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NDA/NA(II) Exam 2015 Mathematics Previous Year Paper

NDA/NA(I) Exam 2015 Mathematics Previous Year Paper
July 3, 2019
NDA/NA(I) Exam 2016 Mathematics Previous Year Paper
July 3, 2019

NDA/NA(II) Exam 2015 Mathematics

Q. 1 Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is

A. an equivalence relation

B. reflexive and transitive but not symmetric

C. symmetric and transitive but not reflexive

D. reflexive and symmetric but not transitive

 

Q. 2 The matrix A will have inverse for every real number x except for

A. x = (11±√5)/2

B. x = (9±√5)/2

C. x = (11±√3)/2

D. x = (9 ±√3)/2

 

Q. 3 If the value of the determinant is positive, where a≠b≠c, then value of abc

A. cannot be less than 1

B. is greater than -8

C. is less than -8

D. must be greater than 8

 

Q. 4 consider the following statements respect of the determinant where α,β are complementary angles

1. The value of the determinant is 1/√2 cos(α-β)/2

2. the minimum value of the determinant is 1/√2

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 5 What is (1000000001)₂ – (0.0101)₂ equal to ?

A. (512.6775)₁₀

B. (512.6875)₁₀

C. (512.6975)₁₀

D. (512.0909)₁₀

 

Q. 6 If A is the matrix, then the matrix X for which 2X + 3A = 0 holds true is:

A. a

B. b

C. c

D. d

 

Q. 7 If z₁ and z₂ are complex numbers with Iz₁I = Iz₂I, then which of the following is/are correct?

1. z₁ = z₂

2. real part of z₁ = real part of z₂

3. imaginary part of z₁ = imaginary part of z₂

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. 3 only

D. none

 

Q. 8 If A and B are two matrices given, then which of the following is/are correct?

1. A and B are commute

2. AB is a null matrix

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 9 The number of real roots of the equation x² – 3IxI + 2 = 0 is

A. 4

B. 3

C. 2

D. 1

 

Q. 10 If the sum of roots of the equation ax² + bx + c=0 is equal to the sum of their squares, then

A. a²+b² = c²

B. a² + b² = a+ b

C. ab + b² = 2ac

D. ab – b² = 2ac

 

Q. 11 If A ={xεR: x²+6x-7<0} and B = {xεR:x²+9x+14>0}, then which of the following is/are correct?

1. )A∩B) = (-2,1)

2. (A∖B)=(-7,-2)

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 12 A, B,C and D are four sets such that A∩B = C ∩ D =φ.consider the following:

1. A U C and B U D are always disjoint.

2.A ∩ C and B ∩ D are always disjoint.

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 13 If A is an invertible matrix of order n and k is any positive real number, then the value of [det(KA)]⁻¹ det A

A. k⁻ⁿ

B. k⁻¹

C. kⁿ

D. nk

 

Q. 14 The value of the infinite product 6½ x 6½ x 6⅜ x 6¼ x… is

A. 6

B. 36

C. 216

D. ∞

 

Q. 15 If the roots of the equation x² – nx + m = 0 differ by 1, then

A. n²-4m-1=0

B. n²+4m-1=0

C. m²+4n+1=0

D. m²-4n-1=0

 

Q. 16 If different words are formed with all the letters of the ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary among themselves as in a dictionary, the word at the 50th place will be

A. NAAGI

B. NAAIG

C. IAAGN

D. IAANG

 

Q. 17 The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

A. 165

B. 364

C. 1001

D. 1365

 

Q. 18 In the expression of (√x + 1/3x²)¹⁰ the value of constant team (independent of x ) is

A. 5

B. 8

C. 45

D. 90

 

Q. 19 The value of sin² 5⁰ + sin² 10⁰ + sin² 15⁰ +sin² 20⁰ +…+sin² 90⁰ is

A. 7

B. 8

C. 9

D. 19

 

Q. 20 On simplifying (sin³ A + sin 3A)/sin A + (cos³ A – cos 3A)/cos A, we get

A. sin 3A

B. cos 3A

C. sin A + cos A

D. 3

 

Q. 21 The value of tan(2 tan⁻¹ 1/5 – π/4) is

A. -7/17

B. 5/16

C. 5/4

D. 7/17

 

Q. 22 Two poles are 10 m and 20 m high. The line joining their tops makes an angle of 15⁰ with the horizontal. The distance between the poles is approximately equal to

