List of top Questions asked in COMEDK UGET- 2025

Simplified expression of \[ 1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y} \]

The length of the perpendicular from the point \( P(1, -1, 2) \) to the given line \[ \frac{x + 1}{2} = \frac{y - 2}{-3} = \frac{z + 2}{4} \]

If \( A(\text{adj} A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix} \), then the value of \( |A| + |\text{adj} A| \) is equal to :

The point on the line \( x + y = 4 \) that lie at a unit distance from the line \( 4x + 3y = 10 \) is

If \[ A = \begin{bmatrix} 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 \end{bmatrix} \] then \( A + 2A^T = \)

The area of the region bounded by the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) is

Differentiate \( \log_a x \) with respect to \( a^x \)

Quadrilateral PQRS is inscribed inside a rectangle of dimensions \( 10 \, \text{cm} \times 8 \, \text{cm} \). The value of \( x \), if the area of the quadrilateral is minimum, is

On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is

A bag contains \( (n + 1) \) coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is \( \frac{7}{12} \), then the value of \( n \) is :

The function \( f(x) = \left\{ \begin{array}{ll} \frac{|x|}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{array} \right. \) is discontinuous at

If \[ y = (\sin^{-1} x)^2 + (\cos^{-1} x)^2, \] then \[ (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = \]

If \[ \binom{n+2}{8} : \, \binom{n-2}{4} = 57 : 16, \text{ then } n \text{ is } \]

The equations \( x = a(\theta + \sin \theta) \) and \( y = a(1 - \cos \theta) \) represent the equation of a curve. If \( \theta \) changes at a constant rate \( k \), then the rate of change of the slope of the tangent to the curve at \( \theta = \frac{\pi}{3} \) is

Integrating factor of the differential equation \[ \frac{dy}{dx} + y = \frac{x^3 + y}{x} \]

If \( \cos A = \frac{3}{4} \), then \( 32 \sin \frac{A}{2} \sin \frac{5A}{2} = \text{?} \)

The area of the region enclosed by the lines \( 2x + y = 10 \), \( y = 1 \), \( y = 5 \) and the y-axis is

The length of the latus rectum of a conic \( 49y^2 - 16x^2 = 784 \) is

The curve \( 4y = 3x^4 - 2x^2 \) attains

If \( A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1} \frac{1}{2} & \tan^{-1} \frac{x}{\pi} \sin^{-1} \frac{x}{\pi} & \cot^{-1} \sqrt{3} \end{bmatrix} \), then \( A - B \) is:

What is the velocity of light in vacuum if the velocity of light in a medium of refractive index 1.2 is \( v \, ms^{-1} \)?

Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability of all five persons leaving at different floors is:

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is 4, and the difference between third and fifth term is \( \frac{32}{81} \), then which of the following is not true?

Let \( A = \{x : x = 4n + 1, n \in \mathbb{Z}, 0 \leq n < 4 \} \)
Let \( B = \{x : x = 15n + 4, n \in \mathbb{N}, n \leq 3 \} \)
Let \( C = \{x : x \text{ is a prime number}, x \in A \cup B \} \)
Then the cardinal number of set \( C \) is

For real numbers \( x \) and \( y \), \( xRy \iff x - y + \sqrt{2} \) is an irrational number. Then the relation \( R \) is: