CBEAS

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1. The value of cos (sin-1 4/5 + tan-1 5/12) is:

65/16 16/65 12/13 13/12
2. If 2 cos A = sin B : sin C then the triangles are:

isosceles equilateral right angled none
3. The value is equal to:

1/120 1/60 120 140
4. If α and β are the roots of the equation x2 – 2x + 4 = 0 then:

(α β)n = 2n+1 α nβn = 2n-1Cos(n/3) α n + βn=2n + 1Cos(n/3) α n + βn = 2n-1cos(/4/3)
5. A fair of dices is cast then the probability that two dices show the same number is:

1/36 1/6 2/36 1/3
6. Let the function f:R→R be defined by then f(-1) is equal to:

3f(-3) -f(-3) -f(-3)/3 f(-3)
7. If a, b, c be in HP then a/b+c, b/c+a, c/a+b are in

HP GP AP ii and iii both
8. The value of α lying between θ = 0 to θ = 9 and the equation

are

7/24 11/24 5/11 i and ii both
9. The value is:

log (5/4) log (5/4)/log(4/3) log(4/5)/log(3/4) log (9/7)
10. The value of is equal to:

none
11. The value of ∫3x2dx/√(9-16x6) is equal to:

1/4 sin-1 (4/3 x3) 1/4 sin-1(x3/3) sin-1(4x3/5)/4 sin-1(4x3/3)
12. The area enclosed between the parabola y2=4ax & x2=4by is:

4ab/3 16a2/3 16ab/3 14ab/5
13. If y=logx/x in 0<x<∞ then the maximum value is equal to:

1/e -e 0 e
14. Let and be the two vectors then the angle between them is:

π/4 π/6 π/3 π/2
15. Resolve into partial fraction (3x + 5)/(x3 + x2 - x - 1)

2/(x - 1) - 2/(x + 1) - 1/(x - 1)2

2 / (x - 1) - 2 / (x + 1) - 1 / (x + 1)2

2 / (x - 1) + 2/(x + 1) - 1 / (x - 1)2

1 / (x - 1) - 1 / (x + 1) - 1 / (x + 1)2
16. The sum of n terms of the series 5 + 55 + 555 + ...

{50(10n – 1)} / 81 {50(10n – 1)} / 81 {50(10n-1)} / 81 – 5n/9 {50(10n – 1)} / 81 + 5n/9
17. What type of locus is represented by {√(ax) + √(by)}2 = 0 is:

two perpendicular lines two separate lines two coincident lines i and ii both
18. The locus of the pole of the line lx + my + n = 0 with respect to the variable circle which touches Y-axis at the origin is:

nx + my = 0 nx – my mx2 = (lx – n)y mx2 = (lx + n)y
19. If the ellipse is given by 5x2+7y2 = 11 then the point (4, -3) lies:

outside the ellipse on the ellipse within the ellipse inside the ellipse
20. A plane meets the coordinate axis at PQR such that the centroid of the triangle PQR is the point (a, b, c). The equation of the plane is:

x/3 + y/3 + z/3 = 1 x/a + y/b + z/c = 3 3x + 3y + 3z = 1 none
21. The solution of the equation cos2x-2cos x-4sin x + sin 2x = 0 where 0< x <  is:

-sin-11/2 n + tan-1(-1/2) n - tan-1(-1/2) none
22. If the covariance between the variables x & y is 18 and the variable of x & y are 16 and 81 respectively. Then the coefficient of correlation between them is:

1 1.5 - 0.5 0.5
23. For a group of 10 items, Σx=452, Σx2=24270 and mode=43.7 then the Personian Coefficient of skewness:

0.77 0.8 0.09 0.077
24. A stone of mass 500g is thrown vertically upwards. If potential energy at the highest point is 56.25 J. Then the height is:

11.25 m 1.125 m 22.5 m 12.25 m
25. A constant force of 10 N acting on an object reduces velocity from 15 ms-1 to 5 ms-1 in 2 seconds then the mass of the object is:

5 Kg 4 Kg 3 Kg 2 Kg
26. Let ƒ(x) = (1– cos ax) / (x sin x) when x ≠ 0 and ƒ(0) = 1/2. If ƒ continues at 0 then a is equal to:

1 2 1 or 2 1 or -1
27. P–R is equal to:

R – P P U R P∩R P–(P∩R)
28. If ƒ(x)=x2 + x–2 and 1/2(ƒog)x = 2x2–5x + 2 then g(x) is equal to:

2x–3 2x + 3 i and ii 3x2–3x–1
29. The determinant of is

0 1 512 5/2
30. Solve the system of equation: 2sinx+cosy = 1  16sin2x + cos2x=4

x = n + (-1)n/6, y = 2n ± 2/3 (/3, 2/3) x = n + (-1)n/4, y = 2n + 2/3 x = n + (-1)n/2, y = n + (-1)n /4
31. The value of a in 4 log93 + 9log24=10 log a83

5 6 8 10
32. If sin-15/a + sin-112/a = /2 then the value of a is equal to:

12 13 -13 ±13
33. The value of (sin x + i cos x)-4 is equal to:

sin4x + cos4x sin4x–i cos4x cos4x + i sin4x cos4x - i sin4x
34. In triangle ABC, tan A can be expressed as:

4Δ/(b2+c2-a2)
4Δ/(a2+b2-c2)
4S/(b2+c2-a2)
5Δ/a2+b2-c2)
35. The direction cosine of the line AB which is joint of A (2, 3, 5) and B(-1, 3, 2) is:

(-1/√2, 0, -1/√2) (-1/2, 0, 1/2) (1/2, 0, -1/2) (1/3√2, 1/3√2, )
36. The equation of the plane through (3, 2, 1) and ┴ to the line joining (-5, 3, 7) and (2, -4, 5) is:

x – y – 2z = 5 x + y + 2z = 5 7x – 7y – 2z = 5 i and ii both
37. A sphere having position vector and radius is 4 units then equation of the sphere is:

x2 + y2 + z2 = 2 x2 + y2 + z2 – 2x – 2y – 2z = 2 x2 – 2y2 + z2 – 2x + 3y + 4z = 2 x2 + y2 + z2 – 2x – 4y + 6z = 2
38. If yx = xsiny then dy/dx is equal to:

xsinx/logx
y/x * {(xlogy + siny)/(ylogx cosy – x)}
y/x * {(xlogy – siny)/(ylogx cosy – x)}
none
39. For the curve y = xex the point is:

x = 1 is a max x = -1 is min x =0 is min x = 0 is max
40. The value of is

(√2 + 1)
(√2 – 1)
/2(√2 + 1)
(√2 – 3)
41. The area enclosed between the parabola y2 = 4ax  x2 = 4by is equal to:

27/2 sq. unit

2/27 sq. unit
27 sq. unit

i and ii both
42. If b + c, c + a, a + b are in HP then a2, b2, c2 are in:

HP
GP
AP
none
43. In how many different ways can a hand of three cards be drawn from a speck of cards?

2210
22100
25000
none
44. The value of the correlation coefficient lies in:

-1 < r < 1
-1 < r < 1
-1< r < 1
-1< r < 1
45. If force P is resolved into two forces making angles of 45o and 15o with its direction then the latter force is:

3/√6
3/√6 P
√6/3 P
√3/√6
46. If A and B are like parallel forces. If A is moved parallel to itself through a distance x then the resultant of A and B moves at distance:

Ax/(A + B)
(A + B)/Ax
Ax/(A – B)
i and ii both
47. A body is projected vertically upwards at 39.2 ms-1. When will its velocity be 29.4 ms-1      [g = 9.8ms-2]

5 sec
2 sec
3 sec
1 sec
48. Find the equation of normal to the parabola y2 = 8x which is perpendicular to the line y = 3x – 7

y + 9x + 38 = 0
9x + y – 38 = 0
9x – y – 38 = 0
y – 9x – 38 = 0
49. The line whose length intercepted by the axis is bisected at the point (3, 4) is:

