mid`kj ^d`kæu] vkxjk–2

lEiknd` e≥M¥izfr;ksfxrk niZ.

© izd`kæd`

izd`kæd`mid`kj ^d`kæu(An ISO 9001 : 2000 Company)

2/11 ,] Lonsæh chek uxj ·ækg flusek ds` lkeus‚] vkxjk–282 002√ksu : 4053333, 2530966, 2531101; √SDl # (0562) 4053330, 4031570E-mail : care@upkar.in, Website : www.upkar.in

czkap vkWfœ`l #4845, vUlkjh jksM] nfj;kxat]ubZ fnY¥h%110 002œ`ksu # 011–23251844/66

ihjeksguh pkSd`] d`nedq`vk∑]iVuk%800 003œ`ksu # 0612–2673340

1-8-1/B, vkj\ vkj\ d`kWEI¥sDl ·lqUnjS;k ikdZ`ds` ikl] eulk ,UD¥so xsV ds` cx¥ eÍ‚]ckx f¥axeiY¥h] gSnjkckn%500 044 ·vk\ iz\‚œ`ksu # 040–66753330

28, pkS|jh ¥su] ';ke cktkj]esV_ks LVsæu ds` fud`V] xsV ua\ 4d`ks¥d`krk%700004 (W.B.)œ`ksu # 033–25551510

B-33, C¥aV LDok;j] d`kuiqjVSDlh LVS≥M ¥su] eoba;k]¥[u˜%226 004 (U.P.)œ`ksu # 0522–4109080

● bl iqLrd` d`ks izd`kfær d`jus eÍ izd`kæd` }kjk iw.Z lko|kuh cjrh xbZ gS] fœ`j Hh fd`lh(qfV ds` f¥, izd`kæd` ftEesnkj ugÓ gksxk\

● bl iqLrd` d`ks vFkok blds` fd`lh vaæ d`ks fcuk ^d`kæd` d`h f¥f[r vuqefr ds`] fd`lh HhÔi%œ`ksVksxzkœ`h] fo»qr-xzkfœ`d`] ;kfU(d`h vFkok vU; Ôi eÍ fd`lh Hh ^d`kj ls mi;ksx ds`f¥, ugÓ Nkik tk ld`rk gS\

● fd`lh Hh ifjokn ds` f¥, U;kf;d` {ks( ds`o¥ vkxjk gh gksxk\

ISBN : 978-93-5013-059-9

ewY; # 80·00 ek((Rs. Eighty Only)

Code No. 1496

eqnzd` # mid`kj ^d`kæu ·f^afVax ;wfuV‚ ckbZ-ikl] vkxjk

tokgj uoksn; fo»k¥;^osæ ijh”k ·d`”k IX‚

d`k g¥ ^'u-i(·Le~fr ij vk|kfjr‚

2014

vuqHkx–I

fgUnhfunsZæ%(i) vkBoÍ iz'u d`k m®j mlds` lkƒ fn, gq,

[k¥h Lƒku ij gh f¥[Í\

(ii) æs" lHh iz'ukÍ ds` lkƒ muds` pkj-pkj m®j fn,gß\ bueÍ ls ds`o¥ ,d` lgh gS\ lgh m®j d`ks bafxr d`hft,\

1. fuEuf¥f[r okD;kÍ eÍ ls d`kSulk okD; v'kq* gS =

(A) vki d`gk∑ tk,∑xs =

(B) d`jks¥ ckx tk˜∑xk\

(C) eßus Hh ogÓ tkuk gS\

(D) Bhd` gS] p¥rs gß\

2. lc¥ gks ;k ˙˙˙˙˙˙˙˙ \ d`kuwu lcds` f¥, leku gS\

mi;qZDr okD; eÍ fjDr-Lƒku ds` f¥, d`k¥s Nis æCnd`k mi;qDr fo¥kse ·'kCn‚ gksxk%

(A) nqcZ¥ (B) ^c¥

(C) fucZ¥ (D) vc¥

3. ‘ckn¥’ d`k i;kZ;okph æCn gS%

(A) t¥n (B) t¥t

(C) t¥f| (D) t¥fuf|

4. ekxZ eÍ vkus ok¥h d`fBukb;kÍ d`k lkeuk d`jks\mi;qZDr okD; eÍ ‘d`fBukb;kÍ’ d`h O;kd`jf.d` d`ksfV·in-Hsn‚ D;k gS =(A) fo'ks". (B) f∂`;k-fo'ks".(C) loZuke (D) laKk

5. d`kSulk 'kCn ‘e|qj’ ls cuh mi;qDr Hkookpd` laKkugÓ gS =(A) e|qjrk (B) ek|q;Z(C) e|qjkbZ (D) ek|q;Zrk

6. ‘ohj ;ks*k j.Hwfe eÍ ^k. ns nsrs gß] ij gkj d`jHkxrs ugÓ\’

mi;qZDr okD; eÍ d`k¥s Nis vaæ ds` f¥, mi;qDreqgkojk gksxk%

(A) ihB ugÓ fn[krs

(B) eq∑g d`h ugÓ [krs

(C) gok ugÓ gks tkrs

(D) ck¥ Hh ck∑d`k ugÓ gksus nsrs

7. gekjs nsæ eÍ vc Hh ‘t;pUn’ gß] tks nq'eukÍ d`hlgk;rk d`jrs gß] rHh rks d`gk tkrk gS ˙˙˙˙˙˙˙˙ .

