1
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
2
IIT-JEE 1983
+1
-0.25
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
+2
-0.5
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
+2
-0.5
The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx$$
A
$$-1$$
B
$$2$$
C
$$1 + {e^{ - 1}}$$
D
none of these
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination