1
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
Limit of the following sequence as $$n \to \infty $$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$
A
$$0$$
B
$$1$$
C
$$\infty $$
D
$$ - \infty $$
2
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$
A
$${1 \over 4}$$
B
$$0$$
C
$${{ - 1} \over 4}$$
D
$$1$$
3
GATE CE 2002
MCQ (Single Correct Answer)
+1
-0.3
The value of the following definite integral in $$\int\limits_{{\raise0.5ex\hbox{$\scriptstyle { - \pi }$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}} {{{Sin2x} \over {1 + \cos x}}dx = \_\_\_\_\_\_\_\_.} $$
A
$$-2log$$ $$2$$
B
$$2$$
C
$$0$$
D
None
4
GATE CE 2002
MCQ (Single Correct Answer)
+2
-0.6
The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$
A
$$4/5$$
B
$$4$$
C
$$2/5$$
D
$$1$$
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