mi;qZDr okD; ds` fjDr-Lƒku ds` f¥, mi;qDr¥ksd`ksfDr gksxh%

(A) ?j d`k Hsnh ¥ad`k

tokgj uoksn; (IX) 2014 | 3

fæf”r gks tkrs gß\ vPNk LokLF; cgqr dq̀ N gekjh fnup;kZvkSj vPNs [ku-iku ij Hh fuHZj gS] tks ¥ksx lw;ksZn; lsiwoZ tkxrs gß] fu;fer Vg¥us tkrs gß] O;k;ke d`jrs gßvkSj LoPN t¥ ls Luku d`jrs gß] os vf|d`rj ¥Eck vkSjLoLƒ thou ^kIr d`jrs gß\

9. LokLF; d`ks vueks¥ lEif® D;kÍ d`gk gS =

(A) og vewY; gksrk gS

(B) og vPNs thou d`k vk|kj gksrk gS

(C) og bZ'oj d`h nsu gS

(D) og geÍ lq[h cukrk gS

10. vuqPNsn eÍ ‘d`ksjs d`kxt’ ls rkRi;Z gS%

(A) nhu-ghu (B) nqcZ¥

(C) ig¥oku (D) vui

4 | tokgj uoksn; (IX) 2014

vuqHkx–III

xf.rfunsZæ%·^'u 20 ls 54 rd`‚ ^R;sd` ^'u ds` f¥, pkj

lEHkfor m®j fod`Yi fn, x, gß] ftueÍ ls ds`o¥ ,d`lgh gS\ vkid`ks lgh m®j pqud`j mlds` lkƒ fn, x,v”jkad` ij xks¥k cukuk gS%

20. √⎯⎯⎯⎯⎯0·0625 + √⎯⎯⎯0·09 cjkcj gS%(A) 0·28 (B) 0·55(C) 2·8 (D) 0·028

21.729 + 625

729 – 625 d`k eku gS%

(A)126

(B)127

(C) 26 (D) 24

22. lj¥ d`hft,%

31757615625

× 625676

(A) 1 (B)2526

(C)2625

(D)676625

23. 77175 d`ks fd`l NksVh-ls-NksVh la“;k ls xq.k fd`;ktk, fd` ifj.keh la“;k ,d` iw.Z ?u la“;k gks =(A) 5 (B) 15

(C) 9 (D) 45

24. ⎣⎢⎢⎡

⎦⎥⎥⎤( )1 127216

–13

2

d`k eku gS%

(A)76

(B)3649

(C)4936

(D)1312

25. (243)– 15 + [ ](64)

–13

12 d`ks lj¥ d`jus ij ifj.ke

vkrk gS%

(A)78

(B)43

(C)65

(D)56

26. 3x3 + 2y2 + 4xy2 d`k eku tc x = –2 rƒk y = 2gkÍ] gS%(A) 16 (B) 44(C) 52 (D) – 48

27. ;fn (1 – x–2) d`ks (x–1 + 1) ls Hkx fn;k tk,] rksifj.ke gS%

(A)x + 1

x(B)

x – 1x

(C)x

x – 1(D)

xx + 1

28. ;fn a2 + 1a2

= 62 gS] rks 3( )a + 1a d`k |ukRed`eku gS%(A) 8 (B) 16(C) 24 (D) – 8

29. 4x2 + y2 – z2 – 4xy d`k ,d` xq.u[≥M gS%(A) x + y – z (B) 2x + y – z(C) 2x – y – z (D) x + 2y – z

30. 7x2 – 11x – 6 ds` xq.u[≥M gß%(A) (7x – 3), (x + 2)(B) (7x – 3), (x – 2)(C) (7x + 3), (x – 2)(D) (7x + 3), (x + 2)

31. 8x3 – 27y3 ds` xq.u[aMu ls ^kIr gksrk gS%

(A) (2x – 3y) (4x2 + 9y2 + 6xy)

(B) (2x – 3y) (4x2 + 9y2 – 6xy)

(C) (2x – 3y) (4x2 + 9y2 + 12xy)

(D) (2x + 3y) (4x2 + 9y2 + 6xy)

32. ik∑p ∂`ekxr fo"e la“;kvkÍ] ftud`k ;ksxœ`¥ 75 gS]eÍ ls lcls NksVh la“;k gS%(A) 15 (B) 19

(C) 13 (D) 11

33. ;fn x – a

b =

x – ba

, a ≠ b, gS] rks x d`k eku gS%

(A) a – b (B) a + b

(C) b – a (D) a2 – b2

34. ,d` d`ks. vius iwjd` d`ks. d`k ik∑p xquk gS\ d`ks. d`heki gS%(A) 30° (B) 45°(C) 60° (D) 75°

tokgj uoksn; (IX) 2014 | 5

35. vkÎ`fr eÍ] ;fn AB || CD, ∠ABE = 100° vkSj∠BED = 25° gS] rks ∠CDE d`h eki gS%

E

25°

100°

A C

B D

(A) 75° (B) 100°(C) 125° (D) 135°

36. vkÎ`fr eÍ] AB || CD gS\ ;fn ∠ABE = 120° rƒk∠CDE = 140° gS] rks ∠BED d`h eki gS%

B

DC

A

E140°

120°

(A) 90° (B) 100°(C) 120° (D) 140°

37. vkÎ`fr eÍ] ABCD ,d` oxZ gS rƒk Hqtk DC ij,d` leckgq f(Hqt DCE cuk;k x;k gS\ ∠DAE d`heki gS%

CD

E

A B

(A) 60° (B) 45°(C) 30° (D) 15°

38. vkÎ`fr eÍ] ABC ,d` leckgq f(Hqt gS rƒk PQR,d` lef}ckgq f(Hqt gS] ftleÍ PQ = QR gS\ ;fn∠PQR = 50° gS] rks ∠x + ∠y d`k eku gS%

