COMEDK 2026 Afternoon Shift

Cards are numbered from 12 to 51 . Two cards are drawn one after the other without replacement. Find the probability that one card is a multiple of $\mathbf{6}$ and the other card is a multiple of $\mathbf{8}$.

A coffee roaster has $\mathbf{1 2}$ rare coffee beans with intensity scores ranked from $\mathbf{1}$ (mildest) to $\mathbf{1 2}$ (strongest).
You choose 7 beans at random and line them up from mildest to strongest:
$$ C_1< C_2< C_3< C_4< C_...

Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common ratio of the geometric progression is:

If $\boldsymbol{k}$ is the arithmetic mean of two given quantities and $\boldsymbol{p}, \boldsymbol{q}$ are the geometric means between the same two quantities, then $\boldsymbol{p}^{\mathbf{3}}+\boldsymbol{q}^{\mathbf{3}}$ is:

Given the sets $A=\{1,2,3\} ; B=\{2,3,5\}$ and $C=\{4,5,6\}$ identify which of the following statement is incorrect.

Let $A$ and $B$ be two subsets of $\xi=\{\mathbf{1}, \mathbf{2}, \mathbf{3},-------, \mathbf{4 4}, \mathbf{4 5}\}$ such that
$A=\{x: x$ is divisible by 3 and 4$\}$
$B=\{x: x$ is a perfect square number $\}$
Then $n(B-A)$ equals

\(\text { The range of the relation } R=\left\{(x, y): y=x+\frac{6}{x} \text {; where } x, y \in \mathbb{N} \text { and } x<6\right\} \text { is: }\)

A student needs to buy notebooks $(n)$ for a semester. Double the number of notebooks plus 5 must strictly exceed 15 , but the number of notebooks plus 10 must be no more than 22 . What is the range of notebooks they can buy?

The variance of a set of 20 observations is 16 . If 7 is added to each observation, and then $\mathbf{5}$ is subtracted from each resulting observation, what will be the new standard deviation?

Let point Q be the image of point $P(2,-1)$ in the line $3 x+5=4 y$.
Find the area of the circle that has the segment PQ as the diameter.

Let the line $L_1$ be a line passing through the point $(\mathbf{0},-\mathbf{6})$ and making an angle of $\mathbf{1 5 0}^{\circ}$ with the positive $x$-axis. Then the equation of a line $L_2$ parallel to $L_1$ and crossing the $y$-axis 2 un...

A line L passes through the point of intersection of the lines $3 x+y-10=0$ and $x-y-2=0$.
If the perpendicular distance of the line $L$ from the point $(5,1)$ is exactly $\frac{2}{\sqrt{5}}$ units, which of the following represents the cor...

Consider the lines $L_1$ and $L_2$ given by the following vector equations:
$$ L_1: \vec{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(3 \hat{i}+\boldsymbol{t} \hat{j}) \quad L_2: \vec{r}=(4 \hat{i}+\boldsymbol{a} \hat{j}-\hat{k})+\mu(2 \hat{i}+3 \h...

The equation of the perpendicular drawn from the point $A(6,1,3)$ to the line $\frac{x-1}{2}=\frac{2-y}{-1}=\frac{z-3}{2}$ is $\frac{x-6}{\boldsymbol{a}}=\frac{y-1}{\boldsymbol{b}}=\frac{z-3}{\boldsymbol{c}}$. If $\mathbf{a}, \mathbf{b}, \m...

$$ \begin{aligned} &\text { Consider two skew lines in 3D space. }\\ &M_1: \frac{x-1}{1}=\frac{2-y}{1}=\frac{z-5}{1} \text { and } M_2: \frac{x+3}{1}=\frac{y-7}{2}=\frac{z+4}{1} \end{aligned} $$
Let $L_1$ be the line of shortest distance (c...

If $2 \sin \theta=\left(x+\frac{1}{x}\right)$, then $\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=$

Suppose 'a' and 'b' are non-zero constants satisfying the following system of equations $\boldsymbol{a} \sin ^3 x+\boldsymbol{b} \cos ^3 x=\sin x \cos x$ and $\mathbf{a} \sin x-\boldsymbol{b} \cos x=0$, then $\mathbf{2}\left(\boldsymbol{a}^...

$$ \text { The expression } \frac{\tan \left(x-\frac{\pi}{2}\right) \cos \left(\frac{3 \pi}{2}+x\right)-\sin ^3\left(\frac{7 \pi}{2}-x\right)}{\cos \left(x-\frac{\pi}{2}\right) \tan \left(\frac{3 \pi}{2}+x\right)} \text { simplifies to: } $...

\(\text { If }(\vec{a}+\vec{b}) \perp \vec{b} \text { and }(\vec{a}+2 \vec{b}) \perp \vec{a} \text {, then }\)

\(\text { If the projection of } \vec{a}=5 \hat{\imath}+\hat{\jmath}+\lambda \hat{k} \text { on } \vec{b}=2 \hat{\imath}+6 \hat{\jmath}+3 \hat{k} \text { is } 4 \text { units, then } \lambda=\)

An electronic device operates at 2 MHz . The oscillating circuit has an inductance $20 \times 10^{-5} \mathrm{H}$. What is the capacitive reactance of the resonant circuit?

A source of alternating emf $\varepsilon=\varepsilon_0 \sin (\omega t)$ is connected to a capacitor. Then the instantaneous current in the circuit is: ˋ

In a given circuit, the instantaneous values of the alternating voltage and current are $V=0.5 \sin \left(80 \pi t+\frac{\pi}{3}\right)$ volt and $I=0.5 \sin (80 \pi t)$ ampere respectively. Find the average power consumed in that circuit.