A. 36.3 m

B. 37.3 m

C. 38.3 m

D. 39.3 m

 

Q. 23 If g(x) = 1/f(x) and f(x) = x, x ≠ 0, then which one of the following is correct?

A. f(f(f(g(g(f(x)))))) = g(g(f((g(f(x)))))

B. f(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

C. f(g(f(g(g(g(f(x))))) = g(g(f(g(f(x)))))

D. f(f(f(g(g(f(x))))) = f(f(f(g(f(x))))

 

Q. 24 consider the following :

1. sin⁻¹ 4/5 + sin⁻¹ 3/5 = π/2

2. tan⁻¹ √3 + tan⁻¹ 1 = -tan⁻¹ (2+π√3)

which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 25 If A is an orthogonal matrix of order 3 and B, then which of the following is/are correct?

1.IABI = ± 47

2. AB = BA

select the correct answer using the code given below

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 26 If a,b,c are the sides of a Δ ABC, then (refer figure) where p > 1 a

A. always negative

B. always positive

C. always zero

D. positive if 1<p<2 and negative p>2

 

Q. 27 Id a,b,c are real number, then the value of the determinant is

A. 0

B. (a-b)(b-c)(c-a)

C. (a+b+c)²

D. (a+b+c)³

 

Q. 28 If the point z₁ = 1+i where i = √-1 is the reflection of a point z₂ = x+iy in the line iz̅-iz = 5, then the point z₂ is

A. 1+4i

B. 4 + i

C. 1-i

D. -1-i

 

Q. 29 If sin x + sin y= a and cos x + cos y = b, then tan² (x+y)/2+tan² (x-y)/2 is equal to

A. (a⁴ + b⁴+4b²)/(a²b²+b⁴)

B. (a⁴-b⁴+4b²)/(a²b²+b⁴)

C. (a⁴-b⁴+4a²)/(a²b²+a⁴)

D. none of the above

 

Q. 30 A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m. from a point on the field , the angles of elevation of the bottom and tip of the flag staff are 30⁰ and 45⁰ respectively. Which of the following gives the best approximation to the height of the tower?

A. 3.90 m

B. 4.00 m

C. 4.10 m

D. 4.25 m

 

Questions: 31 – 33

For the next three items that follow:

consider the expansion of (1+x)²ⁿ⁺¹

 

Q. 31 If the coefficients of x^r and x^(r+1) are equal in the expansion, then r is equal to

A. n

B. (2n-1)/2

C. (2n+1)/2

D. n+1

 

Q. 32 The average of the coefficients of the two middle terms in the expansion is

A. A

B. B

C. C

D. D

 

Q. 33 The sum of the coefficients of all the terms in the expansion is

A. 2²ⁿ⁻¹

B. 4ⁿ⁻¹

C. 2 x 4ⁿ

D. none of the above

 

Q. 34 The nth term of A.P is (3+n)/4, then the sum of first 105 terms is

A. 270

B. 735

C. 1409

D. 1470

 

Q. 35 A polygon has 44 diagonals. The number of its side sides:

A. 11

B. 10

C. 8

D. 7

 

Q. 36 If p,q,r are in one geometric progression and a,b,c are in another geometric progression then ap, bq, cr are in

A. arithmatic progression

B. geometric progression

C. harmonic progression

D. none of the above

 

Questions: 37 – 38

For the next two items that follow:

consider a triangle ABC satisfying 2a sin² (C/2)+2c sin² (A/2) = 2a+2c-3b

Q. 37 The sides of the triangle are in

A. G.P

B. A.P

C. H.P

D. neither in G.P nor in A.P nor in H.P

 

Q. 38 sin A, sin B, sin C are in

A. G.P

B. A.P

C. H.P

D. neither in G.P nor in A.P nor in H.P.

 

Q. 39 If the p=tan(-11π/6), q=tan (21π/6) and r = cot(283π/6), then which of the following is/are correct?

1. The value of p x r is 2.

2. p,q and r are in G.P.

select the correct answer using the code given below.

