1
GATE EE 2016 Set 2
+2
-0.6
The value of the integral $$\,\,2\int_{ - \infty }^\infty {\left( {{{\sin \,2\pi t} \over {\pi t}}} \right)} dt\,\,$$ is equal to
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
2
GATE EE 2016 Set 1
Numerical
+2
-0
Let $$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$ where $$\,\,\left| \alpha \right| < 1.\,\,$$ The value of $$\alpha$$ in the range $$\,\,0 < \alpha < 1,\,\,$$ such that $$\,\,S = 2\alpha \,\,$$ is ___________.
3
GATE EE 2015 Set 2
Numerical
+2
-0
The volume enclosed by the surface $$f\left( {x,y} \right) = {e^x}$$ over the triangle bounded by the lines $$x=y;$$ $$x=0;$$ $$y=1$$ in the $$xy$$ plane is ________.
4
GATE EE 2014 Set 2
+2
-0.6
To evaluate the double integral $$\int\limits_0^8 {\left( {\int\limits_{y/2}^{\left( {y/2} \right) + 1} {\left( {{{2x - y} \over 2}} \right)dx} } \right)dy,\,\,}$$ we make the substitution $$u = \left( {{{2x - y} \over 2}} \right)$$ and $$v = {y \over 2}.$$ The integral will reduce to
A
$$\int\limits_0^4 {\left( {\int\limits_0^2 {2udu} } \right)dv}$$
B
$$\int\limits_0^4 {\left( {\int\limits_0^1 {2udu} } \right)dv}$$
C
$$\int\limits_0^4 {\left( {\int\limits_0^1 {udu} } \right)dv}$$
D
$$\int\limits_0^4 {\left( {\int\limits_0^{21} {2udu} } \right)dv}$$
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