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1

### 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
2

### 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
3

### 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
4

### IIT-JEE 1981

Let $$a, b, c$$ be non-zero real numbers such that
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx = \int\limits_0^2 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} + bx + c} \right)dx.} }$$
Then the quadratic equation $$a{x^2} + bx + c = 0$$ has
A
no root in $$(0, 2)$$
B
at least one root in $$(0, 2)$$
C
a double root in $$(0, 2)$$
D
two imaginary roots

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NEET

Class 12