COMEDK 2025 Evening Shift

In a game, a man wins ₹ 1000 if he gets an even number greater than or equal to 4 on a fair dice and loses ₹ 200 for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his exp...

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 ...

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?

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

A geometric progression consists of an even number of terms. If the sum of all the terms is five times the sum of the terms occupying the odd places, then the common ratio of the geometric progression is

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

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

Two finite sets have $m$ and $n$ elements. The total number of proper subsets of the first set is 119 more than the total number of subsets of the second set. Find the value of $m-n$

If the standard deviation of $0,1,2,3 \cdots\cdots\cdots9$ is ' $k$ ' then the standard deviation of $10,11,12,13, \cdots\cdots\cdots\cdots19$ will be :

The angle between two lines is $45^{\circ}$ and slope of one line is $\frac{1}{4}$ then which is the possible value of the slope of the other line.

If the line $(3 x+14 y+7)+k(5 x+7 y+6)=0$ is perpendicular to $x$-axis 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 a line 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

The equation of a line passing through origin with direction angles $\frac{2 \pi}{3}, \frac{\pi}{4}, \frac{\pi}{3}$ 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 $P^{\prime}(a, b, c)$. Then $a+b+c=$

If $\sin x+\sin ^2 x=1$ then $\cos ^8 x+2 \cos ^6 x+\cos ^4 x$ is equal to :

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

The value of $\frac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}$ is :

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

For any vector $\vec{p}$, the value of $\left[2\left\{|\vec{p} \times \hat{\imath}|^2+|\vec{p} \times \hat{\jmath}|^2+|\vec{p} \times \hat{k}|^2\right\}\right]$ is

A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 2000 turns. The output power is delivered at 220 V by the transformer. If the current in the primary of the transformer is 2 A...

In a pure inductive circuit, a sinusoidal voltage $V(t)=200 \sin 250 t$ is applied to a pure inductance of $\mathrm{L}=0.02 \mathrm{H}$. The current through the coil is:

A series LCR circuit having $\mathrm{R}=44 \Omega, \mathrm{~L}=2 \mathrm{H}$ and $\mathrm{C}=25 \mu \mathrm{~F}$ is connected to a variable frequency of 220 V . What is the average power transferred to the circuit in one complete cycle if t...

The instantaneous values of alternating current and voltages in a circuit are $\mathrm{I}=\frac{3}{\sqrt{2}} \sin (200 \pi t)$ ampere and $\mathrm{V}=\frac{3}{\sqrt{2}} \sin \left(200 \pi t+\frac{\pi}{6}\right)$ volt. What is the average po...

Select the correct statement from the following:

Which of the following is correct in the case of the Bohr model of atoms?
A. Predicts continuous emission spectra for all atoms
B. Assumes that the angular momentum of electrons is quantised
C. Predicts same emission spectrum for singly ion...

The minimum energy required by a hydrogen atom in ground state to emit radiation in Paschen series is nearly:

When ${ }^{10} \mathrm{~B}_5$ nuclei are bombarded by neutrons, one of the resultant nuclei is ${ }^7 \mathrm{Li}_3$. Then the emitted particle will be:

If the mass numbers of two nuclei are in the ratio $5: 2$ and their diameters are in ratio $2: 6$. Then their nuclear densities will be in the ratio

Radium having mass number 200 and binding energy per nucleon 5.6 MeV , splits into two fragments Cadmium of mass number 112 and Hassium of mass number 108. If the binding energy per nucleon for Cadmium and Hassium is approximately 8.0 MeV ,...

A capacitor of capacitance $4 \mu \mathrm{~F}$ is charged to a potential of 24 V and then connected in parallel to an uncharged capacitor of capacitance $6 \mu \mathrm{~F}$. The final potential difference across each capacitor will be:

A network of capacitors is as shown below. If the voltage supply is 100 V , find the energy stored in the $6 \mu \mathrm{~F}$ capacitor.

$C_1=3 \mu F, C_2=6 \mu F, C_3=3 \mu F$ and $C_4=4 \mu F$

Select the correct statement from the following: The position of the centre of mass of a system :

The velocity - mass graph of body with constant linear momentum is represented by the graph:

A point marked on a ring of radius 2 cm is in contact with a horizontal plane. Now the ring is rolled forward half a revolution along the positive X - direction. Then the angle made by the displacement vector of the point with the X - axis ...

The resistance of a heating element is found to be $120 \Omega$ at room temperature which is $20^{\circ} \mathrm{C}$. If the temperature coefficient of the material of the resistor is $1.6 \times 10^{-4} C^{-1}$ and the resistance is found ...

A galvanometer having a resistance of $50 \Omega$ is shunted by a wire of resistance $10 \Omega$. If the total current is 2 A , the current passing through the shunt is:

The power dissipated across the $16 \Omega$ resistor in the circuit is 2 watts. The power dissipated in watt units across the $4 \Omega$ resistor is:

The net resistance between the points A and B in the circuit given below is:

A student measures the terminal potential difference $V$ of a cell of emf $\varepsilon$ and internal resistance $r$ as a function of the current I flowing through it. Which of the following graphs will give the values of emf $\varepsilon$ a...

The stopping potential when a metal surface is illuminated by light of wavelength $\lambda$ is 15 V . The stopping potential when the same surface is illuminated by light of wavelength $4 \lambda$ is 3 V . The ratio of threshold wavelength ...

A plot of kinetic energy of emitted photoelectrons from a metal versus the frequency of incident radiation gives a straight line, the intercept of which
A. Depends on the nature of the metal used
B. Depends on the intensity of radiation
C. ...

A wire of negligible mass having uniform area of cross section ' A ' and young modulus ' Y ' is used to suspend a point mass ' m '. The point mass executes simple harmonic motion in a vertical plane with a period ' T ', then the length of t...

Select the correct statement from the following:

A rectangular coil of 250 turns has an average area of $20 \mathrm{~cm} \times 15 \mathrm{~cm}$. The coil rotates with a speed of 60 cycles per second in a uniform magnetic field of $2 \times 10^{-2} \mathrm{~T}$ about an axis perpendicular...

A plane electromagnetic wave with frequency 40 MHz travels in free space. At a particular point in space and time, the magnetic field is $2 \times 10^{-8} T$. What will be the electric field at this point?

A bob of a simple pendulum has a mass of 4 g and a charge of $20 \mu \mathrm{C}$. If it is at rest in a uniform horizontal electric field of intensity $1000 \mathrm{Vm}^{-1}$, the angle that the pendulum makes with the vertical at equilibri...

Two electric dipoles of dipole moments $3.9 \times 10^{-30} \mathrm{Cm}$ and $5.2 \times 10^{-30} \mathrm{Cm}$ are placed in two different uniform electric fields of strengths $16 \times 10^4 \mathrm{NC}^{-1}$ and $4 \times 10^4 \mathrm{NC}...

A particle of mass 3 g and charge $60 \mu \mathrm{C}$ is released from rest in a uniform electric field of intensity $10^5 N C^{-1}$. If the value of kinetic energy attained by the particle after moving through a distance of 2 cm is $m \tim...

A uniformly charged conducting sphere of 0.2 m diameter has a surface charge density of $70 \mu \mathrm{Cm}^{-2}$. The electric flux leaving the surface of the sphere is: