Mathematics. Maths. a Directions (Q.1-20) : fueufyf[kr ç'uks esa ç'u fpà

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1 Mthemtics Directions (Q.1-20) : fueufyf[kr ç'uks es ç'u fpà ¼\½ ds LFkku ij D;k vuqekfur eku vkuk pkfg,\ 1. ( dk %) ( dk 22.04%) =? () 289 (b) 296 (c) 278 (d) 221 (e) dk 14.95% dk 19.9% =? () 116 (b) 146 (c) 165 (d) 176 (e) ? = 240 () 105 (b) 173 (c) 113 (d) 234 (e) =? () 6500 (b) 5900 (c) 4300 (d) 3900 (e) dk 54.94% =? () 373 (b) 445 (c) 507 (d) 302 (e) /17 199/13 16/91=? () 650 (b) 700 (c) 770 (d) 820 (e) =? () 380 (b) 420 (c) 350 (d) 410 (e) =? () 2025 (b) 2300 (c) 1925 (d) 2200 (e) =? () 21 (b) 6 (c) 12 (d) 18 (e) =? () 576 (b) 591 (c) 564 (d) 553 (e) = (2)^? () 5 (b) 6 (c) 7 (d) 8 (e) /4 of? +2/3 of 465=60% of 450 () -160 (b) 160/3 (c) -160/3 (d) -160/9 (e) 165/ =? () (b) (c) (d) (e) % of % of 450 =? + 43% of 400 () 125 (b) 216 (c) 343 (d) 120 (e) % of % % of 400 =? () 845 (b) 485 (c) 458 (d) 480 (e) =? () 6500 (b) 6000 (c) 6300 (d) 5700 (e) =? () 680 (b) 610 (c) 925 (d) 435 (e) % of % of =? () 450 (b) 320 (c) 210 (d) 280 (e) (21.98) ² (25.02) ² + (13.03) ² =? () 28 (b) 125 (c) 6 (d) 65 (e) =? () 110 (b) 90 (c) 200 (d) 160 (e) 125 Directions (Q.21-40): fueufyf[kr ç'uks es] nks lehdj.k I vksj II fn, x, gs- vkidks nksuks lehdj.kks dks gy djuk gksxk vksj mùkj nsuk gksxk : () ;fn x < y (c) ;fn x y (b) ;fn x > y (d) ;fn x y (e) ;fn x vksj y ds chp lc/k fu/kkzfjr ugh fd;k tk ldrk 21. I. x² 9x + 18 = 0 II. 5y² 22y + 24 = I. 6x² + 11x + 5 = 0 II. 2y² + 5y + 3 = I. x² + 10x + 24 = 0 II. y² 625=0 24. I. 10x² + 11x + 1 = 0 II. 15y² + 8y + 1 = 0 Mths 1

2 25. I.15x² 11x + 2 = 0 II. 10y² 9y + 2 = x² 9x + 10 = 0 y² 18y + 72 = x² + 11x + 12 = 0 y² 14y + 48 = x² 11x + 30 = 0 y² 4y 12 = x² 32x 21 = 0 8y² + 6y 5 = x² + 48x 9 = 0 y² 2y 15 = x 2 = 4, 3y 2 4y 4 = x 2 5x 6 = 0 2y 2 13y + 20 = x 2 5x = 0 2y 2 + 7y 4 = x 2 + 5x + 2= 0 2y y + 45 = x 2 7x 6 = 0 5y y + 12 = x² + 8x + 3 = 0 4y² 29y + 45 = x² 23x + 21 = 0 y² + 42y = x² 26x + 21 = 0 2y² 17y + 21 = x² 21x = 0 y² 33y = x² 31x = 0 y² 28y = 0 II.(41-75) Study the following informtion crefully nd nswer the questions tht follow: Percentgewise distribution of techers who tech six different subjects Totl Number of Techers = bfrgkl es efgyk vksj iq:"kks dk vuqikr 1 : 1 gs] ;fn 1 f'k{kd tks Hkwxksy i<+krs gs og 3 efgyk;s gsa vksj bzfrgkl vksj ck;ykwth ds izfr'kr,d leku gs] rks crkbz;s Hkwxksy] bfrgkl vksj ck;ykwth es fdrus iq:"k gks xsa bues ls d bz ugè 43. bzfrgkl vksj HkkSfrdh ds dqy Vhpj vksj dseslvªh vksj ck;ykwth ds dqy Vhpj dk vrj fdruk gksxk? bues ls d bz ugè f'k{kd jlk;u es efgyk;s gs] vksj xf.kr es 50% gs] rks jlk;u ds iq:"k Vhpj vksj efgyk;s f'k{kd dk vuqikr D;k gksxk? 44. ;fn : : : : 6 5. bues ls d bz ugè 45. ;fn jlk;u ds Vhpj 50% ls cm+k fn;k tk;s ] vksj xf.kr ds Vhpj dks 25% de dj fn;k tk;s ] rks crkb;s fd jlk;u vksj xf.kr es fdrus f'k{kd gksxsa Direction (66-70) Refer to the Line Grph nd nswer the given questions. Number of Shirts of X brnd sold in Shop A nd Shop B in 6 different months f'k{kd HkkSfrdh es efgyk, gs] rks crkb;s dh HkkSfrd es efgyk;s Hkqxksy es dqy f'k{kd dk fdruk izfr'kr gs A 41. ;fn % 2. 42% % 5. bues ls d bz ugè. 46. B ds }kjk csph xbz 'kvz fdruk izfr'kr cm+h gs] uocj ls nhlecj rda 1. 50% 2. 40% 3. 10% 4. 60% 5. bues ls d bz ugè 47. vdvwcj] Qjojh vksj ekpz rfkk tuojh] uocj vksj fnlecj es csph xbz 'kvz dk nksuks deifu;ks dk vurj fdruk gksxk? Mths 2

3 A ds }kj vdvwcj] uocj vksj fnlcj es csph xbz dqy 'kvz B }kjk bzlh efgus es csph xbz 'kvz ls fdruk izfr'kr ;k T;knk gsa 1. 25/4% 2. 45/4 % 3. 55/4 % 4. 75/4 % 5. None of the Above 49. A ds }kjk vdvwcj] uocj] fnlecj] ekpz vksj Qjojh es csph xbz 'kvz dk vkslr D;k gksxk? B ds }kjk flrecj es csph xbz 'kvz 20% de gs] vdvwcj es csps x;s 'kvz ls vksj B }kjk vizsy es csph 'kvz ekpz ls 20% T;knk gs] rks crkbz;s dh flrecj vksj vizsy es csph xbz 'kvz dk vuqikr D;k gksxk? 1. 2:9 2. 1:5 3. 4:9 4. 2:7 5. 8:5 Directions (51-55): A person purchsed 5 Gdgets from shop nd sold them online. Given below is the dt showing cost price, selling price nd profit/loss percentge. 51. ysivki ds Ø; eqy; VscysV ds foø; eqy; dk yxhkx fdruk izfr'kr gs? () 138% (b) 182% (c) 142% (d) 154% (e) 186% 52. ;fn VscysV ij 12% gkfu dh otg 12% ykhk gksrk gs] rks crkbz;s u;s foø; eqy; iqjkus foø; eqy; ls fdruk T;knk gs? () 5216 (b) 5396 (c) 5336 (d) 5316 (e) bues ls d bz ugè 53. fmthvy dsejk ds ykhk dk izfr'kr fdruk de ;k T;knk gs ysivkwi ds ykhk ds izfr'k ls? () 50% more (c) 33.67% more (b) 33.34% less (d) 50% less (e) 150% less 54. LekVZ okwp vksj LekVZ Qksu ds ykhk dk vuqikr D;k gksxk? () 5 : 3 (b) 3: 2 (c) 3 : 5 (d) 2 : 5 (e) bues ls d bz ugè 55. dqy fdruk ykhk ;k gkfu gqbz? () 22.12% profit (b) 12.12% profit (c) 14.14% profit (d) 33.12% loss (e) 15.15% loss Directions (56-60): Study the tble nd nswer the given questions. Dt relted to the number of employees in five different compnies in December 2012 Note: (I) Employees of the given compnies cn be ctegorised only in three types: Science grdutes, Commerce grdutes nd Arts grdutes (II) A few vlues re missing in the tble (indicted ). A cndidte is expected to clculte the missing vlue, if it is required to nswer the given question, on the bsis of the given dt nd informtion. 56. dyk ds Lukrd vksj fokku ds Lukrd ds chp dk vurj D;k gksxk? () 87 (b) 89 (c) 77 (d) 81 (e) deiuh Q ds dyk ds Lukrd vksj dkwelz ds Lukrd dk vkslr 312 gs rks crkbz;s Q es dqy fdrus dezpkjh gksxs? () 920 (b) 960 (c) 1120 (d) 1040 (e) diuh M ds dkwelz Lukrd vksj dyk Lukrd dezpkfj dk vuqikr 10 : 7 gs] rks M diuh es dqy fdrus dyk ds dezpkfj gksxs? () 294 (b) 266 (c) 280 (d) 308 (e) ;fn diuh N ds 2012 fnlcj ls 2013 fnlcj es 20% dezpkfj c<+ tkrs gs] vksj ;fn 20% diuh N ds fnlecj 2013 ds fokku ds Lukrd gs rks crkb;s fd diuh N es fnlecj 2013 es fokku ds dqy fdrus dezpkjh gksxs? Mths 3

