An engine operates by taking a monatomic ideal
Question: An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to Solution: $\mathrm{W}_{\mathrm{ABCDA}}=2 \mathrm{P}_{0} \mathrm{~V}_{0}$ $\mathrm{Q}_{\text {in }}=\mathrm{Q}_{\mathrm{AB}}+\mathrm{Q}_{\mathrm{BC}}$ $\mathrm{Q}_{\mathrm{AB}}=\mathrm{nC}\left(\mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}\right)$ $=\frac{\mathrm{n} 3 \mathrm{R}}{2}\left(\mathrm{~T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{A}}\right)$ $...
Read More →Two resistors of resistance 400Ω and 800Ω
Question: Two resistors $400 \Omega$ and $800 \Omega$ are connected in series across a $6 \mathrm{~V}$ battery. The potential difference measured by a voltmeter of $10 \mathrm{k} \Omega$ across $400 \Omega$ resistor is close to:$2 \mathrm{~V}$$1.95 \mathrm{~V}$$2.05 \mathrm{~V}$$1.8 \mathrm{~V}$Correct Option: , 2 Solution: So the potential difference in voltmeter across the points $\mathrm{A}$ and $\mathrm{B}$ is $\frac{6}{1185} \times 385=1.949 \mathrm{~V}$...
Read More →Solve this following
Question: A sound source $S$ is moving along a straight track with speed $\mathrm{v}$, and is emitting sound of frequency $\mathrm{v}_{0}$ (see figure). An observer is standing at a finite distance, at the point $\mathrm{O}$, from the track. The time variation of frequency heard by the observer is best represented by : $\left(\mathrm{t}_{0}\right.$ represents the instant when the distance between the source and observer is minimum)Correct Option: , 4 Solution: $\mathrm{f}_{\text {observed }} \Ri...
Read More →When a car is at rest,
Question: When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $\mathrm{v}$, he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta) \mathrm{v}$, this angle changes to $45^{\circ}$. The value of $\beta$ is close to:$0.41$$0.50$$0.37$$0.73$Correct Option: , 4 Solution: Rain is falling vertically downwards. $\overrightarrow{\mathrm{V}}_{\mathrm{r} / \mathrm{m}}=\...
Read More →A point like object is placed at a distance of
Question: A point like object is placed at a distance of $1 \mathrm{~m}$ in front of a convex lens of focal length $0.5 \mathrm{~m}$. A plane mirror is placed at a distance of $2 \mathrm{~m}$ behind the lens. The position and nature of the final image formed by the system is : $1 \mathrm{~m}$ from the mirror, virtual$1 \mathrm{~m}$ from the mirror, real$2.6 \mathrm{~m}$ from the mirror, real$2.6 \mathrm{~m}$ from the mirror, virtualCorrect Option: 1, 4 Solution: Object is at $2 \mathrm{f}$. So i...
Read More →Which of the following will NOT be observed
Question: Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the chosen component is capacitor.Multimeter shows a deflection,accompanied by a splash of light out of connected component in one direction and NO deflection on reversing the probes if the chosen component is LED.Multimeter shows NO deflect...
Read More →A radioactive nucleus decays by two different processes.
Question: A radioactive nucleus decays by two different processes. The half life for the first process is $10 \mathrm{~s}$ and that for the second is $100 \mathrm{~s}$. the effective half life of the nucleus is close to:$9 \mathrm{sec}$$55 \mathrm{sec}$$6 \mathrm{sec}$$12 \mathrm{sec}$Correct Option: 1, Solution: $\frac{1}{\mathrm{~T}_{\text {eff }}}=\frac{1}{\mathrm{~T}_{1}}+\frac{1}{\mathrm{~T}_{2}}$ $\mathrm{T}_{\text {eff }}=\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2...
Read More →A square loop of side
Question: A square loop of side $2 \mathrm{a}$ and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current $\mathrm{I}$ is placed parallel to z-axis and passing through point $(0, b, 0),(ba)$. The magnitude of torque on the loop about z-ax is will be :$\frac{2 \mu_{0} I^{2} a^{2} b}{\pi\left(a^{2}+b^{2}\right)}$$\frac{\mu_{0} I^{2} a^{2} b}{2 \pi\left(a^{2}+b^{2}\right)}$$\frac{\mu_{0} I^{2} a^{2}}{2 \pi b}$$\frac{2 \mu_{0} I^{2} a^{2}}{\pi b}$Corr...
