List of top Questions asked in GATE MN- 2026

Given \( \mathbf{x} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} \), \( \mathbf{b} = \begin{pmatrix} -16 \\ -3 \\ 7 \end{pmatrix} \), \( \mathbf{P}^{-1} = \begin{pmatrix} e & -6 & -7 \\ f & 9 & 11 \\ -1 & -2 & g \end{pmatrix} \) and \( \mathbf{P}\mathbf{x} = \mathbf{b} \).
If \( \mathbf{P}\mathbf{y} = \mathbf{d} \) with \( \mathbf{y} = \begin{pmatrix} y_1 \\ y_2 \\ y_3 \end{pmatrix} \) and \( \mathbf{d} = \begin{pmatrix} -16 \\ 0 \\ 7 \end{pmatrix} \), the value of \( y_2 \) is

The in-situ stresses are determined by the Flat-jack method by making three slots (P, Q, and R) on the wall (ABCD) of a mine gallery as shown. The in-situ stresses \( \sigma_P \), \( \sigma_Q \), and \( \sigma_R \) are determined at slot-P, slot-Q, and slot-R, respectively. If \( \sigma_P > \sigma_Q \), and \( \sigma_R = 0 \), the shear stress on the wall 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 ________.

Exacerbate : Mitigate ::

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

The igneous intrusion along the bedding plane of the coal seam, as indicated by P, is known as

The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

Given the data in the following table, Newton's divided difference interpolation polynomial is
\[ y = b_0 + b_1(x-2) + b_2(x-2)(x-2.5) \]
If the values of \( b_0 \) and \( b_1 \) are 3 and 1, respectively, then the value of \( b_2 \) is

x	2.0	2.5	3.0
y	3.0	3.5	5.0

Following observations were taken using a Tacheometer with staff held vertical. The additive and multiplying constants of the instrument are 0 and 100, respectively. The reduced level (RL) of the staff station R, in \(m\), is . (rounded off to two decimal places)

Instrument station	Staff station	Staff reading (m)	Vertical angle	Remarks
P	Q	1.4, 2.7, 3.9	7°	RL of Q = 102 m
P	R	2.1, 2.8, 3.6	5°

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

The borehole data for resource estimation for an iron ore deposit are shown.

The average grade of the deposit, in %, is . (rounded off to two decimal places)

Suresh said, "I did it yesterday."
Which one of the following options is the correct form of this sentence in indirect speech?

Two blocks P and Q weighing \(100\ \text{kN}\) and \(200\ \text{kN}\), respectively, are connected by a string passing through a massless and frictionless pulley as shown. The friction coefficient between blocks P and Q is 0.4, and that between block Q and surface is 0.3. The minimum force, F, in kN, required to pull the block Q, is . (answer in integer)

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.

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 ________.

Match the distribution with its corresponding probability density/mass function.

Distribution type	Probability 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) \( f(x) = \lambda\exp(-\lambda x), \ x>0 \)

In remote sensing, the order of the wavelength bands of electromagnetic radiation used for data acquisition is

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

The observations from a correlation survey are shown. If the coordinates of points C and D are (East: 375 m, North: 1120 m) and (East: 376 m, North: 1121 m), respectively, the whole circle bearing of the line EF is