UPSC will conduct NDA & NA 2 (II) 2019 Exam on 17^{th} November 2019 or total 415 vacancies in the Indian Army, Navy and Air Force wings of the National Defence Academy and Naval Academy. The written exam of UPSC NDA & NA 2 2019 Recruitment will consist of two papers, i.e., General Ability Test (GAT) & Mathematics. The Mathematics Section of Written Exam will consist of 120 Questions of total 300 Marks. To score high marks in UPSC NDA & NA 2 2019 Exam candidates must start practicing the mock tests for Mathematics Section of the exam. For the ease of the candidates we have created Mathematics Mock test based on the latest exam pattern of the UPSC NDA & NA 2 2019 Exam.
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UPSC NDA 2 2019: Mathematics Mock Test(300 Marks – 120 Questions of 2.5 marks each) 
(a) 3 log_{2} 7
(b) 1 – 3 log_{2} 7
(c) 1 – 3 log_{7} 2
(d) 7/8
2. If an infinite GP has the first term x and the sum 5, then which one of the following is correct?
(a) x <  10
(b) – 10 < x < 0
(c) 0 < x < 10
(d) x > 10
3. Consider the following expressions:
Which of the above are rational expressions?
(a) 1, 4 and 5 only
(b) 1, 3, 4 and 5 only
(c) 2, 4 and 5 only
(d) 1 and 2 only
4. A square matrix A is called orthogonal if
(a) A = A^{2}
(b) A’ = A^{1}
(c) A = A^{1}
(d) A = A’
Where A’ is the transpose of A.
5. If A, B and C are subsets of a Universal set, then which one of the following is not correct?
(a) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
(b) A’ ∪ (A ∪ B) = (B’ ∩ A)’ ∪ A
(c) A’ ∪ (B ∪ C) = (C’ ∩ B)’ ∩ A’
(d) (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C)
Where A’ is the complement of A.
6. Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to
(a) 2480
(b) 2481
(c) 2482
(d) 2483
7. The sum of the series 3 – 1 + (1/3) – (1/9) + …… is equal to
(a) 20/9
(b) 9/20
(c) 9/4
(d) 4/9
Consider the information given below and answer the two (02) items that follow:
A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.
8. How many students like to play all the three games?
(a) 14
(b) 21
(c) 28
(d) 35
9. How many students like to play exactly only one game?
(a) 196
(b) 228
(c) 254
(d) 268
10. If ∝ and β (≠ 0) are the roots of the quadratic equations x2 + ∝x – β = 0, then the quadratic expression – x2 + ∝x + β where x θ R has
(a) Least Value – 1/4
(b) Least Value – 9/4
(c) Greatest Value 1/4
(d) Greatest Value 9/4
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11. What is the coefficient of the middle term in the binomial expansion of (2 + 3x)^{4}?
(a) 6
(b) 12
(c) 108
(d) 216
12. For a square matrix A, which of the following properties hold?
1. (A^{1})^{1} = A
2. det (A^{1}) = 1/det A
3. (λA)^{1} = λA^{1} Where λ is a scalar
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
(a) x  3
(b) x  y
(c) y  3
(d) x  3y
14. What is the Adjoint of the matrix?
(a) 3
(b) 2
(c) 1
(d) 0
16. There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?
(a) C (17, 11)
(b) C (12, 8)
(c) C (17, 5) x C (5, 3)
(d) C (5, 3) x C (12, 8)
17. What is the value of log_{9} 27 + log_{8} 32?
(a) 7/2
(b) 19/6
(c) 4
(d) 7
18. If A and B are two invertible square matrices of same order, then what is (AB)^{1} equal to?
(a) B^{1} A^{1}
(b) A^{1} B^{1}
(c) B^{1} A
(d) A^{1} B
(a) 16
(b) 16
(c) 8
(d) 8
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21. The system of equations
2x + y – 3z = 5,
3x – 2y + 2z = 5 and
5x – 3y – z = 16
(a) is inconsistent
(b) is consistent, with a unique solution
(c) is consistent, with infinitely many solutions
(d) has its solutions lying along xaxis in threedimensional space
22. Which one of the following is correct in respect of the cube roots of unity?
(a) They are collinear
(b) They lie on a circle of radius√3
(c) They form an equilateral triangle
(d) None of the above
(a) 0
(b) 1
(c) (p – q) (q – r) (r – p)
(d) ln u x ln v x ln w
24. Let the coefficient of the middle term of the binomial expansion of (1 + x)^{2n} be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct?
