List of top Questions asked in COMEDK UGET

A gas is taken through the cycle $ A \to B \to C \to A $, as shown in the figure. What is the net work done by the gas?

In the figure, pendulum bob on the left side is pulled aside to a height $ h $ from its initial position. After it is released, it collides with the right pendulum bob at rest, which is of the same mass. After the collision, the two bobs stick together and rise to a height

Two wires of the same material having radius in ratio 2 : 1 and lengths in ratio 1 : 2. If the same force is applied on them, then the ratio of their change in length will be
A thin circular ring of mass $ M $ and radius $ R $ rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity $ \omega $. Four small spheres each of mass $ m $ (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be
One end of the string of length $ l $ is connected to a particle of mass $ m $ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $ v $, the net force on the particle (directed towards the center) will be (T represents the tension in the string)
A transistor is connected in CE configuration. The collector supply is 10 V and the voltage drop across a resistor of 1000 $ \Omega $ in the collector circuit is 0.5 V. If the current gain factor is 0.96, then the base current is
A particle is projected at an angle $30^\circ$ with horizontal having kinetic energy $K$. The kinetic energy of the particle at the highest point is.
The ratio of amplitude of magnetic field to the amplitude of electric field of an electromagnetic wave propagating in vacuum is
A capacitor of capacity 2 $ \mu F $ is charged up to a potential 14 V and then connected in parallel to an uncharged capacitor of capacity 5 $ \mu F $. The final potential difference across each capacitor will be
The mass density of a nucleus varies with mass number $ A $ as
The phase difference between displacement and velocity of a particle in simple harmonic motion is
The mean energy per molecule for a diatomic gas is
If $2f(x^2) + 3f\left( \frac{1}{x^2} \right) = x^2 - 1$, for $x \in \mathbb{R} - \{0\}$, then $f(x^8)$ is equal to

The general solution of $ 2 \cos 4x + \sin^2 2x $= 0  is

The expression $ \frac{2 \tan A}{1 - \cot A} + \frac{2 \cot A}{1 - \tan A} $ can be written as

If $ \cos A = m \cos B $ and $ \cot \left( \frac{A+B}{2} \right) = \lambda \tan \left( \frac{B-A}{2} \right), $  then $ \lambda \text{ is equal to} $

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failures will be
The solution of the differential equation $ \frac{dy}{dx} \tan y = \sin(x + y) + \sin(x - y) $ is
Find $ nC_{21} $, if $ nC_{10} = nC_{12} $
The general solution of $ \left( \frac{dy}{dx} \right)^2 = 1 - x^2 - y^2 + x^2y^2 $ is
The coefficient of $x^{29}$ in the expansion of $ (1 - 3x + 3x^2 - x^3)^{15} $ is}
The differential equation of all non-vertical lines in a plane is
In the expansion of $ (1 + 3x + 3x^2 + x^3)^{2n} $, the term which has the greatest binomial coefficient, is
The value of $ \frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + ... + \frac{99}{100!} $ is equal to
The sum of $ n $ terms of the series, $ \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + ... $ is