Master MathematicsPartII

7/31/2019 Master MathematicsPartII

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Part - II/C/36 ( 4 )

(3) 35

(4) 42

(3) 35

(4) 42

5.53 dk xq .kkRed izfrykse gS

(1) 53

(2)53

(3)35

(4)35

5. Multiplicative inverse of53 is

(1) 53

(2)53

(3)35

(4)35

6. okLrfod la [;kvksadk ;ks T; rRled gS (1) 1

(2) 0

(3) 1

(4) bues als dksbZ ugha

6. Additive identity of real numbers is

(1) 1

(2) 0

(3) 1

(4) None of these

7. 0 'kw U; dk ;ksT; iz fryks e gS(1) 0

(2) 1

(3) 1

(4) ifjHkkf"kr ughagS

7. Additive inverse of 0 (zero) is

(1) 0

(2) 1

(3) 1

(4) Not defined

8. fuEufyf[kr la[;kvksaes a dkSu vifjes; gS

(1)7

22

(2)9

5

(3) 1.312312......

(4)

8. Which of the following number isirrational

(1)7

22

(2)9

5

(3) 1.312312......

(4)

9. ;fn 2562 dks 17 ls Hkkx fn;k tk;] rks'ks "k gksxk

9. When 2562 is divided by 17 , theremainder would be

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Part - II/C/36 ( 5 ) P. T. O.

(1) 1

(2) 14

(3) 16


(1) 1

(2) 14

(3) 16

(4) None of these10. rhu vHkkT; la [;kvksadk ;ksx 100 gSA ;fn

muesals ,d nwljs ls 36 cM+h gS] rkslcls cM+h la [;k gS

(1) 73

(2) 91

(3) 67

(4) 57

10. The sum of three prime numbers is 100 . Ifone of them exceeds the other by 36 ,then largest number is

(1) 73

(2) 91

(3) 67

(4) 57

11. ;fn S izFke 732 vHkkT; la[;kvksadk ;ksx gks] rks S lnSo foHkkftr gks xk

(1) 2 ls

(2) 4 ls

(3) 6 ls

(4) buesals fdlh ls ugha

11. If S is the sum of first 732 primenumbers, then S is always divisible

(1) by 2

(2) by 4

(3) by 6

(4) by none of these

12. ;fn 0,1)(1)( 4nn =+ rks n gS (1) dksbZ /ku iw .kkd

(2) dksbZ _.k iw .kkd

(3) dksbZ fo"ke iw .kkd

(4) dksbZ le iw .kkd

12. If 0,1)(1)( 4nn =+ then n is

(1) any positive integer

(2) any negative integer

(3) any odd integer

(4) any even integer

13. ;fn a = 0.1039 gks] rks3a1)4a(4a 2 ++ dk eku gS

(1) 0.1039

(2) 0.2078

(3) 1.1039

(4) 2.1039

13. If a = 0.1039, then the value of

3a1)4a(4a 2 ++ is

(1) 0.1039

(2) 0.2078

(3) 1.1039

(4) 2.1039

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Part - II/C/36 ( 6 )

14.

=

+

27343

73

1x

es ax dk eku gS

(1) 7

(2) 2

(3) 4

(4) 5

14. The value of x in

=

+

27343

73

1x

is

(1) 7

(2) 2

(3) 4

(4) 5

15. ;fn n ,d le iz kfrd la [;k gks] rksog lcls cM+h izkfrd la [;k ftlls

n(n + 1) (n + 2) foHkkftr gks ldrk gS] gksxh(1) 6

(2) 8

(3) 12

(4) 24

15. If n is an even natural number, then thelargest natural no. by which n(n + 1) (n + 2) is divisible, is

(1) 6

(2) 8

(3) 12

(4) 24

16. 2xx42 ++ dk fuEure eku gS(1) 0

(2) 2

(3) 2

(4) 4

16. Lowest value of 2xx42 ++ is

(1) 0

(2) 2

(3) 2

(4) 4

17. 2xx42 dk vf/kdre eku gS(1) 2

(2) 4

(3) 6

(4) 8

17. Maximum value of ,xx42 2 is

(1) 2

(2) 4

(3) 6

(4) 8

18. fdlh f}?kkr cgqin es a tc (x + 2) ls Hkkx fn;k tk; rks 'ks "kQy 1 nsrk gSvkS j tc

(x 1) ls Hkkx fn;k tk; rks 'ks"kQy4 nsrk gSA tc bldks (x + 2) (x 1) ls Hkkx fn;k tk; rks 'ks "kQy D;k gks xk

(1) 1

18. A quadratic polynomial when divided by(x + 2) leaves a remainder of 1 and whendivided by (x 1) leaves a remainder of 4.What will be the remainder when it isdivided by (x + 2) (x 1)

(1) 1

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Part - II/C/36 ( 7 ) P. T. O.

(2) 4

(3) x + 3

(4) x 3

(2) 4

(3) x + 3

(4) x 3

19. ;fn vkS j cgqin c1)(xpx 2 + ds 'kwU;d gks a] rks ( + 1) ( + 1) cjkcj gS

(1) 1 + c

(2) 1 c

(3) c 1

(4) c

19. If , are the zeros of a polynomialc,1)(xpx2 + then ( + 1) ( + 1) is equal

to

(1) 1 + c

(2) 1 c

(3) c 1

(4) c

20. ;fn a + b + c = 0 gksrks abc

cab

bca 222 ++ dk

eku gS

(1) 0

(2) 1

(3) 2

(4) 3

20. If a + b + c = 0, then value of

abc

cab

bca 222 ++ is

(1) 0

(2) 1

(3) 2

(4) 3

21.ac

a

ccb

c

bba

b

a

x

x

x

x

x

x+++

cjkcj gS

(1) 0

(2) 1

(3) cbax ++

(4) abccba x / )(x ++

21.ac

a

ccb

c

bba

b

a

x

x

x

x

x

x+++

is equal to

(1) 0

(2) 1

(3) cbax ++

(4) abccba x / )(x ++

22. ;fn xy yx = rks x/y

yx

dk eku gS 22. If xy yx = then value of

x/y

yx

is

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Part - II/C/36 ( 9 ) P. T. O.

26. nksvadksaokyh ,d la[;k es a bdkbZdk va d ngkbZds vad dk nqxq uk gSA ;fn la [;k es a36 tks M+usij va dks a dk LFkku cny tkrk gS] rks og la[;k gS

(1) 36

(2) 63

(3) 48

(4) 84

26. In a number of two digits, unit's digit istwice the ten's digit. If 36 is added to thenumber, the digits are reversed, then thenumber is

(1) 36

(2) 63

(3) 48

(4) 84

27. ikp lky igys tfru dh mez fiz;k dsmez dh frxq uh FkhA nl o"kZckn tfru dh mez fiz ;k ds mezdh nqxq uh gksxhA fiz ;k dh orZ eku mez o"kks es a gS

(1) 50

(2) 30

(3) 20

(4) 15

27. Five years ago, Jatin was thrice as old asPriya. Ten years later, Jatin will be twiceas old as Priya. The present age of Priya

is (in years )

(1) 50

(2) 30

(3) 20

(4) 15

28. ekuk 'A' vkS j 'B' nks O;a td gSa ftudk y0 l0 i0 'a' rFkk e0 l0 i0 'b' gSA ;fn

A + B = a + b, rks

(1) a + 2b = A + 2B

(2) 2a + b = 2A + B

(3) 2222 BAba =

(4) 2222 BAba +=+

28. Let 'A' and 'B' are two expressions whoseL.C.M. is 'a' and H.C.F. is 'b'. If A + B = a + b,

then

(1) a + 2b = A + 2B

(2) 2a + b = 2A + B

(3) 2222 BAba =

(4) 2222 BAba +=+

29. O;atdks a 22 y)(xx6y),(xx2 ++ vkS j )y(xx12 223 dk e0 l0 gksxk

(1) 2x

(2) 22 y)(xx6 +

29. H.C.F. of 22 y)(xx6y),(xx2 ++ &)y(xx12 223 will be

(1) 2x

(2) 22 y)(xx6 +

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Part - II/C/36 ( 10 )

(3) 2x6

(4) 2x (x + y)

(3) 2x6

(4) 2x (x + y)

30. O;atdks a 2)x(x2 rFkk 6)x(x2 + dk y0 l0 gS

(1) (x 2) (x + 1)

(2) (x + 3) (x 2)

(3) (x 2)

(4) (x 2) (x + 1) (x + 3)

30. L.C.M. of expressions 2)x(x 2 and6)x(x2 + is

(1) (x 2) (x + 1)

(2) (x + 3) (x 2)

(3) (x 2)

(4) (x 2) (x + 1) (x + 3)

31. ;fn nks cgqinks a dk xq .kuQy8)(x9)(x 32 gks vkSj mudk y0 l0

6)x(x2 + gks] rksmudk e0 l0 gksxk

(1) x 3

(2) (x + 3) (x 2)

(3) (x 3) 4)2x(x2 ++

(4) 42xx2 ++

31. If product of two polynomials is8)(x9)(x 32 and their L.C.M. is

6)x(x2 + , then their H.C.F. is

(1) x 3

(2) (x + 3) (x 2)

(3) (x 3) 4)2x(x2 ++

(4) 42xx2 ++

32. uhpsfn;s x;s ekuksaes a ls K ds fdl eku ds fy, fcUnq A(1, 4), B(2, 5) vkS j C(3, K) la js [kh; gks axs

(1)3

16

(2)163

(3) 5

(4) 1

32. For which value of K given below, pointsA(1, 4), B(2, 5) and C(3, K) are co-linear

(1)3

16

(2)163

(3) 5

(4) 1

33. ;fn fcUnq P(p, q), fcUnq vks a A(a + b, b a) vkSj B(a b, a + b) ls leku nw jh ij gks] rks

(1) ap = bq

33. If the point P(p, q) is equidistant from thepoints A(a + b, b a) and B(a b, a + b), then

(1) ap = bq

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Part - II/C/36 ( 12 )

Tmn gks xk

(1) mn1

(2) n1

m1 +

(3) 1

(4) 0

is

(1) mn1

(2) n1

m1 +

(3) 1

(4) 0

38. fdlh cgqHkqt ds vUr%dks.k lekUrj Js .kh esa gS aA ;fn lcls Nks Vk dks .k 120 dk gks rFkk dks .kks a es a vUrj 5 dk gks] rks cgqHkqt es aHkq tkvks a dh la[;k gks xh

(1) 6

(2) 7

(3) 8

(4) 9

38. The interior angles of a polygon are inA.P. If the smallest angle be 120 andangles differ by 5, then number of sidesin polygon is

(1) 6

(2) 7

(3) 8

(4) 9

39. ;fn a, b vkS j c lekUrj Js.kh esagksarksljy js [kk ax + by + c = 0 ges 'kk ftl fcUnq ls xqtjs xh] og fcUnq gS

(1) (1, 2)

(2) (1, 2)

(3) (1, 2)

(4) (1, 2)

39. If a, b and c are in A.P., then the straightline ax + by + c = 0 always passesthrough the point

(1) (1, 2)

(2) (1, 2)

(3) (1, 2)

(4) (1, 2)

40. ;fn fdlh lekUrj Js .kh dk n ok in(2n 1) gks] rksmlds izFke n inksadk ;ks x

gksxk (1) 1n2

(2) 21)(2n

(3) 2n

(4) 1n2 +

40. If thn term of an A.P. be 2n 1, then thesum of its first n terms is

(1) 1n2

(2) 21)(2n

(3) 2n

(4) 1n2 +

41. ;fn fdlh l0 Js0 ds m rFkk n inks a ds 41. If the ratio of the sums of m and n terms

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Part - II/C/36 ( 13 ) P. T. O.

;ksxksadk vuq ikr 22 n:m gks] rks blds m os a rFkk n os a inksadk vuq ikr gks xk

(1) (2m 1) : (2n 1)

(2) (2m + 1) : (2n + 1)

(3) (2m 1) : (2n + 1)(4) (2m + 1) : (2n 1)

of an A.P. be 22 n:m , then ratio of itsthm term and thn term is

(1) (2m 1) : (2n 1)

(2) (2m + 1) : (2n + 1)

(3) (2m 1) : (2n + 1)(4) (2m + 1) : (2n 1)

42. ;fn bbac

aacb ++ , rFkk c

cba + l0 Js0 es a gksa] rks fuEu es a ls dkS u l0 Js 0 esa gksxk

(1) a, b, c

(2) c1

b1

a1 ,,

(3) 222 c,b,a


42. Ifb

baca

acb ++ , and ccba + are in

A.P. then which of the following is also inA.P.

(1) a, b, c

(2)c

1

b

1

a

1 ,,

(3) 222 c,b,a

(4) None of these

43. ;fn 1n321 a........,,a,a,a + l0 Js 0 es a gks a]

rks 1nn3221 aa

1aa

1aa

1+

+++ ........ gS

(1)1n1 aa

1+

(2)1n1 aa

1n+

(3)1n1 aa

n+

(4)1n1 aa

1n+

+

43. If 1n321 a........,,a,a,a + are in A.P. then

1nn3221 aa1

aa1

aa1

++++ ........ is

(1)1n1 aa

1+

(2)1n1 aa

1n+

(3)1n1 aa

n+

(4)1n1 aa

1n+

+

44. lehdj.k 2xx 1/32/3 =+ dsew y gS a

(1) 1, 8

(2) 1, 1

(3) 1, 2

44. If 2xx 1/32/3 =+ then roots of the equationare

(1) 1, 8

(2) 1, 1

(3) 1, 2

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Part - II/C/36 ( 14 )

(4) bues als dksbZ ugha (4) None of these

45. ;fn cgqin 56kxx2 esa (x 2) ls Hkkx nsusij 'ks "kQy50 gks] rksk dk eku gS

(1) 2

(2) 1

(3) 1

(4) 2

45. If the remainder is 50 when the polynomial56kxx2 is divided by (x 2), then the

value of k is

(1) 2

(2) 1

(3) 1

(4) 2

46. ;fn lehdj.k 0cbxax 2 =++ ds ew yks a dk

vuq ikr r gks] rks r1)(r 2+

dk eku gks xk

(1)bca 2

(2)cab 2

(3)abc 2

(4) abc1

46. If the ratio of the roots of the equation

0cbxax 2 =++ is r, thenr

1)(r 2+ is equal

to

(1)bca 2

(2)cab 2

(3)abc 2

(4) abc1

47. ;fn lehdj.k 0k13x5x 2 =++ ds ew y ,d nwljsds O;qRe gksa] rksk dk eku gksxk

(1) 4

(2) 6

(3) 5

(4) 1/6

47. If the roots of equation 0k13x5x 2 =++ are reciprocal of each other, then thevalue of k is

(1) 4

(2) 6

(3) 5

(4) 1/6

48. ;fn lehdj.k 012pxx2 =++ dk ,d ew y4 gS tcfd lehdj.k 0qpxx2 =++ ds ew y

cjkcj gS a] rks q dk eku gS

(1)494

48. If one root of the equation 012pxx2 =++ is 4, while the equation 0qpxx2 =++ has equal roots, then the value of q is

(1)494

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Part - II/C/36 ( 15 ) P. T. O.

(2)4

49

(3)41

(4) 4

(2)4

49

(3)41

(4) 4

49. lehdj.k 08kxx2 =+ dk ,d ew y nw ljs ew y dk oxZ gS] rks k dk eku gS

(1) 2

(2) 8

(3) 8

(4) 2

49. One root of 08kxx2 =+ is square ofthe other, then the value of k is

(1) 2

(2) 8

(3) 8

(4) 2

50. ;fn p vkS j q lehdj.k 1x2)(x2 = ds ew y gksa] rks 22 qp + dk fuEure lEHko eku gks xk

(1) 0

(2) 3

(3) 4

(4) 5

50. If p and q are the roots of the equation1x2)(x2 = , then the minimum

possible value of 22 qp + is

(1) 0

(2) 3

(3) 4

(4) 5

51. ;fn lehdj.k 0cbxx 2 =+ ds ew y nks ekxr iw.kkd gSa] rks 4c)(b 2 cjkcj gS

(1) 1

(2) 2

(3) 3

(4) 4

51. If the roots of 0cbxx 2 =+ are twoconsecutive integers, then 4c)(b 2 isequal to

(1) 1

(2) 2

(3) 3

(4) 4

52. ;fn lehdj.k 52. If the roots of the equation

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14/48

Part - II/C/36 ( 16 )

1pcosxp)(cosxp)(sin 2 =++

ds eww y okLrfod gksa] rks

(1) p [ , 0 ]

(2) p [ 0, ]

(3) 2

,2

p

(4) mi;qZDr es a dksbZ ugha

1pcosxp)(cosxp)(sin 2 =++ are real, then

(1) p [ , 0 ]

(2) p [ 0, ]

(3) 2

,2

p

(4) None of the above

53. O;a td b)2ax(x2 ++ dk eku /kukRed gksxk ;fn

(1) 04ba 2 >

(2) 04ba 2

53. The expression b)2ax(x 2 ++ haspositive value if

(1) 04ba 2 >

(2) 04ba 2

54. ;fn lehdj.k r1

qx1

px1 =+++ ds ew y

ifjek.k esacjkcj fdUrq fp es a foijhr gksa] rksew yksadk xq.kuQy gks xk

(1) /2)q(p 22 +

(2) /2)q(p 22 +

(3) /2)q(p 22

(4) /2)p(q 22

54. If the roots of the equation

r1

qx1

px1 =+++ are equal in magnitude

but opposite in sign, then product of the

roots will be

(1) /2)q(p 22 +

(2) /2)q(p 22 +

(3) /2)q(p 22

(4) /2)p(q 22

55. ;fn ,22p 1/32/3 += rks

(1) 066pp 3 =+

(2) 066pp 3 =

(3) 066pp 3 =+

55. If ,22p 1/32/3 += then

(1) 066pp 3 =+

(2) 066pp 3 =

(3) 066pp 3 =+

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Part - II/C/36 ( 17 ) P. T. O.

