NDA Previous Year Question Paper 2022-mathematics|
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1. How many four-digit natural numbers are there such that all of the digits are odd?
(a) 625 (b) 400 (c) 196 (d) 120
2. What is ∑_{r=0}^{n} 2^r C(n,r) equal to?
(a) 2^n (b) 3^n (c) 2^(2n) (d) 3^(2n)
3. If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with C?
(a) 302400
(b) 403600
(c) 907200
(d) 1814400
4. Consider the following statements:
1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z
2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N
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
5. Consider the determinant
If a13 = yz, a23 = xz, a33 = xy and the minors of a13, a23, a33 are respectively (z − y), (z − x), (y − x) then what is the value of Λ?
(a) (z − y)(z − x)(y − x)
(b) (x − y)(y − z)(x − z)
(c) (x − y)(z − x)(y − z)(x + y + z)
(d) (xy + yz + zx)(x + y + z)
6. [प्रश्न पाठ अपूर्ण] correct?
1. A + adj A is a null matrix
2. A⁻¹ + adj A is a null matrix
3. A − A⁻¹ is a null matrix
4. A − A⁻¹ is a null matrix
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
7. If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2 then which of the following are correct?
1. (ZY)X is a square matrix having 9 entries.
2. Y(XZ) is a square matrix having 4 entries.
3. X(YZ) is not defined.
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
8. For how many quadratic equations, the sum of roots is equal to the product of roots?
(a) 0
(b) 1
(c) 2
(d) Infinitely many
9. Consider the following statements:
1. The set of all irrational numbers between √2 and √5 is an infinite set.
2. The set of all odd integers less than 100 is a finite set.
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
10. Consider the following statements:
1. 2 + 4 + 6 + … + 2n = n² + n
2. The expression n² + n + 41 always gives a prime number for every natural number n
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
11. Let p, q (p > q) be the roots of the quadratic equation x² + bx + c = 0 where c > 0. If p² + q² − 11pq = 0 then what is p − q equal to?
(a) 3√c (b) 3c
(c) 9√c (d) 9c
12. What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm?
(a) 1 + √2 cm
(b) 2 + √2 cm
(c) 2 + √3 cm
(d) 3 + √3 cm
13. Let A = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16} and let f : A → N be defined by f(x) = the highest prime factor of x
How many elements are there in the range of f?
(a) 4
(b) 5
(c) 6
(d) 7
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14. Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x² = y³}. Which of the following are not correct?
1. (x, x) ∈ R for all x ∈ N
2. (x, y) ∈ R ⇒ (y, x) ∈ R
3. (x, y) ∈ R and (y, z) ∈ R ⇒ (x, z) ∈ R
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
15. Consider the following:
1. A ∩ B = A ∩ C ⇒ B = C
2. A ∪ B = A ∪ C ⇒ B = C
Which of the above is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
DIRECTIONS: Consider the following for the next three (03) items that follow:
Let z = (1 + i sin θ)/(1 − i sin θ) where i = √(−1)
16. What is the modulus of z?
(a) 1
(b) √2
(c) 1 + sin²θ
(d) (1 + sin²θ)/(1 − sin²θ)
17. What is angle θ such that z is purely real?
(a) nπ/2
(b) (2n + 1)π/2
(c) nπ
(d) 2nπ only
where n is an integer
18. What is angle θ such that z is purely imaginary?
(a) nπ/2
(b) (2n + 1)π/2
(c) nπ
(d) 2nπ
where n is an integer
DIRECTIONS: Consider the following for the next three (03) items that follow:
Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B.
Let P : Q = (5n + 4) : (9n + 6)
19. What is the ratio of the first term of A to that of B?
(a) 1/3
(b) 2/5
(c) 3/4
(d) 3/5
20. What is the ratio of their 10th terms?
(a) 11/29
(b) 22/49
(c) 33/59
(d) 44/69
21. If d is the common difference of A and D is the common difference of B, then which one of the following is always correct?
(a) D > d
(b) D < d
(c) 7D > 12d
(d) None of the above
DIRECTIONS: Consider the following for the next three (03) items that follow:
Consider the binomial expansion of (p + qx)⁹
22. What is the value of q if the coefficients of x³ and x⁶ are equal?
(a) p
(b) 9p
(c) 1/p
(d) p²
23. What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?
(a) pq
(b) p/q
(c) 4p/5q
(d) 1/(pq)
24. Under what condition the coefficients of x² and x⁴ are equal?
(a) p : q = 7 : 2
(b) p² : q = 7 : 2
(c) p : q = 2 : 7
(d) p² : q² = 2 : 7
DIRECTIONS: Consider the following for the next three (03) items that follow:
Consider the word 'QUESTION' :
25. How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed?
(a) 36
(b) 144
(c) 576
(d) 864
26. How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?
(a) 288
(b) 576
(c) 1152
(d) 2304
27. How many 8-letter words with or without meaning, can be formed so that all consonants are together?
(a) 5760
(b) 2880
(c) 1440
(d) 720
DIRECTIONS: Consider the following for the next three (03) items that follow :
Let Δ be the determinant of a matrix A
where A = [a11 a12 a13 ; a21 a22 a23 ; a31 a32 a33] and C11, C12, C13 be the cofactors
of a11, a12, a13 respectively.
28. What is the value of
a11 C11 + a12 C12 + a13 C13?
(a) 0
(b) 1
(c) Δ
(d) −Δ
29. What is the value of a21 C11 + a22 C12 + a23 C13?
(a) 0
(b) 1
(c) Δ
(d) −Δ
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30. What is the value of | a21 a31 a11 ; a23 a33 a13 ; a22 a32 a12 |
(a) 0
(b) 1
(c) Δ
(d) −Δ
DIRECTIONS: Consider the following for the next three (03) items that follow:
Let f(x) be a function satisfying f(x + y) = f(x) f(y) for all x, y ∈ E such that f(1) = 2
31. If ∑_{x=2}^{n} f(x) = 2044 then what is the value of n?
(a) 8
(b) 9
(c) 10
(d) 11
32. What is ∑_{x=1}^{5} f(2x − 1) equal to?
(a) 341
(b) 682
(c) 1023
(d) 1364
33. What is ∑_{x=1}^{6} 2^x f(x) equal to?
(a) 1365
(b) 2730
(c) 4024
(d) 5460
DIRECTIONS: Consider the following for the next three (03) items that follow:
A university awarded medals in basket ball, football and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
34. How many received medals in exactly two of the three sports?
(a) 30 − 4x
(b) 35 − 7x
(c) 40 − 7x
(d) 45 − 5x
35. How many received medals in at least two of three sports?
(a) 30 − 6x
(b) 35 − 6x
(c) 40 − 5x
(d) 40 − 6x
36. How many received medals in exactly one of three sports?
(a) 21x − 40
(b) 21x − 35
(c) 20x − 35
(d) 20x − 25
DIRECTIONS: Consider the following for the next three (03) items that follow:
symmetric matrix and Q is skew-symmetric matrix.
37. What is P equal to?
(a) [0 1/2 1/2 ; 1/2 0 1/2 ; 1/2 1/2 0]
(b) [0 1 1 ; 1 0 1 ; 1 1 0]
(c) cos 20 [0 −1 1 ; 1 0 −1 ; −1 1 0]
(d) cos 20 [0 −1/2 1/2 ; 1/2 0 −1/2 ; −1/2 1/2 0]
38. What is Q equal to?
(a) [0 1/2 1/2 ; 1/2 0 1/2 ; 1/2 1/2 0]
(b) [0 1 1 ; 1 0 1 ; 1 1 0]
(c) cos 20 [0 −1 1 ; 1 0 −1 ; −1 1 0]
(d) cos 20 [0 −1/2 1/2 ; 1/2 0 −1/2 ; −1/2 1/2 0]
39. What is the minimum value of determinant of A?
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1
DIRECTIONS: Consider the following for the next three (03) items that follow:
ABC is a triangular plot with AB = 16 m, BC = 10 m and CA = 10 m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45° at the vertex B.
40. What is the height of the lamp post?
(a) 6 m
(b) 7 m
(c) 8 m
(d) 9 m
41. What is AB/sin C equal to?
(a) 17 m
(b) 50/3 m
(c) 40/3 m
(d) 16 m
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42. What is cos A + cos B + cos C equal to?
DIRECTIONS: Consider the following for the next three (03) items that follow :
There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at a distance y from the foot of the tower (x > y). The angles of elevation of the top of the tower from P and Q are 15° and 75° respectively.
