Bangalore University 2010-2nd Year M.C.A Entrance -Year -Maths-Practice -3 - Question Paper
Total Questions: 75 Time allotted 90 minutes
1. If cosec9 = x+ then the value of cosec9 + cot 9 is
4x
(a) 2x (b) -2x
(c) 1/2x (d) -1/2x
2. If sin (A + B + C) = 1,tan (A - B)=-and sec (A + C) = 2, then
\3
(a) A = 900,B = 600,C = 300
(b) A = 1200,B = 600,C = 00
(c) A = 600,B = 300,C = 00
(d) None of these
ft 9n 3n 5n .
3. The value of 2coscos--+ cos--+ cos is
13 13 13 13
(a) 1 (b) 0
(c) -1 (d) None of these
4. The solution of the equation cos2 9 + sin 9 +1 = 0, lies in the interval.
(a) I-?,!) 'b) *
(o (* ,5n) (d) *
5. Solution of the equation 4 cos 29 = cot2 9 - tan2 9 is
n n
(a) 9 = nn+ (b) 9 = nrc +
2 3
n
(c) 9 = nn (d) None of these
4
6. The value of tan-11 + tan-11 is
2 3
(a) (b)
(c) (d) 0
7. sin 1 (cos (sin 1x) + cos 1 )(sin (cos 1x ))isequal
to
(a) (b)
(c) 3y4 (d) 0
8. If (sin 1x) + (cos 1x) = -n_, then x is equal to
(a) 1, 2 (b) -1, 2
(c) y' V? (d) "X0
9. The angle C of the triangle ABC in which (c + a + b)(a + b - c) = ba is
(a) 2n3 (b) n3
(c) n6 (d) n4
ABC
10. In any AABC, abc Ssinsinsin =
2 2 2
(a) A3 (b) 3A2
(c) A2 (d) None of these
11. A person, standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600,when he retreats 40m from the bank, he finds the angle to be 300. The height of the tree and the breadth of the river are
(a) 10V3m,10m (b) 20V3m,10m
(c) 20>/3m, 20m (d) None of these
12. At the foot of the mountain the elevation of its summit is 450, after ascending 1000m towards the mountain up a slope of 30 inclination, the elevation is found to be 600. The height of the mountain is
V3+1 V3 -1
(a)-m (b)-m
22
(c) 1 m (d) None of these
13. If a, p, y are the real roots of the equation x3 - 3Px2 + 3qx -1 = 0 , then the centroid of the triangle
having vertices a, j, p, p j and y, j are
(a) (P, q) (b) (P, -q)
(c) (-P, q) (d) (-P, -q)
14. The equation of the straight line, passing through the point (2, -4) and perpendicular to the line
8x - 4y + 7 = 0 is
(a) x + 2y + 6 = 0 (b) x - 2y + 6 = 0
(c) 2x + y + 6 = 0 (d) 2x - y + 6 = 0
15. If the lines x - 2y - 6 = 0, 3x + y - 4 = 0 and Xx + 4y + X2 = 0 are concurrent, then (a) X = 2 (b) X = -3
(c) X = 4 (d) None of these
16. If the ratio of gradients of the lines, represented by ax2 + 2hxy + by2 = 0 is 1 : 3, then the value of the ratio h2 : ab is
(a) >3 (b) 34
17. If the angle between the two lines represented by 2x2 + 5xy + 3y2 + 6x + 7y + 4 = 0 is tan 1 m, then m =
(a) y5 (b) 1 (c) 75 (d) 7
18. The equation of that diamenter of the circle x2 + y2 - 6x + 2y - 8 = 0, which passes through the origin, is
(a) x - 3y = 0 (b) x + 3y = 0
(c) 3x - y = 0 (d) None of these
19. If the line 2x - y + k = 0 is a diameter of the circle x2 + y2 + 6x - 6y + 5 = 0 then k is equal to (a) 12 (b) 9
(c) 6 (d) 3
20. The locus of a point whose sum of the distances from the origin and the line x = 2 is 4 units is
(a) y2 =-12 (x - 3) (b) y2 = 12 (x - 3)
(c) x2 = 12 (y - 3) (d) x2 =-12 (y - 3)
21. In an ellipse the distance between its foci is 6 and length of its minor axis is 8. Then its eccentricity is
(a) X <> /.f52
(c) X (d) 45
Jl999 / \
22. The eccentricity of the hyperbola 3 (x2 - y2) = 1 is
(a) V2 (b) 2
(c) 2V2 (d) V3
23. Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 is
(a) y = 3x + 5
(b) y = 3x - 5
(c) y = 3x + 5 and y = 3x - 5
(d) None of these
24. The mirror image of the directrix of the parabola y2 = 4 (x +1) in the line mirror x + 2y = 3 is
(a) x = -2 (b) 4y - 3x = 16
(c) 3x - 4y + 16 = 0 (d) None of these
25. If the distance of a point on the ellipse x + y/2 = 1 from the centre is 2, then the eccentric angle is
(a) n3 (b)
(c) (d)
The domain of the function f (x) = Vx-1 +J5-x is
26.