(4) 066pp 3 =++ (4) 066pp 3 =++

56. ;fn lehdj.k 0qpxx2 =++ o 0xx 2 =++ ( p, q) dk ,d ew y

mHk;fu"B gks] rksbl ewy dk eku gS

(1) (q )/(p )(2) ( q + p)/( q)

(3) (q )/( p) or (p q )/(q )

(4) mi;qZDr es a dksbZ ugha

56. If one root of the equations 0qpxx2 =++ and 0xx 2 =++ ( p, q) iscommon then value of this root is

(1) (q )/(p )(2) ( q + p)/( q)

(3) (q )/( p) or (p q )/(q )


57. ;fn lehdj.k 0cbxx 2 =++ ds ew y rFkk gSa] rks lehdj.k

0cx2c)(bcx 22 =++ ds ewy gSa

(1) 22 ,

(2)1,1

(3) 2 , 2

(4) ,

57. If and are the roots of the equation0,cbxx2 =++ then the roots of the

equation 0cx2c)(bcx 22 =++ are

(1) 22 ,

(2)1,1

(3) 2 , 2

(4) ,

58. ;fn ewyks a dk ;ksxQy2 rFkk xq.kuQy5 gks] rksog f}?kkr lehdj.k gS

(1) 025xx2 =+

(2) 052xx2 =+

(3) 052xx2 =+

(4) 025xx2 =+

58. If sum of the roots is 2 and product is 5,then the quadratic equation is

(1) 025xx2 =+

(2) 052xx2 =+

(3) 052xx2 =+

(4) 025xx2 =+

59. lehdj.k 0cbxax 2 =++ ds ewy ,d nw ljs ds O;qRe gksa xs] ;fn

(1) a = b

(2) b = c(3) c = a


59. The roots of the equation 0cbxax 2 =++ will be reciprocal of each other if

(1) a = b

(2) b = c(3) c = a

(4) None of these

60. ;fn fdlh f}?kkr lehdj.k ds ew y] f}?kkr lehdj.k 0cbxax 2 =++ , ds ewyks a dk nqxq uk gks] rksog f}?kkr lehdj.k gS

60. If the roots of a quadratic equation0cbxax 2 =++ are doubled, then the

corresponding quadratic equation is

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Part - II/C/36 ( 18 )

(1) 02c2bxax 2 =++

(2) 04c4bxax 2 =++

(3) 02c4bxax 2 =++

(4) 04c2bxax 2 =++

(1) 02c2bxax 2 =++

(2) 04c4bxax 2 =++

(3) 02c4bxax 2 =++

(4) 04c2bxax 2 =++

61. ;fn lehdj.k 0a2axx2 =+ dk ,d ew y gks] rksnwljk ew y gksxk

(1) /(2 1)

(2) (2 1)/

(3) /(2 + 1)

(4) (2 + 1)/

61. If is one of the roots of the equation0a2axx2 =+ , then the other root is

(1) /(2 1)

(2) (2 1)/

(3) /(2 + 1)

(4) (2 + 1)/

62. ;fn lehdj.k 02a3axx 22 =++ ds ew y vkSj gksavkSj 5 22 =+ gks] rks a dk eku gS

(1) 2

(2) 3

(3) 1

(4) 1/2

62. If , be the roots of 02a3axx 22 =++ and 5, 22 =+ then value of a is

(1) 2

(2) 3

(3) 1

(4) 1/2

63. og la[;k tks vius /kukRed oxZew y ls 12 vf/kd gS] gks xh

(1) 9

(2) 16

(3) 25


63. The number which exceeds its positivesquare root by 12 is

(1) 9

(2) 16

(3) 25

(4) None of these

64. ;fn vkS j lehdj.k 0127xx 2 =+ ds ew y gSa] rks 22 + cjkcj gS

(1) 14

(2) 19

(3) 24

(4) 25

64. If , are the roots of the equation0,127xx2 =+ then 22 + equals

(1) 14

(2) 19

(3) 24

(4) 25

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Part - II/C/36 ( 19 ) P. T. O.

65. ;fn fdlh f}?kkr lehdj.k ds ewyks a dk ;ksx 4 rFkk muds oxksdk ;ksxQy14 gks] rksog

f}?kkr lehdj.k gksxk

(1) 014xx2

=+ (2) 012xx2 =

(3) 013xx2 =

(4) 013xx2 =++

65. The sum of the roots of a quadraticequation is 4 and the sum of theirsquares is 14, then the quadraticequation is

(1) 014xx2

=+ (2) 012xx2 =

(3) 013xx2 =

(4) 013xx2 =++

66. ;fn lehdj.k 03x2x 2 =++ ds ewyks a dk ;ks xQy] muds xq .kuQy ds cjkcj gks] rks =

(1) 4

(2) 4

(3) 6


66. If the sum of the roots of the equation03x2x 2 =++ be equal to their

product, then =

(1) 4

(2) 4

(3) 6

(4) None of these

67. ;fn +++= .......121212x rd] rks x dk ,d eku gS (1) 3

(2) 3

(3) 4

(4) ,d vifjes ; la [;k

67. If +++= .......121212x , then oneroot of x is

(1) 3

(2) 3

(3) 4

(4) an irrational no.

68. ;fn lehdj.k 04kx2)(k32x 2 =+++ , ds ew y ifjek.k esacjkcj fdUrq foijhr fp ds gksa] rksk =

(1) 1

(2) 2

(3) 3

(4) 2/3

68. If the roots of the given equation04kx2)(k32x 2 =+++ , be equal in

magnitude but opposite in sign, then k =

(1) 1

(2) 2

(3) 3

(4) 2/3

69. ;fn lehdj.k 0cbxx2 =++ ds ew yksadk vuq ikr ogh gS tkslehdj.k 0rqxx2 =++ ds ewyks a dk] rks

69. If the ratio of the roots of the equation0cbxx2 =++ is same as that of0,rqxx2 =++ then

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Part - II/C/36 ( 20 )

(1) 22 cqbr =

(2) 22 cqcr =

(3) bqrc 22 =

(4) cqrb 22 =

(1) 22 cqbr =

(2) 22 cqcr =

(3) bqrc 22 =

(4) cqrb 22 =

70. 'm' dk og eku] ftlds fy, lehdj.kks a 042mx3x 2 = rFkk x(x 4m) + 2 = 0

dk ,d mHk;fu"B ew y gks xk] gS(1) 21/

(2) 23/

(3) 1/2

(4) 1/2

70. The value of 'm' so that the equation 042mx3x 2 = and x(x 4m) + 2 = 0

may have a common root is

(1) 21/

(2) 23/

(3) 1/2

(4) 1/2

71. ;fn ,y)(x

4xycosec 2

2

+= rks

(1) x < y

(2) x = y

(3) x > y


71. If ,y)(x

4xycosec 2

2

+= then

(1) x < y

(2) x = y

(3) x > y

(4) None of these

72. ;fn 211

AcotAcosec =+ gks] rks tan A = (1)

2221

(2)1615

(3)44

117

(4)11744

72. If ,11

AcotAcosec 2=+ then tan A =

(1)2221

(2)1615

(3)44

117

(4)11744

73. ;fn 31Atan = vkS j 2

1Btan = gks] rks (A + B) gS (1) /4

(2) 3 /4

(3) 6 /4

73. If31Atan = and ,

21Btan = then (A + B)

is

(1) /4

(2) 3 /4

(3) 6 /4

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Part - II/C/36 ( 21 ) P. T. O.

