COMEDK 2025 Afternoon Shift

A bag contains $(n+1)$ coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is $\frac{7...

Three bags contain a number of red and white balls are as follows.
Bag I: 3 red balls
Bag II: 2 red balls and 1 white ball
Bag III: 3 White balls
The probability that bag $i$ will be chosen and a ball is selected from it is $\frac{i}{6}, i=...

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 o...

The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true

For real numbers $x$ and $y, x R y \Leftrightarrow x-y+\sqrt{2}$ is an irrational number. Then the relation R is:

If $A=\{1,2,4\} \quad B=\{2,4,5\} \quad C=\{2,5\}$ then $(A-B) \cap(B-C)=$

Let $A=\{x: x=4 n+1, n \in Z, 0 \leq n<4\}$
$$\begin{aligned} & B=\{x: x=15 n+4, n \in N, n \leq 3\} \\ & C=\{x: x \text { is a prime number }, x \in A \cup B\} \end{aligned}$$
Then the cardinal number of set C is

The inequality representing the following graph is

If the mean of $4,7,2,8,6$ and $k$ is 7 . Then the mean deviation from the mean of these observations is

The point on the line $x+y=4$ that lie at a unit distance from the line $4 x+3 y=10$ is

In a triangle $A B C$ the coordinate of the vertex $A$ is $(1,2)$. Equations of the median through $B$ and $C$ are respectively $x+y=5$ and $x=4$. Then the equation of side $\mathbf{A B}$ is

The line $A B$ passes through the point $P(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5: 3$ by the point $P$. Given that the point A lies on $x$-axis and B lies on $y$-axis, then the ...

The length of the perpendicular from the point $P(1,-1,2)$ to the given line $\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z+2}{4}$ is

Shortest distance between the lines $\vec{r}=(8+3 \lambda) \hat{\imath}-(9+16 \lambda) \hat{\jmath}+(10+7 \lambda) \hat{k}$ and $\vec{r}=15 \hat{\imath}+29 \hat{\jmath}+5 \hat{k}+\mu(3 \hat{\imath}+8 \hat{\jmath}-5 \hat{k})$ is

If $Q(1,0,1)$ is the image of the point $P(a, b, c)$ in the line $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$ then $a+b+c$ is equal to :

If for real values of $x, \cos \theta=x+\frac{1}{x}$, then $X$

If $\cos A=\frac{3}{4}$, then $\left(32 \sin \frac{A}{2} \sin \frac{5 A}{2}\right)=$

Simplified expression of
$1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ is :

If $|\vec{a}|=2 \sqrt{2}$ and $|\vec{b}|=3$ and angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$. If a parallelogram is constructed with adjacent sides $\vec{p}=2 \vec{a}-3 \vec{b}$ and $\vec{q}=\vec{a}+\vec{b}$ then the product of ...

Position vector of P and Q are $\hat{\imath}+3 \hat{\jmath}-7 \hat{k}$ and $5 \hat{\imath}-2 \hat{\jmath}+4 \hat{k}$ respectively. Then the cosine of the angle between $\overrightarrow{P Q}$ and y -axis 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 ?

In which of the following circuit do we find the current and voltage in phase?

The ratio of the number of turns of the primary coil to the secondary coil of an ideal transformer is $5: 1$. The primary is connected to 220 V supply. What is the output power of the transformer if the output resistance is $11 \Omega$ ?

What is the frequency ' $\nu$ ' of the electron in Bohr's first orbit of radius ' $r$ ' of the hydrogen atom?

Fusion reaction is more energetic than fission reaction because

To get 300 MW electric power for half an hour, how much mass is to be completely converted into energy?

The nucleus of oxygen atom contains 8 protons and 8 neutrons. What is the mass defect in amu?
[Given Mass of proton $=1.00727 \mathrm{amu}$ Mass of neutron $=1.00866 \mathrm{amu}$ and the mass of oxygen nucleus $=15.99053 \mathrm{amu}$. ]

When a dielectric slab of dielectric constant $\mathrm{k}=2$ is used to fill the space between the plates of a parallel plate capacitor, the capacitance of the capacitor is found to be $20 \mu \mathrm{~F}$. What will be the capacitance when...

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

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

A coin is placed on a disc rotating with an angular velocity $\omega$. The co-efficient of friction between the disc and the coin is $\mu$. The maximum distance of the coin from the centre of the disc up to which it will rotate with the dis...

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

A galvanometer of $50 \Omega$ resistance is converted into an ammeter using a shunt resistance of $10 \Omega$. If the same resistance is used to convert the same galvanometer in to a voltmeter, what would be the ratio of the resistance of t...

The wire made of Phosphor bronze is used as the suspension strip in the moving coil galvanometer, because:

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

Ten cells, each having internal resistance $1 \Omega$ and emf 1.5 V are connected in series. But unknowingly 3 cells are connected wrongly in series. The effective internal resistance and emf of the series combination are respectively:

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 velocit...

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

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 wave length associated with the charged particle?

One end of a nylon rope of length 1 and diameter 10 mm is fixed to free limb. A monkey weighing 100 N jumps to catch the free end and stays there. The change in diameter of the rope is (Young's modulus of the wire is Y and Poisson Ratio is ...

A circular coil of area $2 \sqrt{2} \mathrm{~cm}^2$ and resistance $2 \boldsymbol{\Omega}$ is arranged vertically in the east -west direction. A uniform magnetic field 0.2 T is set up across the plane in the north to east direction. Now the...

A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is $2000 \times 10^{-6}$ weber. What is the induced emf in the secondary if the current through the ...

Three point charges $-1 C,+1 C,+1 C$ are placed at points $A, B, C$ respectively of a triangle $A B C$. What is the total potential energy of the system? [given $\mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm}$ and $\mathrm{BC}=3 \mathrm{~cm}$ ]

A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' $v$ '. Then the mass ' $m$ ' of the charged particle is

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 is the dimensional formula for electric flux?

The electric field versus distance graph is shown as given. Select the correct statement from the following.
E- electric field
R-radius
r - distance from the centre

Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$. The cross-sectional area of the tap is $1 \mathrm{~cm}^2$. Assume that the pressure is constant throughout the stream of water and that the flow...

A wind mill converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. The electrical power output P is related to the velocity of wind v as

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