(a) [1,) (c) (1,5)
(b) (-,5) (d) [1,5 ]
27. The period of the function f (x) = sin4 2x + cos4 2x is
(a) n2 (b) n8
(d) None of these
If f (x ) = log (j+xj ,thenf (j2x
(a) f(x)
(c) 3f(x)
28.
+ x (b) 2f(x) (d) 4f(x)
ex -(1 + x) The value of lim--- is
29.
x
(a) X
(c) 0
(b) 1 (d) 1
2 \8x +3
30. The value of lim I * + I is
x2x2 + 5 I
(a) e8 (c) e4
-8
(b) e (d) e-'
r 2 -V 2 + x .
31. lim-, is equal to
2 - 4 - X
(b) -3 <d>
1 - sin x n
-2,x <
3cos x 2
Then f(x) is continuous at x = is
32. If f (x ) =
-n2
b (1 - sinx)'
(n-2x )
(a) a = /'3,b = 2 (b) a = 13,b = 83
(d) None of these
(c) a = X,b = >3
33. The function f (x) = -1-, where u = is discontinuous at the points
v u2 + u - 2 x -1
(a) x = -2, 1, 1/2 (b) x = /, 1, 2
(c) x = 1, 0 (d) None of these
34. If f (x) = (-1) , where [.] denotes the greatest integer Function, then
(a) f(x) is continuous for x = n/:3, where n e 1
<b) f (32 )=1
(c) f1 (x) = 0for -1 < x < 1
(d) None of these
35. If f (x) = |cosx|, then f1 is equal to
(c) 1 (d) None of these
36. If y = sinx, then d-_(cos7 x) is equal to
(a) 35cos3x - 42cos5x (b) 35cos3x + 42cos5x (c) 42cos3 x - 35cos5 x (d) None of these
37. If f(x) = |x - 3| and (x) = (fof)(x), then for x > 10, 1(x) is equal to (a) 1 (b) 0
(c) -1 (d) None of these
-2|x|
38. The equation of the normal to the curve y = e 1 at the point where the curve cuts the line
1
x = is
2
(a) 2e (ex + 2y) = e2 - 4
(b) 2e (ex - 2y) = e2 - 4
(c) 2e (ex - 2x) = e2 - 4
(d) None of these
logx
39. The maximum value of-is
x
(a) % (b) K
(c) 1 (d) d = e
40. If y = f(x) be the equation of an ellipse to which the line y = 2x + 3 is a tangent at the point where x = 2,then
(a) f1 (2) = 2 (b) f (2 ) = 2f1(2)
(c) f (2 ) + f1 (2 ) + f11 (2 ) = 2
(d) None of these
41. The value of [---dx is
J x
x
(b)
(c) -38 (- f + c
(d) None of these
r Vl - x
The value of I-dx is
42.
x
(a) 2V1 + x + 1n 41 + x -1
+ c
-s/1 + x +1 + c
(c) 2V1 + x + c V1 + x -1 V1 + x + 1
(d)
+ c
The antiderivative of the function (3x + 4) |sinx|, where 0 < x < n, is given by
43.
(a) 3sinx - (3x + 4) cos x
(b) 3sinx + (3x + 4) cos x
(c) -3sin x + (3x + 4) cos x
(d) None of these
3n
512
3n2
1024
3n
(b)
(a)
256 (d) None of these
(c)
u,
45. The value of a which satisfies |cos xdx = cos 2a,ae['2n] is
0
(a)
(d) None of these
ft/
(c)
r dx
I-7 is equal to
o [ax + (l-x)b]
(a) ab (b) a/b
(c) b/a (d) l/ab
47. The degree of the differential equation of which y2 = 4a(x + a) is a solution, is
(a) 1 (b) 2
(c) 3 (d) None of these
dy ,
48. Integrating Factor of differential equation cos x.--+ y sin x = 1 is
dx
(a) sin x (b) sec x
(c) tan x (d) cos x
49. The solution of the differential equation 2x--y = 3 represents
dx
(a) circles (b) straight lines
(c) ellipse (d) parabola
(a + ib)2 (a - ib)2
50. If -------x + iy , then x
a - ib a + ib
-2b3 6a2b
(a) --TT (b)
(a2+b2)2 (a2+b2)2
(c) 0 (d) None of these
51. If set A = {5, 15, 20, 30} and B = {3, 5, 15, 18, 20} then AuB is
(a) {3, 5, 15, 18, 20, 30}
(b) {3, 18, 30}
(c) {2, 5, 15, 18, 20}
(d) {5, 15, 20}
52. In a group of people 65% speak German and 45 speak French. If 5% of the people speak neither French nor German, then the percentage of people who can speak both German and French is
(a) 5% (b) 10%
(c) 15% (d) 20%
53. Convert 103 of base to a number of base 3 is (a) 12011 (b) 10211
(c) 10221 (d) 10031
54. If (2311)4 - (1111)2 = (x)5, then x (a) 1131 (b) 1130
(c) 1129 (d) None of these
55. Given A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then (A x B) n (B x C) is
(a) A null set of ordered pairs
(b) {(4, 3)}
(c) {(3, 4)}
(d) {(4, 3),(3,4)}
56. Value of (x +1 + i)(x +1-i)(x-1 + i)(x-1-i) is (a) x4 + 4 (b) x3 + 3
(c) x2 + 2 (d) None of these
57. The multiplicative inverse of the complex number z = 3 - 2i is
32. 3 2 .
