List of top Questions asked in COMEDK UGET- 2025

Two volatile liquids X and Y form an ideal solution at 298 K and have vapour pressures equal to 100 mm and 200 mm of Hg respectively in their pure state. The mole fraction of X in the solution is 0.4 and the mole fraction of Y in the vapour phase is \( \frac{a}{20} \). Calculate the value of \(a\).
0.4 g of propane burns completely at 300 K in a bomb calorimeter. The temperature of the calorimeter and surrounding water rises by \(0.4^\circ C\). If the heat capacity of the calorimeter and contents is \(24 \, kJ \, K^{-1}\), what is the enthalpy for the reaction? Assume that propane gas shows ideal behaviour.
Match the metals in Column II with their characteristic properties given in Column I.
What volume of \(0.2M \, CH_3COOH\) needs to be added to \(100 \, ml\) of \(0.4M \, CH_3COONa\) solution to prepare a buffer of pH equal to \(4.91\)? Given that \(pK_a\) of \(CH_3COOH\) is \(4.76\).
If \( f(x) = \left(\frac{3+x}{1+x}\right)^{2+3x} \), then \( f'(0) = \)
The value of \( \lambda \) for which the angle between lines \( \vec{r} = \hat{i} + \hat{j} + \hat{k} + p(2\hat{i} + \hat{j} + 2\hat{k}) \) and \( \vec{r} = (1+q)\hat{i} + (1+q\lambda)\hat{j} + (1+q)\hat{k} \) is \( \frac{\pi}{2} \)
If \( A(t) = \begin{pmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{pmatrix} \), then the product of \( A(t) \) and \( A(-t) \) is
The range of \( x \) for which the equation \( \sin^{-1}\left(\frac{2x}{1+x^2}\right) = 2\tan^{-1}(x) \) holds true
The value of \( \displaystyle \lim_{x \to 0} \frac{(1-x)^n - 1}{x} \) is
If \( f(x) = \begin{cases} \frac{1-x^m}{1-x}, & \text{for } x \neq 1 \\ 2m-1, & \text{for } x = 1 \end{cases} \) and the function is discontinuous at \( x = 1 \), then
If \( \displaystyle \int \frac{dx}{(x+2)(x^2+1)} = p\log|x+2| + q\log|x^2+1| + r\tan^{-1}x + c \), then \( p+q+r = \)
If the third and fourth terms in the expansion \( (2x + \frac{1}{8})^{10} \) are equal, then the value of \( x \) is
If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is
A solid \(S\) is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are \(x\) cm. The height of the cylinder is \((20-4x)\) cm and the volume of \(S\) is \(V=\frac{1}{3}\pi y\). Find the maximum value of \(y\).
The magnitude of the projection of the vector \( -\hat{i} + 2\hat{j} - \hat{k} \) on the \(z\)-axis is
A line \(L_1\) passing through the point \(A\) with position vector \( \vec{a} = 4\hat{i} + 2\hat{j} + 2\hat{k} \) is parallel to the vector \( \vec{b} = 2\hat{i} + 3\hat{j} + 6\hat{k} \). The length of the perpendicular drawn from a point \(P\) with position vector \( \vec{p} = \hat{i} + 2\hat{j} + 3\hat{k} \) to \(L_1\) is
In an entrance test, there are multiple choice questions. There are four possible answers to each question of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is
If \( \frac{x-1}{3+i} + \frac{y-1}{3-i} = i \) then \( (y,x) = \)
Let \(R\) be a relation on natural numbers defined by \(x+2y=8,\ x,y\in N\). The domain of \(R\) is
Identify the correct statement
Oil from a conical funnel is dripping at the rate of \(5\ \text{cm}^3/\text{s}\). If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is
The solution of the differential equation \( \frac{dy}{dx}+y\log y\cot x=0 \) is
Vasant and Jothi play a game with a coin. Vasant stakes INR 1 and throws the coin four times. If he throws four heads, he gets his stake and INR3 from Jothi. If he throws only three heads and they are consecutive, he gets his stake and INR 2 from Jothi. If he throws only two heads and they are consecutive, he gets his stake and INR 1 from Jothi. In all other cases Jothi takes the stake money. Find the expectation of Vasant's gain.
If \( \tan x^\circ \tan 2^\circ \tan 3^\circ \cdots \tan 88^\circ \tan y^\circ = 1 \), then \( \cot(x+y)= \)
A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must have at least one bottle of each variety is