4 () 224 (b) 266 (c) 294 (d) 252 (e) ;fn diuh P ds dezpkjh O ds dezpkjh dk rhu xquk gs] vksj ;fn diuh P ds dyk Lukrd vksj diuh O ds Hkh dyk Lukrd dk () 1200 (b) 1440 (c) 720 (d) 900 (e) 1080 Direction : The following tble gives the percentge of popultion of Five Sttes UP, MP, Rjsthn, Bihr nd Punjb which re below poverty line nd lso the rtio of mle to femle mong them : Study the tble nd nswer the questions bsed on it 65. ;fn jktlfkku es xjhch js[kk ds uhps dqy 35 fefy;u tul[;k gs] rks jktlfkku es xjhch js[kk ds mij iq:"kks dh l[;k fdruh gksxh? 1) million 2) 36 million 3) million 4) million 5) bues vrj ls d bz 180 ugè gs] rks crkbz;s fd O es dqy fdrus dezpk Directions (Q. 1-5): Study the following grph crefully to nswer these questions. 61. ;w-ih- es xjhch ds Åij dh iq:"k tul[;k D;k gksxh ;fn efgyk tul[;k xjhch js[kk ds uhps ;w-ih es 18 feyh;u gs? 1) 29.6 million 2) 39.6 million 3) 49.6 million 4) 19.6 million 5) bues ls d bz ugè 62. ;fn jktlfkku es dqy 20 feyh;u tul[;k gs] rks crkb;s fd jktlfkku es xjhch js[kk ds uhps fdruh efgyk;s gksxh? 1) 5 million 2) 6 million 3) 3 million 4) 4 million 5) bues ls d bz ugè 63. ;fn fcgkj es xjhch js[kk ds Åij iq:"kks dh l[;k 21 feyh;u gs] rks fcgkj es dqy tul[;k D;k gksxh? 1) 48 million 2) million 3) 75 million 4) million 5) bues ls d bz ugè 64. ;fn e/izns'k es xjhch js[kk ds uhps iq:"kks tul[;k 15 fefy;u gs] vksj itkc es 18 fefy;u gs] rks crkb;s fd e/;izns'k vksj itkc es dqy tul[;k dk vuqikr D;k gksxk? 1) 40 : 27 2) 30 : 27 3) 50 : 27 4) 27 : 50 5) bues ls d bz ugè es xqtjkr dh tul[;k xqtjkr dh lhkh lky dh tul[;k dk fdruk izfr'kr gksxh? ) 8.26 b) 7.26 c) 8.32 d) 7.82 e) bues ls d bz ugè ,2002,2003 es jktlfkku dh dqy tul[;k vksj xqtjkr ds 2005, 2006, 2007 dh dqy tul[;k dk vuqikr D;k gksxk? ) 27:53 b) 54:29 c) 29:54 d) 53:27 e) bues ls d bz ugè 68. fdl izns'k fd tul[;k finys lky dh rqyuk es lcls T;knk gs? ) Gujrt-2003 b) Gujrt-2002 c) Rjsthn-2004 d) Rjsthn-2005 e) bues ls d bz ugè ls 2004 rd xqtjkr dh tul[; fdruh izfr'kr c<+h? ) 16 1/3 b) 16 2/3 c) 18 2/3 d) 18 1/3 e) bues ls d bz ugè 70. jktlfkku dh tul[;k fn, x, lkyks dh tul[;k dk vkslr yxhkx D;k gksxk? ) 65 lkhs b) 50 lkhs c) 48 lkhs d) 58 lkhs e) 52 lkhs I.Study the following grph crefully to nswer the given questions Mths 4

5 71. ;fn N vksj P dsunz ds ym+ds vksj ym+fd;ks dk vuqikr 2 : 3 gs] rks crkbz;s dh N vksj P ds ym+dks vkslr D;k gksxk? bues ls d bz ugè 72. M, O vksj Q es vlqy gksus okys dqy fdrus Nk= gksxs? bues ls d bz ugè 73. dsunz N ds ikl gksus okys ym+ds vksj Qsy gkus okyh ym+fd;ks dk vuqikr D;k gksxk] ;fn N ds ym+fd;kw vksj ym+dks dk vuqikr 16 : 11 gs] 1.121:24 2.7: : :37 5. bues ls d bz ugè 74. Q ds ikl gksus okys vksj M ds Qsy gksus okys Nk=ks dk vurj D;k gksxk? bues ls d bz ugè 75. fdl dsunz ij nwljs lcls de Nk= Qsy gq,? 1.M 2.P 3.O 4.Q 5.N Direction (12-16)- Study the following grph crefully to nswer the given questions 76. P vksj R,d dke dks pkyw djrs gs dqn fnu ckn U Hkh 'kkfey gks tkrk gs] vc lhkh feydj bzl dke dks 10 fnu es iwjk dj ysrs gs] ;fn mudks 600 :i;s bl dke ds fy, fn, tk;s rks crkbz;s dh U dk fgllkk fdruk gksxk? A. Rs.360 B. Rs.385 C. Rs.24 D. cn t be determined 77. Q vksj S,d lkfk 5 fnu dke djrs gs] cps gq, dke dks M nks vksj T;knk fnu es iwjk dj ysrk gs ;fn mudks bzl dke ds fy, A. 200, 250, 300 B. 300, 200, 250 C. 600, 400, 200 D. 600, 400, 500 E. Bues ls d bz ugè 78. ;fn L fd {kerk P dh {kerk ls 25% T;knk gs L vdsyk dke dks pkyw djrk gs ] vksj mlds ckn P dke [kre gksus ds ikp fnu igys vk tkrk gs] rks crkbz;s fd L us fdrus fnu dke fd;k gksxk? A. 9 B. 11 C. 10 D. 25 E R fdlh dke dks pkyw djrk gs vksj dqn le; ckn NksM+ nsrk gs] dsoy 25% dke gh iwjk gksrk gs] vksj Z vk tkrk gs] vksj og 25 es dke dks iwjk dj nsrk gs] rks crkb;s fd R vksj Z,d lkfk bzl dke dks fdrus fnu es iwjk dj nsxsa A. 6 B. 8 C. 10 D. 12 E T vksj V dke pkyw djrs gsa vksj rhu fnu ds ckn Z vk tkrk gs ] og bzl iwjs dke dks 3 fnu es iwjk dj ldrk gs] rk crkbz;s fd og rhuks feydj bzl dke dks fdrus fnu es iwjk dj ysxsa Direction: (61-65) Find the next number , 35, 20, 45,? A.32 B.21 C.10 D.20 E.bues ls d bz ugè Mths 5

6 82. 24, 10, 13,?, 36 A.8 B.10.5 C.12 D.14.5 E ,81,651,?, A.3562 B.3850 C.3911 D.4215 E.bues ls d bz ugè , 115, 224,?, 2708 A.716 B.769 C.679 D.767 E.bues ls d bz ugè , 22, 42, 78,? A.112 B.105 C.118 D.125 E.bues ls d bz ugè ? A. 438 B. 448 C. 488 D. 498 E. bues ls d bz ugè ? A B C D E. bues ls d bz ugè ? A. 342 B. 366 C. 396 D. 291 E. bues ls d bz ugè ? A. 112 B. 132C. 115 D. 117 E. bues ? A. 5 B. 3 C. 2 D. 1 E. bues ls d bz ugè ? 12 A. 2 B. 4 C. 6 D. 7 E. bues ls d bz ugè ? 3525 A. 716 B. 736 C. 746 D. 696 E. bues ls d bz ugè ? A. 245 B. 235 C. 275 D. 255 E. bues ls d bz ugè ? A B C D E. bues ls d bz ugè ? A. 457 B. 592 ls d bz ugè C. 509 D. 529 E. bues ls d bz ugè ? A. 123 B. 103 C. 153 D. 113 E. bues ls d bz ugè ? A. 222 B. 232 C. 242 D. 252 E. bues ls d bz ugè Directions(91-95) : In these questions, number series is given. Only one number is wrong which does not fit in the series. Find out the wrong number , 19, 36, 93, 356 A.19 B. 36 C.93 D.356 E. bues ls d bz ugè , 14, 26, 62,143 A.12 B.14 C.26 D.62 E , 183, 141, 181, 100, 265 A.183 B.141 C.181 D.100 E. bues ls d bz ugè , 10, 23, 73, 297 A.5 B.10 C.73 D.297 E. bues ls d bz ugè , 13, 25, 62,100 A.10 B.13 C.62 D.100 E. bues ls d bz ugè Mths 6

7 1. Solution B Mths 7

8 Mths 8

9 13x² 32x 21 = 0 x = 3, y² + 6y 5 = 0 y = -1.25, B. X < Y Explntion: 2x² 9x + 10 = 0 x = 2.5, 2 y² 18y + 72 = 0 y = 12, B. X < Y Explntion: 2x² + 11x + 12 = 0 x = 4, 1.5 y² 14y + 48 = 0 y = 6, E. X = Y or reltion cnnot be estblished Explntion: x² 11x + 30 = 0 x = 5, 6 y² 4y 12 = 0 y = 6, E. X = Y or reltion cnnot be estblished Explntion: 30. E. X = Y or reltion cnnot be estblished Explntion: 17x² + 48x 9 = 0 x = -3, 0.1 y² 2y 15 = 0 y = 5, E) If X=Y or cnnot be estblished Explntion: x 2 = 4 Gives x = 2, -2 3y 2 4y 4 = 0 3y 2 6y + 2y 4 = 0 Gives y = -2/3, 2 Put on number line -2-2/3 2 When y = 2, y x When y = -2/3, y > x(-2) nd y < x(2) So no reltion 32. B) If X < Y Explntion: 6x 2 5x 6 = 0 6x 2 9x + 4x 6 = 0 Gives x = -2/3, 3/2 2y 2 13y + 20 = 0 2y 2 8y 5y +20 = 0 Gives y = 4, 5/2 Put on number line -2/3 3/2 5/ E) If X=Y or cnnot be estblished Expln tion: 2x 2 5x = 0 x(2x-5) = 0 Gives x = 0, 5/2 3y 2 7y 6 = 0 3y 2 9y + 2y 6 = 0 Gives y = -2/3, 3 Put on number line -2/3 0 5/ A) If X > Y Explntion: 2x 2 + 5x + 2= 0 2x 2 + 4x + x + 2= 0 Gives x = -1/2, -2 2y y + 45 = 0 2y y + 9y + 45 = 0 Gives y= -10/2, -9/2 Put on number line -10/2-9/2-2 -1/2 35. C) If X Y Mths 9

10 Explntion: 5x 2 7x 6 = 0 5x 2 10x + 3x 6 = 0 Gives x = -3/5, 2 5y y + 12 = 0 5y y + 3y + 12 = 0 Gives y = -4, -3/5 Put on number line -4-3/ x² + 8x + 3 = 0 x = -0.5, y² 29y + 45 = 0 y = 2.25, x² 23x + 21 = 0 x = 10.5, 2 y² + 42y = 0 y = -16, x² 26x + 21 = 0 x = 4.2, 1 2y² 17y + 21 = 0 y = 7, x² 21x = 0 x = 13, 8 y² 33y = 0 y = 13, x² 31x = 0 x = 15, 16 y² 28y = 0 y = 13, Answer 1. 57% Number of techers in Physics = 17/100 * 1800 = 306 Number of mle techers in Physics = 7/9 * 306 = 238 Number of techers in Geogrphy = 23/100 * 1800 = 414 % = 238 / 414 * 100 = 57% 42. Answer Number of mle techers who tech Geogrphy = 2/3 * 23/100 * 1800 = 276 Number of mle techers who tech History = /2 * 27/100 * 1800 = 243 % of femle techers who tech Biology = % of femle techers who tech Biology i.e 50% Therefore Number of mle techers who tech Biology = 50/100 * 12/100 * 1800 = 108 Totl = = Answer Totl number of techer who tech History nd Physics = 44% of 1800 Totl number of techer who tech Chemistry nd Biology = 25% of 1800 Difference = 19% of 1800 = Answer : 6 Number of mle techers who tech Chemistry = 2/3 * 13/100 * 1800 =156 Number of femle techers who tech Biotechnology = 1/2 * 8/100 * 1800 =72 Rtio = 156 : 72 = 13 : Answer Totl number of techer who tech Chemistry = = 351 Totl number of techer who tech Mths = 3/4 * 8% of 1800 = 108 Totl number of Chemistry nd Mths techers together = = 459 I.(66-70) 46. Answer 4. 60% = = 120 = (120/200)*100 = 60% 47. Answer Shirts in October, Februry & Mrch = 1700 Shirts in Jnury, November & December = 690 Difference = = Answer 4. 75/4 % Required Percentge = [( )/640]*100 = [120/640]*100 = 75/4% 49. Answer Avg = = 1030 = 1030/5 = Answer 5. 8:5 Shirts sold in Shop B in September = 20% of 120 = 24 = = 96 Shirts sold in Shop B in April = 20% of 50 = 10 = = 60 Rtio = 96 : 60 = 8:5 51. Mths 10

11 Q59. Q60. Q52. Q53. Q54 Q55. Q ; Femle popultion below poverty line = 18 million 5 : 6 = x : 18 x = 15 Totl popultion (below poverty line) = = 33mn Since 20% popultion in up is below poverty line Therefore 80% popultion will be bove poverty line 20 : 40 = 33 : y (Mle popultion bove poverty line) y = : 4 = 33 : y Mle popultion bove poverty line = (132 * 3)/10 = 39.6 million 62. 3; Totl popultion (below poverty line) = 20 35% = 7 million Femle below poverty line = 7/7 * 3 = 3 million 63. 3; Since 7 rtio = 21 1 rtio = 3 Totl ( 7 + 8) 3 = 45 million 60 % = 45 1 = 45/60 * 10 million 64. 3; 50 : ; 66. Q Q Mths 11

12 Answer N:675 =>Boys = 675*3/5 = 405 P:650 =>Boys = 650*3/5 = 390 Avg = /2 = Answer M =768*25%= 192 O= 460*15% = 69 Q = 320*25% = 80 Totl = Answer 1.121: => 400:275 => 16:11 = G:B G:400*12% =48 B:275*88% = :48 = 121: Answer 1.48 Q psse d => 75% of 320 = 240 M filed => 192 Difference = = Answer 4.Q M=192 N=81 O=69 P=130 Q= Answer C. Rs.240 Efficiency of P = 4% Efficiency of R = 2% [(4+2)*10] = 60% The remining work ws done by U = 40%. 40% of 600 = Answer D. 600, 400, 500 Q s 5 dys work = 50% S s 5 dys work = 33.33% M s 2 dys work = 16.66% [100- ( )] Rtio of work of Q, S nd M = 3: 2: 1 Q s totl shre = Rs S s totl shre = Rs M s totl shre = Rs Q s one dy s wge = Rs.600 S s one dy s wge = Rs.400 M s one dy s wge = Rs Answer B. 11 Efficiency (L : P) = 5 : 4 Number of dys(l : P) = 4x : 5x = 4x : 25 Number of dys required by L to finish the work lone = 4x = 4 x 5 = 20. L nd P work together for lst 5 dys = 5 x 9 = 45% Efficiency of L = 5% nd P s efficiency = 4% No. of dys tken by L to complete 55% work = 55/5 = 11dys 79. Answer E. 20 Efficiency of R = (100/50) = 2% Rest work = 75% Efficiency of Z = 75/25 = 3% Combined efficiency of R nd Z = 5% Number of dys required by R nd Z to work together = 100/5 = 20 dys. 80. Answer C.4 dys Efficiency of T nd V = = 16.66% Work done in 3 dys = 3 x = 50% Rest work done by T, V nd Z = 50/50 = 1 dy Work cn be completed in 4 dys. 81. Answer C * 2 = * 3 = * 5 = * 7 = Answer D *0.5 2 = 10 10*1 + 3 = 13 13*1.5 5 = *2 + 7 = Answer C * = * = * = * = Answer C *1+5 = *2-6 = *3+7 = *4-8 = Answer C = 22 Mths 12

13 = = = Answer A ^2-10^2, -8^ Answer C * * 2 4 * Answer D * = 11; 11 * = 46; 46 * = Answer D = 4 * * 1 34 = 11 * * = 34 * * Answer A / 6-10 / 5-8 / Answer D. 7 *2 2 /2 + 2 * Answer D. 696 (5 * 1) + (1 * 9) = 14 (14 * 2) + (2 * 9) = Answer B * 3 1 = 8 8 * = * 3 5 = Answer D / = / 2 2 = / = Answer C * 32 = * 16 = * 8 = Answer B * 1² = * 2² = * 3² = Answer A ³ 12 = 717 8³ + 10 = 522 7³ 8 = Answer B * 1 + (1 * 7) = 19 19* 2 (2 * 6) = * 3 + (3 * 5) = * 4 (4 * 4) = 356 Correct Number: Answer E = = = = 142 Correct Number: Answer C *1 = *2 = *3 = *4 = *5 = 265 Correct Number: Answer A.5 8 * = * = * = * = 297 Correct Number: Answer C * 1² = * 2² = * 3² = 52 Correct Number: 52 Mths 13

14 Resoning Directions (1-5): fueufyf[kr tkudkjh dk lko/kkuhiwozd v/;;u dhft;s vksj ç'uks ds mùkj nhft;s: ;gk lkr c Dl vfkkzr- A] B] C] D] E] F vksj G gs- lhkh c Dl vyx&vyx jx ds gs vfkkzryky] dkys] uhys] ihys] Øhe] csxuh vksj ukjxh ijurq vko';d ugh blh Øe es gks- lhkh c Dl mij ls uhps dh vksj O;ofLFkr fd;s x, gs- c Dl D] ihys jx ds c Dl ds Bhd mij flfkr gs- rhu ls vf/kd c Dl] Øhe jx ds c Dl vksj ukjxh jx ds c Dl ds e/; flfkr gs- ;gk nks c Dl c Dl B vksj c Dl E ds e/; flfkr gs] c Dl E tksfd yky jx dk c Dl gs- ;gk dsoy,d c Dl] c Dl E vksj c Dl G ds e/; flfkr gs- ;gk rhu c Dl c Dl G vksj c Dl A ds e/; flfkr gs] c Dl A tksfd dkys jx dk c Dl gs- ;gk nks c Dl] c Dl A vksj c Dl C ds e/; flfkr gs] c Dl C csxuh jx dk c Dl gs- ukjxh jx dk c Dl] c Dl G ds Bhd mij j[kk gs- rhu ls vf/kd c Dl] ihys jx ds c Dl vksj Øhe jx ds c Dl ds e/; flfkr gs- 1. fueufyf[kr es ls dksu lk c Dl 'kh"kz ij j[kk gs\ () A (c) C (b) B (d) D (e) E 2- c Dl B fdl jx dk gs\ ¼½ csxuh ¼b½ dkys ¼c½ uhyk ¼d½ Øhe ¼e½ v js t 3- fueufyf[kr es ls dksu lk c Dl ihys jx dk gs\ ¼½ D ¼b½ E ¼c½ F ¼d½ G ¼e½ A 4- fdrus c Dl] D vksj uhys jx ds c Dl ds e/; flfkr gs\ ¼½ pkj ¼b½ rhu ¼c½ nks ¼d½,d ¼e½ dksbz ugh- 5-,d fuf'pr vk/kkj ij ;fn B dk lc/k uhy jx ds c Dl ls gs vksj E dk lc/k ihys jx ds c Dl ls gs] rks A fdl ls lecf/kr gksxk\ ¼½ ukjxh jx ds c Dl ¼b½ csxuh jx ds c Dl ¼c½ ihys jx ds c Dl ¼d½ Øhe jx ds c Dl ¼e½ bues ls dksbz ugh Resoning Directions (6-10) : fueufyf[kr tkudkjh dk lko/kkuhiwozd v/;;u dhft;s vksj ç'uks ds mùkj nhft;s: ;gk lkr O;fä vfkkzr P] Q] R] S] T] U vksj V gs- bu lhkh dk vyx&vyx O;olk; gs vfkkzr MsfVLV] dsfelv] QkekZflLV] odhy] fqftf'k;u] vkfdzvsdv vksj bthfu;j ;g lhkh lirkg¼leku lirkg ds½ lkseokj ls jfookj dks efnj tkrs gs ijurq vko';d ugh blh Øe es tkrs gks- çr;sd fnu dsoy,d O;fä efnj tkrk gsog O;fä tks bftfu;j gs] U ds igys efnj tkrk gs ijurq xq#okj ds ckn tkrk gs- nks ls vf/kd O;fä] bftfu;j vksj R ds e/; efnj tkrs gs- og O;fä tks MsfVLV gs] vkfdzvsdv ds Bhd igys efnj tkrk gs- og O;fä tks odhy gs] Q ds Bhd igys efnj tkrk gs- V] exyokj dks efnj ugh tkrk gs- T] xq#okj dks efnj tkrk gs- dsoy,d O;fä T vksj fqftf'k;u ds e/; tkrk gs- P] fqftf'k;u ds Bhd ckn efnj tkrk gs- dsoy rhu O;fä P vksj QkekZflLV ds e/; efnj tkrs gs- dsoy nks O;fä QkekZflLV vksj U ds e/; efnj tkrs gs- 6- fueufyf[kr es ls dksu dsfelv gs\ ¼½ R ¼b½ S ¼c½ P ¼d½ T ¼e½ V 7- fn, x, ikp fodyiks es ls pkj,d fuf'pr vk/kkj ij,d lewg dk fuekz.k djrs gs- bues ls dksu ml lewg ls lecf/kr ugh gs\ ¼½ R&exyokj ¼b½ T&lkseokj ¼c½ Q&jfookj ¼d½ P&'kqØokj ¼e½ U&'kfuokj 8- fueufyf[kr es ls D;k S ds lunhkz es lr; gs\ ¼½ S] R ds Bhd ckn efnj tkrk gs- ¼b½ S] QkekZflLV gs- ¼c½ dsoy nks O;fä S vksj R ds e/; efnj tkrs gs- ¼d½ fn, x, lhkh dfku lr; gs ¼e½ S] jfookj dks efnj tkrk gs- 9- T dk fueu es ls dksu lk O;olk; gs\ ¼½ QkekZflLV ¼b½ MsfVLV ¼c½ vkfdzvsdv ¼d½ odhy ¼e½ bftfu;j 10- nh x;h O;oLFkk ds vk/kkj ij Q dk lc/k QkekZflLV ls gs vksj blh çdkj P dk lc/k bftfu;j ls gs] blh vk/kkj ij] U fdl ls lecf/kr gksxk\ ¼½ og O;fä tks dsfelv gs- 14

