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# NDA/NA(II) Exam 2017 Mathematics Previous Year Paper

July 3, 2019
###### NDA/NA(II) Exam 2018 Mathematics Previous Year Paper
July 3, 2019

NDA/NA(II) Exam 2017 Mathematics

Q. 1 If x + log₁₀ (1 + 2ˣ) = x log₁₀ 5 + log₁₀ 6, then x is equal to

A. 2, -3

B. 2 only

C. 1

D. 3

Q. 2 The remainder and the quotient of the binary division (101110)₂ / (110)₂ are respectively

A. (111)₂ and (100)₂

B. (100)₂ and (111)₂

C. (101)₂ and (101)₂

D. (100)₂ and (100)₂

Q. 3 The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 – y columns. Both AB and BA exists. What are the values of x and y respectively?

A. 8 and 3

B. 3 and 4

C. 3 and 8

D. 8 and 8

Q. 4 If Sₙ = nP + n(n – 1)Q/2, where Sₙ denotes the sum of the first n terms of an AP, then the common difference is

A. P + Q

B. 2P + 3Q

C. 2Q

D. Q

Q. 5 The roots of the equation (q – r)x² + (r – p)x + (p – q) = 0 are

A. (r – p)/(q – r), 1/2

B. (p – q)/(q – r), 1

C. (q – r)/(p – q), 1

D. (r – p)/(p – q), 1/2

Q. 6 If E is the universal set and A = B U C, then the set E – (E – (E – (E – (E – A)))) is same as the set

A. B’ U C’

B. B U C

C. B’ ∩ C’

D. B ∩ C

Q. 7 If A = {x: x is a multiple of 2}, B = {x: x is a multiple of 5} and C = {x: x is a multiple of 10}, then A ∩ (B ∩ C) is equal to

A. A

B. B

C. C

D. {x: x is a multiple of 100}

Q. 8 If α and β are roots of the equation 1 + x + x² = 0, then the given matrix product is equal to

A. a

B. b

C. c

D. d

Q. 9 If lal denotes the absolute value of an integer, then which of the following are correct?

1. labl = lal lbl

2. la + bl <= lal + lbl

3. la – bl >=l lal – lbl l

Select the correct answer using the code given below.

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 10 How many different permutations can be made out of the letters of the word

‘PERMUTATION’?

A. 19958400

B. 19954800

C. 19952400

D. 39916800

Q. 11 Answer the questions given in the image.

A. a

B. b

C. c

D. d

Q. 12 The sum of all real roots of the equation lx – 3l² + lx – 3l – 2 = 0 is

A. 2

B. 3

C. 4

D. 6

Q. 13 It is given that the roots of the equation x² – 4x – log₃ P = 0 are real. For this, the minimum value of P is

A. 1/27

B. 1/64

C. 1/81

D. 1

Q. 14 If A is a square matrix, then the value of adj Aᵀ – (adj A)ᵀ is equal to

A. A

B. 2lAl I, where I is the identity matrix

C. null matrix whose order is same as that of A

D. unit matrix whose order is same as that of A

Q. 15 The value of the product 6¹/² x 6¹/⁴ x 6¹/⁸ x 6¹/¹⁶ x … up to infinite terms is

A. 6

B. 36

C. 216

D. 512

Q. 16 The value of the given determinant for all values of θ is

A. 1

B. cos θ

C. sin θ

D. cos 2θ

Q. 17 The number of terms in the expansion of (x + a)¹⁰⁰ + (x – a)¹⁰⁰ after simplification is

A. 202

B. 101

C. 51

D. 50

Q. 18 In the expansion of (1 + x)⁵⁰, the sum of the coefficients of odd powers of x is

A. 2²⁶

B. 2⁴⁹

C. 2⁵⁰

D. 2⁵¹

Q. 19 If a, b, c are real non-zero numbers, then the inverse of the matrix A is

A. a

B. b

C. c

D. d

Q. 20 A person is to count 4500 notes. Let aₙ denote the number of notes he counts in the nth minute. If a1 = a2 = a3 = … = a10 = 150, and a10, a11, a12, …. are in AP with the common difference -2, then the time taken by him to count all the notes is

A. 24 minutes

B. 34 minutes

C. 125 minutes

D. 135 minutes

Q. 21 The smallest positive integer n for which given equation is correct is

A. 1

B. 4

C. 8

D. 16

Q. 22 If we define the relation R on the set N x N as (a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N x N, then the relation is

A. symmetric only

B. symmetric and transitive only

C. equivalence relation

D. reflexive only

Q. 23 If y = x + x² + x³ + … up to infinte terms, where x < 1, then which one of the following is correct?

A. x = y / (1 + y)

B. x = y / (1 – y)

C. x = (1 + y) / y

D. x = (1 – y) / y

Q. 24 If α and β are the roots of the equation 3x² + 2x + 1 = 0, then the equation whose roots are α + β⁻¹ and β + α⁻¹ is

A. 3x² + 8x + 16 = 0

B. 3x² – 8x – 16 = 0

C. 3x² + 8x – 16 = 0

D. x² + 8x + 16 = 0

Q. 25 The value of 1/log₃ e + 1/log₃ e² + 1/log₃ e⁴ + … upto infinite terms is

A. logₑ 9

B. 0

C. 1

D. logₑ 3

Q. 26 A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

A. 24 x 8! x 8!

B. (8!)³

C. 210 x 8! x 8!

D. 16!

Q. 27 The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k² has no solution if k equals

A. 0

B. 1

C. -1

D. -2

Q. 28 If 1.3 + 2.3² + 3.3³ + …. + n.3ⁿ = [(2n – 1)3ᵃ + b] / 4, then a and b are respectively

A. n, 2

B. n, 3

C. n + 1, 2

D. n + 1, 3

Q. 29 In △PQR, ∠R = π/2; If tan (P/2) and tan (Q/2) are the roots of the equation ax² + bx + c = 0, then which on of the following is correct?

A. a = b + c

B. b = c + a

C. c = a + b

D. b = c

Q. 30 If lz – 4/zl = 2, thn the maximum value of lzl is equal to

A. 1 + √3

B. 1 + √5

C. 1 – √5

D. √5 – 1

Q. 31 The angle of elevation of a stationary cloud from a point 25 m above a lake is 15° and the angle of depression of its image in the lake is 45°. The height of the cloud above the lake level is

A. 25 m

B. 25√3 m

C. 50 m

D. 50√3 m

Q. 32 The value of tan 9° – tan 27° – tan 63° + tan 81° is equal to

A. -1

B. 0

C. 1

D. 4

Q. 33 The value of √3 cosec 20° – sec 20° is equal to

A. 4

B. 2

C. 1

D. -4

Q. 34 Angle α is divided into two parts A and B such that A – B = x and tan A : tan B = p : q. The value of sin x is equal to

A. (p + q) sin α / (p – q)

B. p sin α / (p + q)

C. p sin α / (p – q)

D. (p – q) sin α / (p + q)

Q. 35 The value of sin⁻¹ (3/5) + tan⁻¹ (1/7) is equal to

A. 0

B. π/4

C. π/3

D. π/2

Q. 36 The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30° and 45°. If hₜ is the height of the tower and hₚ is the height of the pole, then which of the following are correct?

1. 2hₜhₚ/(3 + √3) = hₚ²

2. hₜ – hₚ / (√3 + 1) = hₚ/2

3. 2(hₚ + hₜ)/hₚ = 4 + √3

Select the correct answer using the code given below.

A. 1 and 3 only

B. 2 and 3 only

C. 1 and 2 only

D. 1, 2 and 3

Q. 37 In a triangle ABC, a – 2b + c = 0. The value of cot(A/2) cot(C/2) is

A. 9/2

B. 3

C. 3/2

D. 1

Q. 38 √(1 + sin A) = – (sin A/2 + cos A/2) is true if

A. 3π/2 < A < 5π/2 only

B. π/2 < A < 3π/2 only

C. 3π/2 < A < 7π/2

D. 0 < A < 3π/2

Q. 39 In triangle ABC, if (sin² A + sin² B + sin² C) / (cos² A + cos² B + cos² C) = 2 then the triangle is

A. right angled

B. equilateral

C. isosceles

D. obtuse angled

Q. 40 The principal value of sin⁻¹ x lies in the interval

A. (-π/2, π/2)

B. [-π/2, π/2]

C. [0, π/2]

D. [0, π]

Q. 41 The points (a, b), (0, 0), (-a, -b) and (ab, b²) are

A. the vertices of a paralellogram

B. the vertices of a rectangle

C. the vertices of a square

D. colinear

Q. 42 The length of the normal from origin to the plane x + 2y – 2z = 9 is equal to

A. 2 units

B. 3 units

C. 4 units

D. 5 units

Q. 43 If α, β, and γ are the angles which the vector OP (O being the origin) makes with the positive direction of the coordinate axis, then which of the following are correct?

1. cos² α + cos² β = sin² γ

2. sin² α + sin² β = cos² γ

3. sin² α + sin² β + sin² γ = 2

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 44 The angle between the lines x + y – 3 = 0 and x – y + 3 = 0 is α and the acute angle between the lines x – √3y + 2√3 = 0 and √3x – y + 1 = 0 is β. Which one of the following s correct?

A. α = β

B. α > β

C. α < β

D. α = 2β

Q. 45 Let ⃗α = î + 2ĵ – k̂, ⃗β = 2î + ĵ + 3k̂ and ⃗γ = 2î + ĵ + 6k̂ be three vectors. If ⃗α and ⃗β are both perpendicular to the vector ⃗δ and ⃗δ . ⃗γ = 10, then what is the magnitude of ⃗δ?

A. √3 units

B. 2√3 units

C. √3/2 units

D. 1/√3 units

Q. 46 If â and b̂ are two unit vectors, then the vector (â + b̂) x (â x b̂) is parallel to

A. (â – b̂)

B. (â + b̂)

C. (2â – b̂)

D. (2â + b̂)

Q. 47 A force ⃗F = î + 3ĵ + 2k̂ acts on a particle to displace it from the point A(î + 2ĵ – 3k̂) to the point B(3î – ĵ + 5k̂). The work done by the force will be

A. 5 units

B. 7 units

C. 9 units

D. 10 units

Q. 48 For any vector ⃗α, l ⃗α x î l² + l ⃗α x ĵ l² + l ⃗α x k̂ l² is equal to

A. l ⃗α l²

B. 2 l ⃗α l²

C. 3 l ⃗α l²

D. 4 l ⃗α l²

Q. 49 A man running around a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

A. 18π square meters

B. 15π square meters

C. 12π square meters

D. 8π square meters

Q. 50 The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4 is

A. 5/√13 units

B. 3/√17 units

C. √17 units

D. √17/2 units

Q. 51 If the vectors aî + ĵ + k̂, î + bĵ + k̂, î + ĵ + ck̂ (a, b, c ≠ 1) are coplaner, then the value of 1/(1 – a) + 1/(1 – b) + 1/(1 – c) is equal to

A. 0

B. 1

C. a + b + c

D. abc

Q. 52 The point of intersection of the line joining the points (-3, 4, -8) and (5, -6, 4) with the XYplane is

A. (7/3, -8/3, 0)

B. (-7/3, -8/3, 0)

C. (-7/3, 8/3, 0)

D. (7/3, 8/3, 0)

Q. 53 If the angle between the lines whose direction ratios are <2, -1, 2> and is π/4, then the smaller value of x is

A. 52

B. 4

C. 2

D. 1

Q. 54 The position of the point (1, 2) relative to the ellipse 2x² + 7y² = 20 is

A. outside the ellipse

B. inside the ellipse but not at the focus

C. on the ellipse

D. at the focus

Q. 55 The equation of a straight line which cuts off an intercept of 5 units on the negative direction of the y-axis and makes an angle 120⁰ with the positive direction of the x-axis is

A. y + √3x + 5 = 0

B. y – √3x + 5 = 0

C. y + √3x – 5 = 0

D. y – √3x – 5 = 0

Q. 56 The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is

A. 21x + 46y – 180 = 0

B. 21x – 46y + 96 = 0

C. 46x + 21y -155 = 0

D. 46x – 21y – 29 = 0

Q. 57 The equation of the ellipse whose center is at the origin, the major axis is along the x-axis with eccentricity 3/4 and latus rectum 4 units is

A. x²/1024 + 7y²/64 = 1

B. 49x²/1024 + 7y²/64 = 1

C. 8x²/1024 + 49y²/64 = 1

D. x²/1024 + y²/64 = 1

Q. 58 The equation of the circle which passes through the points (1, 0), (0, -6) and (3, 4) is

A. 4x² + 4y² + 142x + 47y + 140 = 0

B. 4x² + 4y² – 142x – 47y + 138 = 0

C. 4x² + 4y² – 142x + 47y + 138 = 0

D. 4x² + 4y² + 150x – 49y + 138 = 0

Q. 59 A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the center of the sphere OABC, O being the origin, is

A. x/a + y/b + z/c = 1

B. a/x + b/y + c/z = 1

C. a/x + b/y + c/z = 2

D. x/a + y/b + z/c = 2

Q. 60 The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7 and perpendicular to the plane x – 5y + 3z = 5 is given by