(4) bues als dksbZ ugha (4) None of these

74. 10cos3

10sin1 dk eku gS

(1) 0

(2) 1

(3) 2

(4) 4

74. 10cos3

10sin1 is equal to

(1) 0

(2) 1

(3) 2

(4) 4

75. ;fn tan + cot = 2 gks] rks cottan 119 + dk eku gS

(1) 1

(2) 3/2

(3) 2


75. If tan + cot = 2, then cottan 119 + is

(1) 1

(2) 3/2

(3) 2

(4) None of these

76. (3 sin + 4 cos ) dk vf/kdre eku gS

(1) 7

(2) 5

(3) 4(4) 2

76. The maximum value of (3 sin + 4 cos )is

(1) 7

(2) 5

(3) 4(4) 2

77. ;fn tan + sin = m vkS j tan sin = n gS] rks 22 nm dk eku gS

(1) 4 mn

(2) (mn)2

(3) (mn)4

(4) (m/n)2

77. If tan + sin = m and tan sin = n, then value of 22 nm is equal to

(1) 4 mn

(2) (mn)2

(3) (mn)4

(4) (m/n)2

78. fuEu es a dkS u lEHko gS

(1)35sin =

(2) tan = 2008

78. Which of the following is possible

(1)35sin =

(2) tan = 2008

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Part - II/C/36 ( 22 )

(3)23sec =

(4) 1)(pp1

p1cos 2

2>

+=

(3)23sec =

(4) 1)(pp1

p1cos 2

2>

+=

79. fuEu es a dkSu lgh gS(1) tan 1 = tan 2

(2) 2tan321tan

=

(3) tan 1 < tan 2

(4) tan 1 > tan 2

79. Which of the following is correct

(1) tan 1 = tan 2

(2) 2tan321tan

=

(3) tan 1 < tan 2

(4) tan 1 > tan 2

80. ;fn sin vkS j cos lehdj.k 0rqxpx

2=++ dsewy gSa] rks

(1) 02prqp 22 =++

(2) 02prqp 22 =+

(3) 2) qpr(p 22 +=

(4) 2) rqr(p 22 =+

80. if sin and cos are roots of the equation

0rqxpx2

=++ then(1) 02prqp 22 =++

(2) 02prqp 22 =+

(3) 2) qpr(p 22 +=

(4) 2) rqr(p 22 =+

81. 1)(sec 4 dk eku gS(1) 1tan 2 +

(2) tantan2 42 +

(3) 1sec 2 +

(4) tantan2 42

81. Value of 1)(sec 4 is

(1) 1tan 2 +

(2) tantan2 42 +

(3) 1sec 2 +

(4) tantan2 42

82.cos1cos1

+

cjkcj gS

(1) cosec + cot

(2) cosec cot

(3) sec + tan

(4) mi;qZDr esadksbZugha

82.cos1cos1

+

is equal to

(1) cosec + cot

(2) cosec cot

(3) sec + tan


83. ;fn c,cosbsina 22 =+ rks tan dk eku gS

(1) c)(ac)(b

83. If c,cosbsina 22 =+ then value oftan is

(1) c)(ac)(b

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Part - II/C/36 ( 23 ) P. T. O.

(2) c)(ab)(c

(3) a)(bc)(a

(4) c)(b

a)(b

+

(2) c)(ab)(c

(3) a)(bc)(a

(4) c)(b

a)(b

+

84. sin 45 cos 15 dk eku gS

(1)2

13

(2)2

13 +

(3)4

13 +

(4) 4 13

84. The value of sin 45 cos 15 is

(1)2

13

(2)2

13 +

(3)4

13 +

(4) 4 13

85. 16 cos 20 cos 40 cos 60 cos 80 dk eku cjkcj gS

(1) 1/2

(2) 1/3

(3) 21/

(4) 1

85. The value of 16 cos 20 cos 40 cos 60 cos 80 is equal to

(1) 1/2

(2) 1/3

(3) 21/

(4) 1

86.

+++

2AcosAcos12AsinAsin

dk eku cjkcj gS

(1) sin A

(2) cos A

(3) tan A

(4) cot A

86. The value of

+++

2AcosAcos12AsinAsin

is equal

to

(1) sin A

(2) cos A

(3) tan A

(4) cot A

87.

++++

3Acos2AcosAcos3Asin2AsinAsin dk eku gS

(1) tan A

(2) tan 2A

(3) tan 3A

(4) tan 4A

87. The value of

++++

3Acos2AcosAcos3Asin2AsinAsin is

(1) tan A

(2) tan 2A

(3) tan 3A

(4) tan 4A

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23/48

Part - II/C/36 ( 25 ) P. T. O.

(1) 1

(2) 1

(3) sin

(4) 0

(1) 1

(2) 1

(3) sin

(4) 0

93. tan 9 tan 27 + cot 63 cot 81 dk eku gS

(1) 1

(2) 0

(3) 31/

(4) 2/3

93. The value of tan 9 tan 27 + cot 63 cot 81 is

(1) 1

(2) 0

(3) 31/

(4) 2/3

94. ;fn 4BA =+ gks] rks (1 + tan A) (1 + tan B)

dk eku gS (1) 0

(2) 1

(3) 2

(4) 3

94. If ,4BA =+ then value of

(1 + tan A) (1 + tan B) is

(1) 0

(2) 1

(3) 2

(4) 3

95. 1)AsinA(cos 44 + cjkcj gS (1) 2 cos A

(2) sin 2A

(3) Asin2 2

(4) Acos2 2

95. 1)AsinA(cos 44 + is equal to

(1) 2 cos A

(2) sin 2A

(3) Asin2 2

(4) Acos2 2

96. tan 1 tan 2 tan 3 .......... tan 88 tan 89 dk eku gksxk

(1) 0

(2)

(3) 1


96. The value of

tan 1 tan 2 tan 3 .......... tan 88 tan 89 is

(1) 0

(2)

(3) 1

(4) None of these

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Part - II/C/36 ( 26 )

97. ;fn ,222

2n2mnm

mn2msin

+++= rks tan dk

eku gks xk

(1)

n)(m2n

2n)(mm

+

(2)n)(m2n

2n)(mm+

(3))n(m2n

2n)(mm22 +

+

(4)n)(m2n

2n)(mm+

+

97. If ,22

2

2n2mnm

mn2msin

+++= then value of

tan is

(1)

n)(m2n

2n)(mm

+

(2)n)(m2n

2n)(mm+

(3))n(m2n

2n)(mm22 +

+

(4)n)(m2n

2n)(mm+

+

98. (sec tan ) (sec + tan ) dk eku gS

(1) 0

(2) 1

(3) 2 sec

(4) 2 tan

98. (sec tan ) (sec + tan ) is equal to

(1) 0

(2) 1

(3) 2 sec

(4) 2 tan

99. ;fn batan = gks] rks

cosasinbcosasinb

+ dk

eku gks xk

(1) 1(2) )b)/(ab(a 2222 +

(3) 0

(4) )a)/(ba(b 2222 +

99. Ifbatan = , then value of

cosasinbcosasinb

+

will be

(1) 1

(2) )b)/(ab(a 2222 +

(3) 0

(4) )a)/(ba(b 2222 +

100. sin 12 sin 48 sin 54 cjkcj gS (1) 1/32

(2) 1/16

(3) 1/8

(4) 1/4

100. sin 12 sin 48 sin 54 is equal to

(1) 1/32

(2) 1/16

(3) 1/8

(4) 1/4

101. fdlh leprq Hkq Zt dk {ks =Qy mlds fod.kks ds xq.kuQy dk k xquk gS] rck dk eku gksxk

(1) 1

101. Area of a rhombus is k times the productof its diagonals, then k is equal to

(1) 1

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Part - II/C/36 ( 27 ) P. T. O.

(2)21

(3)31

(4)41

(2)21

(3)31

(4)41

102. ,d leckgq f=Hkqt] ftldh Hkq tk 4 lseh gS] dk 'kh"kZ yEc gS

(1) 2 lseh

(2) 3 lseh

(3) 32 lseh

(4) 23 lseh

102. The altitude of an equilateral triangle ofside 4 cm is

(1) 2 cm

(2) 3 cm

(3) 32 cm

(4) 23 cm

103. ,d leyEc prqHkq Z t dh lekUrj Hkq tk, 4 lseh vkSj 5 lseh yEch gSa] vkSj mudschp

dh nwjh2 lseh gSA leyEc prq HkqZ t dk {ks =Qy gS

(1) 28 2 lseh

(2) 35 2 lseh

(3) 11 2 lseh

(4) 14 2 lseh

103. Parallel sides of a trapezium are of 4 cm and 5 cm long, and the distance betweenthem is 2 cm . Area of trapezium is

(1) 28 2cm

(2) 35 2cm

(3) 11 2cm

(4) 14 2cm

104. 20 eh Hkq tk okys ,d leckgq f=Hkq tkdkj {ks = dk {ks =Qy gS

(1) 200 2eh

(2) 3200 2eh

(3) 3100 2eh

(4) 350 2eh

104. Area of an equilateral triangular region ofside 20 m is

(1) 200 2m

(2) 2m3200

(3) 2m3100

(4) 2m350

105. lekUrj prqHkqZ t dk {ks=Qy gks rk gS (1) vk/kkj pkbZ (2)

31 vk/kkj pkbZ

(3)21 vk/kkj pkbZ

(4) vklUu Hkqtkvks adk xq .kuQy

105. Area of parallelogram is(1) base height

(2)31 base height

(3)21 base height

(4) product of adjacent sides

106. ,d leyEc dh lekUrj Hkqtk,52 eh o 106. Parallel sides of a trapezium are 52 m and

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Part - II/C/36 ( 28 )

24 eh gSarFkk 'ks "k nks Hkqtk, 30 eh o 26 eh gS aA leyEc prq Hkq Zt dk {ks=Qy gS