P

C

R

BA

Q

x

y50°

(A) 115° (B) 120°(C) 125° (D) 135°

39. vkÎ`fr eÍ] ABCD ,d` prqHqZt gS] ftleÍ ∠A rƒk∠D ds` lef}Hktd` ∂`eæ# AP rƒk DP gß\ x d`keku gS%

P

A

D C

B

60°

130°

x°

(A) 60° (B) 75°(C) 95° (D) 105°

40. ,d` p∂`h; prqHqZt eÍ] ;fn ∠A = (x + 10)°, ∠B =2(x + 5)° rƒk ∠C = 2(4x – 5)° gkÍ] rks ∠ADCd`h eki gS%

BA

D C

(x + 10

)°

2(x + 5)°

2(4x − 5)°

(A) 80° (B) 100°(C) 130° (D) 150°

41. nh xbZ vkÎ`fr eÍ] O o~® d`k ds`Unz gS rƒk ∠AOB =110° gS] rks ∠ACB d`h eki gS%

BA

O C110°

(A) 90° (B) 75°(C) 55° (D) 35°

42. vkÎ`fr eÍ] O o~® d`k ds`Unz gS rƒk CA ,d` O;kl gS\;fn ∠CAB = 55° rƒk ∠DBC = 30° gS] rks x d`keku gS%

O

D A

BCx

55°

30°

(A) 30° (B) 35°(C) 40° (D) 60°

6 | tokgj uoksn; (IX) 2014

43. vkÎ`fr eÍ] O o~® d`k ds`Unz gS rƒk AC d`ks D rd`c

tokgj uoksn; (IX) 2014 | 7

55. fuEuf¥f[r eÍ ls d`kSu rRo gß =

1. lksuk ·xksYM‚ 2. esƒSu

3. ckWDlkbV 4. vkWDlhtu

(A) 1 vkSj 2 (B) 2 vkSj 4

(C) 1, 2 vkSj 4 (D) 1 vkSj 4

56. uhps nh x;h vfHf∂`;k ds` vuqlkj] nks inkƒZ P vkSjQ d`h vfHf∂`;k }kjk rhljk inkƒZ P2Q cuk%

2P + Q → P2Q

mRikn P2Q ds` fo"; eÍ lgh d`ƒu pqfu,%

(A) bl ^d`kj cuk inkƒZ d`ksbZ rRo gS

(B) mRikn P2Q d`ks ;kSfxd`kÍ eÍ oxhZÎ`r ugÓ fd`;ktk ld`rk

(C) mRikn P2Q nksukÍ P rƒk Q ds` xq.|eksÛ d`ksnækZ,xk

(D) bl ^d`kj cus mRikn d`k la?Vu lnSo fuf'prgksxk

57. uhps fn, x, leqPp;kÍ eÍ ls og leqPp; pqfu,]ftleÍ ,d` rRo] ,d` ;kSfxd` vkSj ,d` feJ. mifLƒrgks%

(A) gkbM_kstu] d`kcZu MkbvkWDlkbM] t¥

(B) e~nk] t¥] vkWDlhtu

(C) flYoj ·pk∑nh‚] xksYM ·lksuk‚] esƒsu

(D) ok;q] t¥] lYŒ;wfjd` vE¥

58. uhps fn, x, ;qXekÍ ij fopkj d`hft,%

1. d`kcZu vkSj lYœ`j

2. ghjk vkSj xzsœ`kbV

3. xzsœ`kbV vkSj cd`feUlVj œq`Y¥jhu

4. xzsœ`kbV vkSj lYœ`j

og d`kSulk ;qXe gS] ftuds` lnL;kÍ ds` jklk;fud` xq.leku gß =

(A) 1 vkSj 2 (B) 2 vkSj 3

(C) 3 vkSj 4 (D) 1 vkSj 4

59. i~Foh ds` ok;qe≥M¥ eÍ d`kcZu vius fd`l Ôi eÍ gksrhgS =

(A) vijÔikÍ

(B) ds`o¥ vkWDlkbMkÍ

(C) vkWDlkbMkÍ vkSj d`kcksZusVkÍ

(D) vkWDlkbMkÍ vkSj gkbM_kstu d`kcksZusVkÍ

60. uhps fn, x, d`ƒukÍ d`k v÷;;u d`hft,%

1. CNG ,d` vknæZ bÛ|u gS] ftleÍ d`kcZu ugÓgksrk\

2. vf|d`kaæ d`kcZu-;kSfxd`kÍ ds` mPp x¥ukad` vkSjDoƒukad` gksrs gß\

3. xzsœ`kbV ds` vfrfjDr d`kcZu ds` lHh vijÔifo»qrΩ ds` dq`pk¥d` gß\

4. vf|d`kaæ d`kcZu-;kSfxd` fo»qrΩ ds` dq`pk¥d` gksrsgß\

d`kcZu ds` fo"; eÍ lgh d`ƒu gß%

(A) 1 vkSj 2 (B) 2 vkSj 3

(C) 3 vkSj 4 (D) 1 vkSj 4

61. uhps fn, x, d`ƒukÍ d`k v÷;;u d`hft,%

1. xzsœ`kbV d`k mi;ksx b¥sDV_ksMkÍ d`ks cukus eÍ fd`;ktkrk gS\

2. cgqr ls d`kVus ok¥s vkStkj xzsœ`kbV ls cuk,tkrs gß\

3. xzsœ`kbV d`k mi;ksx Lusgd` ds` Ôi eÍ gksrk gS\

4. xzsœ`kbV d`ks vklkuh ls ugÓ t¥k;k tk ld`rk\

bueÍ lgh d`ƒu gß%

(A) 1 vkSj 3 (B) 2 vkSj 3

(C) 3 vkSj 4 (D) 1 vkSj 4

62. fuEuf¥f[r eÍ ls d`kSulh |krq HwiiZVh eÍ lclsvf|d` ^pqj ek(k eÍ ikbZ tkrh gS =

