1
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Consider the following expression:

z = sin(y + it) + cos(y $$-$$ it)

where z, y, and t are variables, and $$i = \sqrt { - 1} $$ is a complex number. The partial differential equation derived from the above expression is

A
$${{{\partial ^2}z} \over {\partial {t^2}}} + {{{\partial ^2}z} \over {\partial {y^2}}} = 0$$
B
$${{{\partial ^2}z} \over {\partial {t^2}}} - {{{\partial ^2}z} \over {\partial {y^2}}} = 0$$
C
$${{\partial z} \over {\partial t}} - i{{\partial z} \over {\partial y}} = 0$$
D
$${{\partial z} \over {\partial t}} + i{{\partial z} \over {\partial y}} = 0$$
2
GATE CE 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33

For the equation

$${{{d^3}y} \over {d{x^3}}} + x{\left( {{{dy} \over {dx}}} \right)^{3/2}} + {x^2}y = 0$$

the correct description is

A
an ordinary differential equation of order 3 and degree 2.
B
an ordinary differential equation of order 3 and degree 3.
C
an ordinary differential equation of order 2 and degree 3.
D
an ordinary differential equation of order 3 and degree 3/2.
3
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
$$Q\left( t \right) = 1 - {e^{ - t}}$$
4
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
$$ - 2 - 2t - 3{t^2}$$
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