COMEDK 2026 Morning Shift

A teacher has two jars of candy on her desk:
Jar 1: Contains 3 Strawberry candies and 2 Orange candies.
Jar 2: Contains 1 Strawberry candy and 4 Orange candies.
The teacher randomly picks two candies from Jar 1 and drops them into Jar 2.
Th...

Samhita faces a three-headed dragon. She wins a "Tactical medal" if she manages to defeat exactly one of the three heads.
The battle proceeds head-by-head under the following conditions:

The probability of defeating the first head is $\fra...

An engineering team is testing a new prototype drone. The drone has constant success rate of $\frac{\mathbf{2}}{\mathbf{7}}$ for every autonomous landing attempt. Two engineers, Sarah and Swarna, take turns initiating the landing sequence, ...

The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 14 . Find the numbers.

Let ' $\boldsymbol{a}$ ' and ' $\mathbf{b}$ ' be two numbers where $\boldsymbol{a}<\boldsymbol{b}$. The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 24 . Then ...

Consider the following list of ordered pairs: $(1,0),(-2,-1),(7,-6),(-3,4)$ and $(0,2)$
Which of the following options correctly identifies only those pairs that are NOT elements of the relation $R=\{(x, y): y=1-|x| ; x, y \in \mathbb{Q}\}$...

The set expression $A \cup\left(B \cap\left(A^{\prime} \cup B^{\prime}\right)\right)$ is equivalent to

If $A=\{x: x$ is the first three odd numbers $\}$
$B=\{2 x+3: 0 \leq x<5, x \in \mathbb{N}\}$, then which of the following is true

If for a distribution of 20 items, $\sum(x-4)=10$ and $\sum(x-4)^2=85$ then the standard deviation is:

Distance between $8 x+15 y-20=0$ and $8 x+15 y+14=0$ is:

A straight line passes through the point $P\left(\log _2 16, \log _3 27\right)$ such that the portion of the line intercepted between the co-ordinate axes is divided by $P$ in the ratio $1: 2$ internally (starting from the $x$-axis). Then t...

$$ \begin{aligned} &\text { Find the co-ordinates of the orthocentre of the triangle formed by the lines }\\ &\begin{aligned} & L_1: y-x=2 \\ & L_2: y+2 x=8 \\ & L_3: 3 y-x=18 \end{aligned} \end{aligned} $$

If a straight line passing through a fixed point $(a, b)$, where $\boldsymbol{a}, \boldsymbol{b}>\mathbf{0}$, makes positive intercepts OA and OB on the coordinate axes, then the least value of $\mathbf{O A}+\mathbf{O B}$ is:

Let L be the foot of the perpendicular drawn from the point $P(5,3 k-7,-4)$ to the YZ - plane. If the distance of point L from the origin is $\sqrt{41}$ units, then the possible value of ' $\boldsymbol{k}$ ' is:

The angle between the two lines whose direction cosines satisfy the relations $\boldsymbol{l}+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0}$ and $\boldsymbol{l}^{\mathbf{2}}=\boldsymbol{m}^{\mathbf{2}}+\boldsymbol{n}^{\mathbf{2}}$ is

Let $\mathbf{P}$ be a point on the line $L_1: \frac{x-2}{2}=y+1=\frac{z-1}{2}$ such that its distance from the point $A(2,-1,1)$ is 6 units.
Given that $\boldsymbol{x}$-coordinate of $\mathbf{P}$ is greater than $\mathbf{2}$,
Find the coord...

\(\text { The expression } \frac{1-\tan ^2\left(\frac{\pi}{4}-A\right)}{1+\tan ^2\left(\frac{\pi}{4}-A\right)} \text { equals }\)

If $\sin A+\sin 2 A=x$ and $\cos A+\cos 2 A=y$ then the value of the expression $\left(x^2+y^2\right)\left(x^2+y^2-3\right)$ equals

\(\text { The direction ratios of the vector }(\hat{\imath}+\hat{\jmath}) \times(\hat{\jmath}+\hat{k}) \text { are }\)

Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ internally and externally in the ratio 2:3 respectively, then $\overrightarrow{O R}$ and $\overrightarrow{O S}$ are perpe...

An AC generator having 400 turns and an area of cross section of $2 \times 10^{-3} \mathrm{~m}^2$ rotates with an angular speed of $200 \pi \mathrm{rad} \mathrm{s}^{-1}$ in a uniform magnetic field of strength 0.4 T . The generator is conne...

A solenoid having resistance $R=60 \Omega$ and inductance $L=0.4 \mathrm{H}$ is connected to an AC source $V=100 \sqrt{2} \sin 200 t$.
Find the maximum current.

If wattless current flows in an AC circuit, then the circuit is:
A. LR circuit
B. Purely capacitive circuit
C. Purely resistive circuit
D. LCR circuit

An atom has a single electron. Its ground state energy is -30 eV and its first excited state energy is -8 eV . The atom is bombarded with a stream of photons, each of energy 15 eV .
Assuming the atom being in the ground state, which of the ...