(a) α > β + γ
(b) α < β + γ
(c) α ≡ β + γ
(d) α = β + γ
25. Let A = [x ∈ R :  1 ≤ x ≤ 1], B = [y ∈ R :  1 ≤ y ≤ 1] and S be the subset if A x B, defined by S = [(x, y) ∈ A x B : x^{2} + y^{2} = 1].
Which one of the following is correct?
(a) S is a oneone function from A into B
(b) S is a manyone function from A into B
(c) S is a bijective mapping from A into B
(d) S is not a function
26. Let T_{r} be the r^{th} term of an AP for r = 1, 2, 3, …… If for some distinct positive Integers m and n we have T_{m} = 1/n and T_{n} = 1/m, then what is T_{mn} equal to?
(a) (mn)^{1}
(b) m^{1} + n^{1}
(c) 1
(d) 0
27. Suppose f(x) is such a quadratic expression that it is positive for all real x. If g(x) = f(x) + f”(x), then for any real x
(a) g(x) < 0
(b) g(x) > 0
(c) g(x) = 0
(d) g(x) ≥ 0
28. Consider the following in respect of matrices A, B and C of same order:
1. (A + B + C)’ = A’ + B’ + C’
2. (AB)’ = A’B’
3. (ABC)’ = C’B’A’
Where A’ is the transpose of the matrix A.
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
29. The sum of the binary numbers (11011)_{2}, (10110110)_{2} and (10011x0y)_{2} is the binary number (101101101)_{2}. What are the values of x and y?
(a) x = 1, y = 1
(b) x = 1, y = 0
(c) x = 0, y = 1
(d) x = 0, y = 0
30. Let matrix B be the adjoint of a square matrix A, l be the identity matrix of same order as A. If k (≠0) is the determinant of the matrix A, the what is AB equal to?
(a) l
(b) Kl
(c) k^{2}l
(d) (1/k)l
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31. If (0.2)^{x} = 2 and log_{10} 2 = 0.3010, then what is the value of x to the nearest tenth?
(a) – 10.0
(b) – 0.5
(c) – 0.4
(d) – 0.2
32. The total number of 5digit numbers that can be composed of distinct digits from 0 to 9 is
(a) 45360
(b) 30240
(c) 27216
(d) 15120
(a) (x – y) (y – z) (z – x)
(b) (x – y) (y – z)
(c) (y – z) (z – x)
(d) (z – x)^{2} (x + y + z)
(a) The triangle ABC is isosceles
(b) The triangle ABC is equilateral
(c) The triangle ABC is scalene
(d) No Conclusion can be drawn with regard to the nature of the triangle
35. Consider the following in respect of matrices A and B of same order:
1. A^{2} – B^{2} = (A + B) (A – B)
2. (A – I) (I + A) = 0 ↔ A^{2} = I
Where I is the identity matrix and O is the null matrix.
Which of the above is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
36. What is (2 tan θ/1 + tan^{2} θ) equal to?
(a) cos 2θ
(b) tan 2θ
(c) sin 2θ
(d) cosec 2θ
37. If sec (θ  α), sec θ and sec (θ + α) are in AP, where cos α ≠ 1, then what is the value of sin2θ + cos α?
(a) 0
(b) 1
(c)  1
(d) 1/2
38. If A + B + C = 180°, then what is sin 2A – sin 2B – sin 2C equal to?
(a) – 4 sin A sin B sin C
(b) – 4 cos A sin B cos C
(c) – 4 cos A cos B sin C
(d) – 4 sin A cos B cos C
39. A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is 48°. If the height of the balloon above the bridge is 122m, then what is the length of the bridge?
(a) 122 sin 48° m
(b) 122 tan 42° m
(c) 122 cos 48° m
(d) 122 tan 48° m
40. A is an angle in the fourth quadrant. It satisfies the trigonometric equation 3(3 – tan^{2} A – cot A)^{2} = 1. Which one of the following is a value of A?
(a) 300°
(b) 315°
(c) 330°
(d) 345°
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41. If x, x  y and x + y are the angles of a triangle (not an equilateral triangle) such that tan (x  y), tan x and tan (x + y) are in GP, then what is x equal to?
(a) π/4
(b) π/3
(c) π/6
(d) π/2
42. ABC is a triangle inscribed in a circle with centre O. Let a = ∠BAC, where 45° < �� <90°. Let �� = ∠BOC. Which one of the following is correct?
(a) cos β = 1 – tan^{2} α/1 + tan^{2} α
(b) cos β = 1 + tan^{2} α/1  tan^{2} α
(c) cos β = 2tan α/1 + tan^{2} α
(d) sin β = 2 sin^{2} α
43. If a flagstaff of 6 m height placed on the top of a tower throws a shadow of 2√3 m along the ground, then what is the angle that the sun makes with the ground?
(a) 60°
(b) 45°
(c) 30°
(d) 15°
44. What is tan^{1} (1/4) + tan^{1} (3/5) equal to?
(a) 0
(b) π/4
(c) π/3
(d) π/2
45. A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β. What is the height of the centre of the balloon (neglecting the height of the observer)?
(a) r sin β/sin(α/2)
(b) r sin β/sin(α/4)
(c) r sin (β/2)/sin α
(d) r sin α/sin(β/2)
46. If sin (x + y)/sin (x  y) = a + b/a – b, then what is tan x/tan y is equal to?
(a) a/b
(b) b/a
(c) a + b/a – b
(d) a – b/a + b
47. If sin α + sin β = 0 = cos α + cos β, where 0 < β < α < 2π, then which one of the following is correct?
(a) α = π – β
(b) α = π + β
(c) α = 2π – β
(d) 2α = π + 2β
48. Suppose cos A is given. If only one value of cos (A/2) is possible, then A must be
(a) An odd multiple of 90°
(b) A multiple of 90°
(c) An odd multiple of 180°
(d) A multiple of 180°
49. If cos α + cos β + cos γ = 0, where 0 < α ≤ π/2, 0 < β ≤ π/2, 0 < γ ≤ π/2, then what is the value of sin α + sin β + sin γ?
(a) 0
(b) 3
(c) 5√2/2
(d) 3√2/2
50. The maximum value of sin (x + π/5) + cos (x + π/5), where x ∈ (0, π/2), is attained at
(a) π/20
(b) π/15
(c) π/10
(d) π/2
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51. What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3?
(a) 12√17/5
(b) 13√17/5
(c) √17/5
(d) 6√17/5
52. What is the angle between the straight lines (m^{2}  mn) y = (mn + n^{2}) x + n^{3} and (mn + m^{2}) y = (mn  n^{2}) x + m^{3}, where m > n?
(a) tan^{1} (2mn/m^{2} + n^{2})
(b) tan^{1} (4m^{2}n^{2}/m^{4} – n^{4})
(c) tan^{1} (4m^{2}n^{2}/m^{4} + n^{4})
(d) 45°
53. What is the equation of the straight line cutting off an intercept 2 from the negative direction of yyaxis and inclined at 30° with the positive direction of xaxis?
(a) x – 2 √3 y – 3√2 = 0
(b) x + 2 √3 y – 3√2 = 0
(c) x + √3 y – 2√3 = 0
(d) x – √3 y – 2√3 = 0
54. What is the equation of the line passing through the point of intersection of the lines x + 2y – 3 = 0 and 2x – y + 5 = 0 and parallel to the line y – x + 10 = 0?
(a) 7x – 7y + 18 = 0
(b) 5x – 7y + 18 = 0
(c) 5x – 5y + 18 = 0
(d) x – y + 5 = 0
55. Consider the following statements:
1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p^{2} = c^{2}/a^{2} + b^{2}.
