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 2022 Set 1
MCQ (More than One Correct Answer)
+1
-0

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M3 $$-$$ 4M2 $$-$$ 2M

Which of the following is/are the eigenvalue(s) of matrix Q?

A
15
B
25
C
$$-$$20
D
$$-$$30
4
GATE CE 2022 Set 1
Numerical
+1
-0

Consider the following recursive iteration scheme for different values of variable P with the initial guess x1 = 1:

$${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \right)$$, n = 1, 2, 3, 4, 5

For P = 2, x5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x5 is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x5 is __________. (round off to three decimal places)

Your input ____
EXAM MAP