KCET 2023

A bag contains \(2 n+1\) coins. It is known that \(n\) of these coins have head on both sides whereas, the other \(n+1\) coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $$\frac{31}...

Let \(A=\{x, y, z, u\}\) and \(B=\{a, b\}\). A function \(f: A \rightarrow B\) is selected randomly. The probability that the function is an onto function is

If \(A\) and \(B\) are events, such that \(P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}\) and \(P(B / A)=\frac{2}{3}\), then \(P(B)\) is

The area of a triangle with vertices \((-3,0)\), \((3,0)\) and \((0, k)\) is 9 sq units, find the value of \(k\) is

Given that \(a, b\) and \(x\) are real numbers and \(a < b, x < 0\), then

If \(p\left(\frac{1}{q}+\frac{1}{r}\right), q\left(\frac{1}{r}+\frac{1}{p}\right), r\left(\frac{1}{p}+\frac{1}{q}\right)\) are in \(\mathrm{AP}\), then \(p, q, r\)

\(n\)th term of the series \(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+\ldots\) is

Which of the following is an empty set?

Let the relation \(R\) be defined in \(N\) by \(a R b\), if \(3 a+2 b=27\), then \(R\) is

The mean of 100 observations is 50 and their standard deviation is 5. Then, the sum of squares of all observations is

A line passes through \((2,2)\) and is perpendicular to the line \(3 x+y=3\). Its \(y\)-intercept is

If a line makes an angle of \(\frac{\pi}{3}\) with each \(X\) and \(Y\) axis, then the acute angle made by \(\mathrm{Z}\)-axis is

The length of perpendicular drawn from the point \((3,-1,11)\) to the line \(\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) is

The equation of the plane through the points \((2,1,0),(3,2,-2)\) and \((3,1,7)\) is

The point of intersection of the line \(x+1=\frac{y+3}{3}=\frac{-z+2}{2}\) with the plane \(3 x+4 y+5 z=10\) is

If \((2,3,-1)\) is the foot of the perpendicular from \((4,2,1)\) to a plane, then the equation of the plane is

\(|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144\) and \(|\mathbf{a}|=4\), then \(|\mathbf{b}|\) is equal to

If \(\mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0\) and \((\mathbf{a} \times \mathbf{b})+(\mathbf{b} \times \mathbf{c})+(\mathbf{c} \times \mathbf{a})=\lambda(\mathbf{b} \times \mathbf{c})\), then the value of \(\lambda\) is equal to

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\), then

The component of \(\hat{\mathbf{i}}\) in the direction of the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) is

Total impedance of a series \(L\)-\(C\)-\(R\) circuit varies with angular frequency of the \(\mathrm{AC}\) source connected to it as shown in the graph. The quality factor \(Q\) of the series \(L\)-\(C\)-\(R\) circuit is

In series \(L C R\) circuit at resonance, the phase difference between voltage and current is

An ideal transformer has a turns ratio of 10. When the primary is connected to \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) as source, the power output is

In the Rutherford's alpha scattering experiment, as the impact parameter increases, the scattering angle of the alpha particle

Three energy levels of hydrogen atom and the corresponding wavelength of the emitted radiation due to different electron transition are as shown. Then,

A radioactive sample has half-life of 3 years. The time required for the activity of the sample to reduce to \(\frac{1}{5}\)th of its initial value is about

In the following equation representing \(\beta^{-}\) decay, the number of neutrons in the nucleus \(X\) is
\({ }_{83}^{210} \mathrm{Bi} \longrightarrow X+e^{-1}+\bar{v}\)

A nucleus with mass number 220 initially at rest emits an alpha particle. If the \(Q\) value of reaction is \(5.5 ~\mathrm{MeV}\). Calculate the value of kinetic energy of alpha particle

Five capacitance each of value \(1 ~\mu \mathrm{F}\) are connected as shown in the figure. The equivalent capacitance between \(A\) and \(B\) is

A parallel plate capacitor of capacitance \(C_1\) with a dielectric slab in between its plates is connected to a battery. It has a potential difference \(V_1\) across its plates. When the dielectric slab is removed, keeping the capacitor co...

A particle is in uniform circular motion, related to one complete revolution of the particle, which among the statements is incorrect?

A wire of resistance \(R\) is connected across a cell of emf \((\varepsilon)\) and internal resistance \((r)\). The current through the circuit is \(I\). In time \(t\), the work done by the battery to establish the current \(I\) is

For a given electric current the drift velocity of conduction electrons in a copper wire is \(v_d\) and their mobility is \(\mu\). When the current is increased at constant temperature

Ten identical cells each emf \(2 \mathrm{~V}\) and internal resistance \(1 ~\Omega\) are connected in series with two cells wrongly connected. A resistor of \(10 ~\Omega\) is connected to the combination. What is the current through the res...

The equivalent resistance between the points A and B in the following circuit is

The resistance of a carbon resistor is \(4.7 ~\mathrm{k} \Omega \pm 5 \%\). The colour of the third band is

The four bands of a colour coded resistor are of the colours grey, red, gold and gold. The value of the resistance of the resistor is

A moving coil galvanometer is converted into an ammeter of range 0 to \(5 \mathrm{~mA}\). The galvanometer resistance is \(90 \Omega\) and the shunt resistance has a value of \(10 \Omega\). If there are 50 divisions in the galvanometer-turn...

A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is

In an experiment to study photoelectric effect the observed variation of stopping potential with frequency of incident radiation is as shown in the figure. The slope and \(y\)-intercept are respectively

The energy gap of an LED is \(2.4 \mathrm{~eV}\). When the LED is switched ON, the momentum of the emitted photons is

A stretched wire of a material whose young's modulus \(Y=2 \times 10^{11} ~\mathrm{Nm}^{-2}\) has poisson's ratio 0.25 . Its lateral strain \(\varepsilon_l=10^{-3}\). The elastic energy density of the wire is

A square loop of side \(2 \mathrm{~cm}\) enters a magnetic field with a constant speed of \(2 \mathrm{~cm} \mathrm{~s}^{-1}\) as shown. The front edge enters the field at \(t=0 \mathrm{~s}\). Which of the following graph correctly depicts t...

The current in a coil changes from \(2 \mathrm{~A}\) to \(5 \mathrm{~A}\) in \(0.3 \mathrm{~s}\). The magnitude of emf induced in the coil is \(1.0 \mathrm{~V}\). The value of self-inductance of the coil is

A metallic rod of length \(1 \mathrm{~m}\) held along east-west direction is allowed to fall down freely. Given horizontal component of earth's magnetic field \(B_H=3 \times 10^{-5} \mathrm{~T}\). the emf induced in the rod at an instant $$...

The ratio of the magnitudes of electric field to the magnetic field of an electromagnetic wave is of the order of

A positively charged glass rod is brought near uncharged metal sphere, which is mounted on an insulated stand. If the glass rod is removed, the net charge on the metal sphere is

In the situation shown in the diagram, magnitude, if \(q < < |Q|\) and \(r >>>a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively.
(\(p=2 a Q\) is the dipole moment)

A uniform electric field vector \(\mathbf{E}\) exists along horizontal direction as shown. The electric potential at \(A\) is \(V_A\). A small point charge \(q\) is slowly taken from \(A\) to \(B\) along the curved path as shown. The potent...

A cubical Gaussian surface has side of length \(a=10 \mathrm{~cm}\). Electric field lines are parallel to \(X\)-axis as shown in figure. The magnitudes of electric fields through surfaces \(A B C D\) and \(E F G H\) are $$6 ~\mathrm{kNC}^{-...