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1

### IIT-JEE 1990

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
$$0$$
2

### IIT-JEE 1985

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
3

### IIT-JEE 1983

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
4

### IIT-JEE 1982

The area bounded by the curves $$y=f(x)$$, the $$x$$-axis and the ordinates $$x=1$$ and $$x=b$$ is $$(b-1)$$ sin $$(3b+4)$$. Then $$f(x)$$ is
A
$$\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$
B
$$\sin \left( {3x + 4} \right)$$
C
$$\sin \left( {3x + 4} \right) + 3\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$
D
none of these

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Class 12