1
GATE IN 2005
MCQ (Single Correct Answer)
+1
-0.3
The value of the integral $$\int\limits_{ - 1}^1 {{1 \over {{x^2}}}dx} \,\,\,$$ is
A
$$2$$
B
does not exist
C
$$-2$$
D
$$ \propto $$
2
GATE IN 2005
MCQ (Single Correct Answer)
+1
-0.3
$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$
where $$\,\,{a_i}\,\,$$ ($$i=0$$ to $$n$$) are constants then $$x{{\partial f} \over {\partial x}} + y{{\partial f} \over {\partial y}}\,\,\,$$ is
A
$${f \over n}$$
B
$${n \over f}$$
C
$$n$$ $$f$$
D
$$n\sqrt f $$
3
GATE IN 2001
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{x \to {\pi \over 4}} \,\,{{Sin\,\,2\left( {x - {\pi \over 4}} \right)} \over {x - {\pi \over 4}}} = \_\_\_\_\_\_.$$
A
$$0$$
B
$${1 \over 2}$$
C
$$1$$
D
$$2$$
4
GATE IN 1999
MCQ (Single Correct Answer)
+1
-0.3
$$\mathop {Lim}\limits_{x \to 0} \,{1 \over {10}}\,\,{{1 - {e^{ - j5x}}} \over {1 - {e^{ - jx}}}} = \_\_\_\_.$$
A
$$0$$
B
$$1.1$$
C
$$0.5$$
D
$$1$$
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