List of top Questions asked in PSEB XII- 2025

Evaluate \( \int \frac{\sin^{-1}(x)}{1 + x^2} \, dx \)

Evaluate \( \int \frac{2x - 3}{x^2 + 1} \, dx \)

Principal value of \( \sin^{-1}(1) \) is:

If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of matrix \( A^T \) is:

Using integration, find the area bounded by the circle \( x^2 + y^2 = 16 \) in the first quadrant.

Find the critical points of the function \( f(x) = 2x^3 - 3x^2 - 12x + 15 \):

Find the area of the triangle whose sides are given by vectors: \[ \vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \vec{b} = \hat{i} - \hat{j} + 3\hat{k} \]

Evaluate \( \int_{\pi/6}^{\pi/3} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \):

Evaluate \( \int_0^1 \frac{dx}{1 + x^2} \):

Find the order of the differential equation \( \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 3y = 0 \):

If \( A \) is a square matrix of order \( 2 \times 2 \) and \( |A| = 5 \), then \( | \text{Adj}(A) | \) is:

If \( y = \log x \), then \( \frac{dy}{dx} \) is:

The radius of a circle is increasing at the rate of 2 m/s. The rate of change of its circumference is:

Vector equation of the line \( \frac{x - 5}{4} = \frac{y - 3}{5} = \frac{z + 3}{-8} \) is:

Objective function of a linear programming problem is:

Relation \( R = \{(x, y): x<y^2 \text{ where } x, y \in \mathbb{R}\} \) is:

Range of the function \( \cos^{-1} \):

If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:

Name of the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is:

Write any four features of Computer.

Give any four differences between RAM and ROM.

Discuss the usage of multimedia in four different sectors.

Write any four differences between E-Commerce and Traditional Commerce.

Write any four requirements of effective E-Payment system.

Explain any four benefits of Proxy Server in detail.