1. How many meaningful English words can be formed by using letters of the word "ELPA"?
A
One
B
Two
C
Three
D
More than three
The word "ELPA" consists of 4 letters. Let`s analyze how many meaningful English words can be formed using these letters:
So, there are 5 meaningful English words that can be formed using the letters of the word "ELPA".
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2. Express 231 in prime factors
A
3x7x11
B
21x11
C
33x4
D
3x4x11
3x7x11
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3. Find the value of the polynomial 5x - 4x² + 3 at x = -1
A
8
B
-9
C
3
D
-6
-6
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4. if (1, -2) is a solution of the equation 2x -y = p, then find the value of p
A
4
B
0
C
2
D
1
4
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5. The ratio of two sides of a parallelogram in 3:5 and its perimeter is 96 cim. Find the adjacent side of the parallelogram.
A
18 cm
B
20 cm
C
60 cm
D
45 cm
18 cm
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6. Express 0.000532 is standard form
A
532 x 105
B
5.32 x 10-4
C
532 x x 10-3
D
0.532 x 102
5.32 x 10<sup>-4</sup>
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7. How many pieces of length 125 can be cut from a rod 50 m long?
A
35
B
40
C
52
D
28
Given:
length of rod = 50 m, length of each piece = 125 cm
Formula Used:
number of pieces of rod = length of rod/length of each piece
1 m = 100 cm
Calculation:
⇒ length of rod = 50 m = 5000 cm
⇒ number of pieces of rod = 5000/125 = 40
∴ required number of pieces of rod = 40
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8. What is the value of p(t) = 2 + t + 2t2 - t3 for p(0)
A
1
B
2
C
3
D
5
2
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9. The multiplicative inverse of -13 is p/13, then -p is equal to
A
1
B
0
C
-13
D
None of these
1
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10. What should come in the place of question mark(?) in the following question? using BODMAS
(25)2 + (16)2 - (18)2 - (4)2 + (√4)2 - (√121) = ?
A
534
B
524
C
576
D
512
534
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11. √x × 125 = (24646-22771)×11
A
27225
B
29225
C
28225
D
30225
27225
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12. Find the rate of interest when:(%) Principal = Rs.11000, SI = Rs.7040 and time = 8 years
A
10
B
4
C
8
D
6
8
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13. What is the average of first five multiples of 13?
A
39
B
37
C
35
D
41
14. Henry lended a sum of Rs.4950 for 20% per annum at compound interest then the sum of the amount will be Rs.7128 is obtained. After how many years he will get that amount?
A
2
B
1
C
3
D
4
7128 = 4950 (120/100)^x
This equation holds for x = 2
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15. If p(A) = 0.3, p(B) = 0.8 and p(A and B) = 0.7, find p(A or B)
A
0.3
B
0.5
C
0.6
D
0.4
0.4
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16. Find the length of the largest pole that can be placed in a room of dimensions 36 m × 12 m × 9 m
A
43
B
41
C
39
D
45
39
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17. √((68÷17×9)÷16) = ? - 0.5
A
1
B
4
C
2
D
3
2
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18. Find the area of trapezium whose parallel sides are 24 cm and 20 cm long, and the distance between them is 17 cm. (In cm2 )
A
354
B
364
C
374
D
344
19. Find the area of the square whose side is 235 cm. (In cm2
A
54225
B
56225
C
53225
D
55225
20. Find the greatest number of three digits which is divisible by 12, 24, 32 and 30.
A
970
B
990
C
980
D
960
21. If a line passing through the points (k, 3k) and (2, 3) is perpendicular to the line 3x + 4y + 5 = 0, then what is the value of k?
A
4/5
B
2/5
C
3/5
D
1/5
1/5
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22. Which of the following sets is finite?
A
Set of lines perpendicular to x-axis
B
The set of numbers which are multiple of 5
C
Set of letters in English alphabet
D
Set of lines parallel to x-axis
Set of letters in English alphabet
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23. If f(x) = x2 – 8x + 7, then what is the value of f`(4) + 3f`(2)?
A
–18
B
–16
C
–12
D
–20
–12
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24. If f(x) = kx3 + px + 10 and f`(3) = 15 and f`(1) = 10, then what is the value of (k + p)?
A
109/12
B
113/12
C
119/12
D
115/12
115/12
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25. What is the equation of a line passing through (3, 5) and inclined at an angle of 135 degree with the positive direction of x-axis?
A
x + y = 8
B
x – y = –8
C
x + y = –8
D
x – y = 8
x + y = 8
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26. The set builder form of the set A = {3, 9, 27, 81, 243} is ____
A
{x : x = 3n, n ∈ N and 1 < n < 5}
B
{x : x = 3n, n ∈ N and 1 < n ≤ 5}
C
{x : x = 3n, n ∈ N and 1 ≤ n ≤ 5}
D
{x : x = 3n, n ∈ N and 1 ≤ n < 5}
{x : x = 3n, n ∈ N and 1 ≤ n ≤ 5}
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27. Which of the following is correct roaster form of set A = {x : x is an integer and –1 ≤ x < 3}?
A
A = {–1, 0, 1, 2}
B
A = {–1, 0, 1, 2, 3}
C
A = {0, 1, 2}
D
A = {0, 1, 2, 3}
A = {–1, 0, 1, 2}
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28. The length of the latus-rectum of the ellipse x2 + 4y2 + 2x + 16y + 13 = 0 is __
A
2
B
3
C
4
D
1
29. Which of the following is correct form of De-Morgan`s Law?
A
(A ⋂ B )` = A` ∪ B`
B
(A ⋂ B)` = A` ⋂ B`
C
A ∪ B) = A ⋂ B
D
(A ⋂ B) = A` ⋂ B`
(A ⋂ B )` = A` ∪ B`
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30. What is the equation of the line which is parallel to 2x – 3y + 10 = 0 and passes through the point (2, 3)?
A
2x – 3y + 5 = 0
B
2x + 3y + 10 = 0
C
2x – 3y + 10 = 0
D
2x + 3y + 5 = 0
2x – 3y + 5 = 0
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31. Differentiation of sin(4x + 5) with respect to x is ___
A
4sin(4x + 5)
B
4cos(4x + 5)
C
5cos(4x + 5)
D
5sin(4x + 5)
4cos(4x + 5)
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32. What is the slope of the tangent to the curve f(x) = 2x5 + x3 – 2 at x = 1?
A
13
B
11
C
14
D
12
f`(x) =10x4 + 3x2 So at x=1 f`(1)= 10 + 3 = 13
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33. If A and B are two sets such that n(A)= 50, n(B) = 15 and n(A ∪ B) = 60, then what is the value of n(A ∩ B)?
A
5
B
15
C
8
D
10
34. Two vertices of a triangle are (3, 2) and (7, 4). If the centroid of the triangle is (8, 9), then what is the coordinates of the third vertex of that triangle?
A
(14, 21)
B
(21, 23)
C
(16, 19)
D
(15, 23)
(14, 21)
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35. What is the value of the eccentricity of the ellipse 25x2 + 9y2 – 150x – 90y + 225 = 0?
A
2/5
B
3/4
C
3/5
D
4/5
4/5
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36. Which of the following is a finite set?
A
The set of numbers which are multiple of 3
B
The set of even numbers
C
The set of whole number less than 1
D
The set of negative integers
The set of whole number less than 1
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37. If y = ex cosx, then what is the value of (dy/dx) at x = 0?
A
zero
B
2
C
-1
D
1
38. Differentiation of cotx with respect to x is ___
A
–tan2x
B
tan2x
C
cosec2x
D
-cosec2x
-cosec2x
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39. ϕ, {1}, {2}, {1, 2} are the subsets of ___
A
{1, 2}
B
{0, 1, 2}
C
{1}, {2}
D
{1, 3}
{1, 2}
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40. If the angle between two lines is π/4 and slope of one of the lines is 1/3, then what is the slope of the other line?
