KCET 2026

The probability that a man and his wife live after $20$ years are $\dfrac{1}{4}$ and $\dfrac{1}{3}$ respectively. The probability that neither the man nor his wife live after $20$ years is

Probability of obtaining an even prime number on each die when a pair of dice is rolled is

Probability of occurrence of an event A is $\dfrac{1}{2}$ and that of B is $\dfrac{3}{10}$. If A and B are mutually exclusive, then the probability of occurrence of neither A nor B is

Probability of at least one of the events A and B occur is $0.6$. If A and B occur simultaneously with probability $0.2$, then $P(\bar{A}) + P(\bar{B})$ is

The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is

If we insert two numbers between $\sqrt{2}$ and $4$ so that the resulting sequence is in G.P, then the inserted numbers in the order are

Let R be the relation in the set $\mathbb{N}$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is the correct answer?

If $n(A) = 2$ and the number of relations from set A to set B is $1024$, then $n(B)$ is

If $A = \{1, 2, 3, 4, \ldots, 10\}$, then the number of non-empty subsets of A containing only even number is

If $A = \{a, b, c, d, e, f\}$, then the number of subsets of A which contains at least $2$ elements is

The mean and standard deviation of $100$ items are $50$ and $4$, respectively then the sum of all squares of the items is

The line $L_2$ passing through $(3, -1)$ divides the line segment $L_1$ joining the points $(-1, 2)$ and $(3, 6)$ in the ratio $1 : 3$ internally. The equation of line $L_2$ is:

The three points $A(2, 4, 3), B(4, a, 9)$ and $C(10, -1, 7)$ form a right-angled triangle with $\angle B = 90^\circ$, then the value of "a" is

The measure of the angle between the lines $x = k + 1, y = 2k - 1, z = 2k + 3, k \in \mathbb{R}$ and $\dfrac{x - 1}{2} = \dfrac{y - 2}{1} = \dfrac{z - 3}{1}$ is

The angle between the lines whose direction ratios are $a, b, c$ and $b - c, c - a, a - b$ is

If $\alpha$ and $\beta$ are acute angles such that $\alpha - \beta$ and $\alpha + \beta$ satisfy the equation $\tan^2\theta - 4\tan\theta + 1 = 0$, then $\alpha$ and $\beta$ are respectively,

The maximum value of $\sin\left(x + \dfrac{\pi}{6}\right) + \cos\left(x + \dfrac{\pi}{6}\right)$ is attained at $x = $

The value of $\lambda$ for which the vectors $\vec{a} = 2\hat{i} + \lambda\hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}$ are orthogonal is

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{j} - \hat{k}$ and $\vec{a} \times \vec{c} = \vec{b}, \vec{a} \cdot \vec{c} = 3$, then $\vec{c}$ is

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}, \vec{b} = \alpha\hat{i} + \beta\hat{j} + 2\hat{k}$ and $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$, then $\alpha + \beta$ is equal to

A small town with a demand of $900\text{ kW}$ of electric power at $220\text{ V}$ is situated $20\text{ km}$ away from an electric power generating station. Each wire of the two-wire transmission line has a resistance per unit length of $5 ...

A light bulb rated $100$ W is connected to an AC source of $220$ V, $50$ Hz. The rms current through the bulb is

In a circuit containing a pure resistor connected to an AC source,

An electron transition takes place from excited state to ground state in hydrogen atom, then

Bohr's second postulate implies quantisation of

The radius of first orbit in hydrogen atom is $5.3 \times 10^{-11}$ m. The kinetic energy $E_K$, potential energy $E_P$ and total energy $E_T$ of electron in first orbit are

In the circuit shown in the figure, the potential difference across the $4 \mu\text{F}$ capacitor is

A parallel plate capacitor has a uniform electric field '$E$' in the space between the plates. If the distance between the plates is '$d$' and area of each plate is '$A$', the energy stored in the capacitor is

In the figure, the values of currents $I_1, I_2$ and $I_3$ respectively are

Which of the following circuits is correct for verification of Ohm's law?

In a conducting region, $10^{19}$ electrons and $10^{19}$ protons move to the left, while $10^{19}$ $\alpha$-particles move to the right per second. The resulting electric current is $(e = 1.6 \times 10^{-19}\text{ C})$ _________

Current flowing through a wire decreases linearly from $10$ A to zero in $4$ s as shown in the graph. Find the total charge flowing through the wire in the given time interval.

Given below are two statements:Statement-I: The resistivity of a conductor is independent of its temperature.Statement-II: The resistivity of a semiconductor decreases with increase in temperature.Select the correct option.

The number of electrons moving per second through the filament of a lamp of $60$ W operating at $120$ V is nearly $(e = 1.6 \times 10^{-19}\text{ C})$ _____________.

Variation of photoelectric current with anode potential is shown below. Choose the correct option ($V_0$ = stopping potential)

Work function of the metal is

There are two wires of same material and same length while the diameter of second wire is two times the diameter of the first wire. Then the ratio of extensions produced in the wires by applying same load will be

In the figure shown, the conductor PQ of length $l$ is moved from $x = 0$ to $x = b$ and then up to $x = 2b$ with a constant velocity $\vec{v}$. A uniform magnetic field $\vec{B}$ is perpendicular to the plane of the paper and extends from ...

In Faraday-Henry's experiment, a coil is connected to a galvanometer. For the deflection of pointer in the galvanometer, which of the following statement/s is/are WRONG?The pointer in the galvanometer deflects -(a) When the bar magnet is mo...

What range of electromagnetic spectrum is considered as light?

Match the following Maxwell's equations:(The symbols used here have their usual meanings)List-IList-II(a)Gauss' law for electrostatics(i)$\oint \vec{E} \cdot d\vec{A} = \dfrac{Q}{\varepsilon_0}$(b)Gauss' law for magnetism(ii)$\oint \vec{B} ...

A $200$ J of work is done in moving a charge $5$ C from a point A where the potential is $-20$ V to another point B where potential is V volt. The value of V at B is

An electric dipole of dipole moment $\vec{P}$ is placed in the uniform electric field $\vec{E}$. Then which of the following statements are correct?Statement-I: The torque on the dipole is $\vec{P} \times \vec{E}$Statement-II: The potential...

Consider three point charges $-2Q, Q$ and $-Q$ and three surfaces $S_1, S_2$ and $S_3$ as shown in the figure. Match the entries of List-I with that of List-II.List-IList-II(a) Net flux through $S_1$(i) $\dfrac{-2Q}{\varepsilon_0}$(b) Net f...

What will be the total electric flux through the faces of the cube as given in the figure with side of length '$a$' if a charge Q is placed at B midpoint of an edge of the cube (see figure)?

An electron falls through a distance $1.5$ cm in $2.0 \times 10^4$ N/C from rest. The time taken to cover this distance in second is ____$(e = 1.6 \times 10^{-19}\text{ C}, m_e = 9.11 \times 10^{-31}\text{ kg})$

A 30 cm long capillary tube is dipped in water, water rises upto a height of $10$ cm due to capillarity. If this experiment is conducted in a freely falling water in an elevator, then the length of the water column becomes

Instrument fitted in the carburetor of the automobile to provide the correct mixture of air and fuel necessary for combustion works on

Suppose the acceleration due to gravity at the earth's surface is $g \text{ m/s}^2$ and at the surface of moon it is $g' \text{ m/s}^2$. An M kg passenger goes from the earth to the moon in a spaceship moving with a constant velocity (Negle...

Imagine a new planet having the same density as that of the earth, but it is two times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is $g$ and that on the surface of the new planet is $g'$, t...