(A) vk;ju ·¥ksgk‚ (B) ¯td`

(C) lksfM;e (D) ,s¥qfefu;e

63. uhps fn;k x;k og v;Ld`kÍ d`k d`kSulk lewg gS]ftlls vk;ju ·¥ksgs‚ d`k fuÆd`"Z. lj¥rk ls vkSj¥kH^n Ôi eÍ fd`;k tk ld`rk gS =

(A) xS¥suk vkSj eSXusVkbV

(B) fluckj vkSj gsekVkbV

(C) ckWDlkbV vkSj xS¥suk

(D) eSXusVkbV vkSj gsekVkbV

64. |krqd`ehZ; ^f∂`;kvkÍ ·|krq ds` v;Ld` ls æq* |krq^kIr d`jus d`h ^f∂`;k‚ ds` fuEuf¥f[r pj. gß%

1. fuÆd`f"Zr d`juk

2. ifjÆÎ`r d`juk

3. lanf¥r vkSj filkbZ d`juk

4. lkUnz.

8 | tokgj uoksn; (IX) 2014

bu pj.kÍ d`k ;ƒkƒZ ∂`e gS%(A) 3, 1, 2, 4 (B) 3, 4, 1, 2(C) 3, 1, 4, 2 (D) 1, 4, 2, 3

65. lkekU;r# |krq,∑ ruq vE¥kÍ ls vfHf∂`;k d`jds`gkbM_kstu xSl mRiUu d`jrh gß\ uhps nh xbZ d`kSulh|krq ruq gkbM_ksD¥ksfjd` vE¥ ds` lkƒ vfHf∂`;k ugÓd`jrh =

(A) ,s¥qfefu;e (B) d`kWij ·rk∑ck‚

(C) vk;ju ·¥ksgk‚ (D) eSXuhfæ;e

66. |kfRod` vkWDlkbM ”kjh; vkSj v|kfRod` vkWDlkbMvE¥h; gksrs gß\ uhps fn, x, fd`l vkWDlkbM d`kt¥h; fo¥;u uh¥s f¥Vel d`ks ¥k¥ d`j nsxk =

(A) d`kWij vkWDlkbM

(B) vk;ju vkWDlkbM

(C) eSXuhfæ;e vkWDlkbM

(D) lYœ`j MkbvkWDlkbM

67. uhps fn;k x;k d`kSulk lewg lhes≥V cukus ds` f¥,vko';d` ew¥ la?Vd`kÍ d`k gS =

(A) ,s¥qfeuk] vk;ju vkWDlkbM] ftIle] jsr ·ck¥w‚

(B) dS`fYl;e d`kcksZusV] ,s¥qfeuk] ftIle

(C) jsr ·ck¥w‚] fpd`uh feVΩVh] vk;ju vkWDlkbM]dS`fYl;e d`kcksZusV

(D) vk;ju vkWDlkbM] ,s¥qfeuk] dS`fYl;e d`kcksZusV

68. fuEuf¥f[r eÍ ls tSo-fuEuhd`j.h; inkƒksÛ d`k lewgNk∑fV,%

(A) d`ikl] jsæe ·flYd`‚] uk;¥kWu

(B) d`ikl] js;kWu] lkcqu

(C) jsæe ·flYd`‚] d`ikl] viektZd` ·fMVjtSUV‚

(D) ikWf¥,LVj] js;kWu] lkcqu

69. vR;f|d` ek(k eÍ moZjd`kÍ ,oa ihMÈd`ukfæ;kÍ ds` mi;ksxds` fo"; eÍ uhps fn, x, d`ƒukÍ ij fopkj d`hft,%

1. ;s mi;ksxh vkSj i;kZoj. fgrS"h gß\

2. ;s e~nk d`h moZjrk d`ks uÆV d`j nsrs gß\

3. ;s e~nk ds` mi;ksxh la?Vd`kÍ ij cgqr cqjk ^HkoMk¥rs gß\

4. ;s dq`N le; i'pkrΩ [srkÍ d`ks catj cuk nsrs gß\

bueÍ lgh d`ƒu gß%

(A) ds`o¥ 1 vkSj 2 (B) ds`o¥ 3 vkSj 4

(C) ds`o¥ 1 vkSj 4 (D) 2, 3 vkSj 4

70. I¥kfLVd` ekuo fufeZr inkƒZ gS\ I¥kfLVd`kÍ }kjk nækZ,tkus ok¥s vfr lkekU; xq.|eZ gß%

(A) vf∂`;kæh¥rk] fVd`k˜iu] d`e Hkjh

(B) ˜Æek ds` vPNs pk¥d`] fVd`k˜iu] rU;rk

(C) Haxqjrk] oS»qr pk¥d`rk] d`e Hkjh

(D) vf∂`;kæh¥rk] ped`nkj] ˜Æek vkSj fo»qrΩ ds`vPNs pk¥d`

71. vkids` ikl fp( eÍ nækZ, vuqlkj rhu loZle NMÈÍP, Q vkSj R gß] tks est ij fLƒr gß\ NMÈ P pqEcd`gS] ftld`k fljk I m®j |zqo gS] tcfd` vU; nks NMÈÍpqEcd` gks ld`rh gß vkSj ugÓ Hh gks ld`rh] ijUrq;g ik;k x;k fd` bu rhukÍ NMÈkÍ ds` fljs I, II vkSj IIIijLij ,d`-nwljs d`ks vkd`f"Zr d`jrs gß\ fljkÍ II vkSjIII (vƒok Q vkSj R ) ds` fo"; eÍ lgh fuÆd`"Zpqfu,%

Q

R

P

II

III

I

(A) Q vkSj R ¥ksgs d`h NMÈÍ gß

(B) II vkSj III nf”. |zqo gß

(C) R vkSj Q eÍ ls ds`o¥ ,d` gh pqEcd` gS] ftleÍII vƒok III nf”. |zqo gS

(D) fljk II m®j |zqo vkSj III nf”. |zqo gS vkSjbld`k fo¥kser# Hh gks ld`rk gS

72. fd`lh cPps ds` ikl 6 lseh ¥Eck d`ksbZ NMÈ pqEcd` ABgS\ ;g bls jsr ·ck¥w‚ vkSj d`kWij ·rk∑cs‚ d`h jsru ds`feJ. eÍ œs`jrk gS\ og ;g ^s”. d`jrk gS fd` d`kWijd`h jsru%(A) pqEcd` ds` nksukÍ fljkÍ ij leku Ôi ls vkd`f"Zr

gksrh gß(B) pqEcd` d`h vksj fc¥dq`¥ Hh vkd`f"Zr ugÓ gksrÓ(C) ds`o¥ fljs ‘A’ d`h vksj vkd`f"Zr gksrh gß(D) ds`o¥ fljs ‘B’ d`h vksj vkd`f"Zr gksrh gß

73. fd`lh Nk( ds` ikl ,d` 15 lseh ¥Ech pqEcfd`r ¥ksgsd`h iVΩVh gS\ og bls rhu HkxkÍ] ftud`h ¥EckbZ4 lseh] 5 lseh o 6 lseh eÍ d`kVrk gS vkSj fœ`j ^R;sd`Hkx d`k ijh”. d`jrk gS\ og ;g ^s”. d`jrk gS fd`%(A) ^R;sd` Hkx iw.Z pqEcd` d`h Hk∑fr O;ogkj d`jrk gS

tokgj uoksn; (IX) 2014 | 9

(B) 4 lseh ¥Ecs Hkx us viuk pqEcd`Ro [ks fn;k gSvkSj 6 lseh Hkx iw.Z pqEcd` d`h Hk∑fr O;ogkjd`jrk gS

(C) ds`o¥ 5 lseh ¥Eck Hkx pqEcd` d`h Hk∑frO;ogkj d`jrk gS

(D) 4 lseh ¥Eck Hkx nf”.-|zqo d`h Hk∑fr O;ogkjd`jrk gS] tcfd` 6 lseh ¥Eck Hkx m®j-|zqod`h Hk∑fr O;ogkj d`jrk gS

74. d`ksbZ vk;rkd`kj ckWDl fp( eÍ nækZ, vuqlkj] likVi~ÆB ij rhu fofHUu

10 | tokgj uoksn; (IX) 2014

81. blls d`ksbZ vUrj ugÓ iMÈrk fd` vki fd`lh niZ. ds`lkeus fd`ruh nwjh ij gß= vkid`k ^frfcEc gj fLƒfreÍ lh|k fn[kbZ nsrk gS\ ;g niZ. gks ld`rk gS%

(A) ds`o¥ ler¥ niZ.

(B) ds`o¥ m®¥ niZ.

(C) ;k rks ler¥ vƒok m®¥ niZ.

(D) ;k rks ler¥ vƒok vor¥ niZ.

82. fp( eÍ nækZ, vuqlkj ^d`kæ S1, S2, S3 i~ÆBkÍ ijvkifrr gS\ og i~ÆB d`kSulk/ls gS/gß] ftl/ftu ijvkiru d`ks. ijkorZu d`ks. ds` cjkcj gS =

S1

S2

S3

(A) ds`o¥ S1 (B) S1 vkSj S2(C) S1 vkSj S3 (D) S1, S2, S3

83. fp( eÍ nækZ, vuqlkj nks niZ. X vkSj Y ,d`-nwljs ds`¥EcorΩ j[s gß\ d`ksbZ ̂ d`kæ fd`j. PQ niZ. X ij 30°ds` d`ks. ij vkiru d`jrh gS vkSj fœ`j ijkorZu ds`i'pkrΩ niZ. Y ij vkiru d`jrh gS\ niZ. Y lsijkorZu ds` i'pkrΩ bl fd`j. d`k ijkorZu d`ks. gksxk%

P

XQ

Y

90°

30°

(A) 30° (B) 60°(C) 120° (D) 150°

84. fuEuf¥f[r eÍ ls d`kSulh gk¥ gh eÍ mRiUu gksus ok¥hi;kZoj.h; leL;k,∑ gß =1. vkstksu irZ d`k Ökl 2. oSf'od` ˜Æe.3. xzhu gk˜l ^Hko 4. ckn¥ œ`Vuk

5. Hwd`Ei 6. ck

tokgj uoksn; (IX) 2014 | 11

89. uhps fn, x, d`ƒukÍ d`k v÷;;u d`hft,%

I. ck;ksekl ·tSo ek(k‚ ˜tkZ d`k uohd`j.h;lzksr gS\

II. ck;ksxSl d`k ^eq[ la?Vd` ,sƒSu gS\

III. tc œ`l¥kÍ] ouLifr vifæÆVkÍ vkfn d`kvkWDlhtu d`h vuqifLƒfr eÍ vi?Vu gksrk gS]rks xkscj xSl curh gS\

IV. geÍ vf|d` o~” ¥xkus ds` f¥, ^ksRlkfgr d`jukpkfg,] rkfd` LoPN i;kZoj. vkSj tSfod` bÛ|uHh lqfuf'pr gks\

bueÍ lgh d`ƒukÍ d`k leqPp; gS%

(A) I, II, III (B) II, III, IV

(C) I, III, IV (D) I, II, IV

m®j O;k“;k lfgrvuqHkx–I

fgUnh1. (C) 2. (A) 3. (A) 4. (D) 5. (C)6. (A) 7. (A)

8. eß fNid`j fœ`Ye ns[us x;k%eq>s fgUnh fœ`Ye ns[us d`kcMÈk ækSd` gS\ esjs ?j ls d`jhc 500 ehVj d`h nwjh ij‘tkx~fr’ flusek?j gS\ flusek?j ls ƒksMÈh nwjh ijuxjikf¥d`k d`k [s¥ d`k eSnku gS\ bl eSnku ij eßæke d`ks f∂`ds`V [s¥us tk;k d`jrk gw∑\ [s¥ ds` cgkuseß d`Hh-d`Hh flusek?j eÍ fœ`Ye Hh ns[ f¥;k d`jrkƒk\ fœ`Ye ns[us ds` f¥, d`ksbZ-u-d`ksbZ cgkuk cukd`j eßviuh nknh ls ` 40-50 ¥s f¥;k d`jrk ƒk\ fiN¥so"Z d`k 25 vxLr d`k fnu eq>s gesæk ;kn jgsxk\‘tkx~fr’ flusek?j ls vkfej [ku d`h fœ`Ye ‘¥xku’p¥ jgh ƒh\ esjs fe(kÍ us bl fœ`Ye d`h cMÈh ^æalkd`h ƒh\ eßus bl fœ`Ye d`ks ns[us d`k fu'p; fd`;k\eßus viuh nknhth ls f∂`ds`V ck¥ [jhnus d`k cgkukcukd`j ` 75 ¥s f¥,\ æke d`ks 3 cts eß f∂`ds`VcY¥k ¥sd`j f∂`ds`V [s¥us d`k cgkuk cukd`j ?j lsfud`¥k\ eß cY¥k vius lkƒh ds` ?j ij j[d`jflusek?j igq∑p x;k\ fVd`V ¥sd`j ck¥d`uh eÍ cSBx;k\

fœ`Ye æqÔ gksus ok¥h ƒh\ eß insZ d`h vksj Vd`Vd`h¥xk, gq, ns[ jgk ƒk\ eq>s ugÓ ek¥we iMÈk fd` d`cesjs pkpkth vkSj pkphth vkd`j esjh lhV d`h cx¥d`h lhVkÍ ij cSB x,\ pkphth esjh lhV ds` ikl d`h

lhV ij cSBh ƒÓ\ eß cgqr Mj x;k ƒk] ¥sfd`u esjhpkphth us I;kj ls esjs ˜ij gkƒ œs`jk vkSj g∑lrs gq,fœ`Ye ns[us d`ks d`gk\ e÷;kÕ eÍ pkphth us eq>spkWd`¥sV Hh ¥sd`j nh\ fœ`Ye lekIr gksus ij eß pkpk-th ds̀ lkƒ gh mud`h d`kj eÍ ?j vk;k\ jkr d`ks fMujd`jus ds` ckn eß pkphth ds` ikl x;k\ mUgkÍus eq>lsd`gk fd` fcuk ek∑-cki d`ks crk, d`Hh fœ`Ye ns[us utkuk\ eßus Hh ^. fd`;k fd` fcuk vuqefr ds` eßfœ`Ye ns[us ugÓ tk˜∑xk\ eßus jkr d`ks iwjh ?Vuk d`htkud`kjh viuh ek∑ d`ks nh\ mUgkÍus eq>s ekœ` d`jfn;k\ nknhth ds` lkeus eßus d`ku id`MÈd`j ekœ`hek∑xh\ rc ls vc rd` eß fcuk ek∑-cki d`h vuqefrf¥, fœ`Ye ns[us ugÓ x;k gw∑\

9. (B) 10. (D) 11. (B) 12. (A)

vuqHkx–II

English13. (A) Nehru wants that Indira should not hide

anything when she is in doubt aboutwhat is wrong and what is not.

(B) Bapuji was our leader during the greatFreedom Movement.

(C) Nehru advises Indira to be brave becausebrave persons have no fear and theynever do any shameful deed.

(D) According to Nehru Indira will grow upas a child of light, unafraid andundisturbed if she does not do anythingsecretly even in her private life.

(E) To keep secret means to hide.

14. Last Sunday I with my parents and with mylittle sister went to Naini lake for a picnic. Wehired a taxi from Kathgodam to Nainital.Situated in the Kumaon hills, Naini lake is abeautiful lake. Nainital, a beautiful city issituated around the lake. All the four sides ofthe lake looked very charming. Many men,women and children were roaming around thelake, enjoying the beauty of the lake. Thesewas a big playground on one side of the lake.A football match was being played on theground. There were about 30 boats in thelake. People were enjoying boating. Someyoung boys were swimming near the banks ofthe lake. We also enjoyed boating. Visit ofNaini lake was a good experience.

15. The boys were not in the class.

12 | tokgj uoksn; (IX) 2014

16. Gone the days when you could have left yourdoors unlocked.

17. A beautiful flower was given to her by me.

18. I had reached the station before the train left.

19. Have you seen a one rupee note ?

vuqHkx–III

xf.r

20. (B) √⎯⎯⎯⎯⎯0·0625 + √⎯⎯⎯0·09 = 0·25 + 0·30= 0·55

21. (C)729 + 625

729 – 625 =

27 + 2527 – 25

=522

= 26

22. (A) 15625 o 17576 d`k ?uew¥

2 17576 5 15625

2 8788 5 3125

2 4394 5 625

13 2197 5 125

13 169 5 25

13 5

∴ √⎯⎯⎯⎯3

17576 = 26 √⎯⎯⎯⎯3

15625 = 25

vr# √⎯⎯⎯625 = 25 √⎯⎯⎯676 = 263

1757615625

× 625676

=2625

× 2526

= 1

23. (B) 77175 d`k ?uew¥ Kkr d`jus ds` f¥,] 77175 ds`xq.u[≥M]

3 77175

3 25725

5 8575

5 1715

7 343

7 49

7

77175 = 3 × 3 × 5 × 5 × 7 × 7 × 7⎯⎯⎯⎯⎯ ⎯⎯⎯⎯⎯ ⎯⎯⎯⎯⎯⎯⎯⎯⎯

;g LiÆV gS fd` ;fn 77175 d`ks 3 × 5 }kjk xq.kfd`;k tk,] rks vfUre la“;k iw.Z ?u izkIr gksxh\

24. (B) ⎣⎢⎢⎡

⎦⎥⎥⎤( )1 127216

– 13

2

= ⎣⎢⎢⎡

⎦⎥⎥⎤( )343216

– 13

2

= ⎣⎢⎢⎡

⎦⎥⎥⎤( )216343

13

2

= ⎣⎢⎢⎡

⎦⎥⎥⎤( )67

3 × 13

2

= ( )672

= 3649

25. (D) (243)–

15 + [ ](64)– 13

12

= (35)–

15 + [4–1]

12

= 3–1 + 4–

12

=13 +

12

=2 + 3

6

=56

26. (D) tc x = –2 vkSj y = 2, rks 3x3 + 2y2 + 4xy2

d`k eku]

= 3(–2)3 + 2(2)2 + 4(–2) (2)2

= 3 × (–8) + 2 × 4 – 8 × (2)2

= – 24 + 8 – 32

= – 56 + 8

= – 48

27. (B) (1 – x–2) ÷ (x–1 + 1) =1 – x–2

x–1 + 1

=1 –

1x2

1x + 1

=

x2 – 1x2

x + 1x

=x2 – 1

x (x + 1)

=(x + 1) (x – 1)

x (x + 1)

=x – 1

x

tokgj uoksn; (IX) 2014 | 13

28. (C) ge tkurs gß fd`%

( )a + 1a2

= a2 + 1a2

+ 2

∴ ( )a + 1a2

= 62 + 2

∴ ( )a + 1a2

= 64

∴ a + 1a

= 8

·ds`o¥ |ukRed` eku ¥sus ij‚

∴ 3 ( )a + 1a = 3 × 8= 24

29. (C) 4x2 + y2 – z2 – 4xy

= 4x2 – 4xy + y2 – z2

= (2x – y)2 – z2

= (2x – y + z) (2x – y – z)

vr#] (2x – y – z) ,d` xq.u[≥M gS\

30. (C) 7x2 – 11x – 6 = 7x2 – 14x + 3x – 6= 7x(x – 2) + 3(x – 2)= (x – 2) (7x + 3)

31. (A) 8x3 – 27y3 = (2x)3 – (3y)3

= (2x – 3y) (4x2 + 9y2 + 6xy)

32. (D) ekuk ik∑p ∂`ekxr fo"e la“;k,a x, x + 2, x + 4,x + 6 vkSj x + 8 gß\x + x + 2 + x + 4 + x + 6 + x + 8 = 75⇒ 5x + 20 = 75⇒ 5x = 75 – 20⇒ 5x = 55⇒ x = 11vHhÆV lcls NksVh la“;k 11 gS\

33. (B)x – a

b=

x – ba

⇒ a(x – a) = b(x – b)⇒ ax – a2 = bx – b2

⇒ ax – bx = a2 – b2

⇒ x (a – b) = (a + b) (a – b)⇒ x = a + b

34. (D) ekuk d`ks. x gS\ bld`k iwjd` d`ks. (90° – x)gksxk\

∴ x = 5(90° – x)⇒ x = 5 × 90° – 5x

⇒ 6x = 5 × 90°

⇒ x =5 × 90°

6

⇒ x = 75°

35. (C) CD c

14 | tokgj uoksn; (IX) 2014

37. (D) fp(kuqlkj] ABCD ,d` oxZ vkSj DEC ,d`leckgq Δ gS] rks

∠ADE = ∠ADC + ∠EDC∴ ∠ADE = 90° + 60°∴ ∠ADE = 150°

vkSj AD = DE

∴ Δ ADE ,d` lef}ckgq Δ gS

ekuk ∠DEA = x∴ ∠DAE + ∠DEA + ∠ADE = 180°⇒ x + x + 150° = 180°⇒ 2x + 150° = 180°⇒ 2x = 180° – 150°⇒ 2x = 30°⇒ x = 15°

38. (C) Δ ABC leckgq Δ gS\

∴ ∠A = ∠B = ∠C = 60° i.e., x = 60°

Δ PQR lef}ckgq f(Hqt gS PQ = QR

∠P = ∠R = ∠yy + y + 50° = 180°

2y + 50 = 180°2y = 180° – 50°2y = 130°y = 65°

x + y = 60° + 65°∴ x + y = 125°

39. (C) ABCD ,d` prqHqZt gS

∠A + ∠B + ∠C + ∠D = 360°∠A + 130° + 60° + ∠D = 360°

∠A + ∠D = 360° – 190°∠A + ∠D = 170°

⇒12 ∠A +

12 ∠D = 85°

Δ APD eÍ]

∠ A o ∠ D ds̀ lef}Hktd` AP rƒk DP ∂`eæ# gß]rks%

12 ∠A +

12 ∠D + x = 180°

⇒ 85° + x = 180°⇒ x = 180° – 85°⇒ x = 95°

40. (C) fn;k gS fd` ABCD ,d` p∂`h; prqHqZt gS]

