CUET PG 2025 Civil Structural and Transport Engineering Question Paper (March 27, 2025) (Shift-3)

Question 1

The solution(s) of the ordinary differential equation $y'' + y =0$, isA. cos xB. sin xC. 1 + cos xD. 1+ sin x

Accepted Answer

A and B only

Answer

A and D only

Answer

C and D only

Answer

B and C only

Question 2

For the matrix, $A = \begin{bmatrix} -4.0 & 4.0 \ -1.6 & 1.2 \end{bmatrix}$ the eigen values $(\lambda)$ and eigen vectors $(X)$ respectively are :

Accepted Answer

4. $\lambda = \begin{bmatrix} -2.0 \ -0.8 \end{bmatrix}$, $X_1 = \begin{bmatrix} 2 \ 1 \end{bmatrix}$ and $X_2 = \begin{bmatrix} 1 \ 0.8 \end{bmatrix}$

Answer

1. $\lambda = \begin{bmatrix} -6.0 \ -0.5 \end{bmatrix}$, $X_1 = \begin{bmatrix} -1.2 \ 1.4 \end{bmatrix}$ and $X_2 = \begin{bmatrix} 1 \ 0.8 \end{bmatrix}$

Answer

2. $\lambda = \begin{bmatrix} -3.0 \ -0.2 \end{bmatrix}$, $X_1 = \begin{bmatrix} 2 \ 1 \end{bmatrix}$ and $X_2 = \begin{bmatrix} -1.2 \ 1.4 \end{bmatrix}$

Answer

3. $\lambda = \begin{bmatrix} -2.0 \ -0.8 \end{bmatrix}$, $X_1 = \begin{bmatrix} -1.2 \ 1.4 \end{bmatrix}$ and $X_2 = \begin{bmatrix} 1 \ 0.8 \end{bmatrix}$

Question 3

The value of $\int_S \vec{F}.\vec{N} ds$ where $\vec{F} = 2x^2y\hat{i} - y^2\hat{j} + 4xz^2\hat{k}$ and S is the closed surface of region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
(where $\vec{N}$ is unit outward normal to surface S)

Accepted Answer

180

Answer

108

Answer

72

Answer

144

Question 4

The value of integral $\oint_c \frac{z^2 - 6}{2z - i} dz$, where $c: |z|\leq 1$ is

Accepted Answer

$\frac{\pi}{8} - 6\pi i$

Answer

$\frac{\pi}{8} - 5\pi i$

Answer

$\frac{3\pi}{8} - 5\pi i$

Answer

$\frac{5\pi}{8} - 3\pi i$

Question 5

In a Binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of two successes is:

Accepted Answer

0.2048

Answer

0.3402

Answer

0.1543

Answer

0.0564

CUET PG 2025 Civil Structural and Transport Engineering Question Paper (March 27, 2025) (Shift-3)

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