1
GATE IN 2007
+1
-0.3
Consider the function $$\,\,f\left( x \right) = {\left| x \right|^3},\,\,\,$$ where $$x$$ is real. Then the function $$f(x)$$ at $$x=0$$ is
A
continuous but not differentiable
B
once differentiable but not twice.
C
twice differentiable but not thrice.
D
thrice differentiable
2
GATE IN 2007
+1
-0.3
The value of $$\,\int\limits_0^\infty {\int\limits_0^\infty {{e^{ - {x^2}}}{e^{ - {y^2}}}} dx\,dy\,\,\,\,}$$ is
A
$${{\sqrt \pi } \over 2}$$
B
$${\sqrt \pi }$$
C
$$\pi$$
D
$${\pi \over 4}$$
3
GATE IN 2005
+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
$$\propto$$
4
GATE IN 2005
+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
$$n\sqrt f$$
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