43. At what height is the top of the tower above the ground level?
44. If θ is the inclination of the tower to the horizontal, then what is cot θ equal to?
45. What is the length of the tower?
46. What is the value of cos(−73π/3)?
(a) 2/√3
(b) −2/√3
(c) 2
(d) −2
47. What is the value of
cos(5π/17) + cos(7π/17) + 2 cos(11π/17) cos(π/17)
(a) 0
(c) 4 cos(6π/17) cos(π/17)
(d) 4 cos(11π/17) cos(π/17)
48. What is the value of tan(3π/8)?
(a) √2 − 1
(b) √2 + 1
(c) 1 − √2
(d) −(√2 + 1)
49. What is tan⁻¹ cot(cosec⁻¹ 2) equal to?
(a) π/8
(b) π/6
(c) π/4
(d) π/3
50. In a triangle ABC, a = 4, b = 3, c = 2. What is cos 3C equal to?
(a) 7/128
(b) 11/128
(c) 7/64
(d) 11/64
51. What is cos 36° − cos 72° equal to?
(a) √5/2
(b) −√5/2
(c) 1/2
(d) −1/2
52. If sec x = 25/24 and x lies in the fourth quadrant, then what is the value of tan x + sin x?
(a) 625/168
(b) −343/600
(c) 625/168
(d) 343/600
53. What is the value of tan²165° + cot²165°?
(a) 7
(b) 14
(c) 4√3
(d) 8√3
54. What is the value of sin(2nπ + 5π/6) sin(2nπ − 5π/6) where n ∈ Z?
(a) 1/4
(b) −3/4
(c) −1/4
(d) 3/4
55. If 1 + 2(sin x + cos x)(sin x − cos x) = 0 where 0 < x < 360° then how many values does x take?
(a) Only one value
(b) Only two values
(c) Only three values
(d) Four values
56. Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis :
1. The line passes through the point (1, 1/(2 − √3))
2. The line entirely lies in first and third quadrants.
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
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57. If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?
(a) 3x + 4y − 25 = 0
(b) 4x + 3y − 24 = 0
(c) 4x − 3y = 0
(d) 3x − 4y + 7 = 0
58. The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B lies above the origin. What is the equation of line passing through (8, 0) and parallel to the side AC?
(a) x − √3 y − 8 = 0
(b) x + √3 y − 8 = 0
(c) x − √3 x + y − 8√3 = 0
(d) √3 x − y − 8√3 = 0
59. The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line
(a) 2x − y + 1 = 0
(b) 3x − 2y − 1 = 0
(c) 3x − 4y + 6 = 0
(d) 2x + 3y − 26 = 0
60. The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity?
61. An equilateral triangle is inscribed in a parabola x² = √3 y where one vertex of the triangle is at the vertex of the parabola. If p is the length of side of the triangle and q is the length of the latus rectum, then which one of the following is correct?
(a) p = q
(b) p = √3 q
(c) p = 2√3 q
(d) 2√3 p = q
62. Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4) and D(8, 14, 12). Which of the following statements is/are correct?
1. The points are the vertices of a rectangle ABCD
2. The mid-point of AC is the same as that of BD
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
63. Consider the equation of a sphere x² + y² + z² − 4x − 6y − 8z − 16 = 0
Which of the following statements is/are correct?
1. z-axis is tangent to the sphere.
2. The centre of the sphere lies on the plane x + y + z − 9 = 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
64. A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?
< 2/3, 2/3, 1/3 >
< 1/√6, 1/√6, 2/√6 >
< 2/√6, 1/√6, 1/√6 >
65. Consider the following statements:
1. The direction ratios of y-axis can be < 0, 4, 0 >
2. The direction ratios of a line perpendicular to z-axis can be < 5, 6, 0 >
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
66. PQR is a parallelogram. If PR→ = a→ and QS→ = b→, then what is PQ→ equal to?
(a) a→ + b→
(b) a→ + b→
(c) a→ + b→
(d) a→
67. Let a→, b→ and c→ be unit vectors such that a→ + 2b→ and 5a→ − 4b→ are perpendicular. What is the angle between a→ and b→?
68. Let a→, b→ and c→ be unit vectors lying on the same plane. What is {(3a→ + 2b→) × (5a→ − 4c→)} · (b→ + 2c→) equal to?
(a) −8
(c) 8
69. What are the values of x for which the angle between the vectors 2x² i→ + 3y→ + k→ and i→ − 2j→ + x² k→ is obtuse?
(a) 0 < x < 2
(b) x < 0
(c) x > 2
(d) 0 ≤ x ≤ 2
70. The position vectors of vertices A, B and C of triangle ABC are respectively j→ + k→, 3i→ + j→ + 5k→ and 3j→ + 3k→. What is angle C equal to?
(a) π/6
(b) π/3
(c) π/2
71. Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?
(a) −1
(c) 1
72. If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x) then what is the value of k?
(a) 7
(b) 5
(c) 4
(d) 3
73. What is the minimum value of the function f(x) = log₁₀(x² + 2x + 11)?
(a) 0
(b) 1
(c) 2
(d) 10
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74. What is ∫ (x²)² (1 + ln x) dx equal to?
(a) x² x + c
(b) 1/2 x² x + c
(c) 2x² x + c
(d) 1/2 x² x + c
75. What is ∫ e^x (1 + ln x + x ln x) dx equal to?
(a) x e^x ln x + c
(b) x² e^x ln x + c
(c) x + e^x ln x + c
(d) x e^x + ln x + c
76. What is ∫ ((cos x)^1.5 − (sin x)^1.5)/√(sin x cos x) dx equal to?
(a) √(sin x) − √(cos x) + c
(b) √(sin x) + √(cos x) + c
(c) 2√(sin x) + 2√(cos x) + c
(d) 1/2 √(sin x) + 1/2 √(cos x) + c
77. If y = (x√(x² − 16))/2 − 8 ln |x + √(x² − 16)| then what is dy/dx equal to?
(a) x√(x² − 16)
(b) x − √(x² − 16)
(c) √(x² − 16)
(d) 4√(x² − 16)
78. If y = (x^x)^x then which one of the following is correct?
(a) dy/dx + xy(1 + 2 ln x) = 0
(b) dy/dx − xy(1 + 2 ln x) = 0
(c) dy/dx − 2xy(1 + 2 ln x) = 0
(d) dy/dx − 2xy(1 + 2 ln x) = 0
79. What is the maximum value of 3(sin x − cos x) + 4(cos³x − sin³x)?
(a) 1
(b) √2
(c) √3
(d) 2
80. What is the area of the region (in the first quadrant) bounded by y = √(1 − x²), y = x and y = 0?
(a) π/4
(b) π/6
(c) π/8
(d) π/12
81. What is the area of the region bounded by x − |y| = 0 and x − 2 = 0?
(a) 1
(b) 2
(c) 4
(d) 8
82. If f(α) = √(sec²α − 1), then what is (f(α) + f(β))/(1 − f(α) f(β)) equal to?
(a) f(α − β)
(b) f(α + β)
(c) f(α) f(β)
(d) f(αβ)
83. If f(x) = ln(x + √(1 + x²)), then which one of the following is correct?
(a) f(x) + f(−x) = 0
(b) f(x) − f(−x) = 0
(c) 2f(x) = 2f(−x)
(d) f(x) = 2f(−x)
84. What is lim_{x→0} x/√(1 − cos⁴x) equal to?
(a) 1/(2√2)
(b) −1/(2√2)
(c) √2
(d) Limit does not exist
85. What is lim_{x→1/2} (4x − 2π)/cos x equal to?
(a) −4
(b) −2
(c) 2
(d) 4
86. If f(x) = (x² + x + |x|)/x then what is lim_{x→0} f(x) equal to?
(a) 0
(b) 1
(c) 2
(d) lim_{x→0} f(x) does not exist
87. What is lim_{h→0} (sin²(x + h) − sin²x)/h equal to?
(a) sin²x
(b) cos²x
(c) sin²x
(d) cos²x
88. Let f(x) be a function such that f(x) = g(x) and f⁻(x) = −f(x). Let h(x) = {f(x)}² + {g(x)}². Then consider the following statements:
1. h(3) = 0
2. h(1) = h(2)
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
89. In y = ln²((x² − x + 1)/(x² + x + 1)), then what is dy/dx at x = 0 equal to?
(a) −2
(b) 0
(c) 1
(d) 2
90. If d(1 + x⁴ + x⁸)/dx(1 − x² + x⁴) = ax + bx³, then which one of the following is correct?
(a) a = b
(b) a = 2b
(c) a + b = 0
(d) 2a = b
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91. Under which one of the following conditions does the function f(x) = (p sec x)² + (q sec x)² attain minimum value?