A
3
B
1
C
2
D
4
41. If y = x2sinx, then what is the value of (dy/dx) at x = π/2?
A
π
B
π/4
C
π/6
D
π/2
42. If 5p – 7q + r = 11, 6p – 8q – r = 15 and 3p + 2q – 6r = 7, then what is the value of (p + q + r)?
A
–2
B
–3
C
zero
D
–1
43. What is the equation of the parabola whose focus is (2, 0) and the directrix is x + 5 = 0?
A
y2 = 21x – 14
B
y2 = 14x – 21
C
y2 = 14x + 21
D
y2 = 21x + 14
y2 = 14x + 21
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44. Differentiation of 4x + x5 + 31 with respect to x is ___
A
4x log2 + 5x5
B
5x log4 + 5x4
C
4x log4 + 5x4
D
4x log2 + 4x5
4x log4 + 5x4
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45. Set builder form of the set {1, 8, 27, 64, 125} is ___
A
{x : x = n3 and 1 ≤ n ≤ 15}
B
{x : x = n3 and 1 ≤ n ≤ 5}
C
{x : x = 3n and 1 < n ≤ 15}
D
{x : x = 3n and 1 ≤ n ≤ 505}
{x : x = n3 and 1 ≤ n ≤ 5}
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46. Which of the following states that A = B?
A
A = {2, 7, 9} and B = {7, 9, 2}
B
A = {a, e, f} and B = {f, e}
C
A = {2, 4, 6, 8} and B = {4, 8}
D
A = {a, b, c, d, e} and B = {e, c, b, a}
A = {2, 7, 9} and B = {7, 9, 2}
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47. A circle of radius 2 units touches the coordinate axes in the first quadrant. What is the equation of its image in the line y = 0?
A
x2 + y2 – 4x + 4y + 4 = 0
B
x2 + y2 + 4x – 4y + 8 = 0
C
x2 + y2 + 4x + 4y + 8 = 0
D
x2 + y2 + 4x – 4y + 4 = 0
x2 + y2 – 4x + 4y + 4 = 0
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48. If A = {1, 2, 3, 4, 5, 6}, then which of the following statements is correct?
A
{1, 2, 3} ∈ A
B
{3, 4} ∈ A
C
{3, 4} ⊂ A
D
1 ⊂ A
{3, 4} ⊂ A
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49. The roster form of the set of all letters in the word “MATHEMATICS” is ___
A
{M, A, T, H, E, M, A, T, C, S}
B
{M, A, T, H, E, I, S}
C
{M, A, T, E, H, I}
D
{M, A, T, H, E, I, C, S}
{M, A, T, H, E, I, C, S}
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50. A rod having length of √5 metre slides with its ends on two perpendicular lines. What is the locus of the mid-point of rod?
A
4x2 + 4y2 = √5
B
4x2 – 4y2 = 5
C
4x2 + 4y2 = 5
D
4x2 – 4y2 = √5
4x2 + 4y2 = 5
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51. What is the equation of the circle whose coordinates of centre is (2, 3) and radius is 4?
A
x2 + y2 – 4x – 6y – 3 = 0
B
x2 + y2 + 4x – 6y – 3 = 0
C
x2 + y2 – 4x + 6y + 3 = 0
D
x2 + y2 – 4x – 6y + 3 = 0
x2 + y2 – 4x – 6y – 3 = 0
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52. Differentiation of logtanx with respect to x is ___
A
2cosec2x
B
2sec2x
C
2sin2x
D
2cos2x
2cosec2x
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53. If the coordinates of the mid-points of the sides of a triangle are (1, 2), (2, 4) and (3, 5), then what is the value of coordinates of its centroid?
