1
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value
A
$${{ - 1} \over 3}$$
B
$${{ 1} \over 4}$$
C
$${{ 1} \over 2}$$
D
$$1$$
2
GATE EE 2004
MCQ (Single Correct Answer)
+1
-0.3
The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.
A
$${1 \over 8}$$
B
$${1 \over 6}$$
C
$${1 \over 3}$$
D
$${1 \over 2}$$
3
GATE EE 1997
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{\theta \to 0} \,{{\sin \,m\,\theta } \over \theta },$$ where $$m$$ is an integer, is one of the following :
A
$$m$$
B
$$m\pi $$
C
$$m\theta $$
D
$$1$$
4
GATE EE 1995
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{x \to \infty } \,x\sin {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle x$}} = \_\_\_\_\_.$$
A
$$ \propto $$
B
$$0$$
C
$$1$$
D
Does not exist
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