Test Paper for Go Defence

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NDA MODEL TEST PAPER - ITime Allowed : 2½ hour Maximum Marks : 300

KAKADEO, KIDWAI NAGAR, KANPUR

PAPER - I (Mathematics)1. Suppose A represents the symbol 1, B represents the

symbol 0, C represents the symbol 1, D represents thesymbol 0 and so on. If we divide INDIA by AGRA,then which one of the following is the remainder in BinaryRepresentation?(a) (1101)2 (b) (101)2(c) (11)2 (d) (110)2

2. How many number of digits are there in 298 ? (Given thatlog102 = 0.30103)(a) 98 (b) 99(c) 30 (d) 29

3. What is the area of the triangle on the Argand diagramformed by the complex numbers z, –iz, z – iz ?(a) | z |2 (b) 2 | z |2(c) | z |2/2 (d) | z |2/4

4. In a quadratic equation, with leading coefficient 1, Sheelareads the coefficient 16 of x wrongly as 19 and obtains theroots as –15 and –4. Which of the following are the correctroots of the equation ?(a) 8, 8 (b) 6, 10(c) –6, –10 (d) 12, 5

5. Out of 40 children 30 can swim, 27 can play chess and only5 can do neither. How many children can swim only ?(a) 30 (b) 22(c) 12 (d) 8

6. Both the roots of a quadratic equation x2 – mx + 121 = 0 aregreater than 10. What is the minimum value of m ?(a) 21 (b) 22(c) 23 (d) cannot be determined

7. What is the simplified representation of)()()( CACBCBA where A, B, C are

subsets of a set X ?(a) A (b) B(c) C (d) )( CBAX

8. Which one of the following is the domain of the relation Rdefined on the set N of natural numbers as

?},;3032:),{( NnmnmnmR (a) {2, 4, 6, 8} (b) {3, 7, 11, 15}(c) {3, 6, 9, 12} (d) {3, 6, 9, 12, 15}

9. How many terms are there in the expansion of

?)( 10zyx (a) 11 (b) 33(c) 66 (d) 310

10. Which one of the following is correct ?(a) The relation R0 defined on the set of Real numbers asR0 = {(a, b) such that a2 + b2 = 1 for all a, b R} is anequivalence relation.(b) The relation R0 defined on the set of Real numbers asR0 = {(a, b) such that 3/1|| ba for all Rba , } is anequivalence relation(c) The relation I0 defined on the set of integers as I1I0I2 : I1

2

– 3I1I2 + 2I22 = 0 for all I1, I2 I is an equivalence relation.

(d) We define AEcB by the open sentence : A is cardinallyequivalent to B on the family of sets. Then the relation Econ family of sets is an equivalence relation.

11. How many arrangements can be made out of the letters ofthe word MOTHER taken four at a time so that eacharrangement contains the letter M ?(a) 240 (b) 120(c) 60 (d) 360

12. What are the values of k if the term independent of x in the

expansion of 10

2

xkx is 405 ?

(a) 3 (b) 6

(c) 5 (d) 4

13. If the equations (1) 02 qpxx and (2) 02 srxxhave a root in common and the second equation has equalroots then q + s is equal to which one of the following ?(a) pr/2 (b) 2pr(c) pr (d) p2r

14. If the pth, qth and rth terms of a GP are again in GP, thenwhich of the following is correct ?(a) p, q, r are in AP (b) p, q, r are in GP(c) p, q, r are in HP(d) p, q, r are neither in AP nor in GP nor in HP

15. In how many ways can 10 lions and 6 tigers be arranged ina row so that no two tigers are together ?(a) 10! × 11P6 (b) 10! × 10P6

(c) 6! × 10P7 (d) 6! × 10P6

16. The Geometric Mean of two numbers is 6. Their ArithmeticMean A and Harmonic Mean H satisfy the equation90A + 5H = 918.Which one of the following is correct ?(a) A = 10 (b) A = 1/5, A = 10(c) A = 5; A = 10 (d) A = 1/5, A = 5

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17. Eighteen football teams take part in the nationalchampionship and every team meets the same oppponenttwice. How many matches are played during thechampionship ?(a) 306 (b) 300(c) 72 (d) 153

18. If x, y, z are distinct positive numbers different from 1 suchthat (logyx . logxx – logxx) + (logxy . logzy – logyy) +(logxz . logyz – logzz) = 0, what is the value of xyz ?(a) 2 (b) 1(c) –1 (d) 0

19. Which one of the following is the union of the closed sets?

?,.......2,1,110,12

n

nn(a) [2, 10] (b) (2, 10)(c) [2, 10) (d) (2, 10]

20. Indicate which one of the points given below is not a partof the solution of the inequation ?

?0,0;1243 yxyx(a) (4, 2) (b) (1, 3)(c) (2, 1) (d) (2/3, 11/4)

21. If A is a square matrix of order n × n and k is a scalar, thenadj(kA) is equal to which one of the following ?(a) k adj A (b) k2 adj A(c) kn–1adj A (d) kn adj A

22. For what value of k, the system of linear equationsx + y + z = 2, 2x + y – z = 3, 3x + 2y + kz = 4has a unique solution ?(a) k is any real number other than zero(b) k is any real number(c) k is any integer(d) k = 0

23. If the determinant of a non-singular matrix

333

222

111

cbacbacba

is denoted by , what is the determinant of the matrix

?443443443

33333

22222

11111

cbcbacbcbacbcba

(a) (b) –(c) 7 (d) 4

24. What is the value of the determinant ?111

2

2

2

abcccabbbcaa

(a) abc (b) ab + bc + ca(c) 0 (d) (a – b)(b – c)(c – a)

25. If A is a non-singular matrix of order n × n, then which oneof the following is equal to |adj A| ?(a) |A|n + 1 (b) |A|n

(c) |A|n – 1 (d) |A|n – 1

26. If

zyx

M and ]543[G are two matrices, then

which one of the following is correct ?(a) In the product matrix MG = [hij], the element h32 is 5y.(b) In the product matrix MG = [hij], the element h32 is3x + 4y + 5z.(c) In the product matrix MG = [hij], the element h32 is 4z.(d) In the product matrix MG = [hij], the element h32 doesnot exist

27. If ,0010

A then which one of the following is equal to

(aI + bA)n ?

(a) bAnaIa nn 1 (b) bAnaa nn 1

(c) bAaIa nn 1 (d) nnn AbIa 28. If A is a non-singular matrix such that A–1 = AT, then which

one of the following represents A ? (Here AT denotes thetranspose of A)

(a)

122112221

31

(b)

122212221

31

(c)

122112221

21

(d)

122112221

21

29. The matrix X satisfies the following equation

1011

1031

X

Which one of the following represents X ?

(a)

01

41(b)

0141

(c)

10

41(d)

1021

30. The matrix

113321210

M and its inverse N = [nij]. What

is the element n23 of the matrix N ?(a) 2 (b) –2 (c) 1 (d) –1

31. If ,2

3sinsinsin 111 zyx then what is the value

of ?zyx (a) –3 (b) 3 (c) –1/3 (d) 1/3

32. If ,9011 0Y then what is the value of the expression

YYYYYYYYY 9tan8tan7tan6tan5tan4tan3tan2tantan

?10tan Y(a) 0 (b) –1 (c) 1 (d) 2

3

33. If pA sin and qB sin where |p| and |q| are both lessthan 1, then what are the total number of possible (anddistinct) values of sin (A + B) ?(a) 1 (b) 2(c) 3 (d) 4

34. If cossincossin 33 yx and ,cossin yx

then which one of the following is correct ?

(a) 022 yx (b) 122 yx

(c) 022 yx (d) 122 yx35. If sin C and cos C are the two roots of a quadratic equation

012 2 pxx where ,2

0 C then how many

possible values can p have ?(a) 1 (b) 2(c) 3 (d) 4

36. Let n be a natural number such that n > 4 and

.cossin XXU nnn Which one of the following is

correct ?

(a) XXUUU nnn22

42 cossin

(b) XXUUU nnn cossin32

(c) XXUUU nnn22

24 cossin

(d) XXUUU nnn cossin2 42 37. The three angles A, B and C of a triangle ABC are in AP and

c2 = a2 + b2. If c = 50 metres, then what is the area of thetriangle is square metres ?

