List of top Questions asked in PSEB XII

Order of differential equation \( \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 3y = 0 \) is:
If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:
Name of the inequality \( |\vec{a} \cdot \vec{b}| \le |\vec{a}| |\vec{b}| \) is:
Direction ratios of the straight line \( \vec{r} = 2\hat{i} - 3\hat{j} + \hat{k} + m(9\hat{i} - 2\hat{j} + 5\hat{k}) \) are:
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:
If \( y = e^{\log x} \), then \( \frac{dy}{dx} \) is:
If \( y = \tan x \), then at \( x = \frac{\pi}{4} \), \( \frac{dy}{dx} \) is equal to:
Radius of a circle is increasing at the rate of \( 2 \text{ m/s} \). Rate of change of its circumference is:
\( \int_{\pi/6}^{\pi/3} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx \) is equal to:
\( \int_0^1 \frac{dx}{1+x^2} \) is equal to:
Range of function \( \cos^{-1} x \) is:
Principal value of \( \sin^{-1}(1) \) is:
If \( A \) is a square matrix of order \( 2 \times 2 \) and \( |A| = 5 \), then \( |Adj(A)| \) is:
If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of the matrix \( (A')' \) is:
State Gauss’s theorem. Using this theorem, derive electric field intensity due to thin uniformly charged infinite plane sheet.
Define capacitance. Derive capacitance of a parallel plate capacitor having dielectric slab between its plates.
With help of labelled diagram, write principle of astronomical telescope and derive expression for magnifying power of an astronomical telescope, when final image is formed at least distance of distinct vision.
What is interference of light? Derive an expression for the fringe width in the Young’s double slit experiment.
Relation \( R = \{(x, y) : x<y^2 \text{ where } x, y \in \mathbb{R}\} \) is:
Find the coefficient of mutual inductance of a pair of coils if a current of 3 A in one coil causes the flux in the second coil of 1000 turns to change by \( 10^{-4} \, \text{weber} \) in each turn.
What is total internal reflection? Write necessary conditions for it.
Define binding energy per nucleon. Draw and explain the curve between binding energy per nucleon and mass number.
With the help of a circuit diagram, explain the V-I characteristics of a PN junction diode in forward biasing.
A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of magnetic field inside the solenoid?