1
GATE ME 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Find the solution of $${{{d^2}y} \over {d{x^2}}} = y$$ which passes through origin and the point $$\left( {ln2,{3 \over 4}} \right)$$
A
$$y = {1 \over 2}{e^x} - {e^{ - x}}$$
B
$${1 \over 2}\left( {{e^x} + {e^{ - x}}} \right)$$
C
$$y = {1 \over 2}\left( {{e^x} - {e^{ - x}}} \right)$$
D
$${1 \over 2}{e^x} + {e^{ - x}}$$
2
GATE ME 2015 Set 1
Numerical
+2
-0
Simpson's $${1 \over 3}$$ rule is used to integrate the function $$f\left( x \right) = {3 \over 5}{x^2} + {9 \over 5}\,\,$$ between $$x=0$$ and $$x=1$$ using the least number of equal sub-intervals. The value of the integral is __________.
Your input ____
3
GATE ME 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Given two complex numbers $${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$ and $${z_2} = {2 \over {\sqrt 3 }} + 2i,$$ the argument of $${{{z_1}} \over {{z_2}}}$$ in degrees $$i$$
A
$$0$$
B
$$30$$
C
$$60$$
D
$$90$$
4
GATE ME 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is
A
$${5 \over {{s^2} - 4s + 29}}$$
B
$${5 \over {{s^2} + 5}}$$
C
$${{s - 2} \over {{s^2} - 4s + 29}}$$
D
$${5 \over {s + 5}}$$
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