At an angle of 30° to the magnetic meridian,

Question: At an angle of $30^{\circ}$ to the magnetic meridian, the apparent dip is $45^{\circ}$. Find the true dip :$\tan ^{-1} \sqrt{3}$$\tan ^{-1} \frac{1}{\sqrt{3}}$$\tan ^{-1} \frac{2}{\sqrt{3}}$$\tan ^{-1} \frac{\sqrt{3}}{2}$Correct Option: , 4 Solution: $A \tan \delta=\tan \delta^{\prime} \cos \theta$ $=\tan 45^{\circ} \cos 30^{\circ}$ $\tan \delta=1 \times \frac{\sqrt{3}}{2}$ $\delta=\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$...

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m

Question: A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water $f_{\mathrm{w}}=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ and Density of air $f_{\mathrm{a}}=1.2 \mathrm{~kg} \mathrm{~m}{ }^{-3}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ Coefficient of viscosity of air $=1.8 \times 10^{-5} \ma...

The nuclear activity

Question: The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial value in 30 years. The half-life of radioactive element is __________ years. Solution: $\mathrm{A}=\mathrm{A}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$ $\frac{\mathrm{A}_{0}}{8}=\mathrm{A}_{0} \mathrm{e}^{-\lambda \mathrm{t}} \Rightarrow \lambda \mathrm{t}=\ln 8$ $\lambda t=3 \ln 2$ $\frac{\ln 2}{\lambda}=\frac{\mathrm{t}}{3}=\frac{30}{3}=10$ years...

Consider a binary star system of star A and star B

Question: Consider a binary star system of star A and star B with masses $\mathrm{m}_{\mathrm{A}}$ and $\mathrm{m}_{\mathrm{B}}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$, respectively. If $T_{A}$ and $T_{B}$ are the time period of star $A$ and star $B$, respectively, then:$\frac{\mathrm{T}_{\mathrm{A}}}{\mathrm{T}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}\right)^{\frac{3}{2}}$$\mathrm{T}_{\mathrm{A}}=\mathrm{T}_{\mathrm{B}}$$\mathrm{T}_{\mathrm...

In a semiconductor,

Question: In a semiconductor, the number density of intrinsic charge carriers at $27^{\circ} \mathrm{C}$ is $1.5 \times 10^{16} / \mathrm{m}^{3}$. If the semiconductor is doped with impurity atom, the hole density increases to $4.5 \times 10^{22} / \mathrm{m}^{3}$. The electron density in the doped semiconductor is __________ $\times 10^{9} / \mathrm{m}^{3}$. Solution: $\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}}=\mathrm{n}_{\mathrm{i}}^{2}$ $\mathrm{n}_{\mathrm{c}}=\frac{\mathrm{n}_{\mathrm...

The expected graphical representation of the variation of angle of deviation

Question: The expected graphical representation of the variation of angle of deviation ' $\delta$ ' with angle of incidence ' $i$ ' in a prism is :Correct Option: , 2 Solution: Standard graph between angle of deviation and incident angle....

For a certain radioactive process the graph

Question: For a certain radioactive process the graph between In $\mathrm{R}$ and $\mathrm{t}(\mathrm{sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately: $9.15 \mathrm{sec}$$6.93 \mathrm{sec}$$2.62 \mathrm{sec}$$4.62 \mathrm{sec}$Correct Option: , 4 Solution: $\mathrm{R}=\mathrm{R}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$ $\ell \mathrm{nR}=\ell \mathrm{nR}_{0}-\lambda \mathrm{t}$ $-\lambda$ is slope of straight line $\lambda=...

A solid disc of radius

Question: A solid disc of radius $20 \mathrm{~cm}$ and mass $10 \mathrm{~kg}$ is rotating with an angular velocity of $600 \mathrm{rpm}$, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in $10 \mathrm{~s}$ is ___________ $\pi \times 10^{-1} \mathrm{Nm}$. Solution: $\tau=\frac{\Delta \mathrm{L}}{\Delta \mathrm{t}}=\frac{\mathrm{I}\left(\omega_{\mathrm{f}}-\omega_{\mathrm{i}}\right)}{\Delta \mathrm{t}}$ $\ta...