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 40 The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

A. 1140

B. 3420

C. 6840

D. 8000

 

Q. 41 What is the sum of n terms of the series √2+√8+√18+√32+…?

A. [n(n-1)]/√2

B. √2n(n+1)

C. [n(n+1)]/√2

D. [n(n-1)]/2

 

Q. 42 The coefficient of x⁹⁹ in the expansion of (x-1)(x-2)(x-3)…(x-100) is

A. 5050

B. 5000

C. -5050

D. -5000

 

Q. 43 zz̅+(3-i)+(3+i)z̅+1=0 represents a circle with

A. centre (-3,-1) and radius 3

B. centre (-3,1) and radius 3

C. centre (-3,-1) and radius 4

D. centre (-3,1) and radius 4

 

Q. 44 The number of 3 digit even numbers that can be found from the digits 0,1,2,3.4 and 5 repetition of digits being out allowed is

A. 60

B. 56

C. 52

D. 48

 

Q. 45 If log₈ m + log₈ 1/6 = 2/3, then m is equal to

A. 24

B. 18

C. 12

D. 3

 

Q. 46 The area of the figure formed by the lines ax+by+c=0, ax-by-c=0,ax+by-c=0 and ax-by-c=0 is

A. c²/ab

B. 2c²/ab

C. c²/2ab

D. c²/4ab

 

Q. 47 If a line is perpendicular to the line 5x-y=0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is

A. x+5y±5√2=0

B. x-5y±5√2=0

C. 5x+y±5√2=0

D. 5x-y±5√2=0

 

Q. 48 Consider any point P on the ellipse x²/25 + y²/9 = 1 in the first quadrant. Let r and s represent its distances from (4,0) and (-4,0) respectively, then (r+s) is equal to

A. 10 unit

B. 9 unit

C. 8 unit

D. 6 unit

 

Q. 49 A straight line x=y+2 touches the circle 4(x²+y²)=r². The value of r is

A. √2

B. 2√2

C. 2

D. 1

 

Q. 50 The three lines 4x+4y=1,8x-3y=2,y=0 are

A. the sides of an isosceles triangle

B. concurrent

C. mutually perpendicular

D. the sides of an equilateral triangle

 

Q. 51 The line 3x+4y-24=0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is

A. (2,3)

B. (3,3)

C. (4,3)

D. none of the above

 

Q. 52 The eccentricity of the hyperbola 16x²-9y²=1 is

A. 3/5

B. 5/3

C. 4/5

D. 5/4

 

Q. 53 The product of the perpendiculars from the two points (±4,0) to the line 3x cos φ +5y sin φ =15 is

A. 25

B. 16

C. 9

D. 8

 

Q. 54 If the centre of the circle passing through the origin is (3,4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

A. 3 unit and 4 unit

B. 6 unit and 4 unit

C. 3 unit and 8 unit

D. 6 unit and 8 unit

 

Q. 55 The lines 2x=3y=-z and 6x=-y=-4z

A. are perpendicular

B. are parallel

C. intersect at an angle 45⁰

D. intersect at an angle 60⁰

 

Q. 56 Two straight lines passing through the point A(3,2) cut the line 2y=x+3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

A. 7x+y-21=0

B. x+7y+21=0

C. 2x+y-8=0

D. x+2y+8=0

 

Q. 57 The radius of the sphere 3x²+3y²+3z²-8x+4y+8z-15=0 is

A. 2

B. 3

C. 4

D. 5

 

Q. 58 The direction ratios of the line perpendicular to the lines with direction ratios<1,-2,-2>and <0,2,1> are

A. <2,-1,2>

B. <-2,1,2>

C. <2,1,-2>

D. <-2,-1,-2>

 

Q. 59 What are the co-ordinates of the foot of the perpendicular drawn from the point (3,5,4) on the plane z=0

A. (0,5,4)

B. (3,5,0)

C. (3,0,4)

D. (0,0,4)

 

Q. 60 The lengths of the intercepts on the co-ordinate axes made by the plane 5x+2y+z-13=0 are 

A. 5,2,1 unit

B. 13/5, 13/2, 13 unit

C. 5/13, 2/13, 1/13 unit

D. 1,2,5 unit

 

Q. 61 The area of the square, one of whose diagonals is 3î+4j is

A. 12 square unit

B. 12.5 square unit

C. 25 square unit

D. 156.25 square unit

 

Q. 62 ABCD is a parallelogram and P is the point of intersection of the diagonals. If the O is the origin, then

A. a

B. b

C. c

D. d

 

Q. 63 If b̅ and c̅ are the position vectors of the point B and C respectively, then the position vector of the point D such that

A. 4(c̅ – b̅)

B. -4(c̅ – b̅)

C. 4c̅-3 b̅

D. 4c̅ + b̅

 

Q. 64 If the position vector a̅ of the point (5,n) is such that I a̅I=13, then the value/values of n can be

A. ±8

B. a±12

C. 8 only

D. 12 only

 

Q. 65 If Ia̅I = 2 and I b̅ I = 3, them Ia̅ x b̅ I² + Ia̅.b̅I² is equal to

A. 72

B. 64

C. 48

D. 36

 

Q. 66 Consider the following inequilities in the respect of vectors a̅ and b̅:

1.I a̅ + b̅ I ≤ I a̅ I + I b̅ I

2. I a̅ – b̅ I ≥ a̅ I – I b̅ I

Which of the above is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 67 If the magnitude of difference of two unit vectors is √3 , then the magnitude of sum of the two vectors is

A. 1/2 unit

B. 1 unit

C. 2 unit

D. 3 unit

 

Q. 68 If the vectors αî + αĵ + γk̂, î + k̂, and γî + γĵ + βk̂ lie on a plane, where α, β, and γ are distinct non-negative numbers, then γ is

A. Arithmetic mean of α and β

B. geometric mean of α and β

C. Harmonic mean of α and β

D. none of the above

 

Q. 69 The vectors a̅, b̅, c̅ and d̅ are such that a̅ x b̅ = c̅ x d̅. Which of the following is/are correct?

1.(a̅ – d̅) x (b̅ – d̅) = 0

2. (a̅ x d̅) x (c̅ x d̅) = 0

select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 70 The value of the integral where a+b=0 is

A. 2b-a sin (b-a)

B. a+3b cos(b-a)

C. sin a – (b-a)cos b

D. 0

 

Q. 71 If f(x)=√(25-x)², the what is the value is equal to?

A. 1/5

B. 1/24

C. √24

D. -1/√24

 

Q. 72 consider the function

f(x) = { ax-2, for -2< x < -1

-1, for -1 ≤ x ≤ 1

a+2(x-1)², for 1 < x < 2

what is the value of a for which f(x) is continuous ar x = -1 and x = 1?

A. -1

B. 1

C. 0

D. 2

 

Q. 73 The function f(x) = (1-sin x+cos x)/(1+sin x+cos x) is not defined at x= π. The value of f(π) so that f(x) is continuous at x=π is

A. -1/2

B. 1/2

C. -1

D. 1

 

Q. 74 consider the following functions:

1. f(x) = { 1/x is x ≠ 0

0 if x=0

2. f(x) = { 2x+5 if x> 0

x²+2x+5 if x ≤ 0

which of the above is/are derivable at x =0?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 75 The domain of the function f(x) = 1/√(IxI-x) is

A. [0,∞]

B. (-∞,0)

C. [1,∞)

D. (-∞,0]

 

Q. 76 consider the following statements :

1. The function f(x)= x² + 2 cos x is increasing in the interval (0,π)

2. The function f(x) = ln (√( 1 + x² ) – x ) is decreasing in the interval (-∞,∞)

which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 77 The derivative of ln(x+sin x) with respect to (x+cos x) is

A. (1+cos x)/(x+sin x)(1-sin x)

B. (1-cos x)/(x+sin x)(1+sin x)

C. (1-cos x)/(x-sin x)(1+cos x)

D. (1+cos x)/(x-sin x)(1-cos x)

 

Q. 78 If y = cot⁻¹ [(√(1+sin x)+√(1-sin x))/(√(1+sin x)-√(1-sin x))] where 0 < x < π/2, then dy/dx is equal to

A. 1/2

B. 2

C. sin x+cos x

D. sin x-cos x

 

Q. 79 The function f(x) = x/e^x is monotonically increasing if

A. x < 0 only

B. x > 2 only

C. 0 < x < 2

D. x ∈(-∞,0) U (2,∞)

 

Q. 80 If x^a .y^b = (x-y)^(a+b), then the value of dy/dx – y/x is equal to

A. a/b

B. b/a

C. 1

D. 0

 

Q. 81 If f: R—> R, g:R—> R be two functions given by

f(x) = 2x-3 and g(x) = x³+5, then (fog)⁻¹(x) is equal to

A. [(x+7)/2]⅓

B. [(x-7)/2]⅓

C. [(x – 7/2)]⅓

D. [(x + 7/2)]⅓

 

Q. 82 If 0 < a < b, then the value of

A. IbI – I a I

B. I a I – I b I

C. I b I/I a I

D. 0

 

Q. 83 the value of the integral is equal to

A. 8/15

B. 16/15

C. 32/15

D. 0

 

Q. 84 If f(x) = sin(e^(x-2)-1)/ln (x-1), then

A. -2

B. -1

C. 0

D. 1

 

Q. 85 Consider the following statements:

1. f(x) = ln x is an increasing function on (0,∞)

2. f(x) = e^x – x (ln x) is an increasing function on (1,∞).