A. x + 2y + 3z – 6 = 0

B. x + 2y + 3z + 6 = 0

C. 3x + 4y + 5z – 8 = 0

D. 3x + 4y + 5z + 8 = 0

Q. 61 The inverse of the function y = 5ˡⁿ ˣ is

A. x = y¹/ˡⁿ ⁵, y > 0

B. x = yˡⁿ ⁵, y > 0

C. x = y¹/ˡⁿ ⁵, y < 0

D. x = 5 ln y, y > 0

Q. 62 Which one is correct in respect of the given function?

A. f(x) is continuous at x = 0 but not differentiable at x = 0

B. f(x) is continuous as well as differentiable at x = 0

C. f(x) is discontinuous at x = 0

D. None of the above

Q. 63 Answer as per instructions given in the image.

A. – y²tan x / (1 – y ln(cos x))

B. y²tan x / (1 + y ln(cos x))

C. y²tan x / (1 – y ln(sin x))

D. y²sin x / (1 + y ln(sin x))

Q. 64 Consider the following:

1. x + x² is continuous at x = 0.

2. x + cos 1/x is discontinuous at x = 0.

3. x² + cos 1/x is continuous at x = 0.

Which of the above are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 65 Consider the following statements:

1. dy/dx at a point on the curve gives the slope of the tangent at that point.

2. If a(t) denotes acceleration of a particle, then ∫a(t) dt + c gives a velocity of the particle.

3. If s(t) gives a displacement of a particle at a time t, then ds/dt gives its acceleration at that instant.

Which of the above statement(s) is/are correct?

A. 1 and 2 only

B. 2 only

C. 1 only

D. 1, 2 and 3

Q. 66 If y = sec⁻¹ [(x + 1)/(x – 1)] + sin⁻¹ [(x – 1)/(x + 1)], then dy/dx is equal to

A. 0

B. 1

C. (x – 1)/(x + 1)

D. (x + 1)/(x – 1)

Q. 67 What is ∫ tan⁻¹ (sec x + tan x) dx equal to?

A. πx/4 + x²/4 + c

B. πx/2 + x²/4 + c

C. πx/4 + πx²/4 + c

D. πx/4 – x²/4 + c

Q. 68 Which one of the following is correct in respect of the derivative of the function, i.e. f'(x)?

A. f'(x) = 2x for 0<x≤1

B. f'(x) = -2x for 0<x≤1

C. f'(x) = -2x for 0<x<1

D. f'(x) = 0 for 0<x<∞

Q. 69 Which one of the following is correct in respect of the function f(x) = x(x – 1)(x + 1)?

A. The local maximum value is larger than local minimum value.

B. The local maximum value is smaller than local minimum value.

C. The function has no local maximum.

D. The function has no local minimum.

Q. 70 Consider the following statements:

1. A derivative of f(x) may not exist at some point.

2. A derivative of f(x) may exist finitely at some point.

3. A derivative of f(x) may be infinite (geometrically) at some point.

Which of the above statement(s) are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 71 The maximum value of (ln x)/x is

A. e

B. 1/e

C. 2/e

D. 1

Q. 72 The function f(x) = lxl – x³ is

A. odd

B. even

C. both even and odd

D. neither even nor odd

Q. 73 Answer as per instructions given in the image.

A. l₁ ≠ l₂

B. d/dx(l₃) = l₂

C. ∫ l₃ dx = l₂

D. l₃ = l₂

Q. 74 The general solution of dy/dx = (ax + h)/(by + k) represents a circle only when

A. a = b = 0

B. a = -b ≠ 0

C. a = b ≠ 0, h = k

D. a = b ≠ 0

Q. 75 Answer as per instructions given in the image.

A. l = 1, m = 1

B. l = 2/π, m = ∞

C. l = 2/π, m = 0

D. l = 1, m = ∞

Q. 76 Answer as per instructions given in the image.

A. 8

B. 4

C. 2

D. 0

Q. 77 The area bounded by the curve lxl + lyl = 1 is

A. 1 square unit

B. 2√2 square units

C. 2 square units

D. 2√3 square units

Q. 78 If x is any real number, then x²/(1 + x⁴) belongs to which one of the following intervals?

A. (0, 1)

B. (0, 1/2]

C. (0, 1/2)

D. [0, 1]

Q. 79 The left hand derivative of f(x) = [x] sin (πx) at x = k; where k is an integer and [x] is the greatest integer function; is