Two deuterons are fused to form one alpha particle. If binding energy per nucleon of deuterium is 1.05 MeV and that of alpha particle is 7 MeV , what is the energy released in the formation of one alpha particle from the fusing of two deute...

An atom with one electron has ionization energy of 24 eV . An electron in this atom makes a transition from an excited energy level, where $\mathrm{E}=-15 \mathrm{eV}$, to the ground state. What is the wavelength of the emitted photon from ...

A mercury-198 nucleus is bombarded by a neutron, which causes a nuclear reaction
\(n_0^1+\mathrm{Hg}_{80}^{198} \longrightarrow A u_{79}^{197}+X\)
What is the unknown product particle $X$ ?

A nucleus of uranium -235 absorbs a slow neutron and undergoes nuclear fission according to the reaction: ${ }_{92}^{235} U+{ }_0^1 n \rightarrow{ }_{56}^{141} B a+{ }_{36}^{92} K r+3{ }_0^1 n+Q$
If the average energy released per fission i...

What is the charge on $15 \mu F$ in the circuit given?

A motor cyclist starts from the top of an inclined plane of height $h$ to go around a globe of death trap of radius $r$. The ratio of minimum height ' $h$ ' of the inclined plane to the radius ' $r$ ' of the death globe in order to go aroun...

Genetic Engineering is related to the principle of

A wire of length 1 m has a resistance of $20 \Omega$ at $0^{\circ} \mathrm{C}$. It is uniformly stretched so that its length increases by $21 \%$. Assuming the volume of the wire remains constant, the percentage change in resistance is $n \...

Current in a conductor is expressed as $I=8 t^3+3 t^2+2$, where current I is measured in amperes and time t is measured in seconds. What is the charge that flows through a cross-section of the conductor between time $t=1 \mathrm{~s}$ to $t=...

A current of 3 A enters one vertex P of an equilateral triangle PQR having three resistors of $1 \Omega$ each forming the sides of the equilateral triangle as shown. The value of $i_2$ in amperes is:

In the given circuit, an ideal voltmeter connected across $6 \Omega$ reads 5 V . The internal resistance $r$ of each cell is:

A monochromatic beam of photons of intensity to $1.5 \mathrm{Wm}^{-2}$ and energy 11.2 eV is incident on a material of work function 4.8 eV . What is the maximum speed of photoelectrons emitted due to photoelectric effect if, only $0.53 \%$...

What is the ratio of de Broglie wavelength of an electron to that of proton if the velocity of proton is $\frac{1}{6}$ the velocity of electron?

A light rod of length 1 m is suspended from ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of material $X$ and is of cross-section $0.1 \mathrm{~cm}^2$. and the other of materi...

A square loop of wire 2.2 cm on each side contains 2 turns and has a total resistance of $0.0002 \Omega$. It is located 22 cm from a long straight current carrying wire. If the current in the straight wire is increased at a steady rate from...

A circular coil of radius 7 cm and 40 turns is rotated about its vertical diameter with an angular speed of 40 radians per second in a uniform horizontal magnetic field of $4 \times 10^{-2} T$. What is the maximum current induced in the coi...

Which of the following is incorrect for displacement current
A. Displacement current exists only when electric field changes with time
B. Displacement current obeys ohm's law
C. Displacement current produces magnetic field just like conduct...

A uniform electric field $E=3 \hat{i}+6 \hat{j}+\hat{k}$ passes through a closed cuboidal surface. One face of the cuboid has an area $4 m^2$ and an outward unit normal given by $\frac{2 \hat{i}+2 \hat{j}+3 \hat{k}}{\sqrt{17}}$. If the elec...

Two-point charges of equal magnitude 0.01 C and opposite in sign are separated by 0.2 mm , forming an electric dipole. The electric dipole moment of the dipole is:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $45^{\circ}$ with each other. When the system is immersed in a liquid of relative density 0.8 , the angle between the strings remains unch...

Two conducting spherical shells $A$ and $B$ of radii 4 cm and 6 cm respectively are placed with their centres 17 cm apart in air. Initially, sphere A was given a -20 nC charge while sphere B was uncharged. The spheres are then connected by ...

Two charges 1 C and 2 C are placed at coordinates $(0,3)$ and $(4,3)$ respectively in an XY plane. What is the work done to put a 30 C charge at the origin of the coordinate system?

Point charge $\sqrt{2} C, \sqrt{2} C$, and $-2 C$ are placed at the three vertices of a right-angled triangle in air. [as shown in the figure below]
What is the electric field at a point $P$ on the hypotenuse that is equidistant from all th...

A small hollow vessel which has a small circular hole of radius $r$ in its base, is immersed in a tank of oil of density $\rho$ and surface tension $T$. The oil will penetrate into the vessel at a depth of

Two spheres of masses $M_1$ and $M_2$ are in air separated by a distance of d m . The gravitational force of attraction between them is $F$. If the space around the masses is filled with a liquid of density $\rho$, the force between the mas...

A body is projected vertically upwards from the surface of earth with a velocity ' $v$ ' to reach a height of $10 R$, where $R$ is the radius of the earth, then $v$ is