1
IIT-JEE 1995 Screening
+1
-0.25
If $$f\left( x \right)\,\,\, = \,\,\,A\sin \left( {{{\pi x} \over 2}} \right)\,\,\, + \,\,\,B,\,\,\,f'\left( {{1 \over 2}} \right) = \sqrt 2$$ and
$$\int\limits_0^1 {f\left( x \right)dx = {{2A} \over \pi },}$$ then constants $$A$$ and $$B$$ are
A
$${\pi \over 2}$$ and $${\pi \over 2}$$
B
$${2 \over \pi }$$ and $${3 \over \pi }$$
C
$$0$$ and $${-4 \over \pi }$$
D
$${4 \over \pi }$$ and $$0$$
2
IIT-JEE 1993
+1
-0.25
The value of $$\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}}$$ is
A
$$0$$
B
$$1$$
C
$$\pi /2$$
D
$$\pi /4$$
3
IIT-JEE 1990
+2
-0.5
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
$$0$$
4
IIT-JEE 1985
+2
-0.5
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
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