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 86 If s = √(t² + 1), then d²s / d²t is equal to

A. 1/s

B. 1/s²

C. 1/s³

D. 1/s⁴

 

Q. 87 Consider the following statements:

statement 1: the function f : R—> R such that f(x) = x³ for all x R is one-one.

statement 2: f(a) = f(b) ⇒ a = b for all a,b ε R if the function f is one-one.

which of the following is correct in respect of the above statement?

A. both the statements are true and statement 2 is the correct explanation of statement 1.

B. both the statements are true and statement 2 is not the correct explanation of statement 1

C. statement 1 is true but statement 2 is false

D. statement 1 is false but statement 2 is true

 

Q. 88 ∫ dx/1+e^-x is equal to

where c is the constant of integration

A. 1+e^x+c

B. ln(1+e^-x)+c

C. ln(1+e^x)+c

D. 2 ln(1+e^-x)+c

 

Q. 89 The value of integration

A. 0

B. 2/3

C. 2

D. -2

 

Q. 90 The area bounded by the coordinate axes and the curve √x + √y = 1, is

A. 1 square unit

B. 1/2 square unit

C. 1/3 square unit

D. 1/6 square unit

 

Questions: 91 – 92

for the next two items that follow

consider the function f(x) = (1/x)^(2x^2), where x > 0

Q. 91 At what value of x does the function attain maximum value?

A. e

B. √e

C. 1/√e

D. 1/e

 

Q. 92 The maximum value of the function is

A. e

B. e^(2/e)

C. e^(1/e)

D. 1/e

 

Questions: 93 – 94

For the next two items that follow

consider f'(x) = x²/2 -kx+1 such that f(0) = 0 and f(3) = 15.

Q. 93 The value of k is

A. 5/3

B. 3/5

C. -5/3

D. -3/5

 

Q. 94 f”(-2/3) is equal to

A. -1

B. 1/3

C. 1/2

D. 1

 

Q. 95 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is an increasing function in the interval

A. (-2,-1)

B. (-∞,-2)

C. (-1,2)

D. (-1,∞)

 

Q. 96 For the next two items that follow

f(x) = -2x³ – 9x² -12x + 1

The function f(x) is a decreasing function in the interval

A. (-2,-1)

B. (-∞,-2) only

C. (-1,2) only

D. (-1,∞) U (-1, ∞)

 

Questions: 97 – 98

For the next two items that follow:

consider the integrals

Q. 97 which one of the following is correct?

A. A = 2B

B. B = 2A

C. A = B

D. A = 3B

 

Q. 98 What is the value of B?

A. π/4

B. π/2

C. 3π/4

D. π

 

Questions: 99 – 100

consider the function for the next two items that follow

f(x) = { -2 sin x if x ≤ -π/2

A sin x + B is -π/2 < x < π/2

cos x if x ≥ π/2

which is continuous everywhere.

 

Q. 99 The value of A is

A. 1

B. 0

C. -1

D. -2

 

Q. 100 The value of B is

A. 1

B. 0

C. -1

D. -2

 

Q. 101 The degree of the differential equation dy/dx – x = (y-x dy/dx)⁻⁴ is

A. 2

B. 3

C. 4

D. 5

 

Q. 102 The solution of dy/dx = √(1-x²-y² + x²y²) is

A. sin⁻¹ y = sin⁻¹ x + c

B. 2 sin⁻¹ y = √(1-x²)+ sin⁻¹ x+ c

C. 2 sin⁻¹ y = x√(1-x²)+ sin⁻¹ x + c

D. 2 sin⁻¹ y = x√(1-x²)+ cos⁻¹ x + c

 

Q. 103 The differential equation of the family of circles passing through the origin and having centres on the x-axis is

A. 2xy dy/dx = x²-y²

B. 2xy dy/dx = y²-x²

C. 2xy dy/dx = x²+y²

D. 2xy dy/dx+x²+y²=0

 