A
2, (11/3)
B
5, (11/6)
C
3, (11/4)
D
4, (9/4)
2, (11/3)
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54. If P and Q are the two sets containing 3 and 6 elements respectively, then what can be the maximum number of elements in P ⋃ Q?
A
10
B
9
C
12
D
11
55. If the circles x2+ y2 = K and x2 + y2 – 8x – 6y + 9 = 0 touches externally, then what is the value of K?
A
1
B
2
C
3
D
4
56. The equation of the directrix of the parabola y2 = 4x + 4y is ______.
A
x + 6 = 0
B
x + 3 = 0
C
x + 5 = 0
D
x + 2 = 0
x + 2 = 0
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57. The roster form of the set P = {x : x is an integer and x2 – 81 = 0} is ______.
A
{49, –81}
B
{9, –9}
C
{81, –81}
D
{8, –8}
{9, –9}
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Wrong Answered :
58. Differentiation of e-x with respect to x is ______.
A
-e-x
B
-ex
C
ex
D
e-x
-e-x
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Wrong Answered :
59. Which of the following pairs of sets are equal?
A
A = {1, 2, 3, 4, 5, 6, 7, 8}, B = {x : x is a natural number and x < 8}
B
A = {3, 6, 9, 12}, B = {x : x = 3n and 1 ≤ n ≤ 4}
C
A = {2, 4, 6, 8}, B = {8, 6, 4, 1}
D
A = {a, e, i, o, v}, B = {e, a, u, i, o}
A = {3, 6, 9, 12}, B = {x : x = 3n and 1 ≤ n ≤ 4}
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60. What is the length of latus-rectum of the parabola y2 = 16x?
A
16
B
12
C
20
D
8
61. If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}, then what is the value of A ∩ B?
A
{1, 2, 3, 4, 5, 6}
B
{2, 4, 6}
C
{2, 4}
D
ϕ
{2, 4, 6}
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62. If f(x) = 5x4 – 7 and f(0) = 5, then what is the anti-derivative of f(x)?
A
x4 – 7x + 2
B
x5 – 7x + 6
C
x4 – 7x + 5
D
x5 – 7x + 5
x5 – 7x + 5
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Wrong Answered :
63. The radius of the circle having centre at (3, –4) and touching the line 3x + 4y – 8 = 0 is
A
3
B
2
C
4
D
5
64. In a school 40 percent of the students travels by bus, 30 percent travels by car and 5 percent travels by both bus and car. What percent of total students travel by bus or car?
A
65 percent
B
70 percent
C
60 percent
D
55 percent
65 percent
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Wrong Answered :
65. Differentiation of x3 + cosx + (1/x3 ) with respect to x is ______.
A
3x2 – sinx – (3/x4 )
B
3x2 – sinx + (2/x3 )
C
3x2 + sinx + (2/x3 )
D
3x2 + sinx – (2/x3 )
3x2 – sinx – (3/x4 )
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66. If P = {1, 2, 4, 5, 6}, then the number of subset of P is ______.
A
64
B
32
C
8
D
16
67. If f(x) = xn+2 and f`(1) = 14, then what is the value of n?
A
14
B
12
C
11
D
10
68. What is the distance between the points (4, 5) (7, 9)?
A
6
B
5
C
4
D
3
69. Which of the following is an example of equivalent set?
A
P = {3, 6, 9, 12, 15} and Q = {x : x = 3n and 1 ≤ x < 6}
B
P = {5, 25, 125, 625} and Q = {x : x = 5n and 1 ≤ x ≤ 3}
C
P = {a, b, c, d} and Q = {d, c, a, b, e}
D
P = {2, e, 4, 5, g} and Q = {g, 1, 2, 4, 5, 6}
P = {3, 6, 9, 12, 15} and Q = {x : x = 3n and 1 ≤ x < 6}
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70. If f(x) = [(x + 3)/(x2 + 1)], then what is the value of f`(1)?
A
–3/2
B
5/2
C
–5/2
D
3/2
–3/2
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Wrong Answered :
71. Which of the following includes all the subsets of set {a, b}?
A
ϕ, {a}, {b}, {a, b}
B
ϕ, {a}, {b}
C
{a}, {b}, {a, b}
D
{a}, {b}
ϕ, {a}, {b}, {a, b}
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72. For what value of K, the points (K, 2), (3, 5) and (9, 8) are collinear?
A
3
B
-3
C
-6
D
6
73. If the equation of the base of an equilateral triangle is x + y – 6 = 0 and the coordinates of its opposite vertex is (1, 3), then what is the area of the triangle?
A
2/√3
B
1/√3
C
5/√3
D
4/√3
2/√3
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Wrong Answered :
74. If p + 2q + r = 7, p + 3r = 11 and 2p – 3q = 1, then what is the value of (p2 + q2 + r2 )?
A
11
B
9
C
14
D
10
75. Which of the following includes all the elements of set B = {x : x is an integer, x2 ≤ 4}?
A
{–1, 0, 1, 2, 3}
B
{0, 1, 2, 3, 4}
C
{–2, –1, 0, –1}
D
{–2, –1, 0, 1, 2}
{–2, –1, 0, 1, 2}
Correct Answered :
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76. The coordinates of the vertex of the parabola y = x2 – 2x + 3 is ______
A
(2, 4)
B
(1, 3)
C
(2, 3)
D
(1, 2)
(1, 2)
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Wrong Answered :
77. The objects in a set are called:
A
Numbers
B
Terms
C
Elements
D
None of these
Elements
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Wrong Answered :
78. Which of the following sets has only one subset:
A
{x,y}
B
{x}
C
{y}
D
{ }
{ }
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Wrong Answered :
79. Which of the following statement is correct:
A
The inverse of the inverse is the original matrix itself
B
The inverse of the inverse is always null matrix
C
The inverse of the inverse is not possible
D
None of the above
The inverse of the inverse is the original matrix itself
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80. What is the probability of at least two heads on three tosses of a fair coin:
A
0.125
B
0.5
C
1
D
0.25
Sample space: {HHH, HTH,THH,TTH, HHT, HTT,THT,TTT}
Total number of possible outcomes=8
Probability of getting at least two heads is:
P(A)=P(getting two heads)+P(getting 3 heads)
= 3/8 + 1/8
= 4/8 = 1/2 = 0.5
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Wrong Answered :
81. Revised probability is also know as:
A
Prior Probability
B
Posterior probability
C
Joint probability
D
None of the above
A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information. The posterior probability is calculated by updating the prior probability using Baye`s theorem.
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Wrong Answered :
82. Determine the probability of drawing either an ace or a heart from a standard deck of 52 cards:
A
16/52
B
17/52
C
4/52
D
13/52
16/52
Correct Answered :
Wrong Answered :
83. If A and B be two matrices of the same order, then
A
A + B ≠ A + B
B
A = B
C
A + B = B + A
D
none of the above
A + B = B + A
Correct Answered :
Wrong Answered :
84. A sum of money doubles itself at compound interest in 15 years. It will become 8 times in
A
60 years
B
45 years
C
40 years
D
30 years
45
Correct Answered :
Wrong Answered :
85. What sum of money lent out at compound interest will amount to Rs. 968 in 2 years at 10% per annum, interest being charged annually?
A
900
B
800
C
825
D
780
800
Correct Answered :
Wrong Answered :
86. A sum of Rs. 1600 lent at simple interest at 12.5% per annum will become double in
A
7.5 years
B
6 years
C
8 years
D
9 1/4years
8 years
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Wrong Answered :
87. The simple interest on a certain sum of money for 4 years at 4 percent per annum exceeds the compound interest on the same sum for 3 years at 5 percent per annum by Rs. 57. Find the sum.
