Bangalore University 2010-2nd Year M.C.A Entrance -Year -Maths-Practice -1 - Question Paper
TEST PAPER 1
Total Questions: 75 Time allotted 90 minutes
1. The set of all integers x such that |x - 3| < 2 is equal to (a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4}
(c) {2, 3, 4} (d) {-4, -3, -2}
The Range of the function f(x) = -2 is
2.
2 - x
(b) R - {1} (d) R - {-1}
(a) R (c) (-1)
3. The value of (i)i is (a) ra (c) e-n/2
(b) ra2
(d) 2V2
(cos9 + isin9)4 .
is equal to (icos9 + sin9)
(a) cos- isin 9 (c) sin 9-icos 9
4.
(b) cos99- isin 99 (d) sin99- icos99
The roots of the quadratic equation ax2 + bx + c = 0 will be reciprocal to each other if (a) a = 1/c (b) a = c
(c) b = ac (d) a = b
5.
6.
If a, p are the roots of ax2 - 2bx + c = 0 then a3p3 +a2p3 +a3p2 is
c2 (c + 2b)
(b)
(a)
a
a
(d) None of these
a
7. The sixth term of a HP is 1/61 and the 10 term is 1/105. The first term of the H.P. is (a) 1/39 (b) 1/28
(c) 1/17 (d) 1/6
Let Sn denote the sum of first n terms of an A.P.. If S2n = 3Sn, then the ratio S3n / 5n is equal to
(b) 6 (d) 10
(a) 4 (c) 8
11. A lady gives a dinner party to six quests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
10. If the product of n positive numbers in 1, then their sum is (a) a positive integer (b) divisible by n
(c) equal to n + (d) never less than n
9. Solution of |3 - x| = x - 3 is
(a) x < 3 (b) x > 3
(c) x > 3 (d) x < 3
n
(a) 112 (b) 140
(c) 164 (d) None of these
12. For 1 < r < n, the value of nCr +n 1 Cr +n 2 Cr +___+r Cr is
(a) nCr+1 (b) n+1Cr
(c) n+1Cr+1 (d) None of them.
13. 2.42n+1 + 33n+1 is divisible by
(a) 2 (b) 9
(c) 11 (d) 27
P
14. If Pn denotes the product of the binomial coefficients in the expansions of (1 + x)n, the -n equals
Pn
/ \ n +! n
(a) (b)
n! n!
/ n+1 / -\n+1
(c) t+f- (d) t+lL.
n! (n +1)
15. If x is very large and n is a negative integer or a proper fraction, then an approximate value of
' 1 + xN
is
(a) 1 + * (b) 1+n
n x
(c) 1 + (d) n [1 +
x x
16. If 4 log93 + 9 log24 = 10log x 83, (x e R)
(a) 4 (b) 9
(c) 10 (d) None of these
17. The sum of the series log;; - log;; + log26____to is
(a) e2 (b) loge2 + 1
(c) loge3 - 2 (d) 1 - loge2
18. tan 5x tan 3x tan2x is equal to
,, . sin5x - sin3x -sin2x (a) tan5x - tan3x - tan2x (b)
cos5x - cos3x - cos2x (c) 0 (d) None of these
19. If a = tan60 tan 420 and B = cot660 cot 780 (a) A = 2B (b) A = -3-B
(c) A = B (d) 3A = 2B.
20. The value of cos+ cos+ cos is
7 7 (a) 1 (b) -1
(c) 1/2 (d) -1/2
(b) --a 4
, 1-. 3n n
(d)---
8 2
(c) --a 8
22. If sin9 + cos9 = \/2sin9 , then
(a) V2cos 9 (b) -V2sin9
(c) -42 cos 9 (d) None of these
,, . sin2200 + cos4200 .
