79. If and , then the value of is

a) b)

c) d)

Ans. c

.

80. The unit vector which is orthogonal to the vector ans is coplanar with the vectors and is

a) b)

c) d)

Ans. c

Let , , , then required unit vector will be along .

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81. If f(x) is differentiable and strictly increasing function, then the value of is

a) 1 b) 0

c) -1 d) 2.

Ans. c

Using L'Hospital rule.

82. An infinite G.P. has 1st term 'x' ans sum '5', then

a) x < -10 b)

c) d) x > 10

Ans. c

The sum of an infinite (given)

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83. If one of the diameters of the circle is a chord to the circle with centre ( 2, 1), then the radius of the circle is

a) b)

c) 3 d) 2

Ans. c

Centre is ( 1, 3) and radius = 2

If r = radius of second circle then .

84. If y is a function of x and log (x + y) - 2xy = 0, then the value of is equal to

a) 1 b) -1

c) 2 d) 0

Ans. a

At x = 0, y = 1

log (x + y) - 2xy = 0

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