71. The value of the integral is

a) b)

c) -1 d) 1

Ans. b

Let . Put , then .

72. If and , then is

a) b)

c) d)

Ans. c

73. If

a) b)

c) d)

Ans. d

74. If , then g(f(x)) is invertible in the domain

a) b)

c) d)

Ans. b

which
is invertible in

75. If , , then equals

a) 1/3 b) 2/3

c) -1/3 d) 1.

Ans. a

.

Putting x = 0 and y = 1, we get c = 4.

.

76. If the lines and intersect, then the value of k is

a) 3/2 b) 9/2

c) -2/9 d) -3/2

Ans. b

General points on the lines are and

Equating the coresponding coordinates, we get k = 9/2.

77. Given 2x - y + 2z = 2, x - 2y + z = -4, then the value of such that the given system of equation has no solution, is

a) 3 b) 1

c) 0 d) -3.

Ans. b

As , for no solution .

78. If the line touches the

hyperbola , then the point of contact is

a) b)

c) d)

Ans. d

Equation of tangent is

on comparing with , we get and .