1
GATE CSE 2015 Set 1
+1
-0.3
$$\,\,\mathop {\lim }\limits_{x \to \infty } \,{x^{1/x}}\,\,$$ is
A
$$\infty$$
B
$$0$$
C
$$1$$
D
Not defined
2
GATE CSE 2015 Set 1
+1
-0.3
If $$g(x)=1-x$$ & $$h\left( x \right) = {x \over {x - 1}}\,\,$$ then $$\,\,{{g\left( {h\left( x \right)} \right)} \over {h\left( {g\left( x \right)} \right)}}\,\,\,$$ is
A
$${{h\left( x \right)} \over {g\left( x \right)}}$$
B
$${{ - 1} \over x}$$
C
$${{g\left( x \right)} \over {h\left( x \right)}}$$
D
$${x \over {{{\left( {1 - x} \right)}^2}}}$$
3
GATE CSE 2014 Set 3
Numerical
+1
-0
If $$\int_0^{2\pi } {\left| {x\sin x} \right|dx = k\pi ,}$$ then the values of $$k$$ is equal to _________ .
4
GATE CSE 2014 Set 1
+1
-0.3
Let the function
$$f\left( \theta \right) = \left| {\matrix{ {\sin \,\theta } & {\cos \,\theta } & {\tan \,\theta } \cr {\sin \left( {{\pi \over 6}} \right)} & {\cos \left( {{\pi \over 6}} \right)} & {\tan \left( {{\pi \over 6}} \right)} \cr {\sin \left( {{\pi \over 3}} \right)} & {\cos \left( {{\pi \over 3}} \right)} & {\tan \left( {{\pi \over 3}} \right)} \cr } } \right|$$

Where $$\theta \in \left[ {{\pi \over 6},{\pi \over 3}} \right]$$ and $$f\left( \theta \right)$$ denote the derivative of $$f$$ with repect to $$\theta$$. Which of the following statements is/are TRUE?

$${\rm I})$$ There exists $$\theta \in \left[ {{\pi \over 6},{\pi \over 3}} \right]$$ such that $$f\left( \theta \right)$$ $$= 0$$.
$${\rm I}{\rm I})$$ There exists $$\theta \in \left[ {{\pi \over 6},{\pi \over 3}} \right]$$ such that $$f\left( \theta \right)$$ $$\ne 0$$.

A
$${\rm I}$$ only
B
$${\rm I}$$$${\rm I}$$ only
C
Both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$
D
neither $${\rm I}$$ nor $${\rm I}$$$${\rm I}$$
GATE CSE Subjects
EXAM MAP
Medical
NEET