.
− 8 A¡V$g¡ L¡$ v$pX$d L$fsp 2 õV²$p¡b¡fu h^pf¡ R>¡
6 A\hp õV²$p¡b¡fu L$fsp 2 v$pX$d Ap¡R>p R>¡.
2

27

`pR>m NZu_¡ bpv$bpL$u : S>¡ R>¡ëgu L|$L$fu KQL¡$ s¡
lpfu Åe.
_uQ¡ Ap`¡gu fds sy„ fdu Å¡.

dpfu `pk¡ Ap L$p¡óV$L$ R>¡. s¡_p `f
49 L|$L$fu d|L$uiy„. A¡L$ kde¡ 5 A\hp 5
L$fsp„ Ap¡R>u L|$L$fu D`pX$hu. v$f¡L$ hMs¡ 1
sL$ dmi¡ `Z i|Þe L|$L$fu KQL$u iL$pi¡
_l].

fdpA¡ fds_u iê$Aps L$fu.
s¡Z¡ 49\u `pR>m S>sp„ NZu_¡
4 L|$L$fu KQL$u. h^u 45 L|$L$fu. lh¡
ei L|$L$fu KQLi¡. Ap âdpZ¡ fdsp
R>¡ëgu L|$L$fu ei¡ KQL$u, s¡\u fdp
Æsu NC.

`lg¡ p„ lsp gu^p hÝep `lg¡ p„ lsp gu^p hÝep
49 − 4 = 45 23 − 5 = 18

fdp fdp

45 − 5 = 40 18 − 5 = 13

ei ei

40 − 5 = 35 13 − 5 = 8

fdp fdp

35 − 4 = 31 8 − 4 =4

ei ei

31 − 3 = 28 4 − 3 =1

fdp fdp

28 − 5 = 23 1 − 1 =0

ei ei

28

kyf¡i A_¡ fd¡i¡ qv$hpmu dpV¡$ c¡V$ L$pX®$ s¥epf L$fhp_y„ _½$u L$e¯y. s¡ dpV¡$ kprlÐe gphhp_y„
ls„y. kyf¡i `pk¡ 9 ê$r`ep lsp. fd¡i L¡$V$gpL$ ê$r`ep gpìep¡. b„_¡_p dmu_¡ Ly$g 14
ê$r`ep \ep. fd¡i L¡$V$gp ê$r`ep gpìep¡ ?
fdp : A¡V$g¡ L¡$ 14dp„\u 9 bpv$ L$fhp_p R>¡.
ei : d¢ 14 hsy®m v$p¡ep®. s¡dp„\u 9 hsy®m R>¡¼ep. lh¡ 5 hsy®mp¡ hÝep. A¡V$g¡ fd¡i

5 ê$r`ep gpìep¡.
fdp : d¢ 9\u ApNm 14 ky^u ¾$d\u k„¿ep NZu. dpfp¡ S>hpb `Z 5 R>¡.

L$p¡_u NZsfu kl¡gu R>¡ s¡_p rhi¡ hN®dp„ QQp® L$fp¡.

bpv$bpL$u L$fsu hMs¡ k„¿epf¡Mp_p¡ D`ep¡N L$fu_¡ ApNm A\hp `pR>m NZu_¡ `Z
bpv$bpL$u L$fu iL$pe R>¡. 14 - 9 Ap bpv$bpL$u Å¡.
9 + 5 = 14 A¡V$g¡ 14 - 9 = 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 - 9 = 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

D`f_u `l¡gu ApL©$rsdp„ 9\u 14 ky^u S>dZu bpSy> 5 L|$v$L$p \ep; buÆ ApL©$rsdp„
14\u X$pbu bpSy> 9 L|$v$L$p dpep®, 5 D`f Aphu_¡ AV$¼ep. b„_¡ L©$rsdp„ S>hpb 5 S>
R>¡. b„_¡ âL$pf_u k„¿epf¡Mp hX¡$ bpv$bpL$u L$fu iL$pe. A¡_p¡ Aæepk L$fhp dpV¡$
_uQ¡_u bpv$bpL$u L$f.

