List of top Questions asked in GATE AG- 2026

Two square matrices \( \mathbf{A} \) and \( \mathbf{B} \) of the same order are such that \( \det[\mathbf{A} \cdot \mathbf{B}] = -80 \) and \( \det[\mathbf{A}] = 5 \). Here, \( \mathbf{A} \cdot \mathbf{B} \) is the product of \( \mathbf{A} \) and \( \mathbf{B} \). The value of \( \det[\mathbf{B}^T] \) is

A plough attachment, which is a miniature plough bottom that cuts a narrow, shallow furrow ahead of the shin and moves trash and roots toward the main furrow so that they are completely covered by the mouldboard, is called as

Identify the following partial differential equations in the given order based on their generic form where \( c \) is a constant, and \( u_1 \) and \( u_2 \) are functions of \( (x, t) \) and \( (x, y) \), respectively:
(i) \[ \frac{\partial^2 u_1}{\partial t^2} = c^2 \frac{\partial^2 u_1}{\partial x^2} \] (ii) \[ \frac{\partial u_1}{\partial t} = c^2 \frac{\partial^2 u_1}{\partial x^2} \] (iii) \[ \frac{\partial^2 u_2}{\partial x^2} + \frac{\partial^2 u_2}{\partial y^2} = 0 \]

A box contains one red ball and two blue balls. One ball is drawn at random, its colour is noted and the ball is returned to the box. The process is repeated. In the first two draws, blue ball appears each time. The probability of drawing blue ball again in the third draw is

The general solution to the ordinary differential equation \( \dfrac{d^2y}{dx^2} = \cos 2x \) 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 \( \angle O_1 O_3 O_2 \) 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 ______.

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 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 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 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 below, is ________.
Starting Arrangement: (H) (H) (H) (T) (T) (T)
Final Arrangement: (T) (T) (T) (H) (H) (H)

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

To continue the sequence of tiles shown, the tile indicated by the question mark should be

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

Which plant hormone is mainly responsible for apical dominance?

Which nutrient is most commonly deficient in Indian soils?

The duty of water is defined as:

In Mendelian inheritance, the phenotypic ratio of a dihybrid cross is:

The permanent wilting point of soil corresponds approximately to which soil moisture tension?

Which one of the following crops is most sensitive to photoperiod?

The efficiency of irrigation system is maximum in: