COMEDK 2025 Morning Shift

Vasant and Jothi play a game with a coin. Vasant stakes ₹ 1 and throw the coins four times.
If he throws four heads, he gets his stake and ₹3 from Jothi.
If he throws only three heads and they are consecutive, he gets his stake and ₹2 from ...

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

The solution set of the system of inequalities $5-4 x \leq-7$ or $5-4 x \geq 7, x \in R$ is

$0.2+0.22+0.022+\ldots \ldots \ldots$. up to $n$ terms is equal to

The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in rev...

Let R be a relation on natural numbers defined by $x+2 y=8, x, y \in N$. The domain of R is

Identify the correct statement

If $n(A)=3$ and $n(B)=7$ and $A \subseteq B$ then the number of elements in $A \cap B$ is equal to

The variance of 25 observations is 8 . If each observation is multiplied by 3 , then the new variance of the resulting observations is

If two vertices of a triangle are $(3,-2)$ and $(-2,3)$ and its orthocentre is $(-6,1)$.
Then the difference between ordinate and abscissa of the third vertex of the triangle is

A line $L_1$ passes through the points $(h, k),(1,2)$ and $(-3,4)$. The points $(4,3)$ and $(h, k)$ lie on the line $L_2$. Given $L_1 \perp L_2$ then $(k-h)$ equals to

Distance of the point $(-2,3)$ from the line $12 x-5 y-2=0$ is $\frac{41}{k}$. Then the value of $k$ is

P is a point on the line joining the points $(3,5,-1)$ and $(6,3,-2)$. If $y$ coordinate of point P is 2 , then $x$ coordinate will be

The value of $\lambda$ for which the angle between lines $\vec{r}=\hat{\imath}+\hat{\jmath}+\hat{k}+p(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})$ and $\vec{r}=(1+q) \hat{\imath}+(1+q \lambda) \hat{\jmath}+(1+q) \hat{k}$ is $\frac{\pi}{2}$

The value of $\frac{1}{2 \sin 10^{\circ}}-2 \sin 70^{\circ}$ is

If $\sin A+\sin B=-\frac{21}{65}, \cos A+\cos B=-\frac{27}{65}$ and $\pi

If $\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . . \tan 88^{\circ} \tan y^{\circ}=1$ then $\cot (x+y)=$

The magnitude of the projection of the vector $-\hat{\imath}+2 \hat{\jmath}-\hat{k}$ 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 vect...

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $a \neq 0$ and $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c}),|\vec{a}|=|\vec{c}|=1,|\vec{b}|=4$ and $|\vec{b} \times \vec{c}|=\sqrt{15}$ if $\vec{b}-2 \vec{c}=\lambda \vec{a}$ t...

An LCR series ac circuit is at resonance with 10 V each across $\mathrm{L}, \mathrm{C}$ and R . If the resistance is halved, the respective voltage across $R, C$ and $L$ are

An ideal inductor is connected across a capacitor. Oscillations of energy $K$ are set up in the circuit. The capacitor plates are slowly drawn apart such that the frequency of oscillations is quadrupled. The work done in the process is

A bulb of resistance 280 Ohm is supplied with a voltage $\mathrm{V}=400 \sin \pi \mathrm{t}$. The peak current is

If $R$ and $L$ denote resistance and inductance of a material, then the dimension of $L R$ will be:

In a nuclear fusion reaction, two nuclei, $A$ and $B$ fuse to produce a nucleus $C$, releasing an amount of energy $\Delta \mathrm{E}$ in the process. If the mass defects of the three nuclei are $\Delta M_A, \Delta M_B$ and $\Delta M_C$ res...

According to Bohr's theory of hydrogen atom, the speed of the electron, its energy and radius of its orbit vary with the principal quantum number $n$, respectively as

Which, of the following is true of the Balmer series of the hydrogen spectrum?
a. The series is in the visible region.
b. The entire series falls in the ultraviolet region
c. The entire series falls in the infrared region
d. The series is p...