(a) 2

625(b)

22625

(c) 2

3625 (d) 625

38. If 4

)14( nyx (where n is an integer) and x + y is not

an odd multiple of /2, then what is the value of the

following expression ?2cos2cos2sin2sin

yxyx

(a) –1 (b) 0(c) 1/2 (d) 1

39. From the top of a tower 60 metres high, the angles ofdepression of two objects which are on the horizontalplane and in a line with the foot of the tower are and with > .What is the distance between the two objects inmetres?(a) ecec coscos)sin(60

(b) secsec)cos(60

(c) )cot(cot60

(d) )tan(tan60 40. The points (3, 4) and (2, –6) lie on opposite sides of which

one of the following lines ?(a) 10x – y = 26 (b) 5x + 3y = –9(c) 3x – 4y = 8 (d) x – y = 10

41. Two equal parabolas have the same vertex and their axesare at right angles. What is the angle between the tangentsdrawn to them at their point of intersection (other thanvertex) ?(a) /4 (b) tan–12(c) /3 (d) tan–1(3/4)

42. Which one of the following is the nearest point on the line3x – 4y = 25 from the origin ?(a) (–1, –7) (b) (3, –4)(c) (–5, –8) (d) (3, 4)

43. Which one of the following is the reflection of the point(4, 3) on the line x + y = 0 ?(a) (–4, 3) (b) (–3, –4)(c) (–3, 4) (d) (4, –3)

44. Which one of the following is the orthocentre of thetriangle whose sides are x = 0, y = 1 and x + y – 2 = 0 ?(a) (1, 1) (b) (0, 1)(c) (–1, 0) (d) (0, –1)

45. What is the length of the focal distance from the point t ofthe parabola y2 = 4ax ?(a) at2 (b) a(1 + t2)

(c) 21

tta (d) 2at

46. Which of the following are the equations of circles whichtouch the x-axis at a distance 3 from the origin andintercept a distance 6 on the y-axis ?

(a) 0926622 yxyx

(b) 0926622 yxyx

(c) 0926622 yxyx

(d) 0962622 yxyx47. Under what condition the lines x = ay + b, z = cy + d and

,byax dycz are perpendicular to each other?

(a) 0// ccaa (b) 1 ccaa(c) 1// ccaa (d) 1 ccaa

48. What is the range of the function ?)2cos3()( 1 xxf(a) [1/4, 1] (b) (1/4, 1/2)(c) [–1/4, –1/2] (d) [1/4, 1/2]

49. Let f : R R be defined as f(x) = x|x|. Which one of thefollowing is correct ?(a) f is only onto (b) f is only one-one(c) f is neither onto nor one-one(d) f is one-one and onto

50. What is the value of ?13 3

x

x xxLim

(a) e2 (b) e3

(c) e4 (d) e–4

51. If Ax

xLimx

1sin and ,1sin0

Bx

xLimx

then which

one of the following is correct ?(a) A = 1 and B = 0 (b) A = 0 and B = 1(c) A = 0 and B = 0 (d) A = 1 and B = 1

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52. What is the value of ?sin

152100 xx

Limxxx

x

(a) (ln 2) (ln 5) (b) (ln 3) (ln 5)(c) (ln 10) (ln 5) (d) 0

53. Let f(x) = [x], where [x] denotes the greatest integercontained in x. Consider the following statements :I. f(x) is not onto. II. f(x) is continuous at x = 0.III. f(x) is discontinuous for all positive integral values of x.Which of the statements given above are correct ?(a) I and II (b) I and III(c) II and III (d) I, II and III

54. If nmnm yxyx )( then what is the value of dy/dx ?(a) x/y (b) xy(c) y/x (d) 1

55. For what values of p the function

111)(

2

xx

ifif

pxpxxf

is derivable at x = 1 ?(a) 1/2 (b) 2 (c) –1/2 (d) –2

56. What is the derivative of ?log 2 xx

(a) 1/x (b) zero(c) 1/2x (d) 1/2

57. A function f : R R satisfies f(x + y) = f(x) f(y) for allx, y R and 0)( xf for all x R. If f(x) is differentiable

at x = 0 and 2)0( f then )(xf is equal to which oneof the following ?(a) f(x) (b) –f(x)(c) 2f(x) (d) f(x)/2

58. Let f(x) be a differentiable even function. Consider thefollowing statements :I. )(xf is an even function.

II. )(xf is an odd function.

III. )(xf may be even or odd.Which of the above statements is/are correct ?(a) I only (b) II only(c) I and III (d) II and III

59. What is the derivative of |4||1| xx at x = 3 ?(a) –3 (b) 3(c) 0 (d) 2

60. Let g(x) be the inverse of an invertible function f(x) whichis differentiable at x = c. Which one of the following isequal to ?)]([ cfg

(a) )(cf (b) )(/1 cf (c) f(c) (d) 1/f(c)

61. If ,53

3523)(

xxxxf then which one of the following

is correct ?

(a) )()(1 xfxf (b) )()(1 xfxf

(c) xxfof )()( (d) )(191)(1 xfxf

62. The population of a country doubles in 50 years.Assuming that the rate of increase of population ofproportional to the number of inhabitants, in how manyyears would the population become three times ?

(a) 2ln3ln50 (b)

3ln2ln50 (c) 6ln50 (d) 75

63. Which one of the following represents the differentialequation of all parabolas having the axes of symmetrycoincident with the axis of x ?

(a) 02

2

2

dxdy

dxydy (b) 0

2

2

2

3

3

dxyd

dxydy

(c) 02

2

2

dxyd

dxdyy (d) 0

2

3

3

dxyd

dxdyy

64. Which one of the following definite integrals representsthe area included between the parabola 4y = 3x2 and thestraight line 2y = 3x + 12 ?

(a) 4

2

2

43 dxx (b)

4

02

43

2123 dxxx

(c)

4

22

43

2123 dxxx (d)

2

22

43

2123 dxxx

65. What is the value of ?)(

cos0 44

dx

xxx

(a) zero (b) (c) /4 (d) /2

66. What is the value of ?|sin|100

0

dxx

(a) 100 (b) 100(c) 200 (d) 200

67. What is the integration of ?)(4

3/13

xxx

(a) cx

3/4

2 1183

(b) cx

3/4

2 1183

(c) cx

3/4

211

81 (d) c

xxx

4

3/13 )(

68. What is the integration of ?xe

(a) cxe x )1( (b) cxe x )1(2

(c) cxe x )1(2 (d) ce x 69. Which one of the following equations represents the

differential equation of circles, with centres on the x-axisand all passing through the origin ?

(a) xy

yxdxdy

2

22 (b)

xyyx

dxdy

2

22

(c) xy

xydxdy

2

22 (d)

yx

dxdy

5

70. What is the degree of the differential equation

?0453 2

23/2

3

3

dxdy

dxyd

dxyd

(a) 3 (b) 2/3(c) 2 (d) 6

71. If x m

m dxxI1

)(ln satisfies the relation

,)(ln 1 mm

m IlxxI then which one of the following iscorrect ?(a) l = m – 1 (b) l = m(c) l = m + 1 (d) l = m2 + 1

72. What is the integration of ?ln xax ee

(a) xae)( (b) )(ln

)(ae

ae x(c)

)ln1( aex

(d)

)(ln aex

73. If cba ,, are three mutually perpendicular vectors each

of magnitude unity, then what is the magnitude of

?cba

(a) 3 (b) 1 (c) 3 (d) 1/374. For what value of k, the points with position vectors

jiji ˆ8ˆ40,ˆ3ˆ60 and jik ˆ52ˆ are collinear ?(a) k = 40 (b) k = –40 (c) k = –30 (d) k = 20

75. If ba

, and c are three vectors of which every pair is

non-collinear. If the vectors ba

and cb

are collinearwith the vectors c and a respectively, then which one ofthe following is correct ?

(a) cba

is a null vector

(b) cba

is a unit vector

(c) cba

is a vector of magnitude 2 units

(d) cba

is a vector of magnitude 3 units

76. If ,1|||||| baba then what is the angle between the

vectors a and b

?(a) /6 (b) /3 (c) /2 (d) /4

77. What is the area of the parallelogram having diagonals

kjia ˆ2ˆˆ3 and ?ˆ4ˆ3ˆ kjib

(a) 52 square units (b) 43 square units(c) 53 square units (d) 103 square units

78. If kjbjia ˆˆ2,ˆˆ and babrabar

,

then what is the value of ?|| r

r

(a) 11

)ˆˆ3ˆ( kji (b)

11)ˆˆ3ˆ( kji

(c) 11

)ˆˆ3ˆ( kji (d)

11)ˆˆ3ˆ( kji

79. Which one of the following vectors represents the unitvector parallel to the YZ plane and perpendicular to the

vector ?ˆ2ˆ4ˆ3 kji

(a) 6

)ˆˆˆ2( kji (b)

5)ˆ2ˆ( kj

(c) 2

)ˆˆ( kj (d) 94

)ˆ9ˆ3ˆ2( kji

80. In an experiment two variables X and Y are observed onsome units. It was recorded that x = 2y. Which one of thefollowing statements is correct ?(a) The regression coefficient of Y on X is four times theregression coefficient of X on Y(b) The regression coefficient of Y on X is equal to theregression coefficient of X on Y(c) The regression coefficient of X on Y is four times theregression coefficient of Y on X(d) The value of correlation coefficient exceeds unity

81. An electric device consists of two bulbs A and B. Fromprevious testing procedure, the following results areknown:P[A is fused] = 0.20;P[B is fused alone] = 0.15;P[A and B are fused] = 0.15.What is the probability that bulb A is fused alone ?(a) 0.15 (b) 0.20(c) 0.05 (d) 0.25

82. Which one of the following statistical measures cannot bedetermined graphically ?(a) Median (b) Mode(c) Harmonic Mean (d) Arithmetic Mean

83. The following relative frequency distribution shows thedistribution of 50 members of a country social programmeaccording to their age :Age (in years) Relative frequency30 - 39 0.0240 - 49 0.0650 - 59 0.1660 - 69 0.3270 - 79 0.2080 - 89 0.1690 - 99 0.08What is the number of members who are older than 50 ?(a) 4 (b) 8(c) 46 (d) 16

84. Match List I with List II and select the correct answerusing the codes given below the Lists :List I List II

I. Average shoe size (a) Geometric MeanII. Average speed for equal (b) Harmonic Mean

distances coveredIII. Average speed for equal (c) Arithmetic Mean

times spentIV. Average rate of population (d) Mode

growth(a) I-A, II-B, III-C, IV-D (b) I-A, II-C, III-B, IV-D(c) I-D, II-B, III-C, IV-A (d) I-D, II-B, III-A, IV-C

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85. If the variates are independent, then which one of thefollowing is correct ?(a) The covariance is negative(b) The covariance is positive(c) The covariance is zero(d) The covariance cannot be calculated

86. What is the value of

termsupto 198......411log

311log

211log 101010

(a) 100 (b) 10(c) 2 (d) 0

87. If ,1i what is the value of ?i

(a) 2

1 i(b)

21 i

(c) 2

2 i(d)

22 i

88. If the two quadratic equations 02 cbxx and

02 cxbx have a common root, what is the value ofthe common root ?

(a) ccbb (b)

bbcc

(c) cc

bb

(d) bbcc

89. What is the sum of numbers lying between 107 and 253,which are divisible by 5 ?(a) 5220 (b) 5210(c) 5200 (d) 5000

90. A man on the top of a rock rising on a sea-shore observesa boat coming towards it. If it takes 10 minutes for the angleof depression to change from 300 to 600, how soon will theboat reach the shore ?(a) 20 minutes (b) 15 minutes(c) 10 minutes (d) 5 minutes

91. If ,seccos 22 x then which one of the following iscorrect ?(a) x = 2 (b) x < 2(c) x > 2 (d) 2x

92. If 2524sin and ,900 00 then what is the value of

?)2/sin((a) 12/25 (b) 7/25(c) 3/5 (d) 4/5

93. If ,4sectan then what is the value of ?sin

(a) 15/28 (b) 8/15(c) 15/17 (d) 3/5

94. In a triangle ABC, b2 = c2 + a2, then what is the value of?tantan CA

(a) tan B (b) tan A . tan C(c) b/ac (d) b2/ac

95. M and G are two matrices such that

321

321

321

pppnnnmmm

M

and

321

321

321

spprrrqqq

GM

What type of matrix G is ?(a) Null matrix (b) Scalar matrix(c) Lower triangle matrix (d) Upper triangle matrix

96. There are three matrices E = [lij], F = [fij] and G = [gij] suchthat EF = G. The element guv of the matrix G is zero. Whichone of the following conclusions is correct ?(a) All elements of uth column of the matrix E are zero(b) All elements of uth column of the matrix F are zero(c) All elements of uth row of the matrix F are zero(d) All elements of uth row of the matrix E are zero

97. If /2, /2, /2 are the angles with which a line makes withpositive x, y, z axes respectively, what is the value of

coscoscos ?(a) 1 (b) –1(c) 2 (d) 3

98. An equilateral triangle is inscribed in a parabola y2 = xwhose one vertex is the vertex of the parabola. What is thelength of side of the triangle ?(a) 3 units (b) 23 units(c) 33 units (d) 1 unit

99. The lines 5x – 12y – 5 = 0 and 10x – 24y + 3 = 0 are tangentsto the same circle. What is the diameter of the circle ?(a) 1 unit (b) 5 units(c) 8 units (d) 1/2 unit

100. What is the difference of the focal distances of any pointon the hyperbola ?(a) Eccentricity (b) Distance between foci(c) Length of transverse axis(d) Length of semi-transverse axis.

101. What is the radius of the sphere if the sphere

04222 222 cxbxyzyax passes through

origin, where a, b, c are constants ?(a) 1 unit (b) 2 units(c) 3 units(d) cannot be determined as the values of a, b, c are notgiven

102. Which one of the following points is on the line ofintersection of the planes x = 3z – 4, y = 2z – 3 ?(a) (4, 3, 0) (b) (–3, –4, 0)(c) (3, 2, 1) (d) (–4, –3, 0)

103. ABC is a triangle and AD is the median. If the coordinatesof A are (4, 7, –8) and the coordinates of centroid of thetriangle ABC are (1, 1, 1), what are the coordinates of D ?(a) (–1/2, 2, 11) (b) (–1/2, –2, 11/2)(c) (–1, 2, 11) (d) (–5, –11, 19)

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104. If the points (5, –1, 1), (–1, –3, 4) and (1, –6, 10) are the threevertices of a rhombus taken in order, then which one of thefollowing is the fourth vertex ?(a) (7, –4, 11) (b) (3, –7/2, 11/2)(c) (7, –4, 7) (d) (7, 4, 1)

105. What is the area of the triangle whose vertices are (0, 0, 0),(3, 4, 0) and (3, 4, 6) ?(a) 12 square units (b) 15 square units(c) 30 square units (d) 36 square units

106. What is the shortest distance from the point (2, –7) to the

circle ?0151101422 yxyx(a) 2 units (b) 3 units(c) 5 units (d) 7 units

107. P, Q, R, S are the middle points of the respective sides of aquadrilateral EFGH and vectors proportional to and alongthe sides SR, SP, QP, QR are acting. Which one of thefollowing is correct ?(a) Resultant vector is a unit vector(b) Resultant vector is a null vector(c) Resultant vector is a vector whose magnitude is greaterthan unity(d) Resultant vector is neither a unit vector nor a nullvector

108. A vector v of magnitude 4 units is equally inclined to the

vectors .̂ˆ,ˆˆ,ˆˆ ikkjji Which one of the following iscorrect ?

(a) )ˆˆˆ(3

4 kjiv

(b) )ˆˆˆ(3

4 kjiv

(c) )ˆˆˆ(3

4 kjiv

(d) )ˆˆˆ(4 kjiv

109. If )3,2,1( a

and )2,1,3( b

then which one of the

following vectors is perpendicular to ?ba

(a) ba

2 (b) ba

2

(c) ba

2 (d) ba

110. How many unit vectors are there perpendicular to both the

vectors kji ˆ4ˆ3ˆ2 and ?ˆ3ˆ2ˆ kji (a) 1 (b) 2(c) zero (d)

111. Three dice are rolled. What is the probability of gettingdifferent faces ?(a) 1/3 (b) 1/4(c) 5/9 (d) 4/9

112. If the correlation coefficient between X and Y is 0.7, what isthe correlation coefficient between U = 4X + 3 and

?2

43

YV

(a) 0.6 (b) 0.7(c) 0.8 (d) 1

113. If in 6 trials, X is a binomial variable which follows therelation 9P(X = 4) and P(X = 2), then what is the probabilityof success ?(a) 3/4 (b) 1/4(c) 3/8 (d) 1/8

114. Ten numbered balls are placed in an urn. Balls numbered 1to 4 are red and rest of the 6 balls are blue. The probabilityof drawing the ball numbered 3, of course, is 0.1. A ball isdrawn and it is red. Which one of the following statementsis correct ?(a) P(ball drawn is numbered 3 | ball drawn is red) > 0.1(b) P(ball drawn is numbered 3 | ball drawn is red) = 0.1(c) P(ball drawn is numbered 3 | ball drawn is red) < 0.1(d) P(ball drawn is red | ball drawn is numbered 3) = 0.25Directions (115 - 120) : The following questions consistof two statements, one labelled as the Assertion (A), andthe other as Reason (R). You are to examine these twostatements carefully and select the correct answers to theseitems using the codes given below :(a) Both A and R are individually true and R is the correctexplanation of A.(b) Both A and R are individually true but R is not thecorrect explanation of A(c) A is true but R is false(d) A is false but R is true

115. Assertion (A) : ,. nnn

nn

xLimnLimnxLim

where |x| < 1

Reason (R) : )(.)()()( xgLimxfLimxgxfLimnnn

(a) (b) (c) (d)116. Assertion (A) : Mean deviation can never be nagative.