A force of

Question: A force of $\mathrm{F}=(5 \mathrm{y}+20) \hat{\mathrm{j}} \mathrm{N}$ acts on a particle. The workdone by this force when the particle is moved from $\mathrm{y}=0 \mathrm{~m}$ to $\mathrm{y}=10 \mathrm{~m}$ is Solution: $\mathrm{F}=(5 \mathrm{y}+20) \hat{\mathrm{j}}$ $\omega=\int F d y=\int_{0}^{10}(5 y+20) d y$ $=\left(\frac{5 y^{2}}{2}+20 y\right)_{0}^{10}$ $=\frac{5}{2} \times 100+20 \times 10$ $=250+200=450 \mathrm{~J}$...

The correct relation between the degrees of

Question: The correct relation between the degrees of freedom $f$ and the ratio of specific heat $\gamma$ is :$f=\frac{2}{\gamma-1}$$f=\frac{2}{\gamma+1}$$f=\frac{\gamma+1}{2}$$f=\frac{1}{\gamma+1}$Correct Option: 1 Solution: $\gamma=1+\frac{2}{f}$ $f=\frac{2}{\gamma-1}$...

From the given data,

Question: From the given data, the amount of energy required to break the nucleus of aluminium ${ }_{13}^{27} \mathrm{Al}$ is ____________$\mathrm{x} \times 10^{-3} \mathrm{~J}$. Mass of neutron $=1.00866 \mathrm{u}$ Mass of proton $=1.00726 \mathrm{u}$ Mass of Aluminium nucleus $=27.18846 \mathrm{u}$ (Assume $1 \mathrm{u}$ corresponds to $\mathrm{x} \mathrm{J}$ of energy) (Round off to the nearest integer) Solution: $\Delta \mathrm{m}=\left(Z \mathrm{~m}_{\mathrm{P}}+(\mathrm{A}-\mathrm{Z}) \ma...

If time (t), velocity (v),

Question: If time $(t)$, velocity $(v)$, and angular momentum $(l)$ are taken as the fundamental units. Then the dimension of mass (m) in terms of $t, v$ and $l$ is :$\left[t^{-1} v^{1} l^{-2}\right]$$\left[t^{1} v^{2} l^{-1}\right]$$\left[t^{-2} v^{-1} l^{1}\right]$$\left[t^{-1} v^{-2} l^{1}\right]$Correct Option: , 4 Solution: $\mathrm{m} \propto \mathrm{t}^{\mathrm{a}} \mathrm{v}^{\mathrm{b}} \ell^{\mathrm{c}}$ $\mathrm{m} \propto[\mathrm{T}]^{\mathrm{a}}\left[\mathrm{LT}^{-1}\right]^{\mathrm...

An electron and proton are separated by a large distance.

Question: An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 Å. What is the maximum kinetic energy of the emitted photoelectron?7.61 eV1.41 eV3.3 eVNo photoelectron would be emittedCorrect Option: 2, Solution: Initially, energy of electron = +3eV finally, in ...

Question: Two circuits are shown in the figure (a) \ (b). At a frequency of $\mathrm{rad} / \mathrm{s}$ the average power dissipated in one cycle will be same in both the circuits. Solution: For figure (a) $P_{\text {avg }}=\frac{v_{\mathrm{rms}}^{2}}{R}$ $\frac{\mathrm{v}_{\mathrm{rms}}^{2}}{\mathrm{Z}^{2}} \times \mathrm{R}=\frac{\mathrm{v}_{\mathrm{rms}}^{2}}{\mathrm{R}} \times 1$ $\mathrm{R}^{2}=\mathrm{Z}^{2}$ $25=\left(\sqrt{\left(\mathrm{x}_{\mathrm{C}}-\mathrm{x}_{\mathrm{L}}\right)^{2}+...

Solve this

Question: A $16 \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ supply having internal resistance of $1 \Omega$ is connected across one of its sides. The potential drop across the diagonals of the square loop is ____________$\times 10^{-1} \mathrm{~V}$ Solution: here assume current as By KVL in outer loop $9-12 i-4 i=0$ $16 i=9$ $8 i=\frac{9}{2}=4.5$ $=45 \times 10^{-1}$...

A message signal

Question: A message signal of frequency $20 \mathrm{kHz}$ and peak voltage of 20 volt is used to modulate a carrier wave of frequency $1 \mathrm{MHz}$ and peak voltage of 20 volt. The modulation index will be : Solution: Modulation index $\mu=\frac{A_{m}}{A_{c}}=\frac{20}{20}=1$...

A body rolls down an inclined plane without slipping.

Question: A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \%$ of its translational kinetic energy. The body is :Solid sphereSolid cylinderHollow cylinderRingCorrect Option: , 2 Solution: $\frac{1}{2} \mathrm{I} \omega^{2}=\frac{1}{2} \times \frac{1}{2} \mathrm{mv}^{2}$ $I=\frac{1}{2} m R^{2}$ Body is solid cylinder...

An electron having de-Broglie wavelength

Question: An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:(1) 0 $\frac{2 m^{2} c^{2} \lambda^{2}}{h^{2}}$$\frac{2 m c \lambda^{2}}{h}$$\frac{\mathrm{hc}}{\mathrm{mc}}$Correct Option: , 3 Solution: $\lambda=\frac{h}{m V}$ kinetic energy, $\frac{\mathrm{P}^{2}}{2 \mathrm{~m}}=\frac{\mathrm{h}^{2}}{2 \mathrm{~m} \lambda^{2}}=\frac{\mathrm{hc}}{\lambda_{\mathrm{c}}}$ $\lambda_{\mathrm{C}}=\frac{2 \mathrm{~m} \lambda^{...

In a uniform magnetic field,

Question: In a uniform magnetic field, the magnetic needle has a magnetic moment $9.85 \times 10^{-2} \mathrm{~A} / \mathrm{m}^{2}$ and moment of inertia $5 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^{2}$. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is___________ $\mathrm{mT}$. [Take $\pi^{2}$ as $9.85$ ] Solution: $T=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{MB}}}$ $\mathrm{B}=80 \times 10^{-4}=8 \mathrm{mT}$...

A light beam

Question: A light beam of wavelength $500 \mathrm{~nm}$ is incident on a metal having work function of $1.25 \mathrm{eV}$, placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$, with maximum kinetic energy are bent into circular arc of radius $30 \mathrm{~cm}$. The value of $B$ is _______$\times 10^{-7} \mathrm{~T}$. Given hc $=20 \times 10^{-26} \mathrm{~J}-\mathrm{m}$, mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ Solution: By photoelec...

A particle is making simple harmonic motion along

Question: A particle is making simple harmonic motion along the $\mathrm{X}$-axis. If at a distances $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$ from the mean position the velocities of the particle are $v_{1}$ and $v_{2}$ respectively. The time period of its oscillation is given as :$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}+\mathrm{x}_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}$$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}+\mathrm{x}_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}$$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x...

The amplitude of upper and lower side bands of A.M.

Question: The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency $11.21 \mathrm{MHz}$, peak voltage $15 \mathrm{~V}$ is amplitude modulated by a $7.7 \mathrm{kHz}$ sine wave of $5 \mathrm{~V}$ amplitude are $\frac{\mathrm{a}}{10} \mathrm{~V}$ and $\frac{\mathrm{b}}{10} \mathrm{~V}$ respectively. Then the value of $\frac{\mathrm{a}}{\mathrm{b}}$ is____________ Solution: $\frac{\mathrm{a}}{10}=\frac{\mathrm{b}}{10}=\frac{\mu \mathrm{A}_{\mathrm{C}}}{2}$ $\Ri...

A system consists

Question: A system consists of two types of gas molecules A and $\mathrm{B}$ having same number density $2 \times 10^{25} / \mathrm{m}^{3}$. The diameter of $\mathrm{A}$ and $\mathrm{B}$ are $10A $ and $5A $ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule $A$ to that of $B$ between two successive collision is $\times 10^{-2}$ Solution: $\because$ mean free path $\lambda=\frac{1}{\sqrt{2} \pi \mathrm{d}^{2} \mathrm{n}}$ $\frac{\lambda...

Which of the following graphs represent the behavior

Question: Which of the following graphs represent the behavior of an ideal gas ? Symbols have their usual meaning.Correct Option: , 3 Solution: $\mathrm{PV}=\mathrm{nRT}$ $P V \propto T$ Straight line with positive slope $(\mathrm{nR})$...

Two vectors

Question: Two vectors $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ have equal magnitude. The magnitude of $(\vec{X}-\vec{Y})$ is $n$ times the magnitude of $(\overrightarrow{\mathrm{X}}+\overrightarrow{\mathrm{Y}})$. The angle between $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ is :$\cos ^{-1}\left(\frac{-n^{2}-1}{n^{2}-1}\right)$$\cos ^{-1}\left(\frac{n^{2}-1}{-n^{2}-1}\right)$$\cos ^{-1}\left(\frac{n^{2}+1}{-n^{2}-1}\right)$$\cos ^{-1}\left(\frac{n^{2}+1}...