1
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements is correct?
A
$$a = 1,\,b = 4$$
B
$$\,a = 0.5,\,b = 1$$
C
$$a=0,$$ $$b=1$$
D
$$a=1,$$ $$b=-1$$
2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is
A
$$Q\left( t \right) = {e^{ - t}} - 1$$
B
$$\,Q\left( t \right) = 1 + {e^{ - t}}$$
C
$$Q\left( t \right) = 1 - {e^t}$$
D
$$Q\left( t \right) = 1 - {e^{ - t}}$$
3
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following second $$-$$order differential equation : $$\,y''\,\, - 4y' + 3y = 2t - 3{t^2}\,\,\,$$
The particular solution of the differential equation is
A
$$ - 2 - 2t - {t^2}$$
B
$$ - 2t - {t^2}$$
C
$$2t - 3{t^2}$$
D
$$ - 2 - 2t - 3{t^2}$$
4
GATE CE 2017 Set 1
Numerical
+1
-0
Consider the following partial differential equation: $$\,\,3{{{\partial ^2}\phi } \over {\partial {x^2}}} + B{{{\partial ^2}\phi } \over {\partial x\partial y}} + 3{{{\partial ^2}\phi } \over {\partial {y^2}}} + 4\phi = 0\,\,$$ For this equation to be classified as parabolic, the value of $${B^2}$$ must be ____________.
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