(1) 12 - 8 = (2) 32 - 1 = (3) 15 - 10 =

(4) 43 - 2 = (5) 13 - 11 = (6) 39 - 3 =

(7) 20 - 18 = (8) 44 - 40 = (9) 11 - 2 =

43 - 2 bpv$bpL$u L$fsu hMs¡ 2\u 43 ky^u S>dZu bpSy> L|$v$L$p dpfhp kl¡gp `X¡$
L¡$ 43\u X$pbu bpSy> 2 L|$v$L$p dpfhp kl¡gp `X¡$ ?
44 - 40 Ap bpv$bpL$u L$fsu hMs¡ 44\u S>dZu bpSy>A¡ 40
L|$v$L$p dpfhp kl¡gp `X¡$ L¡$ 40\u S>dZu bpSy>A¡ 44 ky^u L|$v$L$p

dpfhp kl¡gp `X¡$ ?

29

kfhpmp-bpv$bpL$u_u Å¡X$u

10 + 12 = 22

22 - 10 = 12 22 – 12 = 10

kfhpmp_pâÐe¡L$Dv$plfZdp„ 71 + 22 = 93
bpv$bpL$u_p b¡ Dv$plfZ dm¡
R>¡ L¡$, A¡ QL$pku Å¡.

93 - 71 = 22 93 - 22 = 71

Qp¡fk cf. 5 + 5 = 10 dp„\u 10 - 5 = 5 A¡
12 A¡L$ S> bpv$bpL$u dm¡ R>¡.

99 87 + 12 = 99
87 99 − 12 = 87    99 − 87 = 12

50 34 + =
84 =    −
34 − =

+= − =
75 − =    − =



Ap âdpZ¡ sy„ A¡L$ Dv$plfZ s¥epf L$f A_¡ NZ.

+=

− =   

3300

• h¡v$îuA¡ `yõsL$_p 9 `p_p„ hp„Ãep„. buÅ L¡$V$gp„ `p_p„ hp„Q¡ sp¡ 15 `p_p„ h„Qpe

S>i¡ ? iy„ L$fuiy„ : kfhpmp¡
iy„ Apàey„ R>¡ ? hp„Qhp_p„ Ly$g `p_p„, hp„Qu gu^¡gp„ `p_p„, L¡$ bpv$bpL$u
iy„ `|Rey„ R>¡ ? buÅ L¡$V$gp„ `p_p„ hp„Qhp_p„ R>¡.

lz„ bpv$bpL$u L$fy„ Ry>„. lz„ lz„ ApNm NZu_¡
15dp„\u 9 L$pYy„$ Ry>„. kfhpmp¡ L$fy„ Ry>„, s¡_p
L¡$V$gp h^¡ R>¡ s¡ Å¡CA¡. `f\u bpv$bpL$u_p¡

DÑf dmi¡.

15 − 9 =   9 + = 15
dpV¡$ 15 - 9 = 6

• lk_¡ 30 bu S>dp L$ep® R>¡. s¡dp„\u L¡$V$gp„L$ bu QuLy$_p R>¡. h^¡gp 22 bu
kuspam_p R>¡. sp¡ QuLy$_p L¡$V$gp bu R>¡ ?

iy„ Apàey„ R>¡ ?

iy„ `|Rey„ R>¡ ?

− 22 = 22 + = 30

dpV¡$ - =

NZ : − 9 = 8 A_¡ 17 − 8 =
8 + = 17 dpV¡$ − 3 = 29 A_¡ 32 − 29 =
29 + = 32 dpV¡$ − 7 = 42 A_¡ 49 − 42 =
42 + = 49 dpV¡$

31

hpsp®dp„ bpv$bpL$u

• h¥ipgu 54 dZL$p gphu lsu. dpmp b_pìep `R>u s¡_u `pk¡ 21 dZL$p hÝep.
sp¡ dpmpdp„ L¡$V$gp dZL$p `fp¡ìep R>¡?
iy„ Apàey„ R>¡? 54 dZL$p gpìep, 21 dZL$p hÝep
iy„ `|R>ey„ R>¡? dpmpdp„ L¡$V$gp dZL$p `fp¡ìep

iy„ L$fuiy„? bpv$bpL$u

v$iL$ A¡L$d

−5 4 dZL$p gpìep
2 1 dZL$p hÝep

3 3 dZL$p dpmpdp„ `fp¡ìep

• D`f_u `Ý^rs\u bpv$bpL$u L$f.

