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MATHEMATICS
1. Solve: tan  + tan 4tan tantan 4tan 7. =
(1) nn/12
(2) /12
(3) n
(4) n/2 2. If tan-1 x + tan-1 y+ tan-1 z =/2 then xy + yz + zx =
(1) xyz
(2) 0
(3) 1
(4) x + y + z 3. Solve: cos-1 x + sin-1 x/2 =/6 , x =
(1) +1
(2) +3
(3) 0
(4) 1/2 4. The points of discontinuity of f(x) = tan ( x/x+1) other than x =-1 are:
(1) x = 2m +1/1 - 2m m is any integer
(2) x =2m -1/2m + 1
(3) x = 0
(4) x =  5. If y = log I (log x), dy/dx =
(1) 1/x log (log x)
(2) none of these
(3) 1/ log (log x)
(4) 1/x log x.log (log x) 6. 2 is a group of all points rationals under the operation *
defined by a* b = ab/2. The identify of 2 is:
(1) 0
(2) 1/2
(3) 2
(4) 1 7. To be a sub-group the elements of a subset of a group must obey the axioms
of:
(1) Closure and inverse
(2) Closure and associatively
(3) Closure and identify
(4) Associativity and commutativity 8. The distance between the parallel lines x2 +
2xy + y2 -6x -6y + 8 =0 is:
(1) 2
(2) 1/2
(3) 1
(4) 2 9. The radius of the circle 3x(x-2) + 3y(y+1) =4 is:
(1) 15/4
(2) 31/12
(3) 2
(4) 3 10. If the two circles x2 + y2 + 7x + 16y -3 =0 and 2x2 -6x-4y + k =0 cut each
other orthogonally , k =
(1) 17
(2) -37
(3) 27
(4) -47 11. If x = a(cos sin ), y = a (sin  cos cos ) d2y/dx2=
cos 
(1) a
3
(2) sec2/a
(3)sec3/a
(4) sec2/ 12. If x = t2 +t +1 and y = sin/2 t + cos /2t then at t = 1, dy/dx =
/3
(2) /4
(3) /2
(4) -/6 13. S = tan-1 (1 + x2-1/x) and T = tan-1 x then dS/dT =
(1) 1/2
(2) 2
(3) 1
(4) -1 14. The equation to the tangent to the curve y = b e-x/a at the point where it
crosses the y -axis is:
(1) x + y =ab
(2) x/a + y/b=1
(3) ax + by =1
(4) x + y = a+ b 15. The angle of intersection curves y2 = 2x and x2 = 16y at (0,0) is:
(1) /3
(2) tan-1 (3/5)
(3) /2
(4) /4 16. The length of the intercept that the circle x2 + y2 + 10x - 6y + 9 =0 makes
on the x - axis is:
(1) 4
(2) 2
(3) 8
(4) 6 17. A parabola has its focus at (-4,0) and its directrix is x = 4. Its equation is:
(1) y2=-16x
(2) x2=-8y
(3) y2=8x
(4) x2=9y 18. The eccentricity of the hyperbola 36x2 - 25y2 = 900 is :
(1) 5
(2) 61/5
(3) 31/5
(4) 6 19. The straight line y = 4x + k touches the hyperbola x2/64 - y2/49 =1. Then
k=
(1) +_ 500
(2) 56
(3) 251
(4) + 975 20. An ellipse has a minor axis of length 6 and the distance between its
foci is 8. Its equation is:
(1) x2/6 + y2/9 =1
(2) x2/6 + y2/5 =1
(3) x2/25 + y2/9 =1
(4) x2/9 + y2/25 =1 21. dx/1+cot x=
(1) 0
(2) 
(3)/4
(4) /2 22. The area bounded by the curve y = 4x -x2 and the x-axis is:
(1) 32/3
(2) 16
(3) 32
(4) 21 1/3 23.
(1) 1/3
(2) /4
(3) 1
(4) log 2 24. dx/x(xn+1) =
(1) n log (x/xn+1)
(2) n/x log (xn+1)
(3) log (xn /xn+1)
(4) 1/n log (xn /xn+1) 25. Identify the non-A belian group among the following :
(1) The set of all n-square, non-singular matrices under multiplication
(2) The set of all integer under addition
(3) The set of all m X n matrices under addition
(4) All n-square complex matrices under multiplication 26.
(1)
(2)
(3)
(4) 27. For what value of are the vector
are coplanar?
(1) -4
(2) -3
(3) 4
(4) 2a 28.
