List of top Questions asked in GATE MN- 2026

Match the distribution with its corresponding probability density/mass function.
Distribution typeProbability density/mass function
(P) Binomial Distribution(1) \( f(x) = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\left(-\dfrac{1}{2}\left(\dfrac{x-\mu}{\sigma}\right)^2\right), \ \sigma>0 \)
(Q) Poisson Distribution(2) \( f(x) = \dbinom{n}{x}p^x(1-p)^{n-x}, \ x=0,1,2,...,n \)
(R) Normal Distribution(3) \( f(x) = \dfrac{\mu^x}{x!}\exp(-\mu), \ x=0,1,2,... \)
(S) Exponential Distribution(4) \( f(x) = \lambda\exp(-\lambda x), \ x>0 \)
If \( I \) is an identity matrix, the polynomial equation that satisfies the Cayley-Hamilton theorem for the matrix \[ P = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix} \] is
Which one of the following is a non-linear, second-order, and first-degree differential equation?
As per the Mohs scale of hardness, the correct sequence is
As per the UNFC mineral resources classification system, the highest category of resource is indicated by
In a population, patients who have high cholesterol also have high blood pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,

1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.

Then the number of patients who have both diabetes and high BP is
Exacerbate : Mitigate ::

Choose the option with the correct pair of words to fill the blank.
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?

Four people P, Q, R, and S, of different ages, make the following observations.

P: I am younger than S.
Q: I am neither the youngest nor the oldest.
R: P is older than me.

Based on these observations, the youngest person is .
Circles \(C_1\), \(C_2\), and \(C_3\), with centers \(O_1\), \(O_2\), and \(O_3\), and radii \(r_1\), \(r_2\), and \(r_3\), respectively, touch each other as shown in the following figure. Given \(r_1 = 2\) cm, \(r_2 = 1\) cm and the angle \(\angle O_1O_3O_2\) is \(90^\circ\), \(r_3 = \) cm.

To continue the sequence of tiles shown, the tile indicated by the question mark should be:
The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?
A coin with heads facing up is shown as (H) and a coin with tails facing up is shown as (T).
Six coins are placed in the Starting Arrangement, as shown in the figure below. A "step" is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.
Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
Suresh said, "I did it yesterday."
Which one of the following options is the correct form of this sentence in indirect speech?
Which gas is mainly responsible for explosions in coal mines?
The primary purpose of mine ventilation is to:
The Mohr–Coulomb failure criterion is mainly used to describe:
The instrument commonly used for measuring horizontal and vertical angles in mines is:
Which one of the following is the most widely used method for coal extraction in surface mines?
In bord and pillar mining, the main load-bearing elements are:
The machine used for drilling blast holes in hard rock mines is: