1
IIT-JEE 1998
+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
$$1/2$$
2
IIT-JEE 1997
+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
$${{g\left( x \right)} \over {g\left( \pi \right)}}$$
3
IIT-JEE 1995 Screening
+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
$$- 2\pi$$
4
IIT-JEE 1995 Screening
+1
-0.25
If $$f\left( x \right)\,\,\, = \,\,\,A\sin \left( {{{\pi x} \over 2}} \right)\,\,\, + \,\,\,B,\,\,\,f'\left( {{1 \over 2}} \right) = \sqrt 2$$ and
$$\int\limits_0^1 {f\left( x \right)dx = {{2A} \over \pi },}$$ then constants $$A$$ and $$B$$ are
A
$${\pi \over 2}$$ and $${\pi \over 2}$$
B
$${2 \over \pi }$$ and $${3 \over \pi }$$
C
$$0$$ and $${-4 \over \pi }$$
D
$${4 \over \pi }$$ and $$0$$
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12