Two capacitors $\mathrm{C}_1$ and $\mathrm{C}_2$ are charged to 100 V and 120 V respectively. It is found that upon connecting them together in parallel, the potential on each one of them is zero. Therefore

A bomb of mass 20 kg at rest explodes into two pieces of masses 12 kg and 8 kg . If the velocity of 8 kg mass is $6 \mathrm{~ms}^{-1}$, then the kinetic energy of the other mass is:

From a circular disc of radius 2 R , a smaller circular disc is cut with radius of the larger disc as its diameter. The centre of the hole is at a distance of $R$ from the centre of the original disc. The distance of the centre of mass of t...

A student measures the terminal potential difference $V$ of a cell (emf $\varepsilon$ and internal resistance $r$ ) as a function of current I flowing through it, and draws V versus I graph. The slope and intercept of the graph respectively...

If voltage across a bulb rated $220 \mathrm{~V}, 50 \mathrm{~W}$ drops by $5 \%$ of its rated value, the percentage of the rated value by which the power would decrease is

The resistance of a wire is 5 ohm at $25^{\circ} \mathrm{C}$ and 7 ohm at $100^{\circ} \mathrm{C}$. The resistance of the wire at $0^{\circ} \mathrm{C}$ is

Two identical conductors of lengths 1 and 31 respectively are maintained at the same temperature. They are given potential differences in the ratio $1: 3$. The ratio of their drift velocities is

A galvanometer of resistance $50 \Omega$ is connected to a battery of 4 V along with a resistance of $3950 \Omega$ in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 10 ...

Emission of electrons from a metal plate illuminated with monochromatic electromagnetic radiation will always take place provided

A particle of mass $M$ at rest decays into masses $m_1$ and $m_2$ with non-zero velocities. The ratio of de Broglie wavelengths $\lambda_1$ and $\lambda_2$ of the particles is

The magnetic flux $\phi$ through a stationary loop of wire having a resistance R varies with time as $\phi=4 t^2+3 t$. The average emf and total charge flowing in the loop in the time interval $t=0$ to $t=\tau$ respectively are

The electric and magnetic fields associated with an electromagnetic wave propagating along +z axis, can be represented by

Two identical conducting balls having positive charges $q_1$ and $q_2$ are separated by a distance $r$. If they are made to touch each other and then separated to the same distance, the force between them will be

Point charges $-3 Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is

For the charge configuration shown here, which of the following is not true?

A cylindrical tank 0.5 m in radius, rests on a platform 1.5 m high. Initially the tank is filled with water to a height of 2.5 m . A small plug whose area is $10^{-4} \mathrm{~m}^2$ is removed from an orifice located on the side of the tank...

The radius of earth is $R$ and acceleration due to gravity on its surface is $g$. The height at which the acceleration due to gravity becomes $\frac{g}{8}$ is:

A planet is 121 times heavier than moon and has a diameter 9 times that of moon. If the escape velocity on the planet is $v$, then the escape velocity on the moon will be:

A block of metal A is connected in series with another block of metal B such that the two metal blocks have the same area of cross sections. The thermal conductivity of metal A is K and the free end of metal A is at $80^{\circ} \mathrm{C}$....

The mean energy per molecule for a diatomic gas is:

The ratio of specific heat capacities at constant pressure to that at constant volume for a given mass of a gas is $\frac{5}{2}$. If the percentage increase in volume of the gas while undergoing an adiabatic change is $\frac{3}{2}$, then th...

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure below. It absorbs 60 J of heat during the part AB and rejects 80 J of heat during CA . There is no heat exchanged during the process $\mathrm{BC} . \mathrm...

A stone is dropped from a height $h$. It hits the ground with a certain momentum ' $p$ '. If the same stone is dropped from a different height h ' such that percentage change in momentum is $41.4 \%$, then the height from which the stone is...