2. The length p of the perpendicular from the origin to the line x/a + y/b = 1 satisfies the relation 1/p^{2} = 1/a^{2} + 1/b^{2}.
3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1/p^{2} = 1 + m^{2} + c^{2}/c^{2}.
Which of the above is/are correct?
(a) 1, 2 and 3
(b) 1 only
(c) 1 and 2 only
(d) 2 only
56. What is the equation of the ellipse whose vertices are (± 5, 0) and foci are at (± 4, 0)?
(a) x^{2}/25 + y^{2}/9 = 1
(b) x^{2}/16 + y^{2}/9 = 1
(c) x^{2}/25 + y^{2}/16 = 1
(d) x^{2}/9 + y^{2}/25 = 1
57. What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive yaxis equal to twice its intercept on the positive xaxis?
(a) 2x + y = 5
(b) 2x + y = 7
(c) x + 2y = 7
(d) 2x – y = 1
58. Let the coordinates of the points A, B, C be (1, 8, 4), (0,  11, 4) and (2,  3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC?
(a) (3, 4, 2)
(b) (4, 2, 5)
(c) (4, 5, 2)
(d) (2, 4, 5)
59. What is the equation of the plane passing through the points ( 2, 6,  6), ( 3, 10,  9)
and ( 5, 0,  6)?
(a) 2x – y – 2z = 2
(b) 2x + y + 3z = 3
(c) x + y + z = 6
(d) x – y – z = 3
60. A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC?
(a) x^{2} + y^{2} + z^{2} = r^{2}
(b) x^{2} + y^{2} + z^{2} = 4r^{2}
(c) 9 (x^{2} + y^{2} + z^{2}) = 4r^{2}
(d) 3(x^{2} + y^{2} + z^{2}) = 2r^{2}
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61. The coordinates of the vertices P, Q and R of a triangle PQR are (1, 1, 1), (3, 2, 2) and (0, 2, 6) respectively. If ∠RQP = θ, then what is ∠PRQ equal to?
(a) 30° + θ
(b) 45°  θ
(c) 60°  θ
(d) 90°  θ
62. The perpendiculars that fall from any point or the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x  3y = 2 are
(a) 12 and 4 respectively
(b) 11 and 5 respectively
(c) Equal to each other
(d) Not equal to each other
63. The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2, is
(a) Either x + y = 4 or 9x + y = 12
(b) Either x + y = 5 or 4x + 9y = 30
(c) Either x + y = 4 or x + 9y = 120
(d) Either x + y = 5 or 9x + 4 y = 30
64. What is the distance between the straight lines 3x + 4y = 9 and 6x + 8y = 15?
(a) 3/2
(b) 3/10
(c) 6
(d) 5
65. What is the equation to the sphere whose centre is at ( 2, 3, 4) and radius is 6 units?
(a) x^{2} + y^{2} + z^{2} + 4x  6y  8z = 7
(b) x^{2} + y^{2} + z^{2} + 6x  4y  8z = 7
(c) x^{2} + y^{2} + z^{2} + 4x  6y – 8z = 4
(d) x^{2} + y^{2} + z^{2} + 4x + 6y + 8z = 4
(a) 30°
(b) 45°
(c) 60°
(d) 90°
(a) 9p^{2} = 4q^{2}
(b) 4p^{2} = 9q^{2}
(c) 9p = 4q
(d) 4p = 9q
(a) 2
(b) 3
(c) 4
(d) 6
71. Which one of the following is correct in respect of the function f : R → R^{+} defined as f(x) = x + 1?
(a) f(x^{2}) = [f(x)]^{2}
(b) f(x) = f(x)
(c) f(x + y) = f(x) + f(y)
(d) None of the above
72. Suppose f : R → R is defined by f(x) = x^{2}/1 + x^{2}. What is the range of the function?
(a) [10, 1)
(b) [10, 1]
(c) (0, 1]
(d) (0, 1)
73. if f(x) = x + x – 1, then which one of the following is correct?
