KCET 2025

If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})$, then

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?

Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. If she visits temple $A, \frac{1}{3}$ is the probability that she meets her friend, whereas it is $\frac{2}{7}$ if she ...

If $4^{\text {th }}, 10^{\text {th }}$ and $16^{\text {th }}$ terms of a G.P. are $x, y$ and $z$ respectively, then

If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$
$B=\{x: x$ is a natural number and $2 \leq x<5\}$
$\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a prime number $\leq 4\}$
Then $(B-C) \cup A$...

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.
Statement (I): Minimum number of elements in AUB is 3
Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

\(\text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is }\)

Consider the following statements :
Statement(I) : The set of all solutions of the linear inequalities $3 \mathrm{x}+8<17$ and $2 \mathrm{x}+8 \geq 12$ are $\mathrm{x}<3$ and $x \geq 2$ respectively.
Statement(II) : The common set of soluti...

The mean deviation about the mean for the date $4,7,8,9,10,12,13,17$ is

The system of equations $4 x+6 y=5$ and $8 x+12 y=10$ has

A line passes through $(-1,-3)$ and perpendicular to $x+6 y=5$. Its $x$ intercept is

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is

The distance of the point $\mathrm{P}(-3,4,5)$ from yz plane is

If $\cos x+\cos ^2 x=1$, then the value of $\sin ^2 x+\sin ^4 x$ is

Which of the following is not correct?

The minimum value of $1-\sin x$ is

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ are such that $\vec{a}+\lambda \vec{b}$ is perpendicular to $\vec{c}$, then the value of $\lambda$ is

If $|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{~b}}|=2$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=12$, then the value of $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|$ is

Consider the following statements :
Statement (I) : If either $|\vec{a}|=0$ or $|\vec{b}|=0$, then $\vec{a} \cdot \vec{b}=0$
Statement (II) : If $\vec{a} \times \vec{b}=\overrightarrow{0}$, then a is perpendicular to $b$. Which of the follo...

In domestic electric mains supply, the voltage and the current are

A sinusoidal voltage produced by an AC generator at any instant t is given by an equation $\mathrm{V}=311 \sin 314$ t. The rms value of voltage and frequency are respectively

A series LCR circuit containing an AC source of 100 V has an inductor and a capacitor of reactances $24 \Omega$ and $16 \Omega$ respectively. If a resistance of $6 \Omega$ is connected in series, then the potential difference across the ser...

If the radius of first Bohr orbit is $r$, then the radius of the second Bohr orbit will be

\(\text { Match the following types of nuclei with examples shown }\)
$$ \begin{array}{|l|l|} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { A. Isotopes } & \text { i. } \mathrm{Li}^7, \mathrm{Be}^7 \\ \hline \text { B....

Which of the following statements is incorrect with reference of 'Nuclear force'?

During an elastic collision between two bodies, which of the following statements are correct?
I. The initial kinetic energy is equal to the final kinetic energy of the system.
II. The linear momentum is conserved.
III. The kinetic energy d...

Three particles of mass $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed at the vertices A, B and C respectively of an equilateral triangle ABC of side 1 m . The centre of mass of the system from vertex A (located at origin) is

A particle is in uniform circular motion. The equation of its trajectory is given by $(x-2)^2+y^2=25$, where x and y are in meter. The speed of the particle is $2 \mathrm{~ms}^{-1}$, when the particle attains the lowest ' y ' co-ordinate, t...

Given, a current carrying wire of non-uniform cross-section, which of the following is constant throughout the length of wire?

The range of electrical conductivity $(\sigma)$ and resistivity $(\rho)$ for metals, among the following, is

The graph between variation of resistance of a metal wire as a function of its diameter keeping other parameters like length and temperature constant is

\(\text { In the following circuit, the terminal voltage across the cell is }\)

In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit.

He unplugged a resistance of $5200 \Omega$ in R . When $\mathrm{K}_1$ is closed and $\mathrm{K}_2$ ...

Two cells of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2\left(E_2>E_1\right.$ and $\left.r_2>r_1\right)$ respectively, are connected in parallel as shown in figure. The equivalent emf of the combination is $\mathrm{E}_{\tex...

Two similar galvanometers are covered into an ammeter and a milliammeter. The shunt resistance of ammeter as compared to the shunt resistance of milliammeter will be

The variations of resistivity $\rho$ with absolute temperature T for three different materials $\mathrm{X}, \mathrm{Y}$ and Z are shown in the graph below. Identify the materials $\mathrm{X}, \mathrm{Y}$ and Z .

If we consider an electron and a photon of same de-Broglie wavelength, then they will have same

The anode voltage of a photocell is kept fixed. The frequency of the light falling on the cathode is gradually increased. Then the correct graph which shows the variation of photo current I with the frequency $v$ of incident light is

Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of $1: 3$. If they are stretched by the same force, then increase in their lengths will be in the ratio of

When a bar magnet is pushed towards the coil, along its axis, as shown in the figure, the galvanometer pointer deflects towards X . When this magnet is pulled away from the coil, the galvanometer pointer

\(\text { Match the following types of waves with their wavelength ranges }\)
$$
\begin{array}{|l|l|}
\hline \text { Waves } & \text { Wavelength ranges } \\
\hline \text { i. Microwave } & \text { a. } 700 \mathrm{~nm} \text { to } 400 \...

The total energy carried by the light wave when it travels from a rarer to a non-reflecting and nonabsorbing medium

A potential at a point A is -3 V and that at another point B is 5 V . What is the work done in carrying a charge of 5 m C from B to A ?

Match Column-I with Column - II related to an electric dipole of dipole moment $\vec{p}$ that is placed in a uniform electric field $\vec{E}$.



Column - I Angle between


p

→




p

→

vec(p) ...

Which of the following statements is not true?

Which of the following is a correct statement?

Charges are uniformly spread on the surface of a conducting sphere. The electric field from the centre of sphere to a point outside the sphere varies with distance $r$ from the centre as

A metallic sphere of radius $R$ carrying a charge $q$ is kept at certain distance from another metallic sphere of radius $\mathrm{R} / 4$ carrying a charge Q . What is the electric flux at any point inside the metallic sphere of radius R du...

You are given a dipole of charge $+q$ and $-q$ separated by a distance $2 R$. A sphere ' $A$ ' of radius ' $R$ ' passes through the centre of the dipole as shown below and another sphere ' $B$ ' of radius ' $2 R$ ' passes through the charge...