v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d v$iL$ A¡L$d
27 37 68 98

13 25 34 40
− − − −

• Ap_„v¡$ hpsp®_p 28 `yõsL$p¡ hp„Ãep„. kpNf¡ 14 `yõsL$p¡ hp„Ãep„. Ap_„v¡$ kpNf L$fsp
L¡$V$gp `yõsL$p¡ h^pf¡ hp„Ãep„ R>¡?

• ky^uf `pk¡ 46 Np¡V$uAp¡ lsu. s¡dp„_u 12 Np¡V$uAp¡ Mp¡hpC NC, sp¡ lh¡ s¡_u `pk¡
L¡$V$gu Np¡V$uAp¡ li¡?

• V$p¡`gudp„ bpfdpku_p 58 awgp¡ A_¡ Åk|v$_p 32 awgp¡ R>¡. bpfdpku_p awgp¡ L$fsp„
Åk|v$_p awgp¡ L¡$V$gp Ap¡R>p R>¡?

• V$p¡`gudp„ 16 L¡$mp„ lsp. d_âus¡ buÅ L¡$V$gpL$ L¡$mp„ V$p¡`gudp„ d|¼ep„ bpv$ V$p¡`gudp„
29 L¡$mp„ \ep, sp¡ d_âus¡ V$p¡`gudp„ L¡$V$gp L¡$mp„ d|¼ep„ li¡?

3322

hj®_p bpf drl_p

A„N°¡Æ hj®_p drl_p

riepmp¡

qX$k¡çbf ÅÞeyApfu
_h¡çbf 31 qv$hk 31 qv$hk
30 qv$hk 1 a¡b°yApfu
28 A\hp
12 29 qv$hk

Ap¸¼V$p¡bf 11 2 dpQ®

31 qv$hk 10 A„N°¡Æ drl_p 3 31 qv$hk

kàV¡$çbf 9 (N°¡Nqfe_ 4 A¡râg
30 qv$hk hj®) 30 qv$hk

85 D_pmp¡
76
Ap¸NõV$ d¡
31 qv$hk
31 qv$hk Sy>gpC S|>_
Qp¡dpky„ 31 qv$hk 30 qv$hk

hj®_u iê$Aps ÅÞeyApfu drl_p\u \pe R>¡ A_¡ hj® qX$k¡çbf drl_pdp„ `|fy„ \pe R>¡.

  • 30 qv$hk ^fphsp drl_p_p _pd L$l¡.

  • ApMp hj®dp„ 31 qv$hk ^fphsp L¡$V$gp drl_p R>¡ ?

  • a¡b°yApfu drl_pdp„ L¡$V$gp qv$hk lp¡e R>¡ ?

• S|>_ drl_p `l¡gp L$ep¡ drl_p¡ Aph¡ R>¡ ? 30 qv$hk kàV¡$çbf_p,
  • ÅÞeyApfu drl_p `l¡gp L$ep¡ drl_p¡ lp¡e R>¡ ? A¡râg, S|>_ A_¡ _h¡çbf_p
bpL$u_p drl_p 31 qv$hk_p
dpÓ a¡b°yApfu_¡ R>p¡X$u_¡.

3333

cpfsue hj®_p drl_p

hk„s

apNZ Q¥Ó
l¡d„s
riqif

N°uód
dlp h¥ipM

`p¡j 12 1 2 S>¡W$
AN°lpeZ 11 3 AjpY$
(dpNif) 10 cpfsue 4
9 drl_p
8 5

76

L$pfsL$ îphZ

Arð_ cpÖ`v$ hjp®

(Apkp¡) (cpv$fhp¡)

ifv$

hj®_u iê$Aps Q¥Ó drl_p\u \pe R>¡ A_¡ apNZ drl_pdp„ hj® `|fy„ \pe R>¡.
D`f_p rQÓ_y„ r_funZ L$f A_¡ Mpgu Qp¡fk cf.

F>sy hk„s N°uód
`yg _uQ¡_p \p„cgp `pk¡_p X$bp `f L$ep¡ drl_p¡ li¡ ?

Q¥Ó h¥ipM cpv$fhp¡ Apkp¡

34

ipmp_y„ spfurMey„ (L¸$g¡ÞX$f ) fdp : ei, Ap qX$k¡çbf drl_pdp„
qX$k¡çbf 2019
Ap`Zu ipmpdp„ iy„ iy„
frh 1 8 15 22 29
\hp_y„ R>¡ s¡ s_¡ Mbf R>¡ L¡$?

ei : lp. Ap`Zu ipmp_p

kp¡d 2 9 16 23 30 spfurMepdp„ Apàey„ S> R>¡.

fdp : sp¡ L$l¡ Å¡CA¡, ipmpdp„

d„Nm 3 10 17 24 31 rQÓL$gp õ`^p® L$C spfuM¡

R>¡?

by^ 4 11 18 25 ei :

_pspg fdp : A_¡ fds Nds õ`^p® L¡$V$gp

5 12 19 26 qv$hk R>¡?
fds-
Nyfy Nds ei : lh¡ sy„ L$l¡,

õ`^p® 25 qX$k¡çbf¡ L$ep¡ sl¡hpf

6 13 20 27iy¾$fds- R>¡?
Nds rQÓL$gp
õ`^p® õ`^p® fdp : kl¡gy„ R>¡ !

ir_ 7 14 21 28 fdp : Qpg lh¡, lz„ ÅJ Ry>„. Aphsu

h_- L$pg¡ h_cp¡S>_ R>¡. dpf¡

cp¡S>_

s¥epfu L$fhp_u R>¡.

rhQpf L$f :
fdp A_¡ ei hÃQ¡ Ap k„hpv$ L$C spfuM¡ \ep¡ li¡?

L©$rs : L$p¡C`Z A¡L$ L¸$g¡ÞX$f g¡. s¡_p `f\u L$l¡.
• A¡L$pv$ drl_p_p d„Nmhpf¡ Aphsu spfuMp¡dp„ iy„ Nçds S>Zpe R>¡?
• A¡L$pv$ drl_p_p iy¾$hpf¡ Aphsu spfuMp¡dp„ iy„ Nçds S>Zpe R>¡?
rhQpf L$f :
• Å¡ L$p¡C drl_pdp„ by^hpf¡ 4 spfuM lp¡e,
sp¡ `R>u_p by^hpf¡ L$C spfuM li¡?

35

rhcpN buš

k„¿ep_y„ _p_pdp¡V$p`Ï„

b¡ k„¿ep_y„ _p_pdp¡V$p`Ï„ 2, 20
• v$f¡L$ Qp¡fkdp„_u _p_u k„¿ep afs¡ Np¡m L$f.

3, 8 1, 9

• v$f¡L$ Qp¡fkdp„_u dp¡V$u k„¿ep afs¡ Np¡m L$f.

4, 7 2, 7 8, 9

_p_pdp¡V$p`Ï„ v$ip®hsp rQŒp¡_u Ap¡mM
* k„¿ep_y„ _p_pdp¡V$p`Ï„ v$ip®hhp dpV¡$ ‘<’ A\hp ‘>’ rQŒ h`fpe R>¡.
s¡d_p¡ A\® A_¡ D`ep¡N _uQ¡_p Dv$plfZ Üpfp kdÆA¡.

3 < 7    1 < 9    20 > 2   

3 _p_p 7 L$fsp 1 _p_p¡ 9 L$fsp 20 dp¡V$p 2 L$fsp

7 > 3    9 > 1    2 < 20
7 dp¡V$p 3 L$fsp  9 dp¡V$p 1 L$fsp  2 _p_p 20 L$fsp 

72

dNf dp¡V$u k„¿ep_¡ Mpe R>¡.
* L$p¡C`Z b¡, b¡ A„L$u k„¿ep gCA¡, sp¡ s¡d_p hÃQ¡_y„ _p_pdp¡V$p`Ï„ L¡$hu fus¡
_½$u L$fu iL$pe?

S>¡ k„¿epdp„ v$iL$_p¡ A„L$ dp¡V$p¡, s¡ k„¿ep dp¡V$u.

ei : Ap`Z¡ 37 A_¡ 52 gCA¡. 37dp„ 3 v$iL$ R>¡, 52dp„ 5 v$iL$ R>¡. dpV¡$
52 > 37, A¡V$g¡ L¡$ 37 < 52

3366

fdp : bfpbf ! Ap`Z¡ NZhp_u V¡$` `f k„¿ep NZuA¡ Ðepf¡ 37 `l¡gp„ Aph¡ R>¡,
`R>u 52 Aph¡ R>¡, `R>u Aphsu k„¿ep dp¡V$u lp¡e R>¡. `Z b„_¡ k„¿ep_p v$iL$
kdp_ lp¡e sp¡?

v$iL$ kdp_ lp¡e sp¡ A¡L$d_p A„L$ 52\u _½$u L$fpe.

ei : Ap`Z¡ 72 A_¡ 78 gCA¡. 2 < 8 A¡V$g¡ 72 < 78.
k„¿ep_p¡ rhõspf L$fuA¡ A_¡ _p_u dp¡V$u k„¿ep Ap¡mMhp_p¡ r_ed QL$pku Å¡CA¡.

43 A_¡ 28 43 k„¿epdp„ v$iL$õ\p_¡ 4 A„L$ R>¡.
43 = 40 + 3
sp¡ 28 k„¿epdp„ v$iL$õ\p_¡ 2 R>¡.
28 = 20 + 8 43 > 28

31 A_¡ 33 b„_¡ k„¿epdp„ v$iL$õ\p_¡ kdp_
31 = 30 + 1 A„L$ 3 R>¡ `Z 33dp„ A¡L$dõ\p_¡ 3
R>¡. sp¡ 31dp„ A¡L$dõ\p_¡ 1 R>¡.
33 = 30 + 3
31 < 33

lh¡ Ap`¡gu k„¿ep_u Å¡X$uAp¡dp„ _p_u-dp¡V$u k„¿ep Ap¡mMu_¡ < A\hp > A¡hu
r_ip_u L$f.

43, 46     84, 86     67, 57

43 < 46  

30, 50 13, 9 23, 32
 

L$fu Å¡ : Sy>v$u Sy>v$u k„¿epAp¡_u 10 Å¡X$u gp¡. Ap
Å¡X$udp„_u k„¿epAp¡dp„ _p_pdp¡V$p`Ï„ _½$u L$f.

37

k„¿ep_p `pX$p¡iu, sfs `l¡gp_u
A_¡ `R>u_u k„¿ep

k„¿epf¡Mp Aphu lp¡e R>¡.
AL¡ $ fM¡ p_u X$pbu bpS>y A¡ iÞ| e gMg¡ p¡ lp¡e R>.¡ Ðep„\u kyrh^p dyS>b _p_p A„sf gC,
A¡L$ `R>u A¡L$ NZu, kfMp A„sf¡ 1, 2, 3, 4, ... A¡ k„¿epAp¡ gM¡gu lpe¡ R>.¡

0 1  2  3  4  5  6   7
Ap f¡Mp_p¡ L$p¡C`Z cpN Å¡. Ap f¡Mp `f_u L$p¡C`Z A¡L$, ^pfp¡ L¡$ 23 k„¿ep gCA¡.

22 23 24 25 26 27

sfs `l¡gp„_u 22 23 24 sfs `R>u_u.

iy„ Ýep_dp„ Apìey„ ?