(a) f(x) is continuous at x = 0 and x = 1
(b) f(x) is continuous at x = 0 but not at x = 1
(c) f(x) is continuous at x = 1 but not at x = 0
(d) f(x) is neither continuous at x = 0 nor at x = 1
(a) 0
(b) 1
(c) 1
(d) It does not exist
75. What is the area of the region bounded by the parabolas y^{2} = 6 (x  1) and y^{2} = 3x?
(a) √6/3
(b) 2√6/3
(c) 4√6/3
(d) 5√6/3
Consider the following information for the next three (03) items that follow:
Three sides of a trapezium are each equal to 6 cm. Let α ∈ (0, π/2) be the angle between a pair of adjacent sides.
76. If the area of the trapezium is the maximum possible, then what is a α equal to?
(a) π/6
(b) π/4
(c) π/3
(d) 2π/5
77. If the area of the trapezium is maximum, what is the length of the fourth side?
(a) 8cm
(b) 9cm
(c) 10 cm
(d) 12cm
78. What is the maximum area of the trapezium?
(a) 36√3 cm^{2}
(b) 30√3 cm^{2}
(c) 27√3 cm^{2}
(d) 24√3 cm^{2}
(a) e^{π} + 1/2
(b) e^{π}  1/2
(c) e^{π} + 1
(d) e^{π} + ¼
80. If f(x) = x^{2} – 9/x^{2} – 2x – 3, x ≠ 3 is continuous at x = 3, then which one of the following is correct?
(a) f(3) = 0
(b) f(3) = 15
(c) f(3) = 3
(d) f(3) = 1.5
81. The order and degree of the differential equation [1 + (dy/dx)^{2}]^{3} = p2 [d^{2}y/dx^{2}]^{2} are respectively
(a) 3 and 2
(b) 2 and 2
(c) 2 and 3
(d) 1 and 3
82. If y = cos^{1} (2x/1 + x^{2}), then dy/dx is equal to
(a) – 2/1+x^{2} for all x< 1
(b) – 2/1+x^{2} for all x> 1
(c) 2/1+x^{2} for all x< 1
(d) None of the above
83. The set of all points, where the function f(x) = √1e^{x2} is differentiable, is
(a) (0, ∞)
(b) ( ∞, ∞)
(c) ( ∞, 0) ∪ (0, ∞)
(d) (1, ∞)
84. Match ListI with ListII and select the correct answer using the code given below the lists:
List—I 
ListII 
A. sin x + cos x B. 3sin x + 4cos x C. 2sin x + cos x D. sin x + 3cos x 
1. √10 2. √2 3. 5 4. √5 
Code:
(a) A B C D
2 3 1 4
(b) A B C D
2 3 4 1
(c) A B C D
3 2 1 4
(d) A B C D
3 2 4 1
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
86. Which one of the following graph represents the function f(x) = x/x, x ≠ 0?
(a) 251
(b) 250
(c) 1
(d) 0
(a) x(1nx)^{1} + c
(b) x(1nx)^{2} + c
(c) x(1nx) + c
(d) x(1nx)^{2} + c
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 or the jar must be k times the height or the jar. The value of k is
(a) 1
(b) 2
(c) 3
(d) 4
(a) π/4
(b) π/2
(c) π/2√2
(d) π/√2
91. Let g be the greatest integer function Then the function f(x) = (g(x))^{2}  g(x^{2}) is discontinuous at
(a) all integers
(b) all integers except 0 and 1
(c) all integers except 0
(d) all integers except 1
92. The differential equation of minimum order by eliminating the arbitrary 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
93. Consider the following statement:
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 Statement I and Statement are true and Statement II is the correct explanation of Statement
(b) Both Statement I and Statement are true and Statement II is not the correct explanation of Statement
