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1

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$$2 < g\left( 2 \right) < 4$$
2

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$$3$$
3

IIT-JEE 1999

MCQ (Single Correct Answer)
$$\int\limits_{\pi /4}^{3\pi /4} {{{dx} \over {1 + \cos x}}} $$ is equal to
A
$$2$$
B
$$-2$$
C
$$1/2$$
D
$$-1/2$$
4

IIT-JEE 1999

MCQ (Single Correct Answer)
If for a real number $$y$$, $$\left[ y \right]$$ is the greatest integer less than or
equal to $$y$$, then the value of the integral $$\int\limits_{\pi /2}^{3\pi /2} {\left[ {2\sin x} \right]dx} $$ is
A
$$ - \pi $$
B
$$0$$
C
$$ - \pi /2$$
D
$$ \pi /2$$

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