L$p¡C`Z k„¿ep_u X$pbu bpSy>A¡ Aph¡gu A¡V$g¡ L¡$ sfs `l¡gp„_u k„¿ep 1 S>¡V$gu
Ap¡R>u R>¡. Äepf¡ S>dZu bpSy>A¡ Aph¡gu A¡V$g¡ L¡$ sfs `R>u_u k„¿ep 1 S>¡V$gu h^pf¡
R>¡.
Mpgu Qp¡fkdp„ sfs `l¡gp„_u A_¡ sfs `R>u_u k„¿ep gM.

54 79 40

37 62 99

50 78 32

39 30 68

3388

k„¿ep_p¡ QY$sp¡ A_¡
Dsfsp¡ ¾$d

36, 23, 17, Ap k„¿epAp¡_¡ QY$sp ¾$ddp„ L¡$hu fus¡ Np¡W$hpe s¡ Å¡CA¡.
`l¡gp„ (36, 23) (23, 17) (36, 17) Ap Å¡X$uAp¡ s`pkuA¡.

36, 23, 17

17 • 23 < 36, 17 < 23 A_¡

36, 23, 17 17 < 36. A¡V$g¡ L¡$ 17 A¡ kp¥\u
_p_u k„¿ep R>¡. 17 _¡ R>¡L$u _pM

A_¡ s¡ k„¿ep `pV$u `f gM.

17, 23 36, 23, 17 • h^¡gu k„¿epAp¡ 23 A_¡ 36dp„
17, 23, 36 36, 23, 17 23 _p_u k„¿ep R>¡. dpV¡$ 23_¡
R>¡L$u _pM A_¡ s¡_¡ `pV$u `f 17
`R>u gM.

• R>¡hV¡$ h^¡gu k„¿ep 36 _¡ R>¡L$u
_pM A_¡ s¡ k„¿ep `pV$u `f 23
`R>u gM.

A¡ \ep¡ k„¿ep_p¡ QY$sp¡ ¾$d !
s¡_¡ Ap fus¡ gMuA¡.
17 < 23 < 36

D`f âdpZ¡ _uQ¡_u ÓZ k„¿epAp¡_¡ QY$sp ¾$ddp„ Np¡W$h.
(1) 25, 12, 54 (2) 67, 9, 32 (3) 44, 92, 30

3399

36, 23, 48 Ap k„¿epAp¡_¡ Dsfsp ¾$ddp„ L¡$hu fus¡ Np¡W$hpe s¡ Å¡CA¡.

4488 36, 23, 48 • 36, 23 A_¡ 48_y„ r_funZ
L$fu_¡ kp¥\u dp¡V$u k„¿ep _½$u

L$f. kp¥\u dp¡V$u k„¿ep 48 R>¡.

s¡_¡ `pV$u `f gM.

48, 36 36, 23, 48 • lh¡ h^¡gu k„¿epdp„\u dp¡V$u
48, 36, 23 36, 23, 48 k„¿ep _½$u L$fu_¡ s¡ k„¿ep_¡
R>¡L$u _pM A_¡ s¡ k„¿ep `pV$u
`f 48 `R>u gM.

• R>¡hV¡$ h^¡gu k„¿ep_¡ R>¡L$u s¡
k„¿ep `pV$u `f R>¡ëg¡ gM.

Ap \ep¡ k„¿ep_p¡ Dsfsp¡ ¾$d !

s¡_¡ Ap fus¡ gMuA¡.
48 > 36 > 23

_uQ¡_u k„¿epAp¡_¡ QY$sp A_¡ Dsfsp ¾$ddp„ Np¡W$h.

k„¿ep QY$sp¡ ¾$d Dsfsp¡ ¾$d
26, 19, 47 19 < 26 < 47 47 > 26 > 19
62, 85, 50
32, 9, 13 43 < 60 < 76 < 89 89 > 76 > 60 > 43
43, 76, 89, 60
15, 9, 75, 52

rinL$p¡A¡ k„¿epL$pX®$ (A„L$dp„ A_¡ iåv$dp„) s¥epf L$fhp A_¡
rhÛp\}Ap¡_¡ 3 A\hp 4 L$pX®$ Ap`u_¡ s¡_p `f_u k„¿ep QY$sp
A\hp Dsfsp ¾$ddp„ gMhp L$l¡hy„.

40