4x + 3y = 24
4x – 3y – 24 = 0
3x – 4y – 24
4x + 3y + 24 = 0
50. If the line passes ax2 + 2hxy + by2 = 0 and a'x2 + 2h'xy + b'y2 = 0 have the same bisectors then:

(a – b)h = (a' – b')h'
(a + b)h = (a' + b')h
h(a' – b') = h' (a – b)
(a' – b')h' = (a – b)h
51. The function sin (sin x/4) is periodic with period:

4
5
6
8
52. If A and B are any two disjoint then n(A U B) is equal to:

n(A) + n(B) – n(A∩B)
n(A) – n(B)
n(A) + n(B)
none
53. If 3 < x < 4 then:

|x – 4| < 3
x – 3 > 0
(x – 3) / (x – 4) > 1
(x – 3)(x – 4) < 0
54. If then tanx is equal to:

-4
4
-1
3
55. If cot x – tanx – 2tan2x – 4tan4x = 0 then

cot8x
4cot8x
8cot8x
tan8x
56. In triangle XYZ, Z = 30o, Y = √3, X = 1, which one is the another correct angle and side of the triangle?

1, 60o
2, 120o
1, 120o
120o
57. The value of then:

3±i
2±i
1±i
None
58. The value of

1
2
3
0
59. The value of is equal to:

1/√(1-e2√tanx)*e√tanxsec2x
1/√(1-etanx)*e√tanx * sec2x / 2√tanx
e√tanx sec2x /√(1-e2√tanx) (2√tanx)
none
60. The value of ∫log10 xdx is equal to:

x(logx–1)
x(logx + 1)log10e
x(logx–1)ex
x(logx–1)log10e
61. The function ƒ(x) = x3 – 3x2 + 6x + 6 has:

a min.
a max.
i and ii both
neither max. nor min.
62. The parabola 4y = 3x2 cut by the straight line 2y = 3x + 12 then the area is:

9 sq. unit
20 sq. unit
25 sq. unit
27 sq. unit
63. A vector is collinear with the vector = and satisfy . = 3 is  

(2/3, 1/3, 4/3)
(1/3, 2/3, 4/3)
(1, -1/2, -1/2)
(1, 1/2, -1/2)
64. If a > 1, b > 1, c > 1 are in GP then 1/(1 +log a), 1/(1+logb), 1/(1+logc) are in:

H.P.
A.P.
G.P.
All
65. The sum at 1/5√e correct to four places of decimals is:

1.8787
0.08787
0.8187
0.8817
66. How many committees can be formed from a set of 4 boys and 6 girls if each committee contains 2 boys and 3 girls?

130
140
160
120
67. If a, b, c are in A.P. then the straight line ax + by + c = 0 will always passes through the fixed point whose coordinate is:

(1, -2)
(-2, 1)
(-1, -2)
(1, 2)
68. If the lines joining the origin to the point of intersection of y = mx + 1 with x2 + y2 = 1 are perpendicular, then the value of m is:

±1
±2
±3
0
69. The equation of the circum-circle of triangle formed by the lines bx + 4y = ab, x = 0 and y = 0 is:

x2 – y2 – ax – by = 0
x2 + y2 + ax – by = 0
x2 + y2 – ax – by = 0
None
70. In which ratios the lines joining the points (-3, 4, -8), (4, -6, 4) in xy-plane:

1:2
2:1
1:3
4:1
71. If an unbiased coin is tossed six times, what is the probability that the coin will land tells exactly three times?

6/64
1
0.3125
3.125
72. Given that r = 0.72, Cov (x, y) = 8.64 and variance = 16. What is the standard deviation of the variable X?