Q. 104 The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a,0) where a > 0, are respectively

A. 1,1

B. 2,1

C. 1,2

D. 2,2

 

Q. 105 f(xy) = f(x) + f(y) is true for all

A. polynomial functions f

B. trigonometric functions f

C. exponential functions f

D. logarithmic functions f

 

Q. 106 Three digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that product is odd?

A. 2/3

B. 7/48

C. 5/42

D. 5/108

 

Q. 107 Two events A and B are such that P(not B) = 0.8, P(A U B) = 0.5 and p(A/B)=0.4. Then P(A) is equal to

A. 0.28

B. 0.32

C. 0.38

D. none of the above

 

Q. 108 If mean and variance of a Binomial variate X are 2 and 1 respectively , then the probability that X takes a value greater than 1 is

A. 2/3

B. 4/5

C. 7/8

D. 11/16

 

Q. 109 Seven unbiased coins are tossed 128 times . In how many throws would you find at least three heads?

A. 99

B. 102

C. 103

D. 104

 

Q. 110 A coin is tossed five times. What is the probability that heads are observed more than three times?

A. 3/16

B. 5/16

C. 1/2

D. 3/32

 

Q. 111 The geometric mean of the observations x1,x2,x3……… xn is G1. The geometric mean of the observations y1,y2,y3 ….. yn is G2 . The geometric mean of observations is x1/y1 , x2/y2 , x3/y3………….. xn/yn is

A. G1G2

B. ln(G1G2)

C. G1/G2

D. ln(G1/G2)

 

Q. 112 the arithmetic mean of 1,8,27,64 upto n terms is given by

A. n(n+1)/2

B. n(n+1)²/2

C. n(n+1)²/4

D. n²(n+1)²/4

 

Q. 113 An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is / are correct?

1. The probability that no head is observed is 1/16.

2. The probability that the experiment ends with three tosses is 1/8.

Select the correct answer using the code given below:

A. 1 only

B. 2 only

C. both 1 and 2

D. neither 1 nor 2

 

Q. 114 If x∈[ 0 , 5 ] , then what is the probability that x² – 3x + 2 ≥0 ?

A. 4/5

B. 1/5

C. 2/5

D. 3/5

 

Q. 115 A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

A. 5/24

B. 13/24

C. 1/4

D. 2/3

 

Q. 116 A problem in statistics is given to three students A B and C whose chances of solving it independently are 1/2 , 1/3 and 1/4 respectively . The probability that the problem will be solved is

A. 1/12

B. 11/12

C. 1/2

D. 3/4

 

Q. 117 An insurance company insured 2000 scooter drivers , 4000 car drivers and 5000 truck drivers. The probabilities of an accident involving a scooter driver , a car driver and a truck driver are 0.01,0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

A. 1/52

B. 3/52

C. 15/52

D. 19/52

 

Q. 118 A coin is tossed 5 times . The probability that tail appears an odd number of times is

A. 1/2

B. 1/3

C. 2/5

D. 1/5

 

Q. 119 The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

A. 0.48

B. -0.48

C. 0.50

D. -0.50

 

Q. 120 What is the probability that the sum of any two different single digit natural numbers is a prime number?

A. 5/27

B. 7/18

C. 1/3

D. none of the above

Answer Sheet 
Question 1 2 3 4 5 6 7 8 9 10
Answer D A B C B D D B A C
Question 11 12 13 14 15 16 17 18 19 20
Answer A B A B A B C A D D
Question 21 22 23 24 25 26 27 28 29 30
Answer A B B A A B A A B C
Question 31 32 33 34 35 36 37 38 39 40
Answer A B C D A B B B B D
Question 41 42 43 44 45 46 47 48 49 50
Answer C C A C A B A A B B
Question 51 52 53 54 55 56 57 58 59 60
Answer C B C D A A B A B B
Question 61 62 63 64 65 66 67 68 69 70
Answer B A C B D C B B C D
Question 71 72 73 74 75 76 77 78 79 80
Answer D A C B B C A A C D
Question 81 82 83 84 85 86 87 88 89 90
Answer B A C D C C A C A D
Question 91 92 93 94 95 96 97 98 99 100
Answer C C C D A D C B C A
Question  101 102 103 104 105 106 107 108 109 110
Answer D C B A D C C D A A
Question  111 112 113 114 115 116 117 118 119 120
Answer C C C A B D A A B B

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