List of top Questions asked in COMEDK UGET

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:

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?

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

If \( 2y = \left[ \cot^{-1} \left( \frac{\sqrt{3} \cos x + \sin x}{\cos x - \sqrt{3} \sin x} \right) \right]^2 \ \quad \forall x \in \left( 0, \frac{\pi}{2} \right), \text{ then } \frac{dy}{dx} \text{ is equal to:}\)}

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:

A rectangular coil of length 10 cm and breadth 9 cm carries a current of 10 A. A long straight conductor carrying a current of 20 A is placed 1 cm from the coil parallel to its length and in the same plane of the coil. What will be the net force acting on the straight conductor?

For a short magnet, the magnetic field on the axial line at a distance 10 cm from its centre is \( 1.6 \times 10^{-7} \, T \). What is the magnetic field on its equatorial line at the same distance 10 cm from its centre?

By connecting two given capacitors, a technician was able to make two new capacitors having the effective capacitance \( 12.5\mu F \) and \( 2\mu F \). What would be the capacitance of the given capacitors?

What is the kinetic energy of the electron in the \( n \)th level, moving in a plane under the influence of a magnetic field \( B \)? \([ m\text{ - mass of electron},\; h\text{ - Planck's constant},\; e\text{ - electronic charge}]\)

Which of the following statement is wrong regarding the photo electric effect.

In the Young's double slit experiment, when a monochromatic light is used, fringe width obtained is 1 mm. If the wavelength is halved and the slit width is doubled, what will be the new fringe width?

What is the maximum wavelength of EM radiation required to move an electron from the valence band to conduction band of a semiconductor? [Given: Energy gap \( E_g = 1.98 \times 10^{-19} \, J \); Planck's constant \( h = 6.6 \times 10^{-34} \, Js \)]

When a metallic spherical shell of radius 20 cm is charged, the potential on its surface is found to be 5 V. The potential at a point 10 cm from the centre of the spherical shell is:

What should be the value of the inductance of the coil which is to be connected to \( 220 \, V, 50 \, Hz \) supply so that maximum current of \( 3\sqrt{2} \, A \) flows through the circuit?

A monochromatic light of wavelength \( 6000 \, \mathring{A} \) is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in A is \( \frac{1}{2} \) that of B. If the refractive index of A is \( \frac{4}{3} \), find the refractive index of B.

Two wires A and B made of same material having length 10 cm and 40 cm respectively are connected in parallel to the same source of emf 10 V. What will be the ratio of the drift velocity of the electrons in the wire A to the drift velocity in the wire B?

An EM wave of frequency \( 5 \times 10^9 \, Hz \) falls normally on a rectangular slit of width \( 3 \, cm \). What is the total angular width of the central maxima?

The separation between C and O atoms in CO is \( 0.12 \, nm \). The distance of C atom from the centre of mass is

In the expression \( P = E l^2 m^{-5} G^{-2} \) where \( E, l, m \) and \( G \) represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of \( P \) are

Across the \( 220 \, V \) source of internal resistance \( 20\Omega \), how many lamps of \( 40 \, W, 100 \, V \) can be connected in parallel so that all the lamps may glow with full brightness.

de Broglie wave length associated with an electron accelerated through a potential difference \( V \) is \( \lambda \). If the accelerating potential is halved, what will be the new wavelength associated with the charged particle?

An open pipe is in second harmonic with frequency \( f_1 \). One end of the tube is closed and frequency is increased to \( f_2 \) and it resonates again with nth harmonic. For what value of \( n \), the ratio of \( \frac{f_1}{f_2} \) is \( \frac{4}{5} \)?

If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

The resistance of the conductor is \( \sqrt{3}\Omega \) the angle made by the V-I graph with the voltage axis is \( \theta \)