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MATHEMATICS
1. If (1-x + x2)n = a0+ a1x + a2x2+ ...... +a2nx2n then a0 + a2 + a4+.... +a2nequals
1/2
(1) 3n-
(2) 3n+1/2
(3) 3n+1/2
(4) 3n -1/2 2. The fourth, seventh and tenth terms of a G.P. are p, q and r respectively
then
(1) p2 = q2 + r2
(2) p2 = q2
(3) q2 = pr2
(4) r2 = p2 + q2 3. cos 10cos 20cos 30 ........... cos 1790 =
(1) 1/2
(2) 1
(3) 0
(4) 2 4. The sum of the slopes of the lines represented by 4x2 + 2 hxy - 7y2 = 0 is
equal to the product of the slopes. Then h is
(1) -4
(2) 4
(3) -6
(4) -2 5. If f(9) = 9 and (9) = 4 then
(1) 3
(2) 4
(3) 1/2
(4) 2 6. The value of sin2 50 + sin2 100+ sin2 150 +.........+ sin2 850 + sin 900 =
(1)
7
(2) 8
(3) 9
(4) 9 1/2 7. If the equation x2 + y2 + 2gx + 2fy + 1 =0 represents a pair of lines then
(1) f2 -g2 =1
(2) f2 + g2 =1
(3) g2 -f2 =1
(4) f2 + g2 =1/2 8. ABC is right angled at C, then tan A + tan B =
(2) a2/bc
(1) a + b2
(c) c2/ab
(4) b2/ac 9. If the sum of the distances of a point from two perpendicular lines in a
plane is I then its locus is
(1) Circle
(2) square
(3) straight line
(4) intersecting lines 10. The value of cot 540/tan 360 + tan 200/ cot 700 =
(1) 1
(2) 0
(3) 2
(4) 3 11. The Vectors
form a triangle which is
(1) Equilateral
(2) Isosceles
(3) Right angled
(4) Obtuse angled 12.
(1)
(2)
(3)
(4) 13.
(1)
(2)
(3)
(4) 14. If is the angle between the vectors
(1) cot 
(2) - cot 
(3) tan 
(4) -tan  15. If A and B are square matrices of order n x n then (A-B)2 is equal to
(1) A2 - 2AB + B2
(2) A2 - B2
(3) A2 - 2BA + B2
(4) A2 - AB- BA + B2 16. Choose the correct answer
an identity matrix
(1) Every scalar matrix is
(2) Every identity matrix is a scalar matrix
(3) Every diagonal matrix is an identity matrix
(4) A square matrix whose each element is 1 is an identity matrix 17. If f(a) = 2: f' (a)
= 1, g(a) =- g'(a) = 2 then
(1) -5
(2) 1/5
(3) 5
(4) 0 18. The function f(x) = loge (1 + ax) - log ( 1-bx)/x is undefined at x = 0. The
value which should be assigned to f at x = 0 so that it is continuous at x = 0 is
b
(1) a -
(2) a + b/2
(3) a + b
(4) loge(ab) 19. If f(x) = cos (log x) then f(x) -1/2 [f(y/x) + f(xy)] has the value:
(1) 0
(2) 1
(3) 1/2
(4) -2 20. The area of a circle centred at (1,2) and passing through (4, 6) is
5sq. units
(1)
(2) 15sq. units
(3) 25sq. units
(4) 30sq. units 21. The eccentricity of the hyperbola 1999/3 ( x2 + y2) = 1 is
(1) 2
(2) 22
(3) 3
(4) 2 22. In the coaxial system of circles x2 + y2 + 2gx + C = 0 when g is a
parameter, if C > 0 then the circles are of.
(1) non - intersecting type
(2) touching type
(3) intersecting type
(4) orthogonal 23. If the set A has p electrons, B has q elements, then the number of
elements in A x B is
(1) pq
(2) p2
(3) p + q
(4) P + q + 1 24. If is the nth root of unity then I +   n-1 is
(1) 0
(2) 1
(3) -1
(4) 2 25. The contrapositive of (p v q) r is
(1) p(q v r)
(2) r(p v q)
(3) r(p v p)
(4) r(p  q) 26. For the circuits shown below.
(1) (p q) v ( p  q)
(2) (p q) v ( p v q)
(3) (p q)  ( q p)
(4) p q)  ( q p) 27.
(1) X
(2) Y
(3) 
(4) 1 28. if Z = 1 + i then the multiplicative inverse of Z2 is
(1) 1 - i
(2) i/2
(3) -i/2
(4) 2i 29.
(1) loge3
(2) loge2
(3) 0
(4) loge4 30. Let f(x) = 0x t sin t dt then f' (x) =
(1) sin x + cos x
(2) x sin x
(3) x cos x
(4) x2/2 31. The value of0 2sinx/2sin x+2cosx dx is
(2) 
(3) 
(1) 2
(4) /2 32.
(1) 2
(2) loge2
(3) loge2/2
(4) 2 loge2 33. If f(x) = cos-1 [1 - (log x)2/1 + (log x)2 ] then f' (e) =
(1) 2/e
(2) 1/e
(3) 1
(1) /4 - log 2
(4) does not exist 34.