Reason (R) : Mean deviation is the AM of absolutedeviation of the different values from a central tendency.(a) (b) (c) (d)

117. Assertion (A) : There is no practical difference betweenfrequency polygon and frequency curve.Reason (R) : Under frequency polygon the points are joinedby straight lines whereas under frequency curve the pointsare joined by a smooth curve.(a) (b) (c) (d)

118. Assertion (A) : If xxf )( and ,)(2

xxxF then

)()( xfxF always.Reason (R) : At x = 0, F(x) is not defined.(a) (b) (c) (d)

119. Assertion (A) : Perimeter of a regular pentagon inscribedin a circle with centre O and radius x cm equals 12x sin 360

cm.Reason (R) : Perimeter of a regular polygon inscribed in acircle with centre O and radius x cm equals 2nx sin (3600/2n)cm, then it is n-sided, where .3n(a) (b) (c) (d)

120. Assertion (A) : Four consecutive numbers which are notprimes are uniquely given by 122, 123, 124, 125.Reason (R) : Every composite number is divisible by a primeless than its square root.(a) a (b) (c) (d)

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PART - A(English)

Directions (1 - 7) : Each of the following seven itemsconsists of a word in capital letters, followed by four wordsor groups of words. Select the word or group of words thatis most similar in meaning to the word in capital letters.

1. PROCRASTINATE(a) Intimidate (b) Humiliate(c) Predict (d) Postpone

2. ABDOMINABLE(a) Original (b) Detestable(c) Preferable (d) Complimentary

3. RESCIND(a) Cancel (b) Enjoy(c) Praise (d) Receive

4. COLLATERAL(a) Pathetic (b) Tiresome(c) Guarantee (d) Magnanimous

5. KNAVE(a) Novice (b) Dishonest(c) Futuristic (d) Traditional

6. FINESSE(a) Skill (b) Softness(c) Charm (d) Gist

7. ARDOUR(a) Enthusiasm (b) Candidness(c) Discipline (d) FairnessDirections (8 - 14) : Each of the following seven itemsconsists of a word in capital letters, followed by four wordsor groups or words. Select the word or group of words thatis furthest in meaning to the word in capital letters.

8. SAGE(a) Miser (b) Fool(c) Traitor (d) Tyrant

9. FLEDGLING(a) Adversary (b) Callow(c) Social outcast (d) Experienced person

10. PREDILECTION(a) Predicament (b) Afterthought(c) Aversion (d) Postponement

11. HIDEBOUND(a) Strong-willed (b) Open-minded(c) Well-informed (d) Well-to-do

12. ADULATION(a) Criticism (b) Purity(c) Ambiguous (d) accollades

13. ANIMATED(a) Penetrating (b) Modern(c) Dull (d) Similarly

14. ILLUSIVE(a) Not brilliant (b) Not coherent(c) Not deceptive (d) Not obvious

Time Allowed : 2½ hour Maximum Marks : 600Directions (15 - 20) : Each of the following six questionshas a blank space and four words or groups of words aregiven after the sentence. Out of these four choices, selectthe word or group of words which you consider the mostappropriate for the blank space and mark your choice onthe answer Sheet.

15. To the dismay of all the students, the class monitor was.............. berated by the Principal at a school assembly.(a) critical (b) ignominiously(c) prudently (d) fortuitously

16. All attempts to revive the fishing industry were .....failure.(a) foredoomed to (b) heading at(c) predicted for (d) estimated to

17. There are ......... packed outside than yesterday.(a) fewer cars (b) few cars(c) less cars (d) a small number of cars

18. The minister had to ........ some awakard questions fromreporters.(a) fend (b) fend at (c) fend out (d) fend off

19. The ........of evidence was on the side of the plaintiffsince all but one of the witness testified that his story wascorrect.(a) propensity (b) force(c) preponderance (d) brunt

20. Attention to detail is ........... of a fine craftsman.(a) hallmark (b) stamp(c) seal of authority (d) authenticityDirections (21 - 25) : (i) In this section a number ofsentences is given. The sentences are divided in threeseparate parts and each one is labelled (a), (b), (c). Readeach sentence to find out whether there is an error in thatpart. No sentence has more than one error. When you findan error in any one of the three parts (a), (b) or (c), indicateyour response on the separate Answer Sheet at theapproriate space. You may feel that there is no error in asentence. In that case letter (d) will signify a ‘No error’response. (ii) You are to indicate only one response foreach item in your Answer Sheet. (If you indicate more thanone response, your answer will be considered wrong).Errors may be in grammar, word usage or idioms. Theremay be a word missing or there may be a word which shouldbe removed. (iii) You are not required to correct the error.You are required only to indicate your response on theAnswer Sheet.

21. If it weren’t /for you/I wouldn’t be alive today/No error. (a) (b) (c) (d)

22. He looked like a lion/baulked from/its prey/No error. (a) (b) (c) (d)

23. Widespread flooding/is effecting/large areas of the villages./ (a) (b) (c)No errors. (d)

24. She regards / negotiating prices with customers / as her (a) (b)special preserve./ No error. (c) (d)

PAPER - II (General Ability)

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25. Often in political compaigns, a point is reached at which/ (a)

the candidates take out their gloves/and start slugging (b) (c)

with bare fists./ No error. (d)

Directions (26 - 30) : In the following items each passageconsists of six sentences. The first sentence (S1) and thesixth sentence (S6) are given in the beginning. The middlefour sentences in each have been removed and jumbledup. These are labelled P, Q, R and S. You are required tofind out the proper sequence of the four sentences andmark accordingly on the Answer Sheet.

26. S1 : A city tour organised by the airport got our next vote.S6 : “We can ony grow in height as most of our land isreclaimed from the mud brought from neighbouringcountries.” said Bernadette.P : A bumboat ride through the Singapore River gave us avantage view of the country’s prized possession ofskyscrapers in the central business district.Q : The tour is very popular with transit passengers andthere are many such buses doing the route.R : We were greeted into an air-conditioned volvo bus witha bottle of chilled water.S : On the drive through the ‘colonial heart’ of the city, ourguide, Bernadette, pointed out the Parliament House.Supreme Court and City Hall to us.The proper sequence should be :(a) RSQP (b) PQSR(c) RQSP (d) PSQR

27. S1 : But Bhutan is a curious mix of modern and themedieval.S6 : His licence plate reads simply ‘BHUTAN’.P : It was next to a speed limit sign : 8 km an hour.Q : Even the king zips through in a navy blue Toyota LandCruiser.R : I noticed a rusty sign for the Kit Kat chocolate bar andrealised it was the only advertisement I had been.S : Yet in the cities, most middle class people drive brandnew Japanese cars.The proper sequence should be :(a) SQRP (b) RPSQ(c) SPRQ (d) RQSP

28. S1 : His usually fretful features composed, Javagal Srinathannounced his retirement from international cricket.S6 : He finished with 236 wickets in 67 Tests and 315 in 229One-day Internationals.P : He had spent the early years of his 13-year career sittingout nine Tests when he was at his quickest, being remindedof everything he was not.Q : In a classic case of appreciating a good thing when it isgone, the tributes poured in for India’s most successfulpace bowler after Kapil Dev.R : Not aggressive enough, not a non-vegetarian, not anall -rounder.S : Srinath soldiered on, whether wickets were flat or causeslost, as they often were when India toured.The proper sequence should be :(a) QPRS (b) RSQP (c) QSRP (d) RPQS

29. S1 : However, the flower industry also has its share of thorns.S6 : Also, there are no tax concessions from theGovernment.P : Most companies have to individually invest in thetransport, which is very costly.Q : Then there are infrastructural bottlenecks - norefrigerated transport or retail chains and warehouses tostore the highly perishable commodity.R : For one, it is extremely fragmented and dominated bysmall players who don’t have the financial muscle toexpand the business.S : Ferns & Petals claims to be the only flower retailer withmulti-city presence in India.The proper sequence should be :(a) QSRP (b) RPQS(c) QPRS (d) RSQP

30. S1 : One could well be forgiven for momentarily confusingSpencer Plaza, Chennai, with a Dubai Shopping Mall.S6 : Sensing that healthcare plus tourism adds to bigopportunities, corporate hospitals, in cooperation with touroperators, are promoting India as a healthcare destinationfrom the Middle East to far East.P : Having satiated their shopping instincts, many headback, not to a hotel, but to a hospital, and to ailingrelatives.Q : Arabs pour in and out of trendy showrooms, laden withbags full of branded clothes, footwear and cosmetics.R : It is a scenario being replicated across India.S : For these re tourists with a difference, attracted to Indiafor its cutting edge medical expertise more than its charms.The proper sequence should be :(a) QPSR (b) SRQP (c) QRSP (d) SPQRDirections (31 - 35) : In the following items some parts ofthe sentence have been jumbled up. You are required tore-arrange these parts which are labelled P, Q, R and S toproduce the correct sentence. Choose the proper sequenceand mark in your Answer Sheet accordingly.