What is the frequency of the electron in the first orbit of hydrogen atom of orbital radius $0.5 \times 10^{-10} \mathrm{~m}$, if its orbital velocity in that orbit is $2.2 \times 10^6 \mathrm{~ms}^{-1}$.

The main function of cadmium used in the nuclear reactor is:

The atomic mass of an element $10 X^{20}$ is 19.98170 amu. The binding energy per nucleon of that element is: [given mass of neutron = 1.00867amu and mass of proton = 1.00783 amu and 1amu = 931 MeV ]

If the ratio of the nuclear radii of two atoms is $2: 3$ then the ratio of their mass numbers is:

A hydrogen atom absorbs energy and rises to $n=3$ state from its ground state $n=1$. If the potential energy of the atom at its ground state is -13.6 eV , find the wave length emitted by it when it returns to its ground state:
{Planck's con...

A capacitor of capacitance $8 \mu \mathrm{~F}$ is fully charged by connecting it to a source of 200 V . It is then disconnected from the supply and connected to an uncharged capacitor of capacitance $4 \mu \mathrm{~F}$. The electrostatic en...

The dimensional formula for specific resistance is:

A parallel combination of ' $n$ ' cells of emf ' $E$ ' and internal resistance ' $r$ ' each, are connected across the external resistance ' $R$ '. If the external resistance ' $R$ ' is negligibly small, then the current ' $I$ ' through the ...

An electric coil is rated $400 \mathrm{~W}, 200 \mathrm{~V}$. It is cut into two equal parts and connected in parallel to the same source of 200 V . Calculate the percentage increase in energy produced per second.

The voltage - current graph for a metal wire of uniform area of cross section at two different temp $T$ and $T^{\prime}$ is shown.
Then choose the correct statement:

The basic principle used behind the working of electron microscope is:

When metal of work function 1.4 eV is exposed to a radiation, the maximum kinetic energy of the electron emitted is 0.4 eV . The stopping potential required is:

The variation of the stopping potential ( $\mathrm{V}_{\mathrm{o}}$ ) with the frequency of incident radiation( $n$ ) is as given below.
[no - threshold frequency. h - Planck's constant e-electronic charge] then the slope of the graph AB wi...

A wire, made of a certain material of length-l and area of cross section-a can withstand a maximum load $=\mathrm{W}$ without breaking. If, another wire of the same material and crosssectional area is used with double the original length, w...

When a current of 2.5 A passes through the primary coil of a transformer of 200 number turns, the magnetic flux linked with the secondary coil having 400 turns is $600 \times 10^{-6} \mathrm{~T} \mathrm{~m}^2$. Find the induced emf in the s...

A metallic circular loop is placed with its plane perpendicular to a uniform magnetic field of 0.3 T . If the radius of the loop decreases at a constant rate of $2 \mathrm{~mm} \mathrm{~s}^{-1}$, what will be the induced emf in the loop, wh...

Two point charges $P=+25 \mu C$ and $Q=-16 \mu C$ are placed 5 cm apart. Find the position of the point at which the resultant electric field is zero:

A pith ball of mass ' $m$ ' gram and charge ' $Q$ ' is suspended using a mass less silk thread near a large charged conducting metal sheet of area ' $A$ ' and surface charged density ' $\sigma$ '. If the silk thread makes an angle $\Theta$ ...

Uniform electric field of $5 \times 10^3 \mathrm{NC}^{-1}$ is maintained in the positive Y direction. Now a point charge of $2 \times 10^{-4} \mathrm{C}$ at rest is released from the origin. The kinetic energy attained by the charge when it...

In a uniform electric field $10^6 N C^{-1}$ an electric dipole of length 4 cm is placed with its axis making an angle $60^{\circ}$ with the electric field. If the dipole experiences a torque of $8 \sqrt{3} \mathrm{~N} \mathrm{~m}$.
Find the...

Bodies $P, Q, R, S$ are labelled as having charges $Q_P=0.5 \times 10^{-19} C, Q_Q=0.7 \times 10^{-19} C$, $Q_R=2.1 \times 10^{-19} C, Q_S=4.8 \times 10^{-19} C$ respectively.
Select the body having the correct charge.
[Given electronic cha...

A charge of $5 \mu \mathrm{C}$ is placed at the centre of a spherical shell $S_1$ of radius 10 cm . Now this system is enclosed inside another spherical shell $S_2$ of radius 20 cm . The ratio of the electrical flux through the surface $S_2...

Calculate the vapour pressure that can help the formation of a spherical droplet of water of radius $6.25 \times 10^{-5} \mathrm{~m}$ at $22^{\circ} \mathrm{C}$. Given: The surface tension of water at the given temperature is $7.28 \times 1...

Two neutral bodies of masses $m_1$ and $m_2$ are kept at a distance of $r \mathrm{~cm}$ from one another in a vacuum medium. A gravitational force Fracts between the two bodies. The entire set-up is then transferred, as it is, to a water me...

Two particles, one heavy and the other light, placed at 50 cm from each other, are under the influence of gravitational force of one another. If mass of the heavier particle is 4 kg and its acceleration under the influence of gravitational ...

A vessel of volume $27 \times 10^4 \mathrm{cc}$, contains a mixture of Hydrogen (molar mass $=2 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and oxygen (molar mass $=32 \mathrm{~g} \mathrm{~mol}^{-1}$ ) gas at standard temperature and pressure. If the...

Find the mass of oxygen gas with which $1.882 \times 10^{23}$ degrees of freedom are associated at N.T.P. Given: Molar mass of diatomic gas, oxygen is $32 \mathrm{~g} \mathrm{~mol}^{-1}$ and oxygen molecule possess three translational and t...