1
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
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
$$-1/2$$
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
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 1997
MCQ (Single Correct Answer)
+2
-0.5
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
$${{g\left( x \right)} \over {g\left( \pi \right)}}$$
4
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+1
-0.25
The value of $$\int\limits_\pi ^{2\pi } {\left[ {2\,\sin x} \right]\,dx} $$ where [ . ] represents the greatest integer function is
A
$${{ - 5\pi } \over 3}$$
B
$$\pi $$
C
$${{ 5\pi } \over 3}$$
D
$$ - 2\pi $$
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