List of top Questions asked in AP PGECET- 2026

The number of linearly independent solutions of the differential equation $\frac{d^4y}{dx^4} - \frac{d^3y}{dx^3} - 3\frac{d^2y}{dx^2} + 5\frac{dy}{dx} - 2y = 0$ of the form $e^{ax}$ ($a$ is a real number) is}

The general solution of $(x^2 D^2 - xD)y = 0$ is

The inverse Laplace transform of $F(s) = \frac{s^2 - 3s + 4}{s^3}$ is _______}

A plane wall of thickness $0.1\text{ m}$ and thermal conductivity $50\text{ W/m}\cdot\text{K}$ has a surface area of $2\text{ m}^2$. The temperature difference across the wall is $100\text{ K}$. What is the rate of heat transfer through the wall?

The integrating factor of the differential equation $(1 + x^2)\frac{dy}{dx} + 2xy - 4x^2 = 0$ is}

Let $A$ be an $n \times n$ matrix such that $A^3 = A$. Then which one of the following is true?

Diamagnetic materials are:

Let $\vec{f} = x^2 y z \hat{i} + x y^2 z \hat{j} + x y z^2 \hat{k}$ be a vector field. If $\vec{F}(x,y,z) = \text{curl }\vec{f}$, then the vector $\vec{F}(1,-2,1)$ is equal to _______}

The 'Fugacity Coefficient ($\phi = f/P$)' of a real gas approaches unity when

Assertion (A): Gibbs free energy determines spontaneity at constant T and P.
Reason (R): A process is spontaneous when Gibbs free energy is minimum.

A material loses its strong magnetization suddenly at a critical temperature and becomes weakly magnetic. This transition is from

Ferromagnetic materials show:

According to equation of continuity,

Which combination gives highest strength-to-weight ratio?

According to the Boltzmann Equation $S = k_B \ln \Omega$, if a system is in a state of "Perfect Order" (a perfect crystal at $0\text{ K}$), the number of microstates $\Omega$ and the entropy $S$ are

If $\Delta U = 100\text{ J}$ and work done = $40\text{ J}$, heat supplied is:

Which of the following statements is FALSE?

Transparency of glass is due to

The "Glassy" state in ceramics is characterized as

Vacancy diffusion coefficient: $D = D_0 \exp(-Q/RT)$

Centroid of triangle lies at:

If two forces acting at a joint are not along the straight line, then for the equilibrium of the joint

Efficiency of Carnot engine is always:

Which of the following has the highest thermal diffusivity:

Which of the following materials possesses anti-parallel spins of unequal magnitude, resulting in a spontaneous magnetic moment below a critical temperature?