(1) 848 2eh

(2) 912 2eh

(3) 1080 2eh

(4) 1120 2eh

24 m and remaining two sides are 30 m and 26 m . Area of trapezium is

(1) 848 2m

(2) 912 2m

(3) 1080 2m

(4) 1120 2m

107. le:i f=Hkqtksadh la xr Hkqtkvksaes a1 : 4 dk vuq ikr gSA f=Hkqtksads {ks=Qyks a esavuq ikr gS

(1) 1 : 4

(2) 1 : 2

(3) 1 : 16


107. Ratio of corresponding sides of twosimilar triangles is 1 : 4 . The ratio ofareas of triangles is

(1) 1 : 4

(2) 1 : 2

(3) 1 : 16

(4) None of these

108. ,d f=Hkq tkdkj eS nku dh ledks.k cukus okyh Hkq tk, 9 eh vkSj 12 eh dh gS aA eS nku

dk ifjeki gS (1) 56 eh

(2) 50 eh

(3) 46 eh

(4) 36 eh

108. The sides forming the right angle in atriangular field are 9 m and 12 m . The

perimeter of the field is

(1) 56 m

(2) 50 m

(3) 46 m

(4) 36 m

109. ,d vk;r ftldh ,d Hkqtk 10 lseh vkSj fod.kZ 26 lseh gS] dk ifjeki gS

(1) 64 lseh

(2) 72 lseh

(3) 60 lseh

109. The perimeter of a rectangle, one ofwhose sides is 10 cm and diagonal 26 cm, is

(1) 64 cm

(2) 72 cm

(3) 60 cm

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Part - II/C/36 ( 29 ) P. T. O.

(4) 68 lseh (4) 68 cm

110. la yXu fp= esa] DABD cjkcj gS

(1)ABAC

(2)ACAB

(3)ADAB

(4)AB

DA

110. In the adjoining figure,DABD is equal to

(1)ABAC

(2)ACAB

(3)ADAB

(4)AB

DA

111. ;fn X 2 lseh {ks =Qy okys ,d leckgq f=Hkq t vkS j Y 2 lseh {ks=Qy okysoxZds ifjeki cjkcj gks a] rks

(1) X < Y

(2) X > Y

(3) X = Y


111. If an equilateral triangle of area X 2cm and a square of area Y 2cm have thesame perimeter then

(1) X < Y

(2) X > Y

(3) X = Y

(4) None of these

112. ;fn ,d leckgq f=Hkq t ds ekf/;dk dh yEckbZl gks] rks bldk {ks =Qy gksxk

(1) 2l

(2) 2 /2)3( l

(3) 2 /3)3( l

(4) 2 (1/2) l

112. If l is the length of the median of anequilateral triangle, then its area is

(1) 2l

(2) 2 /2)3( l

(3) 2 /3)3( l

(4) 2 (1/2) l

113. ,d ledks.k f=Hkq t dk {ks=Qy 40 oxZlseh vkSj bldk ifjeki 40 lseh gSA blds fod.kZ dh yEckbZgS

(1) 16 lseh

113. The area of a right angled triangle is40 sq. cm and its perimeter is 40 cm . Thelength of its hypotenuse is

(1) 16 cm

C

D

BA

90

90

C

D

BA

90

90

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Part - II/C/36 ( 30 )

(2) 18 lseh

(3) 17 lseh

(4) vkdM+ s vi;kZIr gS a

(2) 18 cm

(3) 17 cm

(4) Data insufficient

114. fuEu fp= es a] js[kk AD BAC dk lef}Hkktd gSABD : DC dk eku gS

(1) 6 : 5

(2) 5 : 6

(3) 3 : 2

(4) 2 : 3

114. In the following figure, the line AD isbisector of BAC. The value of BD : DC is

(1) 6 : 5

(2) 5 : 6

(3) 3 : 2

(4) 2 : 3

115. fdlh f=Hkq t dh Hkq tk, 6 lseh ] 12 lseh rFkk 13 lseh gS aA og f=Hkqt gS

(1) U;w u dks.kh; (2) ledks.kh;

(3) vf/kd dks.kh;

(4) f=Hkqt lEHko ughagS

115. Sides of a triangle are 6 cm, 12 cm and13 cm . This triangle is

(1) acute angled

(2) right angled

(3) obtuse angled

(4) triangle is not possible

116. fdlh f=Hkq t ds e/; - fcUnqvks a dkstksM+us ls cuspkj f=Hkqt gksrsgS a

(1) lef}ckgq f=Hkq t

(2) leckgq f=Hkq t

(3) le:i ijUrq lokxle ugha

(4) lokxle

116. Four triangles formed by joining mid-points of a triangle are

(1) isosceles triangle

(2) equilateral triangle

(3) similar but not congruent

(4) congruent

117. ABC es a] ABC = 90 gSA ;fn M vkSj N 117. In ABC, ABC = 90 . If M and N are mid-

C

B

A6 lseh

5 lseh D

C

B

A 6 cm

5 cm D

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Part - II/C/36 ( 31 ) P. T. O.

e'k%AB vkSj BC ds e/; - fcUnq gS a] rks }(MC){(AN)4 22 + dk eku gS

(1) 2(AC)4

(2) 2(AC)2

(3) 2(AC)3

(4) 2(AC)5

points of AB and BC respectively, thenvalue of }(MC){(AN)4 22 + is

(1) 2(AC)4

(2) 2(AC)2

(3) 2(AC)3

(4) 2(AC)5

118. ;fn ,d f=Hkq t ds dks .k 1 : 2 : 3 ds vuq ikr es agks a rks Hkq tkvks a dk vuqikr gksxk

(1) 1 : 2 : 3

(2) 3:2:1

(3) 2:3:1 (4) 2:2:3

118. If angles of a triangle are in the ratio 1 : 2 : 3, then ratio of the sides is

(1) 1 : 2 : 3

(2) 3:2:1

(3) 2:3:1 (4) 2:2:3

119. fdlh leckgq f=Hkq t ABC esa] Hkq tk BC dk e/; - fcUnq D gSA rc fuEu es als dkSu lgh gS

(1) 22 ADAB =

(2) 22 4AD3AB =

(3) 22 3AD2AB =

(4) AD32AB =

119. In an equilateral triangle ABC, D is mid-point of side BC. Then which of thefollowing is true

(1) 22 ADAB =

(2) 22 4AD3AB =

(3) 22 3AD2AB =

(4) AD32AB =

120. ,d leckgq ABC dh Hkq tkvks aAB o AC ds e/;fcUnq D o E gS aA ;fn D vkS j E dksfeyk fn;k tk;s] rksADE o ABC ds {ks =Qyksa dk vuq ikr gks xk

(1) 1 : 3

(2) 1 : 4

(3) 3 : 1

(4) 4 : 1

120. D and E are mid-points of sides AB andAC of an equilateral triangle ABC. If D andE are joined, ratio of areas of ADE tothat of ABC is

(1) 1 : 3

(2) 1 : 4

(3) 3 : 1

(4) 4 : 1

121. fuEu fp= es a] DEC dk eku gS 121. In the following figure, value of DEC is

D

E

D

E

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Part - II/C/36 ( 32 )

(1) 45

(2) 65

(3) 55

(4) 75

(1) 45

(2) 65

(3) 55

(4) 75

122. ,d o`k dh nksthok, AB rFkk CD ,d nw ljs dkso`k dsckgj fcUnq O ij dkVrh gS aA

;fn AO = 6 lseh ] OB = 12 lseh rFkk OC = 8 lseh ] rks OD dk eku lseh es a gS (1) 4.5

(2) 9

(3) 14


122. Two chords AB and CD of a circleintersect each other at a point O outside

the circle. If AO = 6 cm, OB = 12 cm andOC = 8 cm, then value of OD (in cm) is

(1) 4.5

(2) 9

(3) 14

(4) None of these

123. 28 lseh f=T;k ds o` k dk 22 lseh yEckbZdk pki o`k dsdsUnz ij dks .k vUrfjr djrk gSA rc dk eku gS

(1) 90

(2) 75

(3) 65

(4) 45

123. An arc of length 22 cm of a circle ofradius 28 cm substends an angle at thecentre of circle . Then is(1) 90

(2) 75

(3) 65

(4) 45

124. fdlh o` k] ftldk ds UnzO gS] ds leku yEckbZokysthokvksads e/; fcUnq vks a dk

fcUnq iFk gS(1) ,d ljy js[kk (2) ,d o`k ftldk dsUnz O ls i`Fkd~gS (3) ,d o`k ftldk dsUnz O gS (4) mi;qZDr es a lsdksbZ ugha

124. The locus of middle points of equalchords of a circle with centre at O is

(1) a straight line

(2) a circle with centre different from O

(3) a circle with centre O


125. fdlh o` k dh thok,AB rFkk CD fcUnq O 125. Two chords AB and CD of a circle

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ij izfrPNs fnr djrh gSaA ;fn OA = 8 lseh]OC = 4 lseh rFkk OD = 6 lseh] rks OB gS (1) 3 lseh (2) 4 lseh (3) 6 lseh (4) 12 lseh

intersects at O. If OA = 8 cm, OC = 4 cm and OD = 6 cm , then OB is

(1) 3 cm

(2) 4 cm

(3) 6 cm

(4) 12 cm

126. fdlh o`k dsdsUnzls 5 lseh nw jh ij fLFkr fcUnq ls o`k ij [khapsx;s Li'khZ dh yEckbZ

4 lseh gSA ml o` k dk v)ZO;kl gS(1) 2 lseh

(2) 3 lseh

(3) 4 lseh

(4) 5 lseh

126. The length of tangent from a point at adistance 5 cm from the centre of a circleis 4 cm . The radius of the circle is

(1) 2 cm

(2) 3 cm

(3) 4 cm

(4) 5 cm

127. nkso`kksadsdsUnzksads chp dh nw jh 4.5 lseh gS vkSj mudh f=T;k,e'k%2 lseh vkS j

2.5 lseh gSaA mu o`Rrks a ij [kha ph tk ldus okyh mHk;fu"B Li'kZ js [kkvks a dh la[;k gS

(1) 1

(2) 2

(3) 3

(4) 4

127. The distance between centres of twocircles is 4.5 cm and their radii are 2 cm and 2.5 cm respectively. Number ofcommon tangents that can be drawn tothe circles is

(1) 1

(2) 2

(3) 3

(4) 4

128. 2.5 lseh vkS j 3.5 lseh f=T;k okysnkso` k ckr% Li'kZ djrsgS aA mudsds Unzksads chp dh nwjh gS

(1) 1 lseh (2) 5 lseh (3) 6 lseh (4) 7

lseh

128. Two circles of radii 2.5 cm and 3.5 cm touchexternally. Distance between their centresis

(1) 1 cm

(2) 5 cm

(3) 6 cm

(4) 7 cm

129. 13 lseh vkSj 5 lseh f=T;k okysnkso` k vUr% Li'kZdjrs gSaA mudsds Unz ks a ds chp dh nw jh gS

(1) 18 lseh (2) 12 lseh (3) 9 lseh

129. Two circles of radii 13 cm and 5 cm touchinternally. The distance between theircentres is

(1) 18 cm

(2) 12 cm

(3) 9 cm

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(4) 8 lseh (4) 8 cm

130. fdlh o` k dsds Unzds ,d gh vks j fLFkr nks lekUrj thokvks a dh yEckb;k6 lseh vkS j

8 lseh gS a vkS j muds chp dh nw jh 1 lseh gS] rkso`k dk O;kl gS

(1) 14 lseh (2) 10 lseh (3) 8 lseh (4) 5 lseh

130. If two parallel chords on the same side ofthe centre of a circle are 6 cm and 8 cm and they are 1 cm apart, then diameter ofthe circle is

(1) 14 cm

(2) 10 cm

(3) 8 cm

(4) 5 cm

131. ABCD ,d ph; prq Hkq Zt gSA o` k ds fcUnq vksa A vkSj C ij [khaph x;h Li'kZ js [kk,fcUnq P

ij dkVrh gS aA ;fn ABC = 120 , rks APC dk eku gksxk

(1) 90

(2) 80

(3) 70

(4) 60

131. ABCD is a cyclic quadrilateral. Thetangents drawn at the points A and C ofthe circle intersect at P . If ABC = 120 , then value of APC will be

(1) 90

(2) 80

(3) 70

(4) 60

132. 4 lseh f=T;k okys nksleku o` k ,d nwljs dksbl iz dkj izfrPNs fnr djrs gS a fd iz R;sd nwljs ds dsUnz lsgksdj xqtjrs gSa] rks mHk;fu"B thok dh yEckbZgS

(1) 4 lseh

(2) 32 lseh

(3) 34 lseh

(4) 8 lseh

132. Two equal circles of radius 4 cm intersecteach other such that each passesthrough the centre of the other, thenlength of common chord is

(1) 4 cm

(2) 32 cm

(3) 34 cm

(4) 8 cm

133. 4 lseh v)ZO;kl okyso` k dk {ks =Qy vkafdd :i ls mlds ifjf/k dk fdruk iz fr'kr gks xk

(1) 100

(2) 150

(3) 200

(4) 250

133. The area of a circle of radius 4 cm isnumerically what percent of itscircumference

(1) 100

(2) 150

(3) 200

(4) 250

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134. ,d ifg, okys f[kykS us dk O;kl14 lseh gSA og 15 pDdjksaesafdruh nw jh r; dj ys xk

(1) 880 lseh

(2) 660 lseh

(3) 600 lseh

(4) 560 lseh

134. The diameter of a toy wheel is 14 cm . Thedistance travelled by it in 15 revolutions is

(1) 880 cm

(2) 660 cm

(3) 600 cm

(4) 560 cm

135. ,d o`k dh ifjf/k 100 lseh gSA o` k ds vUrxZr [kha ps x;s,d oxZ dh Hkq tk gksxh

(1) 2100 lseh

(2) 100 lseh

(3) 250 lseh

(4) 250 lseh

135. The circumference of a circle is 100 cm .The side of a square inscribed in thecircle is

(1) 2100 cm

(2) 100

cm

(3) 250 cm

(4) 250

cm

136. pkj cjkcj o`k] ftuesaiz R;s d dh f=T;k 'a'

bdkbZgS] ,d nw ljs dks Li'kZdjrs gSaA muds chp es a f?kjsHkkx dk {ks=Qy] oxZbdkbZ esa] gksxk

(1) 2a3

(2) 2a76

(3) 2a741

(4) 2a71

136. Four equal circles each of radius 'a' unit

touch one another. The area enclosedbetween them, in square units, is

(1) 2a3

(2) 2a76

(3) 2a741

(4) 2a71

137. 784 2 lseh {ks=Qy okyh ,d oxkZdkj dkxt dh 'khV es a ls cjkcj eki okyh pkj cM+h ls cM+h o` kkdkj IysVs a dkV yh tkrh gSaA iz R;s d IysV dh ifjf/k gS

= yhft,

722

(1) 22 lseh

137. Four equal circular plates of maximumsize are cut off from a square paper sheetof area 784 2cm . The circumference of

each plate is

=

722take

(1) 22 cm

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(2) 44 lseh

(3) 66 lseh

(4) 88 lseh

(2) 44 cm

(3) 66 cm

(4) 88 cm

138. fdlh o` k ds,d [k.M dk {ks=Qy] ftldh f=T;k 5 lseh gS rFkk tks ,d3.5 lseh yEcs pki }kjk cuk gS] gks xk

(1) 8.5 2 lseh

(2) 8.75 2 lseh

(3) 7.75 2 lseh

(4) 7.5 2 lseh

138. The area of a sector of a circle of radius5 cm , formed by an arc of length 3.5 cm is

(1) 8.5 2cm

(2) 8.75 2cm

(3) 7.75 2cm

(4) 7.5 2cm

139. ,d h pkbZ okys'kadq dksvk/kkj ls 3h pkbZij] vk/kkj dslekUrj ,d lery ls dkV fn;k tkrk gS] rksbl izdkj cus 'kadq rFkk fNUud ds vk;ruks a dk vuqikr gksxk

(1) 1 : 3

(2) 8 : 19

(3) 1 : 4

(4) 1 : 7

139. A right circular cone of height h is cut bya plane parallel to the base at a distance

3h from the base, then volumes of the

resulting cone and the frustum are in theratio

(1) 1 : 3

(2) 8 : 19

(3) 1 : 4

(4) 1 : 7

140. ,d 12 lseh Hkqtk okys?ku dslHkh lrgksa dksuhys jax lsjx ns us ds ckn]3 lseh Hkq tk okysNksVs?kuksaes a dkV fn;k tkrk gSA bl iz dkj cus Nks Vs ?kuks a dh la[;k] ftldh dks bZ Hkh lrg jxh gqbZ ugha gS] gksxh(1) 8

(2) 12

(3) 16

(4) 24

140. A cube of side 12 cm is painted blue onthe all faces and then cut into the smallercubes, each of side 3 cm . Then totalnumber of smaller cubes having none oftheir faces painted, is

(1) 8

(2) 12

(3) 16

(4) 24

141. ,d ?ku dk vk;ru 216 3eh gSA ,d Qyd dk {ks =Qy cjkcj gS

(1) 48 2eh

(2) 6 2eh

141. Volume of a cube is 216 3m . Area of oneface is

(1) 48 2m

(2) 6 2m

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Part - II/C/36 ( 37 ) P. T. O.

(3) 36 2eh

(4) 12 2eh

(3) 36 2m

(4) 12 2m

142. ?ku dsfod.kZdh yEckbZ 15 lseh gSA ?ku dh dks j dh eki gks xh

(1) 10 lseh

(2) 35 lseh

(3) 5 lseh

(4) 53 lseh

142. Length of diagonal of a cube is 15 cm .Measure of edge of cube will be

(1) 10 cm

(2) 35 cm

(3) 5 cm

(4) 53 cm

143. ,d cs yu dh pkbZrFkk vk/kkj dh f=T;k nks uks a10% c


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Part - II/C/36 ( 38 )

352 2 lseh dh o` f) gks tkrh gSA o` f) - iw oZ xks ys dh f=T;k Fkh


2cm . The radius of the sphere beforeincrease was

(1) 3 cm

(2) 4 cm

(3) 5 cm

(4) 6 cm

147. nksxksyks a dk vk;ru 8 : 27 ds vuqikr es a gSaA muds i`"Bh; {ks=Qyks a dk vuqikr gS

(1) 4 : 9

(2) 2 : 3

(3) 4 : 5

(4) 5 : 6

147. The volumes of two spheres are in theratio 8 : 27 . The ratio of their surfaceareas is

(1) 4 : 9

(2) 2 : 3

(3) 4 : 5

(4) 5 : 6

148. ,d ?ku ds vk;ru dk ml xks ys] tks?ku esa iw .kZ r;k fQV fd;k tk lds xk] dsvk;ru ls vuq ikr gks xk

(1) : 6(2) 6 : (3) 3 : (4) : 3

148. The ratio of volume of a cube to that of asphere, which will fit exactly inside thecube, is

(1) : 6(2) 6 : (3) 3 : (4) : 3

149. ,d ?kukHk dk vk;ru ,d ?ku dsvk;ru dk nq xquk gSA ;fn ?kukHk dh foek, 9 lseh ]

8 lseh rFkk 6 lseh gks a] rks ?ku dk lEiw.kZ i` "Bh; {ks =Qy gksxk

(1) 72 2 lseh (2) 216 2 lseh (3) 432 2 lseh (4) 108 2 lseh

149. The volume of a cuboid is twice that of acube. If the dimensions of the cuboid are9 cm, 8 cm and 6 cm, the total surfacearea of the cube is

(1) 72 2cm

(2) 216 2cm

(3) 432 2cm

(4) 108 2cm

150. 1 lseh O;kl vkSj 8 lseh yEch ,d rk cs dh NM+ dks,dleku O;kl okys ,d rkj ds :i es aifjofrZr fd;k x;k gS] ftldh yEckbZ18eh gSA bl rkj dh f=T;k lseh es a gksxh(1) 1/15

(2) 1/30

(3) 2/15

150. A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniformdiameter and 18 m length. The radius(in cm ) of the wire is

(1) 1/15

(2) 1/30

(3) 2/15

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(4) 15 (4) 15

151. ,d xks ys dk i` "B 64 2 lseh gSA bldk O;kl cjkcj gS


151. The surface area of a sphere 64 2cm .Its diameter is equal to

(1) 16 cm

(2) 8 cm

(3) 4 cm

(4) 2 cm

152. ,d 'ka dq dh pkbZrFkk mldsvk/kkj ds v)Z O;kl nks uks aes a 100% dh o` f) dh tkrh gSA 'ka dq dsvk;ru es ao` f) dk iz fr'kr gks xk

(1) 700

(2) 400

(3) 300

(4) 100

152. Each of the height and base-radius of acone is increased by 100% . The percentageincrease in the volume of the cone is

(1) 700

(2) 400

(3) 300

(4) 100

153. ,d 2 lseh v)Z O;kl okyk xks yk ,d 4 lseh v)Z O;kl dk vk/kkj okys ikuh ls Hkjscs yu esa Mq cks ;k x;k gSA ;fn xks yk iw jh rjg ikuh esa Mw ck gks] rks cs yu es a ikuh dsLrj esao`f) gksxh

(1) 1/3 lseh (2) 1/2 lseh (3) 2/3 lseh (4) 2 lseh

153. A sphere of radius 2 cm is put into watercontained in a cylinder of base-radius4 cm . If the sphere is completelyimmersed in the water, the water level inthe cylinder rises by

(1) 1/3 cm

(2) 1/2 cm

(3) 2/3 cm

(4) 2 cm

154. ;fn ,d csyu ds vk/kkj ds v)ZO;kl dks 50% de djds rFkk mldh pkbZ dks 50%

c


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Part - II/C/36 ( 42 )

(1) 7 : 6

(2) 6 : 7

(3) 3 : 7

(4) 7 : 3

(1) 7 : 6

(2) 6 : 7

(3) 3 : 7

(4) 7 : 3

163. yks gs dh ,d cs yukdkj NM+] ftldh pkbZ mldh f=T;k dh pkj xquh gS] dksfi?kykdj mlh f=T;k dsxks ys cuk, tkrs gS aA cuk;sx;s xks yks adh la [;k gS

(1) 2

(2) 3

(3) 4

(4) 8

163. A cylindrical rod of iron whose height isfour times its radius is melted and recastinto spherical balls of same radius. Thenumber of balls made is

(1) 2

(2) 3

(3) 4

(4) 8

164. /kkrq ls cus ,d Bksl 'ka dq] ftldh pkbZ 10 lseh o vk/kkj dh f=T;k 20 lseh gS] dks

fi?kyk dj 4 lseh O;kl dh xks fy;k cukbZ x;h gS aA bl iz dkj cuh xks fy;ks a dh la [;k gS

(1) 125

(2) 25

(3) 50

(4) 75

164. A solid metallic cone of height 10 cm ,base radius 20 cm is melted to makespherical balls each of 4 cm diameter.The number of such balls which can bemade is

(1) 125

(2) 25

(3) 50

(4) 75

165. fdlh ?kukHk dh Hkq tkvks a dk vuqikr 1 : 2 : 3 vkSj bldk i` "Bh; {ks =Qy 88 2 lseh gSA ?kukHk dk vk;ru gS

(1) 120 3 lseh

(2) 64 3 lseh

(3) 48 3 lseh

(4) 24 3

lseh

165. The edges of a cuboid are in the ratio1 : 2 : 3 and its surface area is 88 2cm .The volume of the cuboid is

(1) 120 3cm

(2) 64 3cm

(3) 48 3cm

(4) 24 3cm

166. oxZ vUrjky10 19 dk oxZ fpg~ u gS

(1) 19

(2) 10

(3) 14.5

166. The class mark of the class interval10 19 is

(1) 19

(2) 10

(3) 14.5

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Part - II/C/36 ( 44 )

171. ;fn x vkSj x1 dk ek/; M gks] rks3x vkS j

3x1 dk ek/; gS

(1)2

3)(MM 3

(2) 3M

(3) 3M3 +

(4) 3)(4MM 2

171. If the mean of x and x1 is M then of 3x

and 3x1 is

(1)2

3)(MM 3

(2) 3M

(3) 3M3 +

(4) 3)(4MM 2

172. vkdM+ksa 8, 7, 15, 12, 10, 8, 9 dh ekf/;dk gksxh

(1) 12(2) 11

(3) 10

(4) 9

172. The median of the data 8, 7, 15, 12, 10, 8, 9 is

(1) 12(2) 11

(3) 10

(4) 9

173. ;fn la [;kvks a27 + x, 31 + x, 89 + x, 107 + x,156 + x dk ek/; 82 gS] rks130 + x, 126 + x,68 + x, 50 + x, 1 + x dk ek/; gksxk

(1) 75

(2) 157

(3) 80

(4) 82

173. If the mean of the numbers 27 + x, 31 + x,89 + x, 107 + x, 156 + x is 82, then meanof 130 + x, 126 + x, 68 + x, 50 + x, 1 + x will be

(1) 75

(2) 157

(3) 80

(4) 82

174. fdlh d{kk ds fo|kfFkZ;ksads kIrka dks a dk vkSlr 68 gSA d{kk esayM+fd;ks a ds kIrka dks a dk vkSlr 80 rFkk yM+dks a dskIrka dks a dk vkSlr 60 gSA d{kk es a fdrus fr'kr fo|kFkhZ

yM+fd;kgSa (1) 40

(2) 60

(3) 65

(4) 70

174. The average of marks scored by thestudents of a class is 68 . The averagemarks of the girls in the class is 80 andthat of boys is 60 . What is percentage of

girls in the class(1) 40

(2) 60

(3) 65

(4) 70

175. rhu la[;kvksaesanwljh la[;k igyh la [;k 175. Out of three numbers, the second is

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Part - II/C/36 ( 45 ) P. T. O.

dh nq xq uh gS vkSj rhljh la [;k dh vk/kh gSA ;fn rhuks a la[;kvksadk vkS lr 56 gks] rks igyh vkS j nwljh la [;kvks a dk vUrj gS

(1) 12

(2) 24

(3) 48

(4) 96

twice the first and half of the third. If theaverage of the three numbers is 56 , thendifference of first and second number is