31. Brazil’s GuaranisP : from being Internet savvyQ : are an ancient tribe who live in the country’s remotejungles,R : excluded themS : but that has not.The proper sequence should be :(a) PSRQ (b) QRSP (c) PRSQ (d) QSRP

32. A game hostP : that could be used at the airport duty-free shopsQ : and the winner walked away withR : shot out ten witty questionsS : vouchers worth 200 Singapore dollars.The proper sequence should be :(a) PSQR (b) RQSP (c) PQSR (d) RSQP

33. And whileP : without adequate international supportQ : the US military has been forced into remaining in IraqR : the overthrow of Saddam Hussein may have been quickS : longer than anticipated.The proper sequence should be :(a) RSQP (b) PQSR (c) RQSP (d) PSQR

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34. The socialist philosophyP : as it is the market philosophyQ : has been given a decent burialR : which is the rage nowS : in political practice.The proper sequence should be :(a) QSPR (b) RPSQ (c) QPSR (d) RSPQ

35. It began as an officially sanctioned project,P : could achieve as a nationQ : but turned into a mass movement and an extraordinaryact of faithR : it it got its act togetherS : which changed not just the lives of millions but thenotions of what India.The proper sequence should be :(a) PSRQ (b) QSRP (c) PRSQ (d) QRSPDirections (36 - 45) : In this section you have three shortpassages. After each passage you will find severalquestions based on the passage. First, read Passage I, andanswer the questions based on it. Then go on to the otherpassage. You are required to select your answers based onthe contents of the passage and opinion of the authoronly.

Passage II was late bloomer and always envied those people whostood out in high school, because I didn’t. I learned earlyon, though, that its essential to set yourself apart from thegroup. Life is one struggle after another to succeed,particularly when you’re starting out. If your bio-data issitting at the bottom of a pile of junk mail, sometimes adistinctive approach will get you noticed, especially if thecompetition is fierce.Once, my partner Jerry and I asked the other freelancewriters of a TV serial what characters they hated to writefor the most. Everybody said the same thing - they dislikedwriting for the minor characters because they felt thatwriting for them wouldn’t help them get others jobs. Jerryand I decided that we would write scripts for the minorcharacters because that’s what was needed and we neededto set ourselves apart.In the first script Jerry and I wrote, a schoolgirl falls in lovewith a boy in her class. The producers love the story. Andwith that one script, Jerry and I were no longer just anothercomedy writing team.

36. The author is of the opinion that(a) one should be part of the group(b) one should be different from others(c) it is important to do well in high school(d) one should heed to the advice of the seniors

37. The author had been(a) into advertising business (b) a comedy writer(c) a music director (d) a newsreader

38. According to the author(a) one should be very meticulous in preparing hisbio-data(b) competition in the job-market is very fierce(c) one should follow a conserative approach in preparinghis bio-data(d) one should try to get noticed by being innovative

39. Jerry and the author wrote scripts for the minor characters(a) to realise their creative potential(b) to earn more money(c) to establish a different image(d) because they did not have enough work

Passage IIWind power has obvious advantages - it is non-polluting,causes no ecological imbalance, requires no throughoutfuel and has extremely low gestation period.After almost a decade of sporadic growth, wind energyfinally seems to be stepping out from shadows ofalternative technology into the commercial mainstream,worldwide. Even though, India now has an installed baseof just over 1,600 MW. This is nothing compared tocountries such as Germany, which meets around 20 percent of its energy requirements from wind energy.Wind power offers long-term price stability too. Not onlyare generation costs of such projects low, the capitalexpenditure is comparable to fossil fuel-based stations.Wind power plants have low operating and maintenancecosts. Long-term economics work out to be quite favourablefor the wind energy. In fact, it is being seen as a solution tosustainable development. By the end of 2001, the installedwind power was almost 25,000 MW.

40. Which one of the following is correct ?(a) Wind-power plants take a long time to get com(b) Maintenance cost of wind-power plants is high(c) Wind-power plants lead to violent vibrations(d) Wind-power plants require no fuel

41. Which one of the following is correct ?(a) Installation of wind-power plants is resisted byenvironmentalists(b) Generation cost of wind-power plants is high(c) Installation cost of wind-power plants is much higherthan that of fossil fuel-based plants(d) Wind power is now being commercially harnessed

42. Which one of the following is correct ?(a) In Germany 25,000 MW of electricity is generated byusing wind power(b) Wind-power plants offer no price stability(c) Wind power is economically viable on long-term basis(d) In America, 20 per cent of the power requirements aremet through wind power

Passage IIIA group of prospective jurors was asked by the judgewhether any of them felt they had ever been treatedunfairly by an officer of the law. “I once got a ticket forrunning a stop sign,” Caroline replied, “even though Idefinitely came to a complete stop.”“Did you pay the fine ?” the judge quesioned.“Yes”“If you thought you were innocent,” the judge went on,“why didn’t you contest it?”“Your Honour,” She replied, “there have been so manytimes I didn’t get a ticket for running a stop sign that Ifigured this evened things out a little.”

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43. Which one of the following is correct ?(a) Caroline was caught travelling without ticket in a localtrain(b) Caroline was caught while driving at a speed above thespeed limit(c) Caroline was driving without a driving license(d) Caroline was fined for jumping the stop signal

44. Which one of the following is correct ?(a) Caroline made a complaint against the traffic inspectorfor his high-handedness(b) Caroline had to pay a bride(c) Caroline was sent to the jail for her crime(d) Caroline decided to pay the fine

45. Which one of the following is correct ?(a) Caroline had been penalised many times before fordriving offences(b) Caroline was an officer of the law(c) Caroline wa a prospective juror(d) Caroline was undergoing police trainingDirections (46 - 50) : In the following passage at certainpoints, you are given a choice of three words/phrasesunderlined and marked (a), (b), (c). Choose the best word/phrase out of the three and indicate your choice in therelevant column of your answer sheet.It hasn’t worked......46...... that way. Indeed, the gapsbetween theory and reality are so numerous that they....47....questions about how much, if at all, the theory will work inthe future. Americans projected their own experience ontothe rest of the world. If prosperity and material progresshad created political cohesion at home - binding together alarge and .......48..... nation - it could do the same abroad.But this marriage between economics and politics may belosing its power. What seemed to be the ascendancy ofAmerican ideas camouflaged new problems and conflicts.The theory may have been .....49..... suited to the cold warthan its aftermath. The most ......50..... problem, of course,involves the outbreak of terrorism.

46. (a) by (b) out(c) off

47. (a) raise (b) arise(c) rise

48. (a) ethically diverse (b) ethnically diverse(c) ethnically wide

49. (a) better (b) aptly(c) much

50. (a) conspicuous (b) conscientious(c) conscious

PART - B(General Knowledge)

51. In the map given alongside, four areas/regions are markedas 1, 2, 3 and 4. Which of these is/are semiarid area(s) ?(a) 1 only (b) 1, 2, 3(c) 2, 3 and 4 (d) 1 and 4

52. Quartzite is a metamorphic form of(a) granite (b) basalt(c) limestone (d) sandstone

53. Which one of the following countries does not broderMediterranean Sea ?(a) Malta (b) Libya (c) Italy (d) Bulgaria

54. Which one of the following statements is correct ?Chemical weathering includes(a) oxidation, reduction and exfoliation.(b) carbonation, oxidation and exfoliation(c) exfoliation, solution and reduction(d) solution, oxidation and reduction

55. Match List I (Agents) with List II (Landforms) and selectthe correct answer using the codes given below the Lists: List I List II(Agents) (Landforms)

I. River (A) CirqueII. Glacier (B) StalagmiteIII. Underground water (C) CraterIV. Wind (D) Meander

(E) Barachan(a) I-E, II-B, III-C, IV-D (b) I-D, II-A, III-B, IV-E(c) I-D, II-A, III-B, IV-E (d) I-E, I-A, III-B, IV-D

56. The deepest oceanic trench ‘Mariana’ is located in(a) Atlantic Ocean (b) Arctic Ocean(c) Pacific Ocean (d) Indian Ocean

57. A type of rainfall which occurs when wind rises up along ahill or mountain barrier is called(a) Anti-cyclonic (b) Convectional(c) Cyclonic (d) Orographic

58. The Tropic of Cancer passes through(a) Bihar (b) Gujarat(c) Uttar Pradesh (d) Orissa

59. The Tibetan river ‘Tsangpo’ enters India through the Stateof(a) Arunachal Pradesh (b) Assam(c) Manipur (d) Nagaland

60. Which one of the following pairs is not correctly matched?Mountains Continents

(a) Rocky : North America(b) The Andes : South America(c) The Alps : Europe(d) Ural : Africa

61. Which one of the following pairs is not correctly matched?(a) Abuja : Nigeria(b) Ashkhabad : Turkmenistan(c) Pretoria : South Africa(d) Rabat : Yemenm

62. Match List I (Cities) with List II (Climate Type) and selectthe correct answer using the codes given below the Lists:List I List II(Cities) (Climate Type)

I. Auckland (A) MediterranenII. Lagos (B) Humid SubtropicalIII. San Francisco (C) Marine West EuropeanIV. Shanghai (D) Equatorial

