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1

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
$$ \pi /2$$
2

IIT-JEE 1998

MCQ (Single Correct Answer)
Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, where $$\left[ x \right]$$ is the integral part of $$x$$. Then $$\int_{ - 1}^1 {f\left( x \right)\,dx} $$ is
A
$$1$$
B
$$2$$
C
$$0$$
D
$$1/2$$
3

IIT-JEE 1998

MCQ (Single Correct Answer)
If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is
A
$$1/2$$
B
$$0$$
C
$$1$$
D
$$-1/2$$
4

IIT-JEE 1997

MCQ (Single Correct Answer)
If $$g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,} $$ then $$g\left( {x + \pi } \right)$$ equals
A
$$g\left( x \right) + g\left( \pi \right)$$
B
$$g\left( x \right) - g\left( \pi \right)$$
C
$$g\left( x \right) g\left( \pi \right)$$
D
$${{g\left( x \right)} \over {g\left( \pi \right)}}$$

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