92. Where does the function f(x) = ∑_{j=1}^{7} (x − j)² attain its minimum value?
(a) x = 3.5
(b) x = 4
(c) x = 4.5
(d) x = 4
93. Consider the following statements in respect of the function
1. The function attains maximum value only at x = 3
2. The function attains local minimum only at x = 0
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
94. What is ∫₀¹ ln(1/x − 1) dx equal to?
(a) −1
(b) 0
(c) 1
(d) ln 2
95. If ∫₀^{π/2} (sin⁴x + cos⁴x) dx = k, then what is the value of ∫₀^{20π} (sin⁴ + cos⁴x) dx?
(a) k
(b) 10k
(c) 20k
(d) 40k
96. What is ∫_{−π/2}^{π/2} (e^{cos x} sin x + e^{sin x} cos x) dx equal to?
97. What is the area of the region enclosed in the first quadrant by x² + y² = π², y = sin x and x = 0?
98. Consider the following statements:
1. The degree of the differential dy/dx + cos(dy/dx) = 0 is 1.
2. The order of the differential equation
(d²y/dx²)³ + cos(dy/dx) = 0
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
99. What is the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis?
(a) x dy/dx + 2y = 0
(b) y dx/dy + 2x = 0
(c) y dx/dy − 2x = 0
100. What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0?
(a) y = tan(x/2) − x + c
(b) y = 1/2 tan(x/2) − x + c
(c) y = 2 tan(x/2) − x + c
(d) y = tan(x/2) − 2x + c
101. Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers.
If x/y = 55/42, then what is the value of n?
(a) 24
(b) 25
(c) 27
(d) 30
102. What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
(a) 7/10
(b) 17/25
(c) 33/50
103. If n > 7, then what is the probability that C(n, 7) is a multiple of 7?
(a) 0
(b) 1/7
(c) −
(d) 1
104. Two numbers x and y are chosen at random from a set of first 10 natural numbers. What is the probability that (x + y) is divisible by 4?
(a) 1/5
(b) 2/9
(c) 8/45
(d) 7/45
105. A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x + 1/x > 2?
(a) 1/n
(b) 1/(2n)
(c) (n − 1)/n
(d) 1
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106. Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?
(a) 1/12
(b) 1/18
(c) 1/36
(d) 1/72
107. If P(A) = 0.5, P(B) = 0.7 and P(A ∩ B) = 0.3 then what is the value of P(A ∩ B′) + P(A ∩ B) + P(A ∩ B′)?
(a) 0.6
(b) 0.7
(c) 0.8
(d) 0.9
108. Five coins are tossed once. What is the probability of getting at most four tails?
109. Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15?
(a) 19/216
(b) 1/12
(c) 17/216
(d) 5/54
110. The probability that a person hits a target is 0.5. What is the probability of at least one hit in 4 shots?
(a) 1/8
(b) 1/16
(c) 15/16
(d) 7/8
111. A box contains 2 white balls, 3 black balls and 4 red balls. What is the number of ways of drawing 3 balls from the box with at least one black ball?
(a) 84
(b) 72
(c) 64
(d) 48
112. During war one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive safely?
(a) 16/625
(b) 32/625
(c) 64/625
(d) 128/625
113. A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are
(a) 9 : 4
(b) 35 : 17
(c) 17 : 35
(d) 4 : 9
114. The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples was noted to be 0.7. Assume that all these couples survive to celebrate the silver jubilee of their marriage. The coefficient of correlation at that point of time will be
(a) 1
(b) 0.9
(c) 0.7
(d) 0.3
115. The completion of a construction job may be delayed due to strike. The probability of strike is 0.6. The probability that the construction job gets completed on time if there is no strike is 0.85 and the probability that the construction job gets completed on time if there is a strike is 0.35. What is the probability that the construction job will not be completed on time?
(a) 0.35
(b) 0.45
(c) 0.55
(d) 0.65
DIRECTIONS : Consider the following for the next two (02) items that follow :
The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below:
Subject Mean Marks SD
Mathematics 40 15
Physics 28 12
Chemistry 38 14
Biology 36 16
116. Which one of the following subjects shows highest variability of marks?
(a) Mathematics
(b) Physics
(c) Chemistry
(d) Biology
117. What is the coefficient of variation marks in Mathematics?
(a) 37.5%
(b) 38.0%
(c) 38.5%
(d) 39.0%
DIRECTIONS: Consider the following for the next three (03) items that follow :
Consider the following grouped frequency distribution :
Class Frequency
0-10 1
10-20 2
20-30 4
30-40 6
40-50 4
50-60 3
118. What is the median of the distribution?
(a) 34
(b) 34.5
(c) 35
(d) 35.5
119. What is mean deviation about the median?
(a) 11.4
(b) 11.1
(c) 10.8
(d) 10.5
120. What is the mean deviation about the mean?
(a) 10.15
(b) 10.65
(c) 11.15
(d) 11.65
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