1
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
JEE Advanced Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12