1
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+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
$$\int\limits_0^4 {\left( {\int\limits_0^{21} {2udu} } \right)dv}$$
2
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The minimum value of the function $$f\left( x \right) = {x^3} - 3{x^2} - 24x + 100$$ in the interval $$\left[ { - 3,3} \right]$$ is
A
$$20$$
B
$$28$$
C
$$16$$
D
$$32$$
3
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the interval $$\left[ {1,6} \right]$$ is
A
$$21$$
B
$$25$$
C
$$41$$
D
$$46$$
4
GATE EE 2010
MCQ (Single Correct Answer)
+2
-0.6
The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,}$$ is
A
$$0$$
B
$$1$$
C
$$e$$
D
$$1/e$$
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