A. (-1)ᵏ (k – 1)π

B. (-1)ᵏ⁻¹ (k – 1)π

C. (-1)ᵏ (kπ)

D. (-1)ᵏ⁻¹ (kπ)

Q. 80 If f(x) = x/2 – 1, then on the interval [0, π] which one of the following is correct?

A. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both continuous

B. tan [f(x)], where [.] is the greatest integer function, and f⁻¹(x) are both continuous

C. tan [f(x)], where [.] is the greatest integer function, and 1/f(x) are both discontinuous

D. tan [f(x)], where [.] is the greatest integer function, is discontinuous but 1/f(x) is

continuous

Q. 81 Answer as per instructions given in the image.

A. 3 and 2

B. 2 and 2

C. 2 and 3

D. 1 and 3

Q. 82 If y = cos⁻¹ (2x/(1 + x²)), then dy/dx is equal to

A. -2/(1 + x²) for all lxl < 1

B. -2/(1 + x²) for all lxl > 1

C. 2/(1 + x²) for all lxl < 1

D. None of the above

Q. 83 The set of all points, where the function f(x) = √(1 – e⁻ˣ²) is differentiable is

A. (0, ∞)

B. (-∞, ∞)

C. (-∞, 0) U (0, ∞)

D. (-1, ∞)

Q. 84 Match List – I with List – II and select the correct answer using the code given.

A. A – 2, B – 3, C – 1, D – 4

B. A – 2, B – 3, C – 4, D – 1

C. A – 3, B – 2, C – 1, D – 4

D. A – 3, B – 2, C – 4, D – 1

Q. 85 If f(x) = x(√x – √(x – 1)), then f(x) is

A. continuous but not differentiable at x = 0

B. differentiable at x = 0

C. not continuous at x = 0

D. None of the above

Q. 86 Which one of the given graphs represent the function f(x) = x/x’, x ≠ 0?

A. a

B. b

C. c

D. d

Q. 87 Answer as per instructions given in the image.

A. 251

B. 250

C. 1

D. 0

Q. 88 Answer as per instructions given in the image.

A. x (ln x)⁻¹ + c

B. x (ln x)⁻² + c

C. x (ln x) + c

D. x (ln x)² + c

Q. 89 A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is

A. 1

B. 2

C. 3

D. 4

Q. 90 The value of given function is

A. π/4

B. π/2

C. π/2√2

D. π/√2

Q. 91 Let g be the greatest integer function. Then the function f(x) = (g(x)² – g(x)) is discontinuous at

A. all integers

B. all integers except 0 and 1

C. all integers except 0

D. all integers except 1

Q. 92 The differential equation of minimum order by eliminating the arbitraty constants A and C in the equation y = A [sin (x + C) + cos (x + C)] is

A. y” + (sin x + cos x)y’ = 1

B. y” = (sin x + cos x)y’

C. y” = (y’)² + sin x cos x

D. y” + y = 0

Q. 93 Consider the following statements:

Statement I – x > sin x for all x > 0

Statement II – f(x) = x – sin x is an increasing function for all x > 0

Which one of the following is correct in respect of the above statements?

A. Both I and II are true and II is the correct explanation of I

B. Both I and II are true and II is not the correct explanation of I

C. I is true but II is false

D. I is false but II is true

Q. 94 Answer as per instructions given in the image.

A. y = x/(∅(x) + c)

B. y = ∅(x)/x + c

C. y = (∅(x) + c) / x

D. y = ∅(x) / (x + c)

Q. 95 If f(x) = (4x + x⁴) / (1 + 4x³) and g(x) = ln [(1 + x)/(1 – x)], then what is the value of f ∘ g [(e – 1)/(e + 1)] equal to?