A
26700
B
12500
C
23050
D
24000
24000
Correct Answered :
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88. A man borrows Rs. 4,000 from a bank at 7 1 2 % interest. At the end of every year, he pays Rs. 1,500 as part repayment of loan and interest. How much does he still owe to the Bank after 3 such annual payments?
A
123.25
B
25
C
124.25
D
125
123.25
Correct Answered :
Wrong Answered :
89. The value of mobile phone which was purchased 2 years ago depreciates at 12% p.a.. If its present value is Rs 9680, for how much was it purchased?
A
12000
B
11500
C
12500
D
10000
12500
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90. Find the compound interest on Rs. 8000 for 3 year at 5% per annum.
A
1261
B
1381
C
1451
D
1151
1261
Correct Answered :
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91. S.I. on Rs. 1500 at 7% per annum for a certain time is Rs. 210. Find the time.
A
3 years
B
1.5 years
C
2 years
D
2.8 years
2 years
Correct Answered :
Wrong Answered :
92. The cost of a machine is estimated to be decreasing at the rate of 15% every year. If it costs Rs. 6,000 now, what will be the estimated value of the machine after 2 years?
A
4335
B
3225
C
3750
D
5000
4335
Correct Answered :
Wrong Answered :
93. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs. 72 more find the sum:
A
1500
B
1000
C
1200
D
1300
1200
Correct Answered :
Wrong Answered :
94. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 1% higher rate, it would have fetched Rs. 24 more. Find the sum.
A
2000
B
1200
C
2400
D
1600
1200
Correct Answered :
Wrong Answered :
95. Find the sum of money which increases 1/10 of itself every year and amounts to Rs. 450 in 5 years at S.I ___
A
250
B
300
C
400
D
350
Rs. 300
Correct Answered :
Wrong Answered :
96. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
A
8925
B
8259
C
8529
D
8952
8925
Correct Answered :
Wrong Answered :
97. The difference in simple interest at 13% and 12% p.a. of a sum in one year is Rs. 110. Then the sum is
A
Rs. 10,000
B
Rs. 15000
C
Rs. 11000
D
Rs. 13000
Rs. 11000
Correct Answered :
Wrong Answered :
98. Simple interest on a certain amount is 9/16 of the principal. If the number representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is:
A
5 ½ years
B
6 ½ years
C
7 years
D
7 ½ years
7 ½ years
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Wrong Answered :
99. If the compound interest on a certain sum of money for 2 ½ years at 5% per annum be Rs. 104.05, what would be the simple interest?
A
Rs. 100
B
Rs. 200
C
Rs. 150
D
Rs. 190
Rs. 100
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Wrong Answered :
100. Ram borrowed Rs. 5,000 from Sanjay with simple interest. After 2 years, Sanjay got Rs. 1,000 more than what he had given to Ram. What was the percentage of interest per annum?
A
15
B
10
C
20
D
5
10
Correct Answered :
Wrong Answered :
101. Let us assume that a student is chosen from a random sample of 80 students, out of which 30 have opted for Maths, 20 opted for physics and 10 have opted for both Maths and Physics. Find the probability that the student has opted for either Maths or Physics.
A
1/2
B
3/2
C
5/2
D
7/2
1/2
Correct Answered :
Wrong Answered :
102. Let us assume set A = {1,2,3,4} and set B = {3,4,5,6,7} find the symmetric difference of set A and Set B?
A
{1,2,3,4,5,6,7}
B
{5,6,7}
C
{1,2,3,4}
D
{1,2,5,6,7}
{1,2,5,6,7}
Correct Answered :
Wrong Answered :
103. Which of the following is an answer for the length of the line segment, given that the coordinates of A is (2,2) and B is (9,11).
A
9.4
B
11.4
C
13.4
D
15.4
Distance = ((11-2) ^ 2 + (9 - 2) ^ 2) ^ 1/2
= (81 + 49)^ 1/2
=130^1/2
=11.4
Correct Answered :
Wrong Answered :