1
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
2
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
3
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
4
IIT-JEE 1981
+2
-0.5
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
EXAM MAP
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