2
1.98
3.12
3
73. The number of permutation of letters in the word STATISTICS is:

7200
10000
5040
50400
74. Two forces P and Q cut at a point; their resultant R is right angled to P. Which one is the angle between the forces?

tan-1 (P/Q)
sin-1(-P/Q)
cos-1(-P/Q)
cos-1(Q/P)
75. If a motorcycle increases its velocity at the rate of 5ms-1 to 30 ms-1 in 4 seconds, then initial velocity is:

10 ms-1
25 ms-1
20 ms-1
12 ms-1
76. The domain of the function √{loge(x2 – 4x + 4)}

(-∞, 2) U [2, ∞)
[-∞, 2) U (2, ∞]
(-∞, 3] U (1, ∞]
(-∞, 1] U [3, ∞)
77. If A and B are any two sets having 4 and 8 distinct elements then minimum numbers of the elements in A U B is

4
8
12
10
78. If  g(x)=x2 + x – 2 and (gof) x = 4x2 – 10x + 4 than f(x) is equal to:

2x - 3
2x + 3
(2x+3)2
2x2 - 5x + 2
79. Let x, y, z are distinct positive real numbers and x2 + y2 + z2 = 1 than xy + yz + zx is:

equal to 2
less than 1
greater than 1
less than or equal to 1
80.  If  b + c, c + a, a + b are in HP, then are in:

GP
HP
AP
none
81. If cos A + cos B + cos C = sin A + sin B + sin C = 0 then cos 3A + cos 3 B + cos 3 C is equal to:

Cos (A + B + C)
3Cos (A + B + C)
3Sin (A + B + C)
ii and iii both
82. If 2n+1Pn-1 : 2n-1Pn = 3:5 then n is equal to:

-1/3
-4
-1/4
none
83. The points (a, b + c), (b, c + a) and (c, a + b) are:

non-coplanar
collinear
i and ii both
straight line
84. In a triangle ABC is inscribed in the circle x2 + y2 = 25. If B and C have coordinate (3, 4) and (-4, 3) respectively then < BAC is equal to:

π/3
π/5
π/6
ϙ/4
85. If x2 - 3xy + ky2 + 3x - 5y + 2 = 0 represents a pair of straight lines then the value of k is:

4
5
2
3
86. If the line x -1 = 0 is the directrix of the parabola y2 - λx + 8 = 0 then one of the value of λ is:

1/4
1/8
1/3
4
87. If e1, e2 be respectively the eccentricity of the ellipse 9x2 + 4y2 = 36 and hyperbola 9x2 - 4y2 = 36 then:

e12 + e22 = 2
e12 + e22 < 4
e12 + e22 > 4
e12 + e22 = 3
88. The equation to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 is:

y = 3x + 5 and y = 3x - 5
y = 3x - 5
y = 3x + 5
none
89. If tanθ + cotθ = 2 then θ =

nπ/3 + π/9
nπ/3 - π/9
nπ/3
π/3
90. The value of is:

2π - x
π + x/2
π/4 - x
π -x/2
91. The value of is equal to:

2/e
3/e
e
1/e
92. Which one is the Second Derivative of ax2 + 2hxy + y2 = 0:

-(ax + hy)/(hx + by)
(h2 - ab)/(hx + by)3
(h2 + ab)/(hx + by)2
none
93. The value of is:

1/√3
√3
π/4
π/2
94. If | + | = | - |, then:

is perpendicular to
||
=
none
95. The probability of an odd number or a 5 in the rolling of a fair dice is:

1/6
3/6
9/12
7/12
96. The area bounded by the curve y = x2 and the line y = 2x is:

4
3/4
4/3
3/2
97. Which one is not the type of average?

median
geometric mean
mode
continuous frequency
98. A lawn roller is pulled with a force of 400 N at an angle of 45o to the lawn through a distance of 20√2m. Then the work done is:

800 J
8000 J
4000 J
none
99. What is the maximum horizontal range of a particle projected with a velocity of 100 ms-1?:

500 m
450 m
1000 m
none
100. The perimeter of a rectangle is 100 m and the area is maximum then the length of its side is:

50 m
40 m
25 m
none

           

 
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