1
GATE EE 2016 Set 1
Numerical
+2
-0
Candidates were asked to come to an interview with $$3$$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $$3$$ pens having the same colour is _______.
Your input ____
2
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A function $$y(t),$$ such that $$y(0)=1$$ and $$\,y\left( 1 \right) = 3{e^{ - 1}},\,\,$$ is a solution of the differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ Then $$y(2)$$ is
A
$$5{e^{ - 1}}$$
B
$$5{e^{ - 2}}$$
C
$$7{e^{ - 1}}$$
D
$$7{e^{ - 2}}$$
3
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 ___________.
Your input ____
4
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\oint\limits_c {{{2z + 5} \over {\left( {z - {1 \over 2}} \right)\left( {{z^2} - 4z + 5} \right)}}} dz$$ over the contour $$\left| z \right| = 1,$$ taken in the anti-clockwise direction, would be
A
$${{24\pi i} \over {13}}$$
B
$${{48\pi i} \over {13}}$$
C
$${{24} \over {13}}$$
D
$${{12} \over {13}}$$
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