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1

IIT-JEE 1993

MCQ (Single Correct Answer)
The value of $$\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}} $$ is
A
$$0$$
B
$$1$$
C
$$\pi /2$$
D
$$\pi /4$$
2

IIT-JEE 1990

MCQ (Single Correct Answer)
Let $$f:R \to R$$ and $$\,\,g:R \to R$$ be continuous functions. Then the value of the integral
$$\int\limits_{ - \pi /2}^{\pi /2} {\left[ {f\left( x \right) + f\left( { - x} \right)} \right]\left[ {g\left( x \right) - g\left( { - x} \right)} \right]dx} $$ is
A
$$\pi $$
B
$$1$$
C
$$-1$$
D
$$0$$
3

IIT-JEE 1985

MCQ (Single Correct Answer)
For any integer $$n$$ the integral ...........
$$\int\limits_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^3}\left( {2n + 1} \right)xdx} $$ has the value
A
$$\pi $$
B
$$1$$
C
$$0$$
D
none of these
4

IIT-JEE 1983

MCQ (Single Correct Answer)
The value of the integral $$\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx} $$ is
A
$$\pi /4$$
B
$$\pi /2$$
C
$$\pi $$
D
none of these

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