(1)
(2)
(3)
(4) 29. The sine of the angle between the vectors
(1) 3/14
(2) 5/7
(3) 5/21
(4) 5/7 30. Simplify
(1) 36
(2) 618
(3) 0
(4) 12 31.
(1) e3
(2) e4
(3) e
(4) e2 32. If x = loga be, y = logb ca and z = logc ab then
(1) ab + bc + ca
(2) abc
(3) x + y+ z
(1) (log 9)2
(4) 1 33.
(2) (log 3)2
(3) log 9
(4) 2 log 9 34. α, β y are the roots of x2 + px + q = 0. Then α3 + β3 + y2 =
(1) -pq
(2) 3pq
(3) -3q
(4) -p 35. The third term of a G.P. is 4. The product of its first five terms is:
3.125
(1)
(2) 32
(3) 1,024
(4) 243 36. If x =-9 is a root of the equation
=0 the other two roots are:
(1) 2,-7
(2) 1, 5
(3) 2,7
(4) -2,7 37. If a b c a root of the equation
(1) x =c
(2) x=0
(3) x =a
(4) x= b 38.
(1)
(2)
(3)
(4) 39. If w is a cube root of unity (1 -w) (1 - w2) (1 - w4) (1 - w8) =
(2) 3
(3) 1
(4) 9 40. The real part of 1/1-cos +i sin is:
(2) 2
(1) tan /2
(1) 
(3) 1/1-cos 
(4) 1/2 41. In a ABC if sin A/sin C = sin( A -B)/sin (B-C) then a2, b2 and c2 are in:
(1) H.P
(2) none of these
(3) A.P
(4) G.P 42. The integral part of (is:
(1) 196
(2) 163
(3) 198
(4) 197 43.
(1)
(2)
(3)
(4)
44. From a group of 5 boys and 3 girls three persons are chosen at random.
Find the probability that there are more girls than boys:
(1) 5/8
(2) 2/7
(3) 3/8
(4) 4/7 45. A and B are two independent events. The probability that both A and B
occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of
A.
(1) 0 or 1
(2) 1/4 or 1/2
(3) 1/2 or 1/3
(4) 1/3 or 1/4 46.  sech x dx =
(1) 
(2) 1
(3) /2 +1
(4) /2 47.  sin x-cos x/1 + sin x cos x dx =
(1) 0
(2) /2
(3) 1
(4) /4 48.
(1) /4
(2) x= 4/I
(3) x + 1
(4) x - 4I 49.  sin x/2 dx =
(1) cos x/2+ sin x/2
(2) 4 cos x/2 -4 sin x/2
(3) -4cos x/4 + 4sin x/4
(4) 4 cos x/4 +4 sin x/4 50. x/(x + 1) ex dx =
(1) (x + 1)e x
(2) none of these
(3) xex
(4) ex/x+1 51. If 15C3r = 15Cr+3, then r:
(1) 1/3
(2) 3/2
(3) 2
(4) 3 52. How many committees of 5 members can be formed from 6 gentlemen and
4 ladies?
(1) 252
(2) 120
(3) 10C5
(4) 10P5 53. How many even numbers can be formed by using all the digits 2, 3, 4, 5 ,
6?
(1) 120
(2) 72
(3) 48
(4) 24 54. There are three copies of each of 4 difference books. In how many ways
can they be arranged in a shelf?
(1) 12/3 +4
(2) 369.600
(3) 369,000
(4) 12 55. The equation of the base of an equilateral triangle is x + y = 2 and the
vertex is (2,-1), Find the length of the side of the triangle.
(1) 2/3
(2) 43/2
(3) 6
(4) 2 3/2 56. The maximum value of f (x) = log x/x, 0 < x < is
(1) 1/e
(2) 2/e
(3) e
(4) e 57. For f(x) = 3 sin x + 3 cos x, the point x = /6 is:
(1) a point of
inflection
(2) none of these
(3) a local minimum
(4) a local maximum 58. If y2 = ax2 + 2bx + c then y3 d2y/dx2 =
(1) ac -b2
(2) 4(b2 + ac)
(3) b2 - 4ac
(4) b2 - ac 59. The speed v of a particle moving along a straight line is given by a +
bv = x2, where x is its distance from the origin. The acceleration of the particle is:
2
(1) x/ab
(2) x/b
(3) ax
(4) abx 60. 2-1 lxl dx =
(2) 1
(3) 5/2
(4) 2
(1) 3/2