CUET PG 2025 Atmospheric Science Question Paper (March 29, 2025) (Shift-3)

Question 1

If $A = \begin{bmatrix} 1 & 2 & -1 \ 3 & 4 & 2 \ 2 & 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \ -4 & 0 \ 2 & 5 \end{bmatrix}$ are two matrices, then which one of the following is incorrect:

Accepted Answer

A - B is defined

Answer

AB is defined

Answer

BA is not defined

Answer

A + B is not defined

Question 2

If $f(t)$ is the inverse Laplace transform of $F(s)=\frac{s+1+\frac{1}{s^2}}{s^2-1}$ then $f(t)$ is

Accepted Answer

$e^t + \sinh t - t$

Answer

$e^t + \sinh t + t$

Answer

$e^t - \sinh t - t$

Answer

$e^t + \cosh t - t$

Question 3

Which of the following statements are correct?
A. In a skew symmetric matrix, all diagonal elements are zero.
B. A square matrix is called a diagonal matrix, if all its non-diagonal elements are one.
C. If the determinant of the matrix is zero, then the matrix is know as non-singular matrix.
D. The product of a matrix A and its adjoint is equal to unit matrix multiplied by the determinant A.
Choose the correct answer from the options given below:

Accepted Answer

A and D only

Answer

B and C only

Answer

A, B and D only

Answer

B, C and D only

Question 4

Match LIST-I with LIST-II LIST-I(Differential Equation)LIST-II(Integrating Factor)(A). $\frac{dy}{dx} = 2x(y-x^2+1)$(I). $x^2e^{x^2}$(B). $x\frac{dy}{dx} + 2(x^2+1)y = 6$(II). $e^{-x^2}$(C). $(x^2+1)\frac{dy}{dx} + 2xy = x\sin x$(III). $x^2$(D). $x^2\frac{dy}{dx} + 2xy = 2x^2e^{x^2}$(IV). $1+x^2$Choose the correct answer from the options given below:

Accepted Answer

A-II, B-I, C - IV, D - III

Answer

A-I, B-II, C-III, D - IV

Answer

A-II, B-III, C-IV, D - I

Answer

A-III, B-IV, C-I, D - II

Question 5

Let $y(t)$ be the solution of differential equation $y''(t) + 4y(t) = 0$, $y(0) = 1$, $y'(0) = 6$, then the Laplace transformation $Y(s)$ of solution $y(t)$ of the differential equation is equal to

Accepted Answer

$\frac{s}{s^2+4} + \frac{6}{s^2+4}$

Answer

$\frac{s}{s^2+4} + \frac{2}{s^2+4}$

Answer

$\frac{s}{s^2-4} + \frac{2}{s^2-4}$

Answer

$\frac{s}{s^2+4} + \frac{1}{s^2+4}$

LIST-I (Differential Equation)	LIST-II (Integrating Factor)
(A). $\frac{dy}{dx} = 2x(y-x^2+1)$	(I). $x^2e^{x^2}$
(B). $x\frac{dy}{dx} + 2(x^2+1)y = 6$	(II). $e^{-x^2}$
(C). $(x^2+1)\frac{dy}{dx} + 2xy = x\sin x$	(III). $x^2$
(D). $x^2\frac{dy}{dx} + 2xy = 2x^2e^{x^2}$	(IV). $1+x^2$

CUET PG 2025 Atmospheric Science Question Paper (March 29, 2025) (Shift-3)

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