64. The value of x for which is

a) 1/2 b) 1

c) 0 d) -1/2

Ans. d

.

65. If and , then in

a) f(x) is strictly increasing function b) f(x) has a local maxima

c) f(x) is strictly decreasing function

d) f(x) is bounded

Ans. a

So f is a strictly increasing function.

66. If be a cube root of unity and , then the least positive vlaue of n is

a) 2 b) 3

c) 5 d) 6

Ans. b

67. If and , then the value of for which Rolle's theorem can be applied in [0, 1] is

a) -2 b) -1

c) 0 d) 1/2

Ans. d

For function to satisfy the condition of Rolle's theorem, it should be continuous in [0, 1]

Also is differentiable in ( 0,1) and f(1) = 0 = f(0).

68. For all 'x' , then the interval in which 'a' lies is

a) a < -5 b) - 5 < a < 2

c) a > 5 d) 2 < a < 5

Ans. b

D < 0

69. The angle between the tangents drawn from the point ( 1, 4) to the parabola is

a) b)

c) d)

Ans. c

Equation of tangent is

Since it passes through ( 1, 4)

,

.

.

70. If one root is square of the other root of the equation , then the relation between p and q is

a)

b)

c)

d)

Ans. a

Let the roots be