(2) /2 + log 2
(3) /2 - log 2
(4) /4 + log 2 35.
(1) /ab
(2) /2ab
(3) ab
(4) 2ab 36. If x + iy = a + ib/ c + id then ( x2 + y2)2 =
(1) a2 - b2/ c2 - d2
(2) a2 + b2/ c2 + d2
(3) a2 + b2/ c2 + d2
(4) c2 + d2/ a2 + b2 37. The matrix
is known as
(1) Symmetric matrix
(2) Diagonal matrix
(3) Upper triangular matrix
(4) Skew symmetric matrix 38. The number of improper subgroups of G = { I, -I, i, i} w.r.t. multiplication is
(1) 1
(2) 2
(3) 3
(4) 4 39. In the group G = { 0, 1, 2, 3, 4, 5 } under addition modulo 6, the value of {3
x 5-1}-1 is
(2) 5
(3) 4
(1) 3
(4) 2 40. An ellipse has its centre at (1, -1) and semi major axis = 8, which passes
through the point (1, 3) Then the equation of the ellipse is
I)2/16 =1
(1) (x + I)2/64 + (y +
(2) (x - I)2/64 + (y + I)2/ 16 =1
(3) (x - I)2/16 + (y + I)2/ 64 =1
(4) (x + I)2/64 + (y - I)2/ 16 =1 41. In the multiplicative group of 2 x 2 matrices of
the form
a and a  R the inverse
is
(1)
(2)
(3)
(4) does not exist 42. The circle x2 + y2 - 8x + 4y + 4 = 0 touches
(1) x - axis
(2) y- axis
(3) both x and y axes
(4) does not touch the axes 43. Focus of the parabola (y- 2)2 = 20 ( x + 3 ) is
(2, 2)
(1)
(2) (-3, 2)
(3) (3, -2)
(4) (2, -3) 44. The locus of the centre of a circle which touches externally the given
two circles is
(1) Circle
(2) Parabola
(3) Ellipse
(4) Hyperbola 45. The line p = x cos α + y sin α becomes tangent to x2/a2 - y2/b2 =1
if
(1) p = a cos α -b sin α
(2) p2 = a2 cos α -b2 sin α
(3) p2 = a2 cos α + b2 sin2 α
(4) p2 = a2 cos2 α -b2 sin2 α 46. Equation of the normal to the hyperbola x2/a2 - y2/b2
=1 at the point (a sec ) is
(1) ax/ sec  by/tan = a2- b2
(2) ax/ sec  by/tan = a2+ b2
(3) ax/ sec  by/tan = a2- b2
(4) ax/ sec   by/tan = a- b 47. If tan-1 (x) + 2 cot-1 (x) = 2/3 then x =
(1) 3
(2) 2
(3) 3 -1/ 3 + 1
(4) 3 48. The angle between the curve y2 = 4x and x2 + y2= 5 at (1, 2) is
(1) /2
(2) /4
(3) tan-1 (3)
(4) tan-1 (2) 49. For the curve yn = an-1 x the subnormal at the point is constant. The
value of n must be
(1) 0
(2) 1
(3) 2
(4) 3 50. The maximum value of the function f(x) = x1/x is
(1) e
(2) e1/e
(3) 1/e
(4) 2/e 51. /sin x + cos x dx is
(1) 1/2 log (x/2 +/8) +C
(2) log tan (x/2 +/8) +C
(3) 1/2 log tan ( x/2 +/8) +C
(4) 1/2 log tan (x +/4) +C 52. ex (I + tan x + tan2 x) dx =
(1) ex tan x + c
(2) ex sec x + c
(3) ex sin x + c
(4) ex cos x + c 53.  a sin x + b cos x/ sin x + cos x dx =
(1) /4
(2) (a + b)/2
(3) (a + b)
(4) (a + b)/4 54.  log (tan x) dx =
(1) /4
(2) /2
(3) 0
(4) 1 55. The area enclosed between the parabolas y2 = 4x and x2 = 4y is
sq. units
(1) 1/16
(2) 16/3 sq. units
(3) 14/3 sq. units
(4) 3/4 sq. units 56. Solution of the differential equation tan y sec2 x dx + tan x sec2 y
dy =0 is
(1) tan x + tan y = k
(2) tan x - tan y = k
(3) tan x /tan y = k
(4) tan x tan y = k 57. The area bounded by the curve y = loge x, the X axis, and the
straight line x = e is
(1) e. sq. units
(2) 1. sq. unit
(3) 1- 1/e. sq. units
(4) 1+ 1/e. sq. units 58. Let f be a polynomial. Then the second derivative of f(ex) is
(1) f" (ex) ex.f'(ex)
(2) f"(ex) e2x + f"(ex)ex
(3) f"(ex)
(4) f" (ex) e2x + f'(ex)ex 59. If m and n are the order and degree of the differential
equation
(1) m = 3 , n = 3
(2) m = 3 , n = 2
(3) m = 3 , n = 5
(4) m = 3 , n = 1 60. The value of
is
(1) 0
(2) a + b + c
(3) 4 abc
(4) abc