List of top Questions asked in COMEDK UGET- 2025

Solution of the differential equation \( \frac{dy}{dx} + x = 0 \) represents a family of

For any vector \( \vec{p} \), the value of \( 2\left[|\vec{p}\times \hat{i}|^2 + |\vec{p}\times \hat{j}|^2 + |\vec{p}\times \hat{k}|^2\right] \) is

For a cell \( 2M(s) + O_2(g) + 4H^+ \rightarrow 2M^{2+}(aq) + 2H_2O(l) \), the \( E^\circ_{\text{cell}} = +1.67\,V \). When \( [M^{2+}] = 1.0 \times 10^{-3} \, M \) and \( p(O_2) = 0.1 \, atm \), the EMF of the cell becomes \( +1.57 \, V \). Calculate the pH of the electrochemical cell.

If \( y = x + e^x \) then \( \frac{d^2 x}{dy^2} = \)

An unbiased die is tossed twice. What is the probability of getting a 4, 5 or 6 on the first toss and a 1, 2, 3 or 4 on the second toss?

Solve the following differential equation \( \cos^2 x \frac{dy}{dx} + y = \tan x \), given that \( y(0)=1 \). Hence find \( y\left(\frac{\pi}{4}\right) \)

If \( \tan \alpha=\frac{1}{7} \) and \( \sin \beta=\frac{1}{\sqrt{10}},\; 0<\alpha,\beta<\frac{\pi}{2} \) then \( 2\beta \) is equal to

The equation of a line passing through origin with direction angles \( \frac{2\pi}{3}, \frac{\pi}{4}, \frac{\pi}{3} \) is

Two lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and \( \frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1} \) intersect at a point. Then the value of \( k \) is

A straight line makes positive intercepts on the coordinate axes whose sum is 5. If the line passes through the point \( P(-3,4) \) then the equation of the line is

If the foci of the ellipse \( \frac{x^2}{16}+\frac{y^2}{b^2}=1 \) and the foci of the hyperbola \( \frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25} \) coincide, then the value of \( b^2 \) is

\( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1+\sqrt{\tan x}}\,dx = \)

A pot contains 5 red and 2 green balls. A ball is drawn at random from this pot. If a drawn ball is green, then a red ball is added to the pot. If a drawn ball is red, then a green ball is added to the pot, while the original ball drawn is not replaced in the pot. Now a second ball is drawn at random from the pot, what is the probability that the second ball drawn is a red ball?

If \( A = \begin{bmatrix} 4 & \lambda & -3 0 & 2 & 5 1 & 1 & 3 \end{bmatrix} \), then \( A^{-1} \) exists if:

If the line \( (3x + 14y + 7) + k(5x + 7y + 6) = 0 \) is perpendicular to x-axis then the value of \( k \) is

If the area under the curve \( y=\sqrt{a^2-x^2} \) included between the lines \( x=0 \) and \( x=a \) is 4 sq units. Then the value of \( a \) is

The image of a point \( P(3,5,3) \) in the line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is \( P'(a,b,c) \). Then \( a+b+c = \)

The function \( y=\frac{\log x}{x^3} \) is strictly increasing function for

If \( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \vec{a}\cdot\vec{b} = |\vec{a}\times\vec{b}| \) then the angle between \( \vec{a} \) and \( \vec{b} \) is

If \( P = \{5m : m \in N\} \) and \( Q = \{5^m : m \in N\} \), where \( N \) is set of natural numbers, then

How many natural numbers are there between 100 and 1000 such that at least one of their digits is 6?

Given that \( n \) number of arithmetic means are inserted between two pairs of numbers \( a,2b \) and \( 2a,b \); where \( a,b \in R \). If the \( m^{th} \) means in the two cases are the same, then the ratio \( a:b \) is equal to

\( \int_{-2}^{2} \frac{|x-3|}{x-3} dx = \)

The relation \( R = \{(1,1),(2,2),(3,3)\ \) on the set \( \{1,2,3\} \) is}