15 ¼b½ og O;fä tks odhy gs- ¼c½ og O;fä tks QkekZflLV gs- ¼d½ og O;fä tks MsfVLV gs- ¼e½ bues ls dksbz ugh- Directions ¼11&15½: fueufyf[kr tkudkjh dk lko/kkuhiwozd v/;;u dhft;s vksj ç'uks ds mùkj nhft;s: ckjg O;fä nks lekukrj js[kk es çr;sd es N: O;fä gs vksj çr;sd vkluu csbus okys O;fä ds e/; leku nwjh gs- js[kk 1 es A] B] C] D] E vksj F csbs gs vksj bu lhkh dk eq[k nf{k.k dh vksj flfkr gsjs[kk&2 es P] Q] R] S] T vksj V csbs gs vksj bu lhkh dk eq[k mùkj dh vksj gs- bl çdkj] nh x;h csbus dh O;oLFkk es,d js[kk es csbs O;fä;ks dk eq[k nwljh js[kk es csbs O;fä;ks ds eq[k dh vksj gs- P] T ds ck;s ls rhljs LFkku ij flfkr gs- u rks P u gh T] js[kk ds vfre Nksj ij flfkr gs- A] E ds nk;s ls nqljs LFkku ij flfkr gs- u rks A u gh E dk eq[k T ;k P dh vksj gs- A] js[kk ds vfre Nksj ij ugh csbk gs- R dk eq[k A dh vksj ugh fg;k R] js[kk ds vfre Nksj ij ugh csbk gs- dsoy,d O;fä F vksj C ds e/; csbs gs- u rks F u gh C dk eq[k T dh vksj ugh gs- C] js[kk ds vfre Nksj ij ugh csbk gs- dsoy,d O;fä V vksj Q ds e/; csbk gs- F] B dk fudvre imkslh ugh gs- A dk eq[k V dh vksj ugh gs- 11- fdrus O;fä V ds nk;s csbs gs\ ¼½,d ¼b½ nks ¼c½ rhu ¼d½ dksbz ugh ¼e½ ikp 12 V dk lc/k B ls gs blh çdkj Q dk lc/k C ls gs- leku isvuz es P dk lc/k fueu es ls fdl ls gksxk\ ¼½ F ¼b½ A ¼c½ D ¼d½ E ¼e½ bues ls dksbz ugh 13- V ds lunhkz es fueu es ls D;k lr; gs\ ¼½ V dk eq[k A dh vksj gs ¼b½ T] V dk fudvre imkslh ugh gs- ¼c½ C dk eq[k V ds ck;s ls nqljs LFkku ij csbs O;fä dh vksj gs ¼d½ V js[kk ds,d vfre Nksj ij csbk gs ¼e½ R] V ds nk;s ls rhljs LFkku ij csbk gs 14- fueufyf[kr es ls dksu js[kk ds vfre Nksj ij csbk gs\ ¼½ D] F ¼b½ V] S ¼c½ Q] S ¼d½ B] D ¼e½ bues ls dksbz ugh 15- fueufyf[kr es ls fdldk eq[k B dh vksj gs\ Resoning () V (c) Q (b) S (d) R (e) T Directions ¼16&20½: fueufyf[kr tkudkjh dk lko/kkuhiwozd v/;;u dhft;s vksj ç'uks ds mùkj nhft;s: lkr Vhpj A,B,C,D,E,F vksj G lkr vyx&vyx fo"k; dks HkkSfrd] vfkz'kkl=] Hkwxksy] thofokku] jlk;u] xf.kr vksj bzfrgkl i<+krs gs] bzudh okf"kzd lsyjh dks rhu Hkkxks es ckwvk x;k gs Øe'k% 3-5 yk[k] 6-8 yk[k vksj yk[k rhu yksxks dh lsyjh yk[k ds chp es gs] F, 12 yk[k :i;s dekrk gs] B vksj G, F ls de dekrs gs] D dsoy 1 Vhpj ls T;knk dekrk gs] tks vfkz'kkl= i<+krk gs]tks Vhpj jlk;u i<+krk gs] og Hkwxksy i<+kus okys ls T;knk i<+krk gs] vksj nksuks dh dqy lsyjh 15 yk[k gs],d gh lsyjh jst es ] 2 yksx 3 ls 5 yk[k lsyjh jst es gs] tks Vhpj bzfrgkl i<+krk gs] og F ls de dekrk gs] vksj ftofokku ls T;knk dekrk gs] F HkkSfrd 'kkl= ugh i<+krk gs] G vksj A rfkk B vksj E dh Øe'k% okf"kzd vk; 17 yk[k vksj 19 yk[k gs D vksj C dh okf"kzd vk; dk vurj 2 yk[k :- gsa 16. fn, x, O;oLFkk es F ckw;ksyksth ls lcf/kr gs] vksj G Hkwxksy ls blh vuqlkj A fdlls lcf/kr gs? A. Mths B. History C. Physics D. Economics E. Chemistry 17. tho fokku vksj HkkSfrd i<+kus okys dh okf"kzd vk; dk vurj D;k gksxk? A. 4 lkh B. 3 lkh C. 6 lkh D. 2 lkh E. 5 lkh 18. dksu lk Vhpj vksj lctsdv dk dkechus'ku lgh gs? A. 7 Chemistry B. 10 History C. 3 Economics D.11 Biology E. 5 Geogrphy 19. bues ls fdl lsyjh D ls nqxwuh gsa A. E B. G C. C D. A E. Other thn those given s options 20. Which of the following represents the sum of the highest nnul income in ech slb? A. 25 lkh B. 20 lkh C. 24 lkh D. 23 lkh E. Other thn those given s options Directions (21-25): Study the following informtion crefully nd nswer the questions 15

16 given below: 8 yksx Q,R, S, T, V, W, Y, Z,d o`rrkdkj Vscy ij csbs gs] mrrkj dh rjq ewwg djds] bues ls rhu iq:"k vksj ikwp efgyk,s gs] dksbz Hkh iq:"k,d lkfk ugh csbs gs] V mlds iruh ds nwljs nkw, ij csbk gs] S, V ds rhljs nk, csbk gs] W mlds ifr Z ds nwljs nk, csbh gqbz gs] Z, V dh iruh dk im+kslh ugh gs] T iq:"k gs] vksj V, Y dk im+kslh ugh gs] R, Q ds nwljs nk, ij csbk gqvk gs A 21. ;fn R ds ck, ls xhuk tk;s rks crkb;s R vksj S ds chp es fdrus yksx csbs gs? () Three (c) Two (b) Four (d) One (e) Five 22. Z dk lc/k Y ls vksj V dk lc/k W ls gs blh Øe es T dk lc/k fdlls gksxk? () R (b) V (c) Q (d) S (e) None of these. 23. V ds rqjr nk;s dksu csbk gs? () S (c) Q (e) None of these (b) R (d) Z 24. Z ds rhljs ck, dksu csbk gs? () Q (c) S (e) None of these (b) V (d) W 25. S ds foijhr dksu csbk gs? () T (b) R (c) Q (d) Y (e) All re true Directions (26-30): Red the following informtion crefully to nswer the questions given below. lkr yksx M, N, O, P, Q, R vksj S lkr ekys okyh edku es jgrs gs] lcls uhps okyh ekyk u- 1 vksj lcls Åij okyk ucj 7 gs] vksj ;g lhkh vyx&vyx jkt; gs] gfj;k.kk] e/;izns'k] rsyxkuk] ;w-ih-] egkjk"vª] jktlfkku vksj itkc gs] ijrq t:jh ugh dh ;g blh Øe es gks O ds Åij rhu ls T;knk yksx jgrs gs] O vksj p ds chp es dsoy,d O;fDr csbk gqvk gs] dsoy 3 O;fDr e/;izns'k vksj itkc ds chp es gs] itkc okyk fo"ke ucj okys ekys ij jgrk gs ijrq e/;izns'k ds uhps O itkc ls ugh gs] M ;w-ih- ls gs] vksj lcls Åij okys ekys ij jgrk gs] M vksj jktlfkku ds chp es rhu ls T;knk yksx jgrs gs] Q vksj R ds chp es dsoy,d O;fDr csbk gqvk R tks rsyxkuk ls gs] rhu e/;izns'k ls ugh gs] tks gfj;k.kk ls gs] og egkjk"vª ls,d efty Åij jgrk gs] ijrq rqjr Åij ugh gs] u rks Resoning P vksj u gh R egkjk"vª ls gs] N, S ds Åij jgrk gs] ijrq fo"ke l[;k okys ekys ija 26. bues ls dksu jktlfkku ds rqjr Åij gs? () M (b) The one who belongs to Telngn. (c) The one who belongs to Punjb. (d) P (e) both c nd d 27. bues ls dksu gfj;k.kk ls gs? () Q (c) M (e) None of these (b) N (d) R 28. ikwpoh efty ij dksu jgrk gs? () R (c) N (e) None of these (b) P (d) M 29. bues ls egkjk"vª ls dksu gs () S (c) N (e) None of these (b) P (d) O 30. nwljh efty ij dksu jgrk gs? () P (c) N (e) R (b) S (d) O Directions (31-35): uhps fn, x, ç'uks es pkj dfku fn, x, gs ftudk vuqlj.k pkj fu"d"kz l[;k I] II] vksj III }kjk fd;k tkrk gs- Kkr rf;ks ls fhkuu gksus ij Hkh vkidks dfku dks lr; ekuuk gslhkh fu"d"kks Z dk lko/kkuhiwozd v/;;u dhft;s vksj fu/kkzfjr dhft;s fd dksu lk fu"d"kz Kkr rf;ks ls fhkuu gksus ij Hkh dfku dk rdziw.kz :i ls vuqlj.k djrk gs- 31- dfku: dqn ykbv LVkj gs- lhkh LVkj isu gsdksbz isu lu ugh gs-dqn lu ewu gsfu"d"kz: I- dqn LVkj lu ugh gs- II- lhkh LVkj ds lu gksus dh lhkkouk gs- III- lhkh LVkj ds isu gksus dh lhkkouk gs- ¼½ dsoy I vuqlj.k djrk gs ¼b½ dsoy III vuqlj.k djrk gs ¼c½ dsoy II vksj III vuqlj.k djrk gs ¼d½ lhkh I] II vksj III vuqlj.k djrk gs ¼e½ bues ls dksbz ugh 32- dfku : lhkh ps;j isv gs-dksbz ps;j ist ugh gslhkh jsm Cyw gsfu"d"kz : I- dqn isv jsm gs- II- dksbz ist isv ugh gs- III- lhkh jsm ds Cyw gksus dh lhkkouk gs- ¼½ dsoy I vksj II vuqlj.k djrk gs? 16

17 ¼b½ dsoy II vksj III vuqlj.k djrk gs ¼c½ dsoy I vksj III vuqlj.k djrk gs ¼d½ dksbz Hkh vuqlj.k ugh djrk gs ¼e½ ;k rks I ;k II vuqlj.k djrk gs 33- dfku : lhkh Vh d Qh gs- lhkh d Qh fmªd gs lhkh fdrkcks dksbz d Qh feyd ugh gs- lhkh feyd okvj gsfu"d"kz : I- lhkh d Qh ds Vh gksus dh lhkkouk gs- () Only III II- lhkh Vh ds fmªd gksus dh lhkkouk gs- (c) Only II III- dqn okvj Vh ugh gs- ¼½ dksbz Hkh vuqlj.k ugh djrk gs ¼b½ dsoy I vuqlj.k djrk gs ¼c½ dsoy II vuqlj.k djrk gs ¼d½ dsoy I nd III vuqlj.k djrk gs ¼e½ dsoy II nd III vuqlj.k djrk gs 34- dfku : dksbz ekml jsv ugh gs- dqn jsv dkå gslhkh dkå fm;j gs- dksbz fm;j M x ugh gsfu"d"kz : () Only II I- dqn jsv M x ugh gs- II- dksbz M x (c) dkå I nd ugh II gs- III- dksbz ekml M x ugh gs- (e) only I, II nd IV ¼½ dksbz vuqlj.k ugh djrk gs 39. dfku % lhkh Nike, Reebok gsa ¼b½ dsoy I vuqlj.k djrk gs lhkh Reebok, Pum gsa ¼c½ dsoy I vksj II vuqlj.k djrk gs dksbz Pum, SKechers ugh gsa ¼d½ dsoy I vksj III vuqlj.k djrk gs dqn Skechers,Wildcrft gsa ¼e½ dsoy II vksj III vuqlj.k djrk gs fu"d"kz % 35- dfku : dksbz Nikem, Skechers ugh gsa dqn u,mk vkxjk gs- lhkh Pum, wildcrft ugh gsa lhkh vkxjk esjb gs- dqn Wikdcrft, Reebok ugh gsa lhkh u,mk dkuiwj gs- dqn reebok, skechers gsa dksbz u,mk iq.ks ugh gs- () Only I nd II (c) Only III nd IV (d) Only II nd III I- dqn esjb iq.ks gs- II- lhkh dkuiwj ds iq.ks gksus dh lhkkouk gs- III- lhkh u,mk ds dkuiwj gksus dh lhkkouk gs- ¼½ dksbz vuqlj.k ugh djrk gs ¼c½ dsoy II vuqlj.k djrk gs ¼e½ dsoy II vksj III vuqlj.k djrk gs 36. dqn?kvs lsd.m gs] dqn lsd.m feuv gs] lhkh feuv jkm.m gs Conclusions fu"d"kz dqn jkm.m?k.vs ugh gsa dqn lsd.m jkm.m gs A dqn jkm.m?k.vs gks ldrs gsa dqn?k.vs feuv gs A () Only I (b) Only II (c) Only I nd IV (d) None follows (e) All follows 37. dfku % dksbz fdrkc] dkih ugh gs A dksbz dkih jftlvj ugh gs dqn jftlvj Qkbys gsa fu"d"kz % dqn Qkby dkih ugh gs A ds QkbZy gksus lehkkouk gsa lhkh QkbZy dkih gks ldrh gsa dksbz fdrkc jftlvj ugh gsa (b) Only I (d) III nd IV (e) All follow 38. dfku % dqn fyuksok eksvks gsa dksbz MI eksvks ugh gsa dqn MI, Micromx gsa fu"d"kz de ls de dqn Motto, MI gsa dqn Micrmx, Motto gsa dqn Lenovo, MI ugh gsa dqn Micormx, Lenove ugh gsa (b) Only III nd II (d) All of these (b) None of these (e) Only III 40. dfku % lhkh ifg;s csx gs] dqn csx czhqdsl ¼b½ dsoy gsa I vuqlj.k djrk gs ¼d½ dsoy dqn III vuqlj.k czhqdsl djrk uhyk gs gs ] lhkh uhyk] Cysd gsa fu"d"kz % lhkh uhyk ds ifg;s gksus lhkkouk gsa dqn dksy dh csx gksus dh lhkkouk gsa dqn czhqdsl] Cysd gsa dqn czhqdsl igh;s ugh gs () Only IV (c) Only II ` (e) None of the bove 41- dfku: dqn d Qh Vh gs- dqn yseu d Qh gsdqn 'ksd Vh gs - (b) Only I nd II (d) Only III or IV Resoning 17

18 I- lhkh yseu 'ksd gs II- dksbz 'ksd yseu ugh gs 42- dfku: dsoy VªS'k ls V gsdqn esy buc Dl ugh gsdqn buc Dl ls V ugh gsfu"d"kz : I- lhkh lsv buc Dl gks ldrs gs II- dqn VªS'k ds buc Dl u gksus dh lhkkouk gs- 43- dfku: dsoy eq cbz fnyyh gsdksbz eqcbz dksydkrk ugh gs dsoy psuubz eqcbz gs I- dqn fnyyh dksydkrk gs II- dksbz fnyyh dksydkrk ugh gs 44- dfku : dqn Vh okvj gs - dsoy d Qh okvj gs dqn okvj isilh gs I- dqn isilh Vh ugh gs- II- dqn Vh ds d Qh gksus dh lehkkouk gs 45- dfku : dqn iizy czkmu gs dqn Cyw xzhu gs dksbz iizy xzhu ugh gs lhkh Cyw czkmu gs I- dqn Cyw iizy ugh gs II- dqn czkmu Cyw gs 46- dfku : lhkh d Qh yseu gs dksbz yseu pk; ugh gs dqn pk; CySd gs - I- dksbz d Qh pk; ugh gs II- dqn CySd d Qh ugh gs 47- dfku : dksbz IykV Vªh ugh gs lhkh Vªh ÝwV gs lhkh ÝwV gcz gs I- dqn Vªh gcz gs II- lhkh gcz IykV gks ldrs gs 48- dfku : dqn b;j efk gslhkh Ms b;j gs Resoning dksbz yhi efk ugh gs I- dqn efk Ms gs II- dksbz efk Ms ugh gs 49- dfku: lhkh xzhu jsm gs lhkh jsm CySd gs lhkh CySd Cyw gs I- dqn jsm Cyw gks ldrs gs II- lhkh Cyw xzhu gs 50- dfku: dqn ykbu jks gs dqn jks d ye gs dksbz ykbu xzkq ugh gs I- dqn ykbu xzkq ugh gs II- dksbz d ye xzkq ugh gs 51- dfku: dqn jke Dohu gs dksbz bfxy'k Dohu ugh gs lhkh jke ';ke gs I- dqn jke ds bfxy'k u gksus dh lhkkouk gs II- dqn bfxy'k jke gs 52- dfku : de ls de dqn ruuq eerk gs dqn uohu t; gs dksbz uohu eerk ugh gs I- dqn uohu ruuq ugh gs II- dqn t; eerk ugh gs 53- dfku : dqn gkml ft;keh gs dqn ysv mcj gs dksbz ft;keh Åcj ugh gs I- lhkh gkml ysv gs II- dksbz ysv gkml ugh gs 54- dfku : dksbz,yvkbzlh ukckmz ugh gs dqn,lchvkbz vkbzchih,l gs lhkh,lchvkbz ukckmz gs I- lhkh vkbzchih,l ukckmz gs II- dqn vkbchih,l ds,ykbzlh gksus dh lhkkouk Fkh 55- dfku : dqn ;syks v js t gs 18