(c) Statement I is true but Statement is false
(d) Statement I is false but Statement is true
95. If f(x) = 4x + x^{4}/1 + 4x^{3} and g(x) = 1n (1+x/1x), then what is the value of f _{° }g[e  1/e + 1] equal to?
(a) 2
(b) 1
(c) 0
(d) 1/2
(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
(a) A^{2} = 2A
(b) A^{2} = 4A
(c) A^{2} = 3A
(d) A^{2} = 4A
99. Geometrically Re (z^{2}  i) = 2, where i = √1 and Re is the real Part, represents
(a)Circle
(b) Ellipse
(c) Rectangular Hyperbola
(d) Parabola
(a) 0
(b) 1
(c) pa + qb + rc
(d) pa + qb + rc + a + b + c
101. A committee of two persons 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
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
103. Let the sample space consist of nonnegative integers up to 50, X denote the numbers which are multiples of 3 and Y denote the 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
(a) 1/6
(b) 1/4
(c) 1/3
(d) 1/2
105. Consider the following statements
1. Coefficient of variation depends on the unit of measurement of the variable.
2. Range is a measure of dispersion.
3. Mean deviation is least when measured about 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
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 or the smallest five observations in the data?
(a) 0
(b) 8
(c) 16
(d) 24
107. Which one of the following can be considered as appropriate pair of values of 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)
(a) 1/5
(b) 1/7
(c) 1/8
(d) 1/10
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
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
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
114. The following table gives the monthly expenditure of two families:

Expenditure (in Rs.) 

Items 
Family A 
Family B 
Food 
3500 
2700 
Clothing 
500 
800 
Rent 
1500 
1000 
Education 
2000 
1800 
Miscellaneous 
2500 
1800 
In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the following ratios?
(a) 1 : 1
(b) 10 : 9
(c) 100 : 91
(d) 5 : 49
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
116. In a multiplechoice 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
117. If x_{1} and x_{2} are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is
(a) x_{1} + x_{2} > 2√x_{1}x_{2}
(b) √x_{1} + √x_{2} > √2
(c) √x_{1}  √x_{2}  > √2
(d) x_{1} + x_{2} < 2(√x_{1}x_{2} + 1)
118. Consider the following statements
1. Variance is unaffected by change of origin and change or scale.
2. Coefficient of variance is independent or 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
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
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
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Answer Key:
UPSC NDA Mathematics Mock Test Answer Key 

Question No. 
Answer 
Question No. 
Answer 
1 
C 
61 
D 
2 
C 
62 
C 
3 
B 
63 
D 
4 
B 
64 
B 
5 
C 
65 
A 
6 
B 
66 
A 
7 
C 
67 
A 
8 
A 
68 
A 
9 
C 
69 
D 
10 
D 
70 
B 
11 
D 
71 
D 
12 
A 
72 
A 
13 
A 
73 
A 
14 
A 
74 
A 
15 
B 
75 
C 
16 
D 
76 
C 
17 
B 
77 
D 
18 
A 
78 
C 
19 
D 
79 
A 
20 
B 
80 
B 
21 
B 
81 
B 
22 
C 
82 
A 
23 
A 
83 
C 
24 
C 
84 
B 
25 
D 
85 
B 
26 
C 
86 
C 
27 
B 
87 
A 
28 
C 
88 
A 
29 
B 
89 
B 
30 
B 
90 
D 
31 
C 
91 
D 
32 
C 
92 
D 
33 
D 
93 
A 
34 
A 
94 
D 
35 
B 
95 
B 
36 
C 
96 
B 
37 
A 
97 
B 
38 
D 
98 
B 
39 
B 
99 
C 
40 
A 
100 
A 
41 
A 
101 
B 
42 
A 
102 
C 
43 
A 
103 
D 
44 
B 
104 
A 
45 
A 
105 
B 
46 
A 
106 
D 
47 
B 
107 
A 
48 
C 
108 
C 
49 
B 
109 
C 
50 
A 
110 
C 
51 
A 
111 
B 
52 
B 
112 
C 
53 
D 
113 
A 
54 
C 
114 
B 
55 
C 
115 
D 
56 
A 
116 
B 
57 
B 
117 
C 
58 
C 
118 
B 
59 
A 
119 
C 
60 
C 
120 
C 