/kzokf"kzd. ijh{kk] 2018&19

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1 vof/k & 3?kaVs v/kz /kzokf"kzd ijh{kk] 2018&19 fgunh d{kk & ik poha iw.kk±d & 80 fnukad & ¼lkseokj½ fo kfkhz dk uke oxz funsz k k & 1½ bl iz ui= esa pkj [kam gsaa 2½ lhkh iz uksa ds mrrj fy[kuk vfuok;z gsa 3½ LoPNrk,oa Li"Vrk ij /;ku nsaa 4½ bl iz u i= esa dqy 05 i`"b gsaa i;k tk p dj ysaa iz-1 iz-2 [k.m & v fn, x, vifbr xn~;ka'k dks /;kuiwozd i<+dj iwns x, iz'uksa ds mrrj nhft, & le; dhkh fdlh ds fy, ugha Bgjrk A bl lalkj esa lcls ewy;oku gs & le; A /ku dks rks ifjje djds iqu% dek;k tk ldrk gsa ^fdarq chrk le; dhkh yksvdj ugha vkrka* bfrgkl lk{kh gs ftlus Hkh le; dk lnqi;ksx fd;k] mls thou esa lqyrk izkir gqbza fon~;kfkhz dky esa rks le; dk vksj Hkh vf/kd egrro gsa mlds fy, le; Lo.kZ ls Hkh vf/kd egùoiw.kz gksrk gsa euksjatu ds uke ij le; dks u V djuk Lo;a dks /kks[kk nsuk gsa /ku ds n~okjk le; ugha dek;k tk ldrk A d½ bl lalkj esa lcls vf/kd ewy;oku fdls crk;k x;k gs \ v½ le; dks c½ /ku dks l½ fon~;kfkhz dks [k½ ifjje ls fdls iqu% dek;k tk ldrk gs \ v½ /ku dks c½ dim+s dks l½ edku dks x½ fon~;kfkhz dk le; fdlls vf/kd egùoiw.kz gs \ v½ Lo.kZ ls c½ uke ls l½ euksjatu ls?k½ ftlus le; dk lnqi;ksx fd;k] mls thou esa D;k izkir gqvk \ v½ lq+yrk c½ vlq+yrk l½ iqjldkj M-½ euksjatu ls gekjk D;k u V gksrk gs \ v½ /ku c½ le; l½ LokLF; fueufyf[kr vifbr in~;ka'k dks i<+dj uhps fy[ks iz'uksa ds mrrj fyf[k, &,d cht Fkk x;k cgqr gh xgjkbz esa cks;k A mlh cht ds varj esa Fkk uugk iks/kk lks;k A ml iks/ks dks ean iou us (1/6)

2 iz-3 vkdj ikl txk;k A uugha&uugha cw nksa us fqj ml ij ty cjlk;k A lwjt cksyk] ^^I;kjs iks/ks funzk nwj Hkxkvks A vylkbz vk [ksa [kksyks rqe mb dj ckgj vkvks A** d½ cgqr gh xgjkbz esa D;k cks;k x;k Fkk \ v½ cht c½ irrk l½ Qwy [k½ ml cht ds varj esa D;k lks;k gqvk Fkk \ v½ Qy c½ iks/kk l½ Qwy x½ iks/ks dks ean iou us ikl vkdj D;k fd;k \ v½ #yk;k c½ f[kyk;k l½ txk;k?k½ uugha&uugha cw nksa us iks/ks ij D;k cjlk;k \ v½ kjcr c½ jl l½ ty M-½ lwjt us uugsa iks/ks ls D;k nwj Hkxkus dks dgk \ v½ vkyl c½ I;kl l½ funzk [k.m & c d½ mfpr laca/k tksfm+, A (½ 6=3) i½ jktk & ckx ii½ lalkj & u`i iii½ unh & liz iv½ cxhpk & nqfu;k v½ k=q & rfvuh vi½ lk i & osjh [k½ fueufyf[kr kcnksa ds foykse kcn fyf[k, & (1 3=3) i½ fon~oku ii½ vknku iii½ vknj x½ uhps fn, x, fp=ksa ds fy, mfpr kcn Nk Vdj fyf[k, & (1 3=3) (i) csy] csy (ii) L=h] bl=h (iii) dikv] div (2/6)

3 iz-4 iz-5 iz-6 iz-7 d½ mfpr lozuke kcnksa ksa n~okjk [kkyh LFkku Hkjks & (1 2=2) i½ ftlus ifjje fd;k gksxk] lqy gksxk A ii½ t+jk ns[kks] ckgj [km+k gsa [k½ fueufyf[kr kcnksa ds opu cnfy, & i½ ydm+h ii½ >amk x½ uhps fn, x, kcnksa ls Hkkookpd lakk, k, cukb, & i½ lkq+ ii½ ew[kz (1 2=2) (1 2=2) fueufyf[kr iz'uksa ds mrrj fyf[k, & ¼dksbZ 3½ 3 (2 3=6) d½ dkjd fdls dgrs gsa \ ;s fdrus izdkj ds gksrs gsa \ [k½ fyax fdls dgrs gsa \ nks mnkgj.k fyf[k, A x½ kcn fdls dgrs gsa \ mnkgj.k nhft, A?k½ Hkk kk esa O;kdj.k dk D;k egùo gs \ [k.m & l fueufyf[kr ifbr i xn~;ka'k dks i<+dj iwns x, iz'uksa ds mrrj fyf[k, & (1 5=5) ds ko nl dk Fkk vksj vksj vhkh viuk dke lh[k gh jgk FkkA firk ds,d ckj djds fn[kk nsus ij og lh/kh ydhjksa okys vksj?kqekonkj fmt+kbu mdsj ldrk FkkA vc rd mlus uddk kh dk tks Hkh dke fd;k Fkk muesa ls bu?kafv;ksa dks cukuk gh lcls T+;knk eqf dy FkkA ds ko tkurk Fkk fd,d fnu rks,slk t+#j vk,xk tc og cgqr ckjhd tkfy;k ] eghu&uq+hl csy&cwvs] dey ds Qwy] ygjkrs gq, lk i vksj bbykdj pyrs gq,?kksm+s & ;s lc irfkj ij mdsj ik,xk] Bhd mlh rjg tsls mlds firk cukrs gsaa dbz lky igys] tc og isnk Hkh ugha gqvk Fkk] mlds ekrk&firk xqtjkr ls vkxjk vkdj cl x, FksA ckn kkg vdcj ml odr vkxjs dk fdyk cuok jgs Fks A d½ ds ko fdrus lky dk Fkk \ [k½ ds ko us tks uddk kh dk dke fd;k Fkk muesa ls lcls T+;knk eqf dy dke dksu&lk Fkk \ x½ ds ko ds ekrk&firk xqtjkr ls vkdj dgk cl x, Fks \?k½ firk ds,d ckj djds fn[kk nsus ij og D;k mdsj ldrk Fkk \ M-½ ml odr vkxjs dk fdyk dksu cuok jgs Fks \ fueufyf[kr ifbr in~;ka'k dks i<+dj iwns x, iz'uksa ds lgh mrrj pqudj fyf[k, & (1 5=5) (3/6)

4 iz-8 og ns[kks ek vkt f[kyksusokyk fqj ls vk;k gsa dbz rjg ds lqanj&lqanj u, f[kyksus yk;k gsa gjk&gjk rksrk fiatm+s esa xasn,d isls okyh NksVh&lh eksvj xkm+h gs lj&lj&lj pyus okyha lhvh Hkh gs dbz rjg dh dbz rjg ds lqanj [ksy pkhkh Hkj nsus ls Hkd&Hkd djrh pyus okyh jsy A xqfm+;k Hkh gs cgqr Hkyh&lh ifgus dkuksa esa ckyh NksVk&lk ^Vh lsv* gs NksVs&NksVs gsa yksvk&fkkyh A d½ f[kyksusokyk D;k ysdj vk;k gs\ [k½ gjk rksrk fdlesa gs \ x½ pkhkh nj nsus ls D;k pyus yxrh gs\?k½ xqfm+;k us dkuksa esa D;k iguh gs \ M-½ eksvj xkm+h dslh gs\ v½ lgh fodyi pqudj fyf[k, & d½ frccr ds crrhlosa jktk dk D;k uke Fkk \ i½ yksuiksxkj ii½ lksuxolsu iii½ vdcj [k½ vkfnoklh vkerksj ij fdldh iwtk djrs gsa \ i½ xk; dh ii½ izd`fr dh iii½ Hkxoku dh x½ ckn kkg vdcj ds csvs dk D;k uke Fkk \ i½ djhe ii½ lyhe iii½ vt+he?k½ byk xqtjkr ds fdl ftys esa jgrh Fkh \ i½ lwjr ii½ Hkqt iii½ Hk:p (½ 6=3) (4/6)

5 M-½ fdlh Hkh txg dk fiu dksm fdrus vadksa dk gksrk gs \ i½ 6 ii½ 7 iii½ 8 p½ rfeyukmq esa Q+lyksa ds R;ksgkj dks D;k dgrs gsa \ i½ vks.ke ii½ iksaxy iii½ chgw c½ [kkyh LFkku Hkfj, & (1 3=3) d½ cgqr iqjkus le; esa ds }kjk lans k Hksts tkrs Fks A [k½ ianzg&lksyg lky dh gksrs&gksrs byk d khnkdkjh esa ekfgj gks xbza x½ jke] dks ky;k vksj rkm+dk dfkk ds ik= gsa A l½ fueufyf[kr kcnksa ds okd; cukb, & (1 3=3) d½ le>nkj [k½ Q+ly x½ igjsnkj n½ fueufyf[kr iz uksa ds mrrj,d kcn esa nhft, & (1 3=3) d½ f[kyksusokyk dfork ds dof;=h dk D;k uke gs \ [k½ yksuiksxkj us ym+dh ls fdrus gkfk yach jk[k dh jllh cukus dks dgk \ x½ xqtjkr esa Q+lyksa ds R;ksgkj ds fnu D;k mm+krs gsa \ iz-9 fueufyf[kr y?kqmrrjh; iz uksa ds mrrj nhft, & ¼dksbZ pkj½ (2 4=8) d½ i= esa uke u gksus ls D;k lel;k vk ldrh gs\ [k½ byk dh d khnkdkjh esa [kkl ckr D;k Fkh \ x½ vdcj dks igjsnkj dh n[kyankt+h vpnh D;ksa ugha yxh \?k½ ek ds vykok?kj esa vksj dksu&dksu gsa tks rqegsa eukrs gsa \ M-½ ckgj ns[kus ls le; dk vankt+k D;ksa ugha gks ik jgk Fkk \ p½ ea=h us vius csvs dks kgj D;ksa Hkstk \ iz-10 fueufyf[kr ufyf[kr nh?kzmrrjh; iz uksa ds mrrj nhft, & ¼dksbZ nks½ (3 2=6) d½,sls rhu R;ksgkj rfkk muls tqm+h fdlh,d dh dgkuh ds ckjs esa fy[kks tks cqjkbz ij vpnkbz dh thr ij cy nsrs gsa \ [k½ *tgk pkg] ogk jkg* ikb ls D;k lh[k feyrh gs \ x½ isny gjdkjksa dks fdl&fdl rjg dh fnddrksa dk lkeuk djuk im+rk gs \ [k.m & n iz-11 xzh ekodk k dh tkudkjh nsrs gq, vius nknk th dks i= fyf[k, A (5) vfkok iqlrd e xokus gsrq izdk kd dks i= fyf[k, A iz-12 fueufyf[kr esa ls fdlh,d fo"k; ij vuqpnsn fyf[k, A (5) d½ o`{kkjksi.k [k½ le; fu;kstu x½ [ksy vksj ge (5/6)

6 iz-13 fn, x, fp= dks ns[kdj rhu&pkj okd; fyf[k, & (3) (6/6)

f}rh; lesfvo vlslesav 20011&12 fo"k; & fgunh le;% 1?k.Vk d{kk & igyh iw.kkzad & 60

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