Codes :(a) I-B, II-A, III-D, IV-C (b) I-C, II-D, III-A, IV-B(c) I-B, II-D, III-A, IV-C (d) I-C, II-A, III-D, IV-B

63. Which one of the following is not an Igneous Rock ?(a) Basalt (b) Dolerite(c) Granite (d) Limestone

64. Which one of the following soils is represented by theshaded portion in the given map ?(a) Alluvial soil (b) Black soil(c) Red and yellow soil (d) Laterite soil

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65. Which one among the following States has the lowest sexratio as per Census 2001 of India ?(a) Haryana (b) Punjab(c) Sikkim (d) Uttar Pradesh

66. Which one of the following pairs is not correctly matched?(a) Alwaye : Fertilisers(b) Ankleswar : Crude Oil(c) Neyveli : Aluminium(d) Nepanagar : Newsprint

67. Match List I (Tourist Place) with List II (State) and selectthe correct answer using the codes given below the Lists:List I List II(Tourist Place) (State)

I. Amber Fort (A) Uttar PradeshII. Auroville (B) PondicherryIII. Buland Darwaza (C) KarnatakaIV. Gol Gumbaz (D) Rajasthan

(E) Madhya Pradesh(F) Tamil Nadu

Codes :(a) I-D, II-F, III-A, IV-B (b) I-A, II-B, III-E, IV-C(c) I-D, II-B, III-A, IV-C (d) I-A, II-F, III-E, IV-B

68. West Bengal shares boundaries with how many foreigncountries ?(a) One (b) Two(c) Three (d) Four

69. Consider the following with reference to the disintegrationand decline of the Mauryan Empire :I. Brahmanical revoltII. King Asoka’s pacifist policiesIII. Invasions from outsideIV. Weakness of Asoka’s successorsWhich of the above reasons led to the disintegration anddecline of the Mauryan Empire ?(a) I, II and IV (b) II and IV(c) I and III (d) I, II, III and IV

70. Who among the following gave the town of Masulipatamto the French ?(a) Asaf Jah (b) Nasir Jang(c) Muzaffar Jang (d) Salabat Jang

71. Consider the following statements :I. The Sikh leader Banda Bahadur was captured and killedduring the reign of Emperor Farrukh Siyar.II. The Marathas fought with Ahmad Shah Abdali atPanipat during the reign of Emperor Shah Alam II.Which of the above statements is/are correct ?(a) I only (b) II only(c) Both I and II (d) Neither I nor II

72. During India’s freedom struggle, the ‘Sepoy Mutiny’started from which one of the following places ?(a) Agra (b) Gwalior (c) Jhansi (d) Meerut

73. Vasco da Gama discovered the sea-route to India in whichone of the following years ?(a) 1498 AD (b) 1492 AD(c) 1494 AD (d) 1453 AD

74. Which one of the following Indian States is the largestproducer of natural rubber ?(a) Tamil Nadu (b) Kerala(c) Assam (d) Andhra Pradesh

75. Who found the Brahmo Samaj ?(a) Debendranath Tagore(b) Keshab Chandra Sen(c) Raja Ram Mohan Roy(d) Ishwar Chandra Vidyasagar

76. Which one of the following Articles of the Constitution ofIndia was provision for the President to proclaimemergency ?(a) Article 352 (b) Article 355(c) Article 356 (d) Article 360

77. Which one of the following offices is held during thepleasure of the President of India ?(a) Vice-President (b) Chief Justice of India(c) Governor of a state(d) Chairman of the Union Public Service Commission

78. Which one of the following pairs is not correctly matched?(a) ‘Purna Swaraj’ Resolution : 1929(b) Martyrdom of Sardar Bhagar Singh : 1931(c) Formation of the Congress Socialist Party : 1938(d) Simla Conference : 1945

79. Who among the following was regarded by MahatmaGandhi as his political ‘Guru’ ?(a) Dadabhai Naoroji (b) Bal Gangadhar Tilak(c) Feroz Shah Mehta (d) Gopal Krishna Gokhale

80. Which one of the following chronological orders of thegiven events is correct ?(a) The Cripps Mission - The Civil DisobedienceMovement - The Cabinet Mission’s Plan(b) The Civil Disobedience Movement - The CrippsMission - The Cabinet Mission’s Plan(c) The Cripps Mission - The Cabinet Mission’s Plan - TheCivil Disobedience Movement(d) The Civil Disobedience Movement - The CabinetMission’s Plan - The Cripps Mission

81. Select the correct chronological sequence of the formationof the given organisations(a) Brahma Sabha - Madras Mahajana Sabha - Arya Samaj(b) Madras Mahajana Sabha - Brahma Sabha - Arya Samaj(c) Brahma Sabha - Arya Samaj - Madras Mahajana Sabha(d) Madras Mahajana Sabha - Arya Samaj - Brahma Sabha

82. The Lingaraja Temple built during the medieval period is at(a) Bhubaneswar (b) Khajuraho(c) Madurai (d) Mount Abu

83. In which one of the following countries Fabian Socialismwas advocated ?(a) United States of America (b) Soviet Union(c) Poland (d) United Kingdom

84. Consider the following statements with reference toIndustrial Revolution :I. Industrial Revolution first took place in FranceII. Capitalists and entrepreneurs in England supportedindustrialisationIII. The Tsarist rule delayed Russia’s industrialisation.Which of the statements given above is/are correct ?(a) I only (b) II only(c) I, II and III (d) II and III

85. Which one of the following is considered an encyclopaediaof Indian medicine ?(a) Charakasamhita (b) Lokayata(c) Brihatsamhita (d) Suryasiddhanta

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86. Which one of the following is not included in the‘eight -fold path’ of Buddhism ?(a) Right speech (b) Right contemplation(c) Right desire (d) Right conduct

87. Central Board of Film Certification comes under which ofthe following Ministries of the Government of India ?(a) Ministry of Tourism and Culture(b) Ministry of Human Resources Development(c) Ministry of Information and Broadcasting(d) Ministry of Youth Affairs and Sports

88. In the year 2003, A.B. Vajpayee had the honour ofaddressing the National Assembly of(a) Indonesia (b) Malaysia(c) Thailand (d) Vietnam

89. Jaouad Gharib who won the gold medal in the Marathon atthe World Athletic Championships held in Aug. 2003 isfrom which one of the following countries ?(a) Morocco (b) Spain(c) Ethiopia (d) Kenya

90. Which one of the following pairs is not correctly matched?Venue of Cricket CountryTest Matches(a) Port of Spain : West Indies(b) Headingley : England(c) Hamilton : New Zealand(d) Kandy : Australia

91. Who is India’s first Woman Grand Master in Chess ?(a) Aarthie Ramaswamy (b) Koneru Humpy(c) S. Meenakshi (d) S. Vijayalakshmi

92. Which one of the following countries has not hostedMinisterial Conference of the WTO so far ?(a) Mexico (b) USA(c) England (d) Singapore

93. Which one of the following groups of players receivedRajiv Gandhi Khel Ratna Award in the year 2003 ?(a) Anju B. George and Anjali Bhagwat(b) Anju B. George, K. Sasikiran and K.M. Beenamol(c) Anjali Bhagwat, K. Sasikiran and K.M. Beenamol(d) Anjali Bhagwat and K.M. Beenamol

94. Who won the Royal Challenge Indian OpenChampionship in Golf in the year 2003 ?(a) Arjun Atwal (b) Jyoti Randhawa(c) Mike Cunning (d) Rick Gibson

95. Who among the following footballers ws declared FIFA’sWorld Player of the Year in 2003 ?(a) David Beckhem (b) Zinedine Zidane(c) Derlei Silva (d) Rivaldo

96. Which one of the following statements is correct ?Vaclav Havel, former President of the Czech Republic, wasrecently in the news in India because he(a) offered to negotiate between China and India to resolvethe border dispute in North-East(b) was awarded the Gandhi Peace Prize for hisoutstanding contribution towards promoting peace anddefending human rights(c) made a good compaign to select India for a permanentseat in the United Naions Security Council(d) made a huge donation to help various voluntaryorganisations to campaign against the spread of HIV/AIDS

Directions (97 - 100) : The following items consist of twostatements, one labelled as the Assertion (A) and the otherlabelled as the Reason (R). You are to examine these twostatements carefully and select the answers to these itemsusing the codes given below :Codes :(a) Both A and R are individually true, and R is the correctexplanation of A.(b) Both A and R are individually true, but R is not thecorrect explanation of A.(c) A is true, but R is false.(d) A is false, but R is true.

