1
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \infty .$$ Then $$P\left\{ {X > 1} \right\}$$ is
A
$$0.368$$
B
$$0.5$$
C
$$0.632$$
D
$$1.0$$
2
GATE IN 2013
MCQ (Single Correct Answer)
+2
-0.6
The maximum value of the solution $$y$$ $$(t)$$ of the differential equation $$\,\,y\left( t \right) + \mathop y\limits^{ \bullet \,\, \bullet } \left( t \right) = 0\,\,\,$$ with initial conditions $$\,\,\mathop y\limits^ \bullet \left( 0 \right) = 1\,\,$$ and $$\,\,y\left( 0 \right) = 1,\,\,$$ for $$\,t \ge 0\,\,$$ is
A
$$1$$
B
$$2$$
C
$$\pi $$
D
$$\sqrt 2 $$
3
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
The type of the partial differential equation $${{\partial f} \over {\partial t}} = {{{\partial ^2}f} \over {\partial {x^2}}}\,\,is$$
A
Parabolic
B
Elliptic
C
Hyperbolic
D
Nonlinear
4
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
While numerically solving the differential equation $$\,{{dy} \over {dx}} + 2x{y^2} = 0,y\left( 0 \right) = 1\,\,$$ using Euler's predictor corrector (improved Euler- Cauchy) method with a step size of $$0.2,$$ the value of $$y$$ after the first step is
A
$$1.00$$
B
$$1.03$$
C
$$0.97$$
D
$$0.96$$
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Graduate Aptitude Test in Engineering
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CBSE
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