1
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\,\int\limits_0^2 {\int\limits_0^x {{e^{x + y}}\,\,dy} } $$ $$dx$$ is
A
$${1 \over 2}\left( {e - 1} \right)$$
B
$${1 \over 2}{\left( {{e^2} - 1} \right)^2}$$
C
$${1 \over 2}\left( {{e^2} - e} \right)$$
D
$${1 \over 2}{\left( {e - {1 \over e}} \right)^2}$$
2
GATE ME 2014 Set 4
Numerical
+1
-0
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. $$500$$ and a standard deviation of Rs. $$50.$$ The percentage of savings account holders, who maintain an average daily balance more than Rs. $$500$$ is
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3
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is
A
$$1 + {e^{ - {x^2}}}$$
B
$$2{e^{ - {x^2}}}$$
C
$$1 + {e^{ {x^2}}}$$
D
$$2{e^{ {x^2}}}$$
4
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
Consider an ordinary differential equation $${{dx} \over {dt}} = 4t + 4.\,\,$$ If $$x = {x_0}$$ at $$t=0,$$ the increment in $$x$$ calculated using Runge-Kutta fourth order multi-step method with a step size of $$\Delta t = 0.2$$ is
A
$$0.22$$
B
$$0.44$$
C
$$0.66$$
D
$$0.88$$
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