List of top Questions asked in GATE PH- 2026

A dielectric sphere carries a uniform polarization \(P = 26\ \mu\text{C}.\text{cm}^{-2}\). The magnitude of the electric field at the center of the sphere is \(E \times 10^{9}\ \text{N}.\text{C}^{-1}\). The value of \(E\) (rounded off to one decimal place) is . \((\epsilon_0 = 8.85 \times 10^{-12}\ \text{C}^{2}.\text{N}^{-1}.\text{m}^{-2})\)

For a scalar field \(\psi(\vec{r})\) and a vector field \(\vec{A}(\vec{r})\), \(\nabla\times(\vec{A}\,\psi)\) is equivalent to the expression

Sketch of a two-dimensional vector field \(\vec{V}\) is shown below. Here, length and arrow head of the arrows denote magnitude and direction of the vector field, respectively.

Which of the following statements is correct for \( \nabla \times \vec{V} \)?

The function \(f(z)\) of the complex variable \(z\) given below,\[ f(z) = \dfrac{z^{2} - 5z + 4}{z^{3} + 4z - z^{2} - 4} \]has singular points at \(z =\)

Which of the following operators is/are self-adjoint?

As shown in the figure, circle \(C_1\) with center \(O_1\) and radius \(r_1\) touches the square \(VWXY\) at points \(P\) and \(Q\) while circle \(C_2\) with center \(O_2\) and radius \(r_2\) touches the square \(VWXY\) at points \(R\) and \(S\). The two circles touch each other at \(T\).

Given \(r_1 = 1\) cm and \(\overline{VY} = \overline{VW} = 4\) cm, \(r_2 =\) ________ cm.

Charity : P :: Retaliation : Q

Choose the appropriate pair of words P and Q that fit the analogy.

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube.

Referring to cubes shown in Panel II, which one of the options is correct?

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____

How many 3-digit numbers can be formed using three distinct single digit prime numbers?

A school has 100 students distributed among 1st to 10th standards.
Based on this, which one of the following statements is always correct?

In the sequence of tiles shown below, the missing tile indicated by the question mark should be:

"He often _____ the numbers. False claims are not going to help. Honesty _____ trust", said the manager.
Choose the option with the correct order of words to fill the blanks.

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative.

All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________

Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:

i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 is the westernmost hill.
iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
iv. Two hills are located to the west of H2.
v. The southernmost hill has at least two hills to its east.

The southernmost hill is ________.

For a particle executing simple harmonic motion, the restoring force is proportional to:

The eigenvalues of the Hamiltonian operator represent the:

The solution of Laplace’s equation satisfies which condition?

Which of the following Maxwell’s equations represents Faraday’s law of electromagnetic induction?

For an ideal gas undergoing an adiabatic process, which quantity remains constant?

Which of the following solids has a completely filled valence band and a large band gap?

Which particle is emitted during beta-minus decay?