19 dqn Cyw CySd gs dqn v jst CySd gs I- dqn ;syks ds CySd u gksus dh lhkkouk gs II- lhkh ;syks CySd gs Directions ¼56&57½ : uhps fn, x, çr;sd ç'u es ] lhkh dfkuks dks lr; ekuuk gs- Kkr dhft;s fd fn, x, fu"d"kz l[;k I] II] III vksj IV es ls dksu fuf'pr :i ls lr; gs vksj vkidk mùkj blh ds vuqlkj gksxk- 56- dfku : M > U > L N; L Y > A I. M Y II. M > N III. N Y IV. M A ¼½ dsoy ;k rks II ;k III lr; gs- ¼b½ dsoy IV nd either I or III lr; gs- ¼c½ dsoy IV lr; gs- ¼d½ dsoy II lr; gsgs- 57- dfku: J A > D = E; L < A < M I. M < J II. J L III. M J IV. E >M ¼½ dsoy II lr; gs- ¼b½ dsoy I vksj III lr; gs- ¼c½ dksbz Hkh lr; ugh gs- ¼d½ dsoy II vksj IV lr; gs- ¼e½ dsoy I vksj II lr; gs- Directions: ¼58&75½: uhps fn, x, ç'uks es ¼e½ dsoy III lr; ] $, #, vksj % dk ç;ksx fofhkuu vfkks Z dks n'kkzus ds fy, fd;k x;k gs- ^P $ Q* dk vfkz ^P] Q ls NksVk ugh gs*- ^P Q* dk vfkz ^P] Q ls u rks cm+k gs u gh cjkcj gs*- ^P # Q* dk vfkz ^P] Q ls u rks NksVk gs u gh cjkcj gs*- ^P % Q* dk vfkz ^P] Q ls cm+k ugh gs*- Q* dk vfkz ^P] Q ls u rks cm+k gs u gh NksVk gs*- vc] uhps fn, çr;sd ç'u es fn, x, dfku dks lr; ekuuk gs vksj Kkr djuk gs fd pkj fu"d"kks Z I] II] III vksj IV es ls dksu lk fuf'pr :i ls lr; gs vksj vkidk mùkj vkids vuqlkj gh gksxk- 58- dfku : R # J, J $ D, K, K % T I. T # D II. D III. R # K IV. J $ T ¼½ dsoy ;k rks I ;k II lr; gs Resoning ¼b½ dsoy III lr; gs ¼c½ dsoy III vksj IV lr; gs ¼d½ dsoy ;k rks I ;k II vksj III lr; gs ¼e½ bues ls dksbz ugh 59- dfku : T % R, R $ M, D, D H I. D % R II. H # R III. T M IV. T % D ¼½ dsoy I lr; gs ¼b½ dsoy I vksj IV lr; gs ¼c½ dsoy I vksj III lr; gs ¼d½ dsoy II vksj IV lr; gs ¼e½ bues ls dksbz ugh 60- dfku : B, B # N, N $ R, R K I. K # B II. R B III. M $ R IV. N M ¼½ dsoy I vksj III lr; gs ¼b½ dsoy I vksj II lr; gs ¼c½ dsoy II vksj IV lr; gs ¼d½ dsoy II] III vksj IV lr; gs ¼e½ bues ls dksbz ugh 61. dfku: G F>A=C<D, A=B E<H fu"d"kz: I.A G II.D>E 62. dfku: G F>A=C<D, A=B E<H fu"d"kz: I.E<G II.H C 63. dfku: P Q<S=T, O>S R fu"d"kz: I.P<O II.Q R 64. dfku: X=Y V<Z, Y<W U fu"d"kz: I.U>V II.X<W 65. dfku: M O>N>Q, R P>N fu"d"kz: I.R M II.Q>P 66. dfku : P<Q<R=U, U T<S, T W I. U>W II. U=W 67. dfku : A = D <G < J >K > F; B < A; K = H I. H>F II. A > J 68. dfku : C = K < X < L > P R; Q C; P = M I. Q L II. L > R 69. dfku : Y U = W < E; W N I. Y < E II. Y N 70. dfku : P < S Q < K = O < R Y; M = Q C I. Y< M II. C < R 71. dfku : A>K>D>L, M C D, L>Q I. C < K II. A > M 72. dfku : T M E, E<O, A>E>S I. T > O II. S < O 73. dfku : G C>U, P=W U, W<N<T I. G > T II. U < N 74. dfku : R>Q>J>D, M C J 19

20 I. D > M II. M D 75. dfku : Z V>U, R=E<U, E>M<O I. Z > E II. U < O Directions (76-80) : bu ç'uks es ] fofhkuu rroks ds e/; fn, x, dfkuks es lc/k n'kkz;k x;k gs- bu dfkuks ds uhps dqn fu"d"kz fn, x, gs - mùkj nhft;s ¼½ ;fn dsoy fu"kd"kz I lr; gs- ¼b½ ;fn dsoy fu"kd"kz II lr; gs- ¼c½ ;fn ;k rks fu"d"kz I ;k II lr; gs- ¼d½ ;fn u rks fu"d"kz I u gh II lr; gs- ¼e½ ;fn nksuks fu"d"kz I vksj II lr; gs- 76. dfku: A>B,D E,C F=G,B C=D fu"d"kz: I.B G II.E G 77. dfku:: T>S Q,T U=V,H T fu"d"kz: I.U H II.S<H 78. dfku: :A>B L,R>B=H fu"d"kz: I.A<L II.R>L 79. dfku: P>K=L,P S<Q,T>K fu"d"kz: I.Q>K II.Q<T 80. dfku: P<H,V S>H,N V fu"d"kz: I.N P II.S>P Direction(81-83) Red the following informtion crefully to nswer the following questions funs'k % & 6 yksx P,Q,R, S, T vksj U,d ifjokj ds lnl; gs] nks firk] rhu HkkbZ vksj,d ekrk gs] R, U dh cgu gs ] T, Q ds ifr dk HkkbZ gs] S, P dk firk gs vksj U dk nknkth gs A 81. Who is the mother in the fmily? ifjokj dh ekrk dksu gs? ) P b) R c) T d) S e) None of these 82. How mny mles re there in the fmily? ifjokj es fdrus iq:"k lnl; gs A ) one b) two c) three d) four e) None of these 83. How is U relted to T? U dk T ls D;k lc/k gsa ) son b) dughter c) niece d) nephew e) None of these Directions (84-85): fueufyf[kr tkudkjh dk lko/kkuhiwozd v/;;u dhft;s vksj ç'uks ds mùkj nhft;s: A] B] C] D] E] F] G] H vksj I iksy gs- C] B ls 2 ehvj iwoz es flfkr gs- A] B ls 1 ehvj mùkj es flfkr Resoning gs vksj H] A ls 2 ehvj nf{k.k es flfkr gs- G] H ds 1 ehvj if'pe es flfkr gs tcfd D] G ds 3 ehvj iwoz es flfkr gs- F] D ds 2 ehvj mùkj es flfkr gs- I] B vksj C ds Bhd e/; flfkr gs tcfd E] H vksj D ds Bhd e/; flfkr gs- 84- E vksj G ds chp dh nwjh fdruh gs\ ¼½ 1 ehvj ¼b½ 3 ehvj ¼c½ 2 ehvj ¼d½ 5 ehvj ¼e½ bues ls dksbz ugh 85- E vksj I dh chp dh nwjh fdruh gs\ ¼½ 1 ehvj ¼b½ 2 ehvj ¼c½ 3 ehvj ¼d½ 4 ehvj ¼e½ 5 ehvj 86- G] iksy F ds lunhkz es fdl fn'kk es flfkr gs\ ¼½ mùkj&if'pe ¼b½ mùkj ¼c½ nf{k.k&iwoz ¼d½ nf{k.k ¼e½ bues ls dksbz ugh 87. R] S dh lkl gs tksfd Q dh fllvj&bu&y gs- P] Q ds firk gs] tksfd T dk,dyksrk HkkbZ gs- P dk fookg R ls gqvk gs- rks R fdl çdkj T ls lecf/kr gs\ ¼½ iruh ¼b½ ekrk ¼c½ vkvh ¼d½ lkl ¼e½ bues ls dksbz ugh 88- E] A dk iq= gs- D] B dk iq= gs- E dk fookg C ls gqvk gs- C] B dh iq=h gs- rks D fdl çdkj E ls lecf/kr gs\ ¼½ HkkbZ ¼b½ vdy ¼c½ llqj ¼d½ cznj bu y ¼e½ bues ls dksbz ugh 89- A ++ B dk vfkz gs A] B dk iq= gs; A B dk vfkz gs A] B dh iruh gs; A B dk vfkz A] B dk HkkbZ gs; A B dk vfkz gs A] B dh ekrk gs vksj A ¾ B dk vfkz gs A] B dh cgu gs rks P + R Q dk vfkz D;k gksxk\ ¼½ Q] P dk HkkbZ gs ¼b½ Q] P dk iq= gs ¼c½ Q] P dk vdy gs ¼d½ Q] P dk firk gs 90- euh"kh 20 fdeh mùkj dh vksj pyrh gs vksj fqj og vius nk;s eqmrh gs vksj 30 fdeh pyrh gs- og fqj ls nk;s eqmrh gs vksj 35 fdeh pyrh gs vksj fqj ck;s eqmrh gs vksj 15 fdeh pyrh gs- og fqj ls ck;s eqmrh gs vksj 15 fdeh pyrh gs- og vius vkjfehkd fcnq ls fdl fn'kk es vksj fdrus fdeh nwj gs\ ¼½ 15 fdeh] if'pe ¼b½ 30 fdeh] iwoz ¼c½ 30 fdeh] if'pe ¼d½ 55 fdeh] iwoz ¼e½ 45 fdeh] iwoz 91- fot; iwoz dh vksj pykuk 'kq: djrk gs

21 ehvj pyus ds ckn] og vius nk;s eqm+rk gs vksj vksj fqj ls 40 ehvj pyrk gs- og fqj ls nk;s eqm+rk gs vksj 35 ehvj pyrk gsvrr: og nk;s eqm+rk gs vksj 20 ehvj pyrk gs- og vkjfehkd fcnq ls fdruh nwj vksj fdl fn'kk es flfkr gs\ ¼½ 20 ehvj] mùkj ¼b½ 35 ehvj] nf{k.k ¼c½ 35 ehvj] mùkj ¼d½ 20 ehvj] nf{k.k ¼e½ bues ls dksbz ugh Solution (1-5): 16. Answer D. Economics 17. Answer E. 5 lkh 18. Answer C. 3 Economics 19. Answer B. G 20. Answer A. 25 lkh 1. Ans.(d) 2. Ans.(d) 3. Ans.(d) 4. Ans.(b) 5. Ans.(e) Solution (6-10): Solution (21-25): V(+)=Y(-) Z(+)=W(-) 21. Ans.(e) 22. Ans.() 23. Ans.(b) 24. Ans.() 25. Ans.(c) Solutions (26-30): 6. Ans.(c) 7. Ans.(e) 8. Ans.() 9. Ans.(d) 10. Ans.(b) Solution (11-15): 26. Ans.(e) 27. Ans.() 28. Ans.(c) 29. Ans.(d) 30. Ans.(b) Solution(31-35): 31. Ans.() 11. Ans.(d) 12. Ans.() 13. Ans.(d) 14. Ans.(b) 15. Ans.(e) Solution(16-20) 32. Ans.(d) 33. Ans.(d) Resoning 21

22 34. Ans.(c) 35. Ans.() Solution(41-45) Resoning 22

23 Solution(51-55) 51. Solution(46-50) Resoning 23

24 Solution (56-57): 56. Ans.(e) 57. Ans.(c) Solution(58-60): Solutions (71-75): 71. Ans.(e) Sol. I. C < K(true) II. A > M(true) 72. Ans.(b) Sol. I. T > O(flse) II. S < O(true) 73. Ans.(b) Sol. I. G > T(flse) II. U < N(true) 74. Ans.(c) Sol. I. D > M(flse) II. M D(flse) 75. Ans.() Sol. I. Z > E(true) II. U < O(flse) 76. B 77. E 78. B 79. A 80. B 81.. Ans.() 82. Ans.(e) 83.. (b) Solution (84-86): 58. Ans.(d) Sol. Sttement= R >J D = K T 59. Ans.() Sol. Sttement= T R M = D < H 60. Ans.(c) Sol. Sttement= M = B > N R < K 61. A 62. A e 65. d Solutions (66-70): 66. Ans.(c) Sol. (I) U > W (Flse) (II) U = W (Flse) 67. Ans.() Sol. (I) H > F (True) (II) A > J (Flse) 68. Ans.(e) Sol. (I) Q L (Flse) (II) L > R (Flse) 69. Ans.(d) Sol. (I) Y < E (True) (II) Y N (True) 70. Ans.(b) Sol. (I) Y < M (Flse) (II) C < R (True) 84. Ans.(c) 85. Ans.() 86. Ans.(e) 87. Ans.(b) Sol. R is the mother of T. 88. Ans.(d) 89. Ans.(d) Sol. 90. Ans.(e) Resoning 24

25 90. Ans.(d) Resoning 25

26 jkt/kkuh v j eqæk Cpitl nd currency Ø- ns k jkt/kkuh eqæk 1- vqxkfulrku dkcwyk vqxkuh 2- E;kekj Uks ;wrkå D;kr 3- ÒwVku ffkiw U;wxLVªkx 4- bm usf k;k tdkrkz :fq;k 5- fdfxzlrku Ckhe dsd Lk e 6- bzjku rsgjku fj;kyk 7- lkbál fud fl;k ;wj 8- tezuh cykêu ;wj 9- nf{k.k d fj;k fl; Yk Ok u 10- fo;ruke gquubz M Ux 11- bztjkbyk Tks:lYke U;wwldsYk 12- nf{k.k vfýdk fidv fj;k js.m 13- fej dk;j Ikkm.M 14- ; xk.mk deikykk flfykx 15- vts±vhuk C;wulvkbfjl Iksl 16- Oksustq,Ykk djdl csfykoj 17- v LVªsfYk;k dsucjkz M Ykj 18- U;wthY.M osfykxvu M Ykj 19- bdokm j D; V M Ykj 20- fpfyk lsfv;kx Iksl jk"vªh; m ku Ntionl Prk Ø- jk"vªh; m ku Áns k 1- dkugk jk"vªh; m ku e/;áns k 2- Tkhok e jk"vªh; m ku e/;áns k 3- Xkk/kh lkxj jk"vªh; m ku e/;áns k 4- dsoykk nsoh jk"vªh; m ku jktlfkku 5- fljldk jk"vªh; m ku jktlfkku 6-?kkuk jk"vªh; m ku jktlfkku 7- nq/kok jk"vªh; m ku mùkjáns k 8- puæáòk jk"vªh; m ku mùkjáns k 9- is p jk"vªh; m ku Ekgkjk"Vª 10- Xkq.kkeYk jk"vªh; m ku Ekgkjk"Vª 11- Ukosxk o jk"vªh; m ku Ekgkjk"Vª 12- xhj jk"vªh; m ku xqtjkr 13- okfyedh jk"vªh; m ku fcgkj 14- LkqUnjou jk"vªh; m ku if pe cxkyk Resoning 26

27 15- Òhrjdfudk jk"vªh; m ku mm+hlk 16- fpydk jk"vªh; m ku mm+hlk 17- ukxktqzu jk"vªh; m ku rsykxkuk 18- dkxsj?kkvh jk"vªh; m ku NÙkhlx<+ 19- unknsoh jk"vªh; m ku mùkjk[k.m 20- bfnjkxk/kh jk"vªh; m ku rfeykukmq 21- jktho xk/kh jk"vªh; m ku dukzvdk fnu Ø- Rkkjh[k fnu 1-12 tuojh jk"vªh; ;qok fnol 2-25 tuojh jk"vªh; ernkrk fnol 3-13 Qjojh fo o jsfm; fnol 4-28 Qjojh jk"vªh; fokku fnol 5-8 ekpz fo o efgykk fnol 6-15 ekpz fo o miò äk fnol 7-18 vásyk fo o fojklr fnol 8-1 ebz etnwj fnol 9-31 ebz Rkckdw fu" /k fnol 10-5 twu fo o i;kzoj.k fnol twu fo o ; xk fnol tqykkbz fo o tul[;k fnol tqykkbz emsykk fnol 14-6 vxlr ghj lhek fnol flrecj jk"vªh; fgunh fnol flrecj v t u fnol 17-2 vdvwcj vfglk fnol 18-8 vdvwcj bfm;u ok;qlsuk fnol uoecj fue fu;k fnol 20-1 fnlecj oymz,m~l fnol fnlecj Ekkuork fnol Dy Mkl Dnce Ø- Mkl Ánss k 1-?kwej jktlfkku 2- dfkd mùkjáns k 3- Yko.kh Ekgkjk"Vª 4- xjck xqtjkr 5- NkÅ fcgkj Resoning 27

28 6- dpph iqm+h vk/kzáns k 7- mm+hlh mmhlk 8- Òkjr ukv~;e rfeykukmq 9- ;{kxku dukzvdk 10- dfkd dykh dsjykk 11- e fguh víse dsjykk 12- fcgw vle 13- ;kxvk Ekf.kiqj 14- /kqegyk TkEewd ehj 15- jklykhykk gfj;k.kk 16- ÒkxMk itkc csd eq[;kyk; Bnk hed qurter Ø- csd LFkku 1- csd v Q bfm;k eqecbz 2- ;wfu;u csd v Q bfm;k eqecbz 3- LksUVªYk csd v Q bfm;k eqecbz 4- nsuk cs d v Q bfm;k eqecbz 5- LVsV csd v Q bfm;k eqecbz 6- itkc us kuyk csd fnyykh 7- itkc v j fl/k csd fnyykh 8- v fj,uvyk csd v Q d elz fnyykh 9- bfm;u csd P sébz 10- bfm;u v ojfll cs d psébz 11- ;wd csd d Ykdkrk 12- ;wukbvsm csd v Q bfm;k d Ykdkrk 13- dsujk csd csxykq: 14- fot;k csd csxykq: 15- csd v Q cm+ nk cm+ nk 16- csd v Q egkjk"vªk iq. 17- vk/kzk csd gsnjkckn 18- ÇlMh dsv csd ef.kikdz 19- dki Zjs ku exykwj 20- bykkgkckn csd d Ykdkrk 21- vkbz-mh-ch-vkbz-csd eqecbz Resoning 28

29 Ekq[;kYk; Orgniztion Ø- llfkk LFkku 1- ;wfulsq U;w;kdZ 2- vkbz-,e-,q Okkf kxvu 3- fo o csd Okkf kxvu 4- MCY;w-,p-v - ftusok 5- MCY;w-Vh-v - ftusok 6- ;wusld isfjl 7- v -bz-lh-mh- isfjl 8- ;wfum fo;uk 9- v isd fo;uk 10- fgvji Yk fyk; u 11- vkbz-,e-v - Yknu 12- ukv cqzlsyk 13-,Q-,-v - j e 14- lkdz dkbekmq 15-,-Mh-ch- efgykk 16- vkfl;ku tdkrkz 17- d euosyfk Yknu 18- NAM usikyk 19- vkbz-,-bz-,- fo;uk 20- GATT tsusok esnku Stdium Ø- esnku LFkku 1- Ckkjkorh dvd 2- dfykxk Òqous oj 3- fqj t kkg d VYkk fnyykh 4- xzhuikdz dkuiqj 5- bfnjk xk/kh fot;okm+k 6- jkthoxk/kh gsnjkckn 7-,e-,- fpnecje psébz 8-,e-fpékLokeh csxykq: 9- lok;s ekuflx Tk;iqj 10- Ek rhckx cm+ njk 11- :iflg XokfYk;j 12- g Ykdj LVsfM;u bn j 13- Okku[ M+s eqecbz 14- bzmu xkmzu d Ykdkrk 15- ÒwisUæ gtkfjdk xqokgkvh 16- YkkYk cgknqj kkóh gsnjkckn Resoning 29

30 17- tokgjykkyk usg: fnyykh 18- Okh-lh-,- ukxiqj 19- cjdkrqyykk Tk /kiqj 20- Ekk/kojko flf/k;k jktd V [ Yk Áfr; fxrk Sports Cup Ø- di [ Yk 1- vkxk [kk g dh 2- /;kupn Vª Qh g dh 3- esg: Vª Qh g dh 4- Ek :xiik di g dh 5- csvu di g dh 6- jxklokeh di g dh 7- j tj di QqVc Yk 8- MwjM di QqVc Yk 9- lqòz r eq[ktê di QqVc Yk 10- Lkr "kvª Qh QqVc Yk 11- dfykxk di QqVc Yk 12- fnykhi Vª Qh fødsv 13- nsonj Vª Qh fødsv 14- j.kthr Vª Qh fødsv 15- bzjkuh Vª Qh fødsv 16- fldsukbzmw di fødsv 17- pïk di csmfe Vu 18- dfudk di csmfe Vu 19- Lk fq;k di csmfe Vu 20- mcsj di csmfe Vu 21- Fkkel di csmfe Vu 22- Ukkjx di csmfe Vu Resoning 30

31 o.kz Z nks o.kksz ;k /ofu;ks ds l;ksx ls gksus okys fodkj (ifjorzu) dks lf/k dgrs gsa lfu/k djrs le; dhkh&dhkh,d v{kj es] dhkh&dhkh nksuks v{kjks es ifjorzu gksrk gs vksj dhkh&dhkh nksuks v{kjks ds LFkku ij,d rhljk v{kj vk tkrk gsa Loj & Loj ds lkfk Loj dk esy gksus ij tks fodkj mriuu gksrk gs mls Loj lf/k dgrs gs 1. nh?kz Loj lf/k & nks lo.khz Lojks dk esy gksus ij tks fodkj mriuu gksrk gs nh?kz Loj lf/k dgykrh gsa o.kks dk l;ksx pkgs glo + âlo gks ;k nh?kz + nh?kz gkss ;fn lo.kz Loj gs rks nh?kz gks tkrk gs A mnkgj.k % iq"i + voyh = iq"ikoyh fge + vky; = fgeky; ek;k + v/khu = ek;k/khu fo k + vky; = fo ky; dfo + bpnk = dohpnk 2. xq.k Loj lf/k & tc v/vk ds vkxs b / bz gks rks nksuks (budss LFkku ij), gks tkrk gs vksj v / vk ds vkxs m / Å gks rks vks gks tkrk gs rfkk v / vk ds vkxs _ gks rks vj~ gks tkrk gs xt + bunz = xtsunz nso + bunz = nsosunz lr; + bunz = lr;sunz ftr + bfunz; = ftrsfunz; uj + bunz = ujsunz 3. o`f)loj lf/k tc v/vk ds vkxs ',' ;k ',s' vkrk gs rks nksuks dk,s gks tkrk gsa blh izdkj tc v/ vk ds vkxs vks / vks vkrk gs rks nksuks dk vks tkrk gsa lnk +,o = lnso rfkk +,o = rfkso olq/kk +,o = olq/kso,d +,d =,dsd Lo +,sfpnd = LoSfPNd 4. ;.k Loj lf/k - tc b] bz] m] Å _ ds vkxs fhky Loj vkrk gsa rks ;s Øe'k% ;~ o~ j es cny tkrk gsa bl ifjorzu dks ;.k Loj lf/k dgrs gsa vfr + vf/kd = vr;f/kd izfr +,d = izr;sd vfr + vyi = vr;yi nsoh + viz.k = nsohiz.k Resoning 31

32 lq + vkxr = Lokxr 5. v;kfn lf/k - tc,],s] vks] vks Loj ds ckn dksbz fhkuu Loj vkrk gs rks, 'v;~',,s dk 'vk;~' vks dk 'vo~' rfkk vks & 'vko' es ifjofrzr gks tkrs gs A ;g v;kfn lf/k dgykrh gsa us + vu = u;u 'ks + vu = 'k;u ps + vu = p;u xs + vu = Xkk;u xs + vd = xk;d O;tu lf/k & O;tu ds lkfk O;tu ;k O;tu ds lkfk Loj dk esy gksus ls tks fodkj mriuu gksrk gsa 1. ;fn Li'kZ O;tuks ds izfke v{kj vfkkzr~ d]p] V]r]"k] ds vkxs dksbz Loj vk;s ;k fdl oxz dk 3, 4 o.kz vk;s rks d] p] V] r] i vius gh o.kz ds rhljs o.kz es cny tkrk gs A fnd~ + xt = fnxxt okd~ + bz'k = okxh'k okd~ + tky = okxtky fnd~ + Hkze = fnxhkze okd + nku = okxnku fnd~ + vcj = fnxcj izkd~ +,sfrgkfld = izkxsfrgkfld fnd~ + n'kzu = fnfxn'kzu fnd~ + fot; = fnfxot; =/d~ + osn = _Xosn folxz lf/k & folxz ds lkfk Loj ;k O;tu ds l;ks x ls tks fodkj gksrk gs] mls folxz lfu/k dgrs gsa ;fn folxz ds ckn p] N] 'k gks rks folxz dk 'k~ gks tkrk gsa nq% + 'kklu = nq''kklu fu% + py = fu'py fu% + fpur = fuf'pur fu% + Ny = fu'ny eu% + fpfdrlk = euf'pfdrlk eu% + psruk = eu'psruk fu% + p; = fu'p; nq% + pfj= = nq'pfj= vr% + psruk = vr'psruk fu% + 'kcn = fu''kcn fu% + 'kd = fu''kd Resoning 32

33 lekl % & ijlij lecfu/kr nks ;k nks ls vf/kd 'kcnks (inks) ds esy dks lekl dgrs gsa vksj bl izdkj feydj cus leiw.kz ;ksfxd 'kcn dks lkekfld in ;k lelr in dgrs gsa lekl ds Hksn % & fgunh O;kdj.k es lekl ds eq[;r% N% Hksn fd;s x;s gs& 1. vo;;h Hkko lekl % & ftl lekl es izfke in vo;; gksus ds lkfk gh iz/kku gksrk gs mls vo;;h Hkko lekl dgrs gs bles nksuks inks dk esy gks tkus ij lelr in Hkh vo;; gks tkrk gs A izfrfnu = fnu&fnu izr;sd =,d&,d ;kotthou = thou gs tc rd vkej.k = ejus rd vktue = tee ls ysdj rriq:"k lekl % & ftl lekl es vfkz dh n`f"v ls iwoz in & xks.k (gydk) rfkk mrj in iz/kku (eq[;) gks] mls rriq:"k lekl dgrs gsa bl lekl es dùkkz,o lecks/ku dh fohkfdr;ks dks NksM+dj 'ks"k N% dkjdks dh fohkfdr;ks yksi gks tkrk gs vksj foxzg djus ij nksuks inks ds chp fohkfdr fpug iqu% vk tkrs gsa fohkfdrk;ks ds yksi ds vk/kkj ij gh rriq:"k lekl ds N% Hksn fd;s x;s gs & dez rriq:"k (dks) dj.k rriq:"k (ls/n~okjk) leiznku rriq:"i (ds fy,) viknku rriq:"k (ls) lecu/k rriq:"k (dk/dh/ds) vf/kdj.k rriq:"k (es/ij/åij) dez rriq:"k (dks) % & ftl rriq:"k lekl es nksuks inks ds chp dez dkjd dh fohkfdr (dks) dk yksi gks] mls dez rriq:"k lekl dgrs gsa ijyks sdxeu = ijyksd dks tkuk xxuhksnh = xxu dks Hksnus okyk xzkexr = xk o dks x;k gqvk d"vkiuu = d"v dks vkiuu (izkir) x`gkxr = xzg dks vk;k gqvk (x`g +vkxr) ;'k izkir = ;'k dks izkir LoxZxr = LoxZ dks x;k gqvk dez/kkj; lekl % & olrqr% ;g lekl rriq:"k dk gh,d mihksn gs vfkkzr~ bles Hkh mùkj in iz/kku gksrk gsa bl lekl dh lcls izeq[k fo'ks"krk ;g gs fd bles nksuks inks ds chp ;k fo'ks"k.k fo'ks"; lecu/k gksrk gs vfkok mies; mieku lecu/k gksrk gsa eq[kpunz = eq[k :ih punz d`".kliz = Ø".k gs tks liz egkjkt = egku gs tks jktk Resoning 33

34 l)hkz uhyxk; = lr~ gs /kez tks = uhyh gs xk; tks f}xq lekl : & ;g lekl Hkh dez/kkj; dk gh,d mihksn gs bl lekl dh fo'ks"krk ;g gs fd bles igyk in l[;kokph fo'ks"k.k gksrk gsa f}xq lekl ds Hkh nks Hksn gs & i) lekgkj f}xq ii) mùkj in iz/kku f}xq i) lekgkj f}xq % & lekgkj 'kcn dk vfkz gs lesvuk ;k lewg / bl lekl es nksuks in viuk lkeku; vfkz cuk;s j[krs gq;s lkekfld in cu tkus ij lewg dk cks/k djkrs gsa pkseklk = pkj eklks dk lewg lrlbz = lr (lkr) lbz (lks) dk lewg 'krkcnh = 'kr (lks) 'kcn (o"kks Z) dk lewg pksjkgk = pkj jkgks dk lewg ipovh = ik p ovks (o`{kks ) dk lewg cgqczhfg lekl : & ftl lekl es vk;s gq;s nksuks inks es ls dksbz Hkh in iz/kku u gks rfkk nksuks inks ds fey tkus ij vr; rhljk in iz/kku gks tk;s mls cgqczhfg lekl dgrs gsa yecksnj = yeck gs mnj ftldk (x.ks'k) pø/kkjh = pø dks /kkj.k djs tks (fo".kq) uhydb = uhyk gs db ftldk (f'ko) n'kkuu = nl gs vkuu ftlds (jko.k) prqjkuu = pkj gs vkuu ftlds (czák) 6) }U} lekl & ftl lekl ds nksuks in iz/kku gks rfkk nksuks inks ds chp "vksj" "vfkok",o ";k" (leqpp; cks/kd vo;; ) dk cks/k gks] mls }U} lekl dgrs gsa bl lekl ds Hkh rhu mihksn gs i) brjsrj }U} lekl % & ftl }U} lekl es nksuks in "vksj" leqpp; cks/kd vo;; ls l;qdr gks rfkk viuk i`fkd &i`fkd vflrro j[krs gks mls brjsrj }U} lekl dgrs gsa jke&y{e.k = jke vksj y{e.k _f"k&eqfu = _f"k vksj eqfu ekrk&firk = ekrk vksj firk xk;&csy = xk; vksj csy HksM+&cdjh = HksM+ vksj cdjh okd;&'kcnks ds lkfkzd lewg dks okd; dgrs gsa &okd; ds nks vx gks srs gs& ¼1½ mn~ns'; ¼2½ fo/ks; ¼1½ mn~ns'; %& okd; es dk;z djus okyk mn~ns'; gksrk gsa vfkkzr dùkkz gh mn~ns'; gksrk gsa ¼2½ fo/ks; %& okd; es mn~ns'; vfkkzr drkz ds }kjk tks dk;z fd;k tkrk gs] og fo/ks; dgykrk gsa bles & dez$fø;k nksuks gksrs gs] ;k okd; es tc dÿkkz ugh gksrk gs rc fø;k fo/ks; gksrh gsa Resoning 34