(a)---i (b) i i
12 13 13 13
3 2 3 2
(c)--+i (d)----i
13 13 13 13
58. If (x + iy)(2-3i) = 4 + i, find (x + y)(y-x)
(a) (b)
9 9
-13
(c) (d) None of these
(2 + 3i )2
59. The conjugate of-- is
2 - i
, 22 9i 22 9i
(a)------(b)---
5 5 5 5
22 9. 22 9.
(c)----1 (d)-- i
5 5 5 5
60. If ra is the cube root of unity then (1 + ra - ra2)7 equals (a) 128 ra (b) -128 ra
(c) 128 ra2 (d) -128 ra2
61. The smallest positive integer for which (1 + i)2n = (1 - i)2n is
(a) 4 (b) 8
(c) 2 (d) 12
62. If a + p = 3, a3 + p3 = 7, then a and p are the roots of (a) 3x3 + 9x + 7 = 0 (b) 9x2 - 27x + 20 = 0
(c) 2x2 - 6x +15 = 0 (d) None of these
63. If one root of the equation ix2 -2(i +1)x + (2-i) = 0 is 2-i, then- the other root is:
(a) -i (b) 2 + i
(c) i (d) 2 - i
64. If the ratio of the roots of the equation Ix2 + nx + n = 0 be P : q, then is equal to:
fn
fn 1
(a) 0 (b)
65. The value of m for which the equation x3 - mx2 + 3x - 2 = 0 has two roots equal in magnitude but opposite in sign is
(a) 1 (b) |
3 4 (c) 7 (d) T
4 5
66. Tn of an A.P. is 5 - 6n. The value of Sn of the same A.P. is:
(a) (n - 3n2) (b) (3n - 2n2)
(c) (n + 3n2) (d) None of these
67. If in an A.P. the sum of 10 items, is 11 and the sum to 11 terms is 19 then the sum of 30 terms is: (a) -20 (b) 20
(c) 30 (d) -30
68. If 9th terms of an A.P. is zero, and 29th term is n times, the 19th term, then value of n is:
(a) 2 (b) 3
(c) 4 (d) 5
69. An A.P. consists of 60 items. If the first and the last term be 7 and 125 respectively its 32nd term is:
(a) 64 (b) 65
(c) 66 (d) 69
70. Let Sn = denote the sum of first n terms of an A.P.. If S2n = 3Sn then the ratio S3n / Sn is equal to (a) 4 (b) 6
(c) 8 (d) 10
71. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is:
(a) 10 (b) 11
(c) 12 (d) None of these
72. The sum of 20 arithmetic means between 7 and 43 is:
(a) 360 (b) 400
(c) 500 (d) 440
73. Number of different signals can be given using any number of flags from 5 flags of different colour is?
(a) 325 (b) 240
(c) 120 (d) None of these
74. In how many ways a committee of 5 members can be selected from 6 men and 5 women, consisting of 3 men and 2 women?
(a) 320 (b) 200
(c) 450 (d) None of these
75. If nC12 = nC8, then n has the value (a) 20 (b) 12 (c) 6 (d) 30
1. (a) 16. (c) 31. (b) 46. (d) 61. (c)
2. (c) 17. (a) 32. (b) 47. (b) 62. (b)
3. (b) 18. (b) 33. (b) 48. (b) 63. (a)
4. (d) 19. (b) 34. (a) 49. (d) 64. (c)
5. (c) 20. (a) 35. (b) 50. (c) 65. (b)
6. (a) 21. (a) 36. (a) 51. (a) 66. (a)
7. (b) 22. (a) 37. (a) 52. (c) 67. (d)
8. (c) 23. (c) 38. (b) 53. (b) 68. (a)
9. (a) 24. (b) 39. (b) 54. (a) 69. (d)
10. (c) 25. (b) 40. (a) 55. (c) 70. (b)
11. (c) 26. (d) 41. (c) 56. (a) 71. (b)
12. (a) 27. (c) 42. (a) 57. (b) 72. (c)
13. (a) 28. (b) 43. (a) 58. (a) 73. (a)
14. (a) 29. (a) 44. (a) 59. (c) 74. (b)
15. (a) 30. (b) 45. (a) 60. (d) 75. (a)
44. | xsin6 x cos4 x dx is equal to
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