A. 2

B. 1

C. 0

D. 1/2

Q. 96 Answer as per the instructions given in the image.

A. (α – β)(β γ)(α – γ)

B. (α – β)(β γ)(γ – α)

C. (α – β)(β γ)(γ – α)(α + β + γ)

D. 0

Q. 97 Answer as per the instructions given in the image.

A. a

B. b

C. c

D. d

Q. 98 Answer as per the instructions given in the image.

A. A² = -2A

B. A² = -4A

C. A² = -3A

D. A² = 4A

Q. 99 Geometrically Re (z² – i) = 2, where i = √-1 and Re is the real part, represents

A. Circle

B. Ellipse

C. Rectangular Hyperbola

D. Parabola

Q. 100 Answer as per instructions given in the image.

A. 0

B. 1

C. pa + qb + rc

D. pa + qb + rc + a + b + c

Q. 101 A committee of two people is selected from two men and two women. The probability that the committee will have exactly one woman is

A. 1/6

B. 2/3

C. 1/3

D. 1/2

Q. 102 Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

A. 1/3

B. 2/3

C. 4/9

D. 5/9

Q. 103 Let the sample space consist of non-negative integers up to 50, X denotes the numbers which are multiples of 3 and Y denote odd numbers. Which of the following is/are correct?

1. P(X) = 8/25

2. P(Y) = 1/2

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. 104 For two events A and B, let P(A) = 1/2, P (A U B) = 2/3 and P (A ∩ B) = 1/6. What is P(A̅ ∩ B) equal to?

A. 1/6

B. 1/4

C. 1/3

D. 1/2

Q. 105 Consider the following statements:

1. The coefficient of variation depends on the unit of measurement fo the variable.

2. A range is a measure of dispersion.

3. Mean deviation is least when measured about the median.

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 106 Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0 respectively. Then which one of the following is the arithmetic mean of the smallest five observations in the data?

A. 0

B. 8

C. 16

D. 24

Q. 107 Which one of the following can be considered as an appropriate pair of values of the regression coefficient of y on x and regression coefficient of x on y?

A. (1, 1)

B. (-1, 1)

C. (-1/2, 2)

D. (1/3, 10/3)

Q. 108 Let A and B be two events with P(A) = 1/3, P(B) = 1/6 and P(A ∩ B) = 1/12. What is P(BlA̅) equal to?

A. 1/5

B. 1/7

C. 1/8

D. 1/10

Q. 109 In a binomial distribution, the mean is 2/3 and the variance is 5/9. What is the probability that X = 2?

A. 5/36

B. 25/36

C. 25/216

D. 25/54

Q. 110 The probability that a ship safely reaches a port is 1/3. The probability that out of 5 ships, at least 4 ships would arrive safely is

A. 1/243

B. 10/243

C. 11/243

D. 13/243

Q. 111 What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?

A. 33/144

B. 17/72

C. 1/144

D. 2/9

Q. 112 It is given that X̅ = 10, Y̅ = 90, σₓ = 3, σᵧ = 12 and rₓᵧ = 0.8. The regression equation of X on Y is

A. Y = 3.2X + 58

B. X = 3.2Y + 58

C. X = -8 + 0.2Y

D. Y = -8 + 0.2X

Q. 113 If P(B) = 3/4, P (A ∩ B ∩ C̅) = 1/3 and P (A̅ ∩ B ∩ C̅) = 1/3, then what is P (B ∩ C) equal to?

A. 1/12

B. 3/4

C. 1/15

D. 1/9

Q. 114 In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the given ratios?

A. 1 : 1

B. 10 : 9

C. 100 : 91

D. 5 : 4

Q. 115 If a variable takes values 0, 1, 2, 3, ……., n with frequencies 1, C(n, 1), C(n, 2), C(n, 3),……, C(n, n) respectively, then the arithmetic mean is

A. 2n

B. n + 1

C. n

D. n/2

Q. 116 In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 – p. The probability of answering a question correctly is 1/m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

A. mp / (1 + mp)

B. mp / (1 + (m – 1)p)

C. (m – 1)p / (1 + (m – 1)p)

D. (m – 1)p / (1 + mp)

Q. 117 If x₁ and x₂ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

A. x₁ + x₂ > 2√(x₁x₂)

B. √x₁ + √x₂ > √2

C. l√x₁ – √x₂l > √2

D. x₁ + x₂ < 2√((x₁x₂) + 1)

Q. 118 Consider the following statements:

1. Variance is unaffected by the change of origin and change of scale.

2. A coefficient of variance is independent of the unit of observations.

Which of the statements given above is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Q. 119 Five sticks of length 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?

A. 0.5

B. 0.4

C. 0.3

D. 0

Q. 120 The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

A. 0.36

B. 0.2

C. 0.6

D. 0.9