23. Value of 40--- is
sin4 200 + cos2 200
(a) 1 (b) 2
(c) V (d) None of these
24. Value of 32cos6200 -48cos4200 + 18cos2200 -1 is
(a) -X (b) >2
(c) "/l (d) None of these
25. If sin9 + cosec9 = 2 , then value of sin3 9 + cosec39 is (a) 2 (b) 4
(c) 6 (d) 8
26. If cosec9 + cot9 = 52 , then the value of tan9 is
(a) 15/6 (b) 2>
16 w /20 21 (d) 2/'21
27. General value of x satisfying the equation -v/3sinx + cosx = ~J3 is given by
/\ i n /i\n n %
(a) nn (b) nn + (-1) I
6 v 4 3
(c) nn (d) nn + (-1)---
3 1 3 6
28. If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ZABC is
, , 120/2 ... 60V2
(a) !cm (b) _!cm
(c) V2cm (d) None of these
23
29. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of depression of 300. After somei traveled by the car during this
depression of 30. After sometimes, the angle of depression becomes 600. The distance (in metres) traveled by the car during this time is
200V3
(a) 100V3 (b)
3
(c) (d) 2003
30. The shadow of a tower of height (l + -v/3) metre standing on the ground is found to be 2 metre
longer when the suns elevation is 30, then when the suns elevation was (a) 30 (b) 45
(c) 60 (d) 75
31. cos1 ( cos-Ej is equal to
32. If coslX + cos1 = , then value of --- + is
2 3 6 4 2V3 9
(a) 34 (b) 1
'4 w /2
(c) 14 (d) None of these
33. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is (a) 7/2 (b) 7/3 (c) 7/5 (d) 7/10
34. The straight lines x + y - 4 = 0, 3x + y - 4 = 0, x + 3y - 4 = 0 form a traigle which is (a) isosceles (b) right angled (c) equilateral (d) None of these
35. Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is
(a) (2D (b) (2.Z
(c) (ii,!1 ) (d) None of these
36. The area bounded by the curves y = |x| - 1 and y = - |x| + 1 is
(a) 1 (b) 2
(c) 2V2 (d) 4
37. The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are
(a) (If) (b) fri
(c) (! T) (d) T
38. Three lines 3x + 4y + 6 = 0, V2"x + V3y + 2V2 = 0 and 4x + 7y + 8 = 0 are
(a) Parallel (b) Sides of a triangles
(c) Concurrent (d) None of these
39. Angle between the pair of straight lines x2 - xy - 6y2 - 2x + 11y - 3 = 0 is
(a) 45, 135
(b) tan-1 2, n = tan-1 2
(c) tan-1 3, n = tan-1 3
(d) None of these
40. If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then locus of its centre is
(a) 2ax + 2by +(a2 + b2 + 4)= 0
(b) 2ax + 2by-(a2 + b2 + 4) = 0
(c) 2ax - 2by + (a2 + b2 + 4) = 0
(d) 2ax - 2by-(a2 + b2 + 4)= 0
41. Centre of circle whose normals are x2 - 2xy - 3x + 6y = 0 is
(a) H) (b) (I-3 (c) H) (d) (-3>f
42. Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is
(a) x2 + y2 - 4x - 6y + 4 = 0
(b) x2 + y2 - 4x - 6y + 5 = 0
(c) x2 + y2 - 4x - 6y - 5 = 0
(d) None of these
43. The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is
(a) (H] (b) (If
(c) (M] (d) (r -2*
44. The line y = mx + 1 is a tangent to the parabola y2 = 4x if (a) m = 1 (b) m = 2
(c) m = 3 (d) m = 4
45. The angle between the tangents drawn from the origin to the parabola y2 = 4a (x - a) is (a) 900 (b) 30
(c) tan-1 (i] (d) 450
46. The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is
(a) >/2a2 (b) 2a2
(c) 4a2 (d) None of these
47. The eccentricity of the eclipse 16x2 + 7y2 = 112 is (a) 4/3 (b) 7/16
(c) 3/VT7 (d) 3/4
2 2
48. A common tangent to the circle x2 + y2 = 16 and an ellipse + = 1 is
49 4
(a) y = x + 4>/5 (b) y = x + V53
49. If the hyperbolas x2 - y2 = a2 and xy = c2 are of equal size, then (a) c2 = 2a2 (b) c = 2a
(c) 2c2 = a2 (d) none of these
50. If a circle cuts rectangles hyperbola xy = 1 in the point (xi, yi), i = 1, :
(a) x1x2x3x4 = 0 (b) yy3y4 =1
(c) yy3y4 = 0 (d) x1x2x3x4 = -1
a b 0 0 a b b 0 a
If
= 0 then
51.
(a) a is a cube root of 1 (b) b is a cube root of 1 (c) a/b is a cube root of 1 (d) a/b is a cube roots of -1
1 + a 1 1 1 1 + b 1 1 11 + c
52. If 1 +1 + - = 0, then
a b c
is equal to
(b) abc
(d) None of these
(a) 0 (c) -abc
cos (a + p) -sin (a + p) cos2B sin a cos a sin p
- cos a sin a cos p
(b) p
(D) Neither a nor p
The determinant (a) a
(c) a and p
is independent of
53.
3 -4 1 -1 3n -4n' n n
|
, the value of An | ||||||
| ||||||
|
(d) None of these |
If A = (a)
54.
3n (-4 )n .1 (-1)
(c)
1
The domain of the function f (x ) =
55.
is
' ' Vx2 - 3x + 2 (b) (-ro,1]u[2, ro)
(d) (1, 2)
(a) (-ro,1)u(2, ro) (c) [-ro,1)u( 2, ro]
sin x2 +1])
- 4 i is
x4 +1
(b) {0} (d) (0, 1)
56. Range of function (a) 0
(c) [-1, 1]
-- 1 - cot x 57. lim- is
x n/4 2 - cotx - cot x
1/
'4
A
(b) 34
(d) None of these
limsec-1 fsinx '] =
x 0 I x 1
(b) 0
(d) Does not exist
(a) 1
(c) V
59. The function y = 3>/x - |x -1| is continuous
(a) x < 0 (b) x > 1
(c) no point (d) None of these
. , . ( 0,x is irrational is The function f (x ) = |
|1,x is rational
(a) continuous at x = 1 (b) discontinuous only at 0
(c) discontinuous only at 0, 1
(d) discontinuous everywhere
Let f : R R be a function defined by f(x) = max. {x, x3}. The set of all points where f(x) is not differentiable is
(a) {-1, 1} (b) {-1, 0}
(c) {0, 1} (d) {-1, 0, 1}
60.
61.
/ \ |(cosx);1*,x 0)
(x)=r ; \ i
[K x = 0J
If the function f (x ) =
is continuous of x = 0 then value of k is
62.
(b) -1
(d) e
(a) 1 (c) 0
f1+dx = 1 + x
63.
(a) 1 - x + x2 - x3 + x4 + c (b) x + - + +
2 3 4 (d) None of these
(c) (1 + x)
f x|x|dx (a) x3 (a)
64.
(b)
3
(d) None of these
(c)
2
1 |x + 2|
N-!dx =
- x + 2
(a1) 1
(c) 0
f log (anx )x
0
65.
(b) 2 (d) -1
66.
(b) (d) 1
67. If a < 0 < b, then fdx
J v
(a) a - b (c) a + b
(b) b - a (d) -a - b
f x2|xdx
0
(a) 5/3 (c) 8/3
68.
(b) 7/3 (d) 4/3
xsinx
69.
dx
+ cos x
(b) n/ (d)
(a)
(c)
The area bounded by curve y = 4x - x and x - axis is
70.
, , 30
(a) sq. units. 32
(c) sq. units.
(b) 37- sq. units.
34
(d) sq. units.
71. The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is
(a) 1 (b) 2
(c) 242 (d) 4
72. The area bounded by the curves y = x4 - 2x3 + x2 - 3 , the x-axis and the two ordinates corresponding to the points of minimum of this Function is
(a) 91/15 (b) 91/30
(c) 19/30 (d) None of these
73. Degree of the differential equation | | + dx ' + = x2 -1, then
6 H dx2) dy dx3
dx3
(a) m = 3, n = 3 (b) m = 3, n = 2
(c) m = 3, n = 5 (d) m = 3, n = 1
74. A solution of the differential equation ) - x.-dl + y = 0 is
(a) y = 2 (b) y = 2x
(c) 4y = x2 + c (d) y = 2x2 - 4
75. The area (in square units) of the parallelogram whose diagonals are a = i + j - 2kandb = i - 3j + 4k (a) -Ju (b) 2V14
(c) 2V6 (d) -738
|
|
46. (c) 61. (d) 47. (d) 62. (a) 48. (d) 63. (b) 49. (c) 64. (b) 50. (b) 65. (b) 51. (d) 66. (c) 52. (b) 67. (c) 53. (a) 68. (c) 54. (d) 69. (a) 55. (a) 70. (c) 56. (b) 71. (b) 57. (b) 72. (b) 58. (d) 73. (d) 59. (d) 74. (c) 60. (d) 75. (a) |
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Attachment: |
| Earning: Approval pending. |
