List of top Questions asked in GATE MN- 2026

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 ________.

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

Exacerbate : Mitigate ::

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

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

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)

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?

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.

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 .

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

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

CD = 3.0 m
CE = 4.2 m
\( \angle DEC = 1'' \)
\( \angle DEF = 170^{\circ} 20' \)

Let \( \hat{i} \) and \( \hat{j} \) be the unit vectors in the x and y direction, respectively. The divergence \( (\nabla . \vec{F}) \) of \( \vec{F} = x^2y\hat{i} + y^3x\hat{j} \) at the point \( (3,2) \) is

A circular curve having a radius of curvature of \(1000\) m is set out by connecting two straights with a deflection angle of \(60^{\circ}\). The apex distance, in \(m\), is . (Rounded off to three decimal places)

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?

Which one of the following is a non-linear, second-order, and first-degree differential equation?

Which of the following statements about Fourier series is/are correct?

Using linear regression (least squares), the best-fit line for the given dataset is \(y = 2.2x + 2.3\). Given the residual sum of squares is 25.8, the coefficient of determination \((r^2)\) is . (rounded off to two decimal places)

x	2	3	4	5
y	8	9	7	16

The value of the determinant of the Hessian of \( f(x, y) = x^2 + y^2 + xy - 8x - 7y \) at its stationary point is