∠A + ∠C = 180°

·foijhr d`ks. lEiwjd` gß‚

x + 10° + 2(4x – 5°) = 180°

⇒ x + 10° + 8x – 10° = 180°

⇒ 9x = 180°

⇒ x = 20°

∠B = 2(x + 5°)

⇒ ∠B = 2(20° + 5°)

⇒ ∠B = 50°

∠B + ∠D = 180°

50° + ∠D = 180°

∠D = 180° – 50°

∠D = 130°

∴ ∠ADC = 130°

41. (C) ge tkurs gß fd` thok }kjk ds`Unz ij cuk;k x;kd`ks.] ifjf| ij cus d`ks. d`k nksxquk gksrk gS\

∴ ∠ACB =12 × 110°

= 55°

42. (B) fn;k gS fd` o~® d`k O;kl CA gS]

∴ ∠ABC = 90°

Δ ABC eÍ]

∠ACB + ∠ABC + ∠BAC = 180°

⇒ x + 90° + 55° = 145°

⇒ x = 180° – 145°

⇒ x = 35°

43. (A) AOBC ,d` prqHqZt gS\

∠ACB = 180° – 82°

∠ACB = 98°

thok AB ds`Unz eÍ ∠ AOB cukrh gS

∠AOB = 2 ∠ACB

∠AOB = 2 × 98°

= 196°

∴ ∠AOB = 360° – 196°

= 164°

tokgj uoksn; (IX) 2014 | 15

44. (A) ∠BOE = 180° – 130°= 50° = ∠OEF

O

D

C B

AF

E130°

75°

∠OED = ∠BEC = 75°∠EDC = ∠OED – ∠OEF

ekuk ∠EDC = y°, y° = 75° – 50°

= 25°

45. (B) o~® d`h ifjf| = 2πr

= 2 × 227

× 35

= 220 lseh

vk;r d`h HqtkvkÍ d`k vuqikr 7 : 4 gS

2(7x + 4x) = 220

∴ 22x = 220∴ x = 10

vr# Hqtk,∑ 70 lseh o 40 lseh gß

46. (B) led`ks. f(Hqt d`h ifjeki = 60 lseh

3x + 4x + 5x = 60

⇒ 12x = 60

⇒ x = 5 lseh

vr# f(Hqt d`h Hqtk,∑ 15 lseh] 20 lseh o 25 lsehgß

f(Hqt d`k ”s(œ`¥ =12 × 15 × 20

= 150 lseh2

47. (B) le¥Ec d`k ”s(œ`¥

=12 ·lekUrj HqtkvkÍ d`k ;ksx‚ × ˜∑pkbZ

=12 (12 + 8) × 6

= 60 lseh2

48. (C) ge tkurs gß fd` ,d` leprqHqZt d`k fod`.Z blsnks cjkcj f(HqtkÍ eÍ ck∑Vrk gS\ f(Hqt d`h Hqtk,∑ 10,10 o 16 lseh gß\

s =10 + 10 + 16

2∴ s = 18vc] s = 18

s – a = 8s – b = 8

vkSj s – c = 2

f(Hqt d`k ”s(œ`¥ = √⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯s(s – a) (s – b) (s – c)

= √⎯⎯⎯⎯⎯⎯⎯⎯⎯18 × 8 × 8 × 2= 48 lseh2

∴ leprqHqZt d`k ”s(œ`¥= 2 × 48

= 96 lseh2

49. (A) oxZ d`k fod`.Z = o~® d`k O;kl

= 7·√⎯ 2 lseh

∴ o~® d`h f(T;k =7

√⎯ 2 lseh

∴ o~® d`k ”s(œ`¥ = πr2

=227

× 7 × 7

2 oxZ lseh

= 77 oxZ lseh50. (D)

15

20 12B

F

G

CD

A

E

iz'ukuqlkj] BC = 3 lseh]

AB = 5 lseh]

BF = 4 lseh

∴?ukH d`k vk;ru = 3 × 5 × 4 ?u lseh

= 60 ?u lseh

51. (B) ekuk cs¥u d`h f(T;k r rƒk ˜∑pkbZ h gks] rks

o∂`i~ÆB = 2πrh = 220

rƒk h = r × 57

⇒ rh =220 × 72 × 22

= 35

∴ r2 =35 × 7

5 = 49

16 | tokgj uoksn; (IX) 2014

∴ r = 7 lseh

∴ h = 5 lseh

∴ vHhÆV vk;ru =227

× 49 × 5 ?u lseh

= 770 ?u lseh

52. (D) cs¥u d`k o∂`i~ÆB = 2πrh

∴ 2π × r × 15 = 660

r =660 × 7

2 × 22 × 15

r = 7 lseh

53. (B) ekuk cs¥u ds` vk|kj d`h f(T;k r rƒk ˜∑pkbZ hgks] rks

cs¥u d`k vk;ru = πr2h

ubZ f(T;k =110100

r = 1·1 r

ubZ ˜∑pkbZ =110100

h = 1·1 h

u;k vk;ru = π(1·1)2 r2 (1·1)h

= π(1·1)3 × r 2h

vk;ru d`h c

tokgj uoksn; fo»k¥;^osæ ijh”k ·d`”k IX‚

d`k g¥ ^'u-i(·Le~fr ij vk|kfjr‚

9th

Publisher : Upkar Prakashan ISBN : 9789350130599 Author : Sampadak MandalPratiyogita Darpan

Type the URL : http://www.kopykitab.com/product/5126

Get this eBook

30%OFF

http://www.kopykitab.com/Jawahar-Navodaya-Vidhyalaya-Pravesh-Pariksha-Solved-Papers-Kaksha-9th-by-Sampadak-Mandal-Pratiyogita-Darpan