1
IIT-JEE 2001 Screening
+3
-0.75
The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}x} \over {1 + {a^x}}}dx,\,a > 0,}$$ is
A
$$\pi$$
B
$$a\pi$$
C
$$\pi /2$$
D
$$2\pi$$
2
IIT-JEE 2000 Screening
+2
-0.5
Let $$g\left( x \right) = \int\limits_0^x {f\left( t \right)dt,}$$ where f is such that
$${1 \over 2} \le f\left( t \right) \le 1,$$ for $$t \in \left[ {0,1} \right]$$ and $$\,0 \le f\left( t \right) \le {1 \over 2},$$ for $$t \in \left[ {1,2} \right]$$.
Then $$g(2)$$ satisfies the inequality
A
$$- {3 \over 2} \le g\left( 2 \right) < {1 \over 2}$$
B
$$0 \le g\left( 2 \right) < 2$$
C
$${3 \over 2} < g\left( 2 \right) \le {5 \over 2}$$
D
$$2 < g\left( 2 \right) < 4$$
3
IIT-JEE 2000 Screening
+3
-0.75
If $$f\left( x \right) = \left\{ {\matrix{ {{e^{\cos x}}\sin x,} & {for\,\,\left| x \right| \le 2} \cr {2,} & {otherwise,} \cr } } \right.$$ then $$\int\limits_{ - 2}^3 {f\left( x \right)dx = }$$
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
4
IIT-JEE 2000 Screening
+3
-0.75
The value of the integral $$\int\limits_{{e^{ - 1}}}^{{e^2}} {\left| {{{{{\log }_e}x} \over x}} \right|dx}$$ is :
A
$$3/2$$
B
$$5/2$$
C
$$3$$
D
$$5$$
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