97. Assertion (A) : In 1773, there arose an armed conflictbetween Americans and the British.Reason (R) : In 1773, when the teaships arrived at NewYork, the Americans threw the tea into the harbour.(a) (b) (c) (d)

98. Assertion (A) : The State of Hyderabad was founded byNizam-ul Mulk, a Wazir of Mughal Emperor.Reason (R) : The Mughal Emperor frustrated all theattempts of Nizam-ul Mulk at reforming the adminnstrationof the empire.(a) (b) (c) (d)

99. Assertion (A) : Isotherms have a general East-West trendaround the globe.Reason (R) : All centres of high and low temperature occurover landmasses.(a) (b) (c) (d)

100. Assertion (A) : The Narmada is the largest among theWest-flowing rivers of Peninsular India.Reason (R) : It flows through the rift valley.(a) (b) (c) (d)

101. A large magnet is broken into two pieces. If the lengths oftwo pieces are in ratio of 3 : 4, what is the ratio of their polesrengths ?(a) 3 : 4 (b) 4 : 3(c) 1 : 3 (d) 3 : 2

102. The current I and voltage V variations for a given metallicwire at two different tempe-ratures T1 and T2 are shown inthe Fig. Then, which one of the following is correct ?

v

I

T1

T2

(a) T1 > T2 (b) T1 < T2

(c) T1 = T2 (d) T1 = 2T2

103. Consider the following statements :I. According to be Broglie hypothesis, particles havewave-like characteristics,II. When an electron and proton have the same de Brogliewavelength, they will have equal momentum.Which of the statements given above is/are correct ?(a) I only (b) II only(c) Both (a) and (b) (d) Neither (a) nor (b)

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104. Which one of the following figures correctly representsthe variation of the potential energy of a body moving upvertically under the influence of gravity ? (PE is thepotential energy and h is the height above ground level)

(a)

h

PE

(b)

h

PE

(c)

h

PE

(d)

h

PE

105. The moon is revolving in a circular orbit around earth witha uniform speed V. If the gravitational force suddenlydisappears, the moon will(a) continue to move with speed V along the original orbit(b) fall downward to Earth with increasing velocity(c) finally come to rest somewhere on the original path(d) move with the velocity V tangentially to the originalorbit

106. A beaker full of hot water is kept in a room and it cools from800C to 750C in t1 minutes and from 750C to 700C in t2minutes and from 700C to 650C in t3 minutes. Then, whichone of the following is correct ?(a) t1 > t2 > t3 (b) t1 = t2 = t3(c) t1 = 1.2 t2, t2 = 1.2 t3 (d) t1 < t2 < t3

107. Alternating current instead of direct current is used inlong-distance electric transmission because(a) it is easy to generate(b) rectification is possible(c) energy losses are minimum(d) it causes fewer accidents

108. In the human eye, the focussing is done by(a) to the fro movement of the eye lens(b) to and fro movement of the retina(c) change in the convexity of the eye lens(d) change in the refractive index of the eye fluids

109. Consider the following statements with reference to X-rays:I. They produce heat when absorbed by matter.II. They are generated when fast moving electrons strike ametal target.III. They can penetrate through a thin sheet of aluminium.Which of the statements given above are correct ?(a) I, II and III (b) I and II(c) II and III (d) I and III

110. Consider the following statements :I. Horsepower is a bigger unit of power than kilowatt.II. One thousand crore is equal to 1010.III. One acre is slightly greater than 5000 square metres.Which of the statements given above is/are correct ?(a) I and II (b) II only(c) I and III (d) II and III

111. Two plane mirrors A and B are placed at a distance 12 cmapart facing towards each other. An object is placed inbetween them at a distance 8 cm from the mirror A. Whatwill be the distance between the first two images formed inthe mirror B ?(a) 4 cm (b) 8 cm(c) 16 cm (d) 20 cm

112. A wire is bent in the form of uniform circular ring. A and B

are two points on the ring such that ,600AOB whereO is the centre of ring. If the equivalent resistance across Aand B is 5, what is the resistance of the whole wire ?(a) 5 (b) 6(c) 30 (d) 36

113. Three similar bulbs A, B, C are connected to a voltagesource as shown in the figure. If C is removed how will theillumination of A and B be affected ?

A

B C

(a) Both A and B will become dimmer(b) Both A and B will become brighter(c) A will become dimmer and B will become brighter(d) A will become brighter and B will become dimmer

114. A body lying at rest suddenly breaks into two parts ofequal masses which start moving. The two parts will movein(a) opposite direction with equal speed(b) same direction with equal speed(c) any direction with unequal speed(d) opposite direction with unequal speed

115. A massless rubber balloon has been inflated by filling itwith 200 grams of water. How much will this balloon weigh,when it is completely immersed in water contained in abucket ? (Take g = 9.8 m/s2)(a) 3.92 N (b) 1.96 N (c) 0.98 N (d) zero

116. Which one of the following pairs of physical quantitieshas the same dimensions ?(a) Surface tension and tension(b) Latent heat and Specific heat(c) Momentum and Impulse(d) Acceleration due to gravity and Gravitational constant

117. In a garden, a boy is swinging in the standing position.How will the time period of the swing be affected if the boysits down on the swing ?(a) Time period will not change(b) Time period will increase(c) Time period will decrease(d) Time period will depend on the weight of the boy

118. Which one of the following statements is correct ?A slab of ice kept in a room(a) does not radiate heat(b) does not radiate heat but absorbs heat from thesurrounding(c) radiates heat but absorbs more heat from thesurrounding(d) radiates heat more than that absorbed by it from thesurrounding

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119. Consider the following statements :The fog during winter season is more on the day whenI. sky is clearII. sky is cloudyIII. wind is blowing.Which of the statements given above is/are correct ?(a) I only (b) II and III(c) II and III (d) II only

120. Consider the following statements regarding electric fusewire :I. It has low melting point.II. It has very high specific resistance.III. It is connected in parallel with the electric circuit.Which of the statements given above is/are correct ?(a) I only (b) I and III(c) I and II (d) II and III

121. Consider the following statements :I. 1 gram of water at 1000C and 1 gram of steam at 1000Ccontain same amount of heatII. 1 m3 of dry air is heavier than 1 m3 of humid air.III. Density of a substance in CGS system is numericallyequal to its specific gravity.Which of the statements given above is/are corrct ?(a) I only (b) III only(c) I and III (d) II and III

122. Match List I and List II and choose the correct answerusing the codes given below the Lists :List I List II

I. Movement of water and minerals (A) Bernoulli’sfrom earth to leaves of plantsthrough roots

II. Lift of an aeroplane during its flight (B) Capillary action

III. Formation of a star in the universe (C) Surface tension

IV. Cleaning action of soap (D) Gravitational force

Codes :(a) I-B, II-A, III-D, IV-C (b) I-B, II-D, III-A, IV-C(c) I-C, II-A, III-B, IV-D (d) I-C, II-D, III-B, IV-A

123. Consider the following statements :I. Atom bomb is based upon the principle of uncontrolled

nuclear fusion.II. Hydrogen bomb is based upon the principle of

uncontrolled nuclear fission.III. Nuclear reactor is based upon the principle of controlled

nuclear fission.Which of the statements given above is/are correct ?(a) III only (b) I and II(c) II and III (d) I, II and III

124. An astronaut of mass 60 kg is revolving around the earthin satellite. What will be his weight inside the satelliteassuming g = 10 m/s2 ?(a) 1200 N (b) 600 N (c) Infinite (d) zero

125. A strong bar magnet is allowed to fall through a ringmade up of copper wire such that its magnetic axis isperpendicular to the plane of the ring. What will be theacceleration of the magnet during its fall ?(a) Equal to g (b) Greater than g(c) Less than g (d) zero

126. The pH of water at 250C is 7. When it is heated to 1000C, thepH of water(a) increase (b) remains same(c) decreases(d) decreases up to 500C and then it increases

127. What is the main constituent of natural gas ?(a) Methane (b) Ethane(c) Butane (d) Hydrogen

128. Which one of the following is not a sulphate ore ?(a) Barytes (b) Calamine(c) Gypsum (d) Epsom salt

129. With reference to the chemical element with atomicnumber 17, consider the following statements :I. It belongs to second period in the periodic table ofchemical elements.II. It forms anion with unit negative charge.Which of the statements given above is/are correct ?(a) I only (b) II only(c) Both (a) and (b) (d) Neither (a) nor (b)

130. Consider the following statements :I. Phosphorus exhibits oxidation states of 3 and 5.II. Iron exhibits oxidation states of 2 and 3.Which of the statements given above is/are correct ?(a) I only (b) II only(c) Both (a) and (b) (d) Neither (a) nor (b)

131. Which one among the following is the most unreactivegas?(a) Hydrogen (b) Oxygen(c) Carbon dioxide (d) Nitrogen

132. The conversion of Fe++ to Fe+++ is :(a) Oxidation (b) Reduction(c) Ionisation (d) Nuclear reaction

133. Which one of the following is obtained in its pure formwhen sugar is treated with sulphuric acid ?(a) Water (b) Carbon(c) Oxygen (d) Hydrogen

134. Consider the following statements :Equivalent weight of a compound is the weight of it thatcombines with or displaces directlyI. 1.008 parts by weight of hydrogenII. 16 parts by weight of nitrogenIII. 35.45 parts by weight of chlorineWhich of the statements given above are correct ?(a) I, II and III (b) I and II(c) II and III (d) I and III

135. Consider the following elements :I. CopperII. GoldIII. PlatinumIV. SilverWhich of the above elements exist free in nature ?(a) I and II (b) II and III(c) I, III and IV (d) III and IV

136. What is the name of the process involved in the burningof hydrogen ?(a) Hydration (b) Reduction(c) Oxidation (d) Hydrogenation

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137. Consider the following statements regarding Bohr atomicmodel :I. It introduces the idea of stationary orbits.II. It assumes that angular momentum of electron is equalto –(1/2) h/2.III. It uses planetary model of the atom involving circularorbits.Which of the statements given above are correct ?(a) I and II (b) II and III(c) I and III (d) I, II and IIIDirections (138 - 140) : The following question consistsof two statements, one labelled as the Assertion (A), andthe other as Reason (R). You are to examine these twostatements carefully and select the correct answers to theseitems using the codes given below :(a) Both A and R are individually true and R is the correctexplanation of A.(b) Both A and R are individually true but R is not thecorrect explanation of A.(c) A is true but R is false.(d) A is false but R is true.

138. Assertion (A) : Glass is a very hard substance.Reason (R) : Silicon is a constituent of glass.(a) (b) (c) (d)

139. Assertion (A) : Carbon forms the largest number ofcompounds.Reason (R) : Carbon shows variable valency.(a) (b) (c) (d)

140. Assertion (A) : When zinc is added to acidified potassiumpermanganate solution the pink colour of the solutiongradually disappears with the evolution of gas.Reason (R) : Manganese has different oxidation states andaddition of zinc changes the oxidation state from the highto the low.(a) (b) (c) (d)

141. The phenomenon by which water molecules move fromthe a weaker solution to a stronger solution through asemi-permeable membrane is called(a) Diffusion (b) Osomosis(c) Transpiration (d) Translocation

142. Consider the following worms :I. Filaria worm II. Guinea wormIII. Hookworm IV. PinwormWhich of the above worms are nematodes ?(a) I and II (b) II, III and IV(c) I, III and IV (d) I, II, III and IV

143. The improper function of which of the following results incondition ‘Myxoedema’ in human beings ?(a) Adrenal gland (b) Pancreas(c) Liver (d) Thyroid gland

144. The Hepatitis-B, which affects liver, is actually a(a) Virus (b) Bacterium(c) Protozoan (d) Helminth

145. Consider the following statements :I. Euglena is a procaryotic organism.II. Blue-green algae are eucaryotic organisms.Which of the statements given above is/are correct ?(a) I only (b) II only(c) Both (I) and (II) (d) Neither (I) nor (II)

146. The corners of the cells of collenchyma tissue in plants arethickened due to the deposition of(a) Lignin and Suberin (b) Suberin and Cutin(c) Cellulose and Pectin (d) Chitin and Lignin

147. Consider the following statements :I. Frogs can breath by means of lungs only when they areadults.II. Reptiles breath by means of lungs right from the birth.Which of the statements given above is/are correct ?(a) I only (b) II only(c) Both (I) and (II) (d) Neither (I) nor (II)

148. In human body, the pancres secretes its enzymes into whichone of the following ?(a) Duodenum (b) Ileum(c) Jejunum (d) Stomach

149. Among the following food items, which one has thehighest amount of carbohydrates ?(a) Apple (b) Banana(c) Cabbage (d) Pea

150. Which among the following is the richest source isascorbic acid ?(a) Apple (b) Bean(c) Carrot (d) Guava

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ANSWERSPAPER - I

1. d 2. c 3. c 4. c 5. d 6. b 7. c 8. c 9. c 10. d 11. c 12. a 13. a 14. a15. a 16. b 17. a 18. b 19. a 20. c 21. c 22. a 23. d 24. c 25. c 26. c 27. b 28. b29. c 30. d 31. b 32. c 33. d 34. b 35. a 36. a 37. c 38. d 39. c 40. c 41. a 42. b43. b 44. b 45. b 46. a 47. a 48. d 49. d 50. c 51. a 52. a 53. b 54. c 55. a 56. b57. c 58. b 59. c 60. b 61. a 62. a 63. a 64. c 65. a 66. c 67. b 68. b 69. c 70. c71. b 72. b 73. c 74. b 75. a 76. b 77. c 78. a 79. c 80. b 81. c 82. c 83. c 84. c85. c 86. c 87. b 88. b 89. a 90. d 91. d 92. c 93. c 94. d 95. d 96. d 97. b 98. b99. d 100. c 101. d 102. d 103. b 104. c 105. b 106. a 107. b 108. b 109. d 110. d 111. c 112. b

113. b 114. a 115. c 116. a 117. a 118. d 119. a 120. c

PAPER - II1. d 2. b 3. a 4. d 5. b 6. a 7. a 8. b 9. d 10. c 11. b 12. a 13. c 14. c

15. b 16. a 17. a 18. d 19. d 20. a 21. c 22. c 23. c 24. a 25. a 26. a 27. a 28. a29. d 30. c 31. d 32. b 33. c 34. a 35. d 36. b 37. b 38. d 39. c 40. d 41. d 42. c43. d 44. d 45. c 46. b 47. a 48. a 49. b 50. a 51. d 52. d 53. d 54. d 55. b 56. c57. d 58. b 59. a 60. d 61. d 62. b 63. d 64. c 65. a 66. c 67. c 68. c 69. d 70. c71. c 72. d 73. a 74. b 75. c 76. a 77. c 78. c 79. d 80. b 81. c 82. a 83. d 84. b85. a 86. c 87. c 88. c 89. a 90. d 91. d 92. c 93. d 94. c 95. b 96. b 97. a 98. a99. c 100. b 101. c 102. b 103. c 104. a 105. d 106. d 107. c 108. c 109. b 110. b 111. c 112. c113. c 114. a 115. d 116. c 117. b 118. b 119. a 120. b 121. c 122. a 123. a 124. d 125. c 126. c127. a 128. b 129. b 130. c 131. a 132. a 133. b 134. d 135. b 136. c 137. c 138. a 139. b 140. a141. b 142. d 143. d 144. a 145. d 146. c 147. c 148. a 149. c 150. d

PAPER - I1. d 2. c 3. c 4. c 5. d 6. b 7. c 8. c 9. c 10. d 11. c 12. a 13. a 14. a

15. a 16. b 17. a 18. b 19. a 20. c 21. c 22. a 23. d 24. c 25. c 26. c 27. b 28. b

29. c 30. d 31. b 32. c 33. d 34. b 35. a 36. a 37. c 38. d 39. c 40. c 41. a 42. b

43. b 44. b 45. b 46. a 47. a 48. d 49. d 50. c 51. a 52. a 53. b 54. c 55. a 56. b

57. c 58. b 59. c 60. b 61. a 62. a 63. a 64. c 65. a 66. c 67. b 68. b 69. c 70. c

71. b 72. b 73. c 74. b 75. a 76. b 77. c 78. a 79. c 80. b 81. c 82. c 83. c 84. c

85. c 86. c 87. b 88. b 89. a 90. d 91. d 92. c 93. c 94. d 95. d 96. d 97. b 98. b

99. d 100. c 101. d 102. d 103. b 104. c 105. b 106. a 107. b 108. b 109. d 110. d 111. c 112. b

113. b 114. a 115. c 116. a 117. a 118. d 119. a 120. c

PAPER - II1. d 2. b 3. a 4. d 5. b 6. a 7. a 8. b 9. d 10. c 11. b 12. a 13. c 14. c

15. b 16. a 17. a 18. d 19. d 20. a 21. c 22. c 23. c 24. a 25. a 26. a 27. a 28. a

29. d 30. c 31. d 32. b 33. c 34. a 35. d 36. b 37. b 38. d 39. c 40. d 41. d 42. c

43. d 44. d 45. c 46. b 47. a 48. a 49. b 50. a 51. d 52. d 53. d 54. d 55. b 56. c

57. d 58. b 59. a 60. d 61. d 62. b 63. d 64. c 65. a 66. c 67. c 68. c 69. d 70. c

71. c 72. d 73. a 74. b 75. c 76. a 77. c 78. c 79. d 80. b 81. c 82. a 83. d 84. b

85. a 86. c 87. c 88. c 89. a 90. d 91. d 92. c 93. d 94. c 95. b 96. b 97. a 98. a

99. c 100. b 101. c 102. b 103. c 104. a 105. d 106. d 107. c 108. c 109. b 110. b 111. c 112. c

113. c 114. a 115. d 116. c 117. b 118. b 119. a 120. b 121. c 122. a 123. a 124. d 125. c 126. c

127. a 128. b 129. b 130. c 131. a 132. a 133. b 134. d 135. b 136. c 137. c 138. a 139. b 140. a

141. b 142. d 143. d 144. a 145. d 146. c 147. c 148. a 149. c 150. d