Category III (2 marks, 1 or more than 1 correct answer)

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Congratulations - you have completed WBJEE - Mathematics (Category - 3) Model Test.
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Question 1

If a>0, the roots of the equation
log_{ a} ax + log_{ x} a^{2} + log_{ a2x} a^{3} = 0, are given by

A

a^{-(4/3)}

B

a^{-(3/4)}

C

a^{-(1/2)}

D

a^{-1}

Question 2

The value of the integral ∫^{1}_{0} e ^{x 2} is

A

< 1

B

> 1

C

< e

D

> e

Question 3

Let f (x) = x^{2} + xg′(1) + g″(2) and g(x) = x^{2} + xf ′(2) + f ″(3), then

A

f ′(1) = 4 + f ′(2)

B

g ′(2) = 8 + g ′(1)

C

g '' (2) + f ″ (2) = 4

D

f ′(1) + g ′(1) = 3

Question 4

If (1 + x)^{n} = C_{0} + C_{1}x + C_{2}x^{2} + ................. + C_{n}x^{n} , where n is a positive integer, then