1
GATE ME 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the following differential equation $${{dy} \over {dt}} = - 5y;$$ initial condition: $$y=2$$ at $$t=0.$$
The value of $$y$$ at $$t=3$$ is
A
$$ - 5{e^{ - 10}}$$
B
$$2{e^{ - 10}}$$
C
$$2{e^{ - 15}}$$
D
$$ - 15{e^2}$$
2
GATE ME 2015 Set 2
Numerical
+2
-0
The values of function $$(x)$$ at $$5$$ discrete points are given below: GATE ME 2015 Set 2 Engineering Mathematics - Numerical Methods Question 20 English

Using Trapezodial rule with step size of $$0.1,$$ the value of $$\,\int\limits_0^{0.4} {f\left( x \right)\,dx\,\,} $$ is __________.

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3
GATE ME 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$
A
$${{s - 5i} \over {{s^2} - 25}}$$
B
$${{s + 5i} \over {{s^2} + 25}}$$
C
$${{s + 5i} \over {{s^2} - 25}}$$
D
$${{s - 5i} \over {{s^2} + 25}}$$
4
GATE ME 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Laplace transform of $$\cos \left( {\omega t} \right)$$ is
A
$${s \over {{s^2} + {\omega ^2}}}$$
B
$${\omega \over {{s^2} + {\omega ^2}}}$$
C
$${s \over {{s^2} - {\omega ^2}}}$$
D
$${\omega \over {{s^2} - {\omega ^2}}}$$
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