(1) 12

(2) 24

(3) 48

(4) 96

176. ;fn oxZ vUrjky10 19, 20 29, 30 39,............., gksrks igysoxZvUrjky dh mPp

lhek gS (1) 19

(2) 19.5

(3) 20


176. If the class intervals are 10 19, 20 29,30 39, ............., then upper limit of firstclass interval is

(1) 19

(2) 19.5

(3) 20

(4) None of these

177. va dks a 3, 5, 7 rFkk 9 dh ckjEckjrk,e'k%x 2,x + 2, x 3 rFkk x + 3 gSA ;fn lekUrj ek/;6.5 gks] rks x dk eku gS

(1) 7.8

(2) 9.5

(3) 18.8

(4) 19.8

177. The numbers 3, 5, 7 and 9 have theirrespective frequencies x 2, x + 2, x 3 and x + 3 . If the arithmetic mean is 6.5 then value of x is

(1) 7.8

(2) 9.5

(3) 18.8

(4) 19.8

178. Fke n kfrd la [;kvks a ds oxks dk ek/; gS

(1) 1)(n2 +

(2) /n1)(n4 +

(3) /61)(2n1)(n ++

(4) /n2)(n1)(n ++

178. The mean of squares of first n naturalnumbers is

(1) 1)(n2 +

(2) /n1)(n4 +

(3) /61)(2n1)(n ++

(4) /n2)(n1)(n ++

179. ;fn x, y, z dk ek/; M gSvkSj y(x + z) = xz, rks 222 z,y,x dk ek/; gS

179. If the mean x, y, z is M and y(x + z) = xz, then mean of 222 z,y,x is

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Part - II/C/36 ( 47 ) P. T. O.

183. ;fn 15, 11, 7, 16, x, 8, 18, 5 dh ekf/;dk 12 gks] rks x dk eku gks xk

(1) 11

(2) 12

(3) 13


183. If median of 15, 11, 7, 16, x, 8, 18, 5 is 12, then value of x will be

(1) 11

(2) 12

(3) 13

(4) None of these

184. ;fn cgqyd vkS j ek/; ds eku e'k%30 o 33 gks] rks ekf/;dk dk eku gS (1) 30

(2) 31

(3) 32

(4) 33

184. If the value of mode and mean is 30 and33 respectively then value of median is

(1) 30

(2) 31

(3) 32

(4) 33

185. 4, 7, 8, 6 vkS j x dk lekUrj ek/; 6 gSA x dk eku gS

(1) 4

(2) 5

(3) 6

(4) 7

185. The arithmetic mean of 4, 7, 8, 6 and x is6. The value of x is

(1) 4

(2) 5

(3) 6

(4) 7

186. rk'k ds 52 ikks a dh xM~Mh esals ,d iRrk ;kn`PN;k [kha pk tkrk gSA ml iRrs ds ckn'kkg ;k csxe gks us dh izkf;drk gS

(1)131

(2)132

(3)41

(4) 261

186. From a pack of 52 cards, one card is drawnat random. The probability that it is a eithera King or a Queen is

(1)131

(2)132

(3)41

(4) 261

187. nksiklksads ,d Qsa d esa 7 ls vf/kd ikusdh iz kf;drk gS

(1) 7/36

(2) 7/12

(3) 5/12

187. In a single throw of two dice, theprobability of getting more than 7 is

(1) 7/36

(2) 7/12

(3) 5/12

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(4) 29/36 (4) 29/36

188. rk'k ds 52 iRrks a dh xM~ Mh esals ,d - ,d djds nks iRrs;kn`PN;k [kha ps tkrs gSaA mu nks uks a ds ckn'kkg gksusdh izkf;drk gS

(1) 2/13

(2) 3/11

(3) 30/221

(4) 1/221

188. Two cards are drawn one by one atrandom from a pack of 52 cards. Theprobability that both of them are king, is

(1) 2/13

(2) 3/11

(3) 30/221

(4) 1/221

189. nksikls ,d lkFk Qsa ds tkrs gSaA nksuksavadksa dk ;ksx 4 dk vioR;Z gks us dh iz kf;drk gS

(1) 1/2

(2) 1/3

(3) 1/8

(4) 1/4

189. Two dice are thrown together. Theprobability that the sum of two numbersis a multiple of 4 is

(1) 1/2

(2) 1/3

(3) 1/8

(4) 1/4

190. 'kCn'PROBABILITY' ls ,d v{kj pq uk tkrk gSA pq us x;s v{kj ds Loj gks us dh iz kf;drk gS

(1) 2/11

(2) 3/11(3) 4/11

(4) 5/26

190. A single letter is selected from the word'PROBABILITY' . The probability that theselected letter is a vowel is

(1) 2/11

(2) 3/11(3) 4/11

(4) 5/26

191. izFke nkslkS /ku iw .kk d la [;kvks a ls ,d la [;k ;kn` PN;k pquh tkrh gSA bl la[;k ds

6 ;k 8 ls HkkT; gksusdh iz kf;drk gS (1) 1/3

(2) 2/3

(3) 3/4(4) 1/4

191. One number is selected at random fromfirst two hundred positive integers. Theprobability that it is divisible by 6 or 8 is

(1) 1/3

(2) 2/3

(3) 3/4(4) 1/4

192. ,d flDds dspkj mNkyks a esade ls de ,d ckj 'kh"kZvkusdh iz kf;drk gS

(1) 1/16

(2) 15/16

192. The probability of getting at least onehead in four throws of a coin is

(1) 1/16

(2) 15/16

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47/48

Part - II/C/36 ( 49 ) P. T. O.

(3) 1/4

(4) 1/8

(3) 1/4

(4) 1/8

193. ik p vadksadh ,d la [;k ;kn` PN;k pq uh tkrh gSA bl ckr dh iz kf;drk] fd lHkh va d vleku gks vkS j fo"ke LFkkuks a ij fo"ke vad rFkk le LFkkuks a ij le vad gksa] gS

(1) 3/65

(2) 1/75

(3) 2/65

(4) 8/75

193. A five digit number is chosen at random.The probability that all the digits aredistinct and digits at odd places are oddand digits at even places are even, is

(1) 3/65

(2) 1/75

(3) 2/65

(4) 8/75

194. ,d iklk Qsa dk tkrk gSvkSj ml ij ,d le

la [;k iz kIr gks rh gSA bl la[;k ds 2 gks us dh iz kf;drk gS(1) 1/2

(2) 1/6

(3) 1/3

(4) 1/12

194. An even number is obtained in a throw of

a dice. Probability of that number to be 2 is

(1) 1/2

(2) 1/6

(3) 1/3

(4) 1/12

195. nksNk=ks a }kjk fdlh iz 'u dks gy dj ysus dh vyx - vyx iz kf;drk, e'k%2/7 rFkk

5/7 gS aA bl ckr dh izkf;drk fd iz 'u gy gks tk,xk] gS

(1) 10/49

(2) 39/49

(3) 0

(4) 1

195. Probability of solving a question by twostudents independently are respectively2/7 and 5/7 . Probability that the questionwill be solved, is

(1) 10/49

(2) 39/49

(3) 0

(4) 1

196. ,d ikls dh rhu Qs dks a es a de ls de ,d ckj 5 dk va d vkus dh iz kf;drk gS

(1) 1/6

(2) 5/6

(3) 91/216

(4) 125/216

196. The probability of getting 5 at least oncein three throws of a dice is

(1) 1/6

(2) 5/6

(3) 91/216

(4) 125/216

197. fdlh vf/ko"kZesa 53 jfookj gks usdh iz kf;drk 197. The probability of being 53 Sundays in a

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48/48

gS (1) 1/7

(2) 2/7

(3) 7/365

(4) 1/365

Leep Year is

(1) 1/7

(2) 2/7

(3) 7/365

(4) 1/365

198. nks flDds ,d lkFk mNkys tkrs gS aA vf/kdre ,d 'kh"kZ vkus dh izkf;drk gS

(1) 1/4

(2) 3/4

(3)21

(4) 1

198. Two coins are tossed simultaneously.Probability of getting at most one head is

(1) 1/4

(2) 3/4

(3)21

(4) 1

199. ,d lk/kkj.k o"kZvf/ko"kZugha es a 53 lks eokj gksusdh iz kf;drk gS

(1) 1/7

(2) 2/7

(3) 53/365


199. The probability of falling 53 Monday in asimple year (not a Leep Year) is

(1) 1/7

(2) 2/7

(3) 53/365

(4) None of these

200. ,d cDls esa 5 yky] 4 gjh rFkk 7 lQs n xs ans a gS aA cDlsls ,d xs a n ;kn`PN;k fudkyh tkrh gSA bl ckr dh izkf;drk fd fudkyh x;h xsa n u rks yky gks vkSj u gh lQsn gks] gS

(1) 5/16

(2) 7/16

(3) 1/4

(4) 3/4

200. A box contains 5 red balls, 4 green ballsand 7 white balls. A ball is drawn atrandom from the box. The probabilitythat the drawn ball is neither red norwhite is

(1) 5/16

(2) 7/16

(3) 1/4

(4) 3/4

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Master MathematicsPartII

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