Read More →Amount of solar energy received on the earth's surface
Question: Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:$\mathrm{ML}^{2} \mathrm{~T}^{-2}$$\mathrm{MLT}^{-2}$$\mathrm{M}^{2} \mathrm{~L}^{0} \mathrm{~T}^{-1}$$\mathrm{ML}^{0} \mathrm{~T}^{-3}$Correct Option: , 4 Solution: $S=\frac{P}{A}=\frac{M L^{2} T^{-3}}{L^{2}}=M T^{-3}$...
Read More →In an adiabatic process, the density of a diatomic gas
Question: In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $\mathrm{n}$ is:326$\frac{1}{32}$32128Correct Option: , 4 Solution: In adiabatic process $\mathrm{PV} \gamma=$ constant $\mathrm{P}\left(\frac{\mathrm{m}}{\mathrm{\rho}}\right)^{\gamma}=\mathrm{constant}$ as mass is constant $P \propto \rho^{\gamma}$ $\frac{P_{f}}{P_{i}}=\left(\frac{\rho_{f}}{\rho_{i}}\right...
Read More →A uniform magnetic field B exists in a direction perpendicular
Question: A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \mathrm{~mm}$ and a total length of $30 \mathrm{~cm}$. The magnetic field changes with time at a steady rate $\mathrm{dB} / \mathrm{dt}=0.032 \mathrm{Ts}^{-1}$.The induced current in the loop is close to (Resistivity of the metal wire is $1.23 \times 10^{-8} \Omega \mathrm{m}$ )$0.61 \mathrm{~A}$$0.34 \mathrm{~A}$$0.43 \mathrm{~A}$$0.53 \mathr...
Read More →A charged particle going around in a circle can be considered
Question: A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge $q$ is moving in a plane with speed $\mathrm{v}$ under the influence of magnetic field $\overrightarrow{\mathrm{B}}$. The magnetic moment of this moving particle:$-\frac{m v^{2} \vec{B}}{B^{2}}$$-\frac{m v^{2} \vec{B}}{2 \pi B^{2}}$$\frac{m v^{2} \vec{B}}{2 B^{2}}$$-\frac{m v^{2} \vec{B}}{2 B^{2}}$Correct Option: , 4 Solution: Magnetic moment $\mathrm{M}=\mathrm{iA}$...
Read More →Particle
Question: Particle $\mathrm{A}$ of mass $\mathrm{m}_{1}$ moving with velocity $(\sqrt{3} \hat{\mathrm{i}}+\hat{\mathrm{j}}) \mathrm{ms}^{-1}$ collides with another particle B of mass $\mathrm{m}_{2}$ which is at rest initially. Let $\overrightarrow{\mathrm{V}}_{1}$ and $\overrightarrow{\mathrm{V}}_{2}$ be the velocities of particles $\mathrm{A}$ and $\mathrm{B}$ after collision respectively. If $m_{1}=2 m_{2}$ and after collision $\overrightarrow{\mathrm{V}}_{1}=(\hat{\mathrm{i}}+\sqrt{3} \hat{\...
Read More →Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.
Question: Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $\mathrm{T}$. The total internal energy, U of a mole of this gas, and the value of $\gamma\left(=\frac{C_{\mathrm{P}}}{C_{\mathrm{v}}}\right)$ given, respectively, by: $\mathrm{U}=\frac{5}{2} \mathrm{RT}$ and $\gamma=\frac{6}{5}$$\mathrm{U}=5 \mathrm{RT}$ and $\gamma=\frac{7}{5}$$\mathrm{U}=5 \mathrm{RT}$ and $\gamma=\frac{6...
Read More →A metallic sphere cools from 50 degree C to
Question: A metallic sphere cools from $50^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in $300 \mathrm{~s}$. If atmospheric temperature around is $20^{\circ} \mathrm{C}$, then the sphere's temperature after the next 5 minutes will be close to:$33^{\circ} \mathrm{C}$$35^{\circ} \mathrm{C}$$31^{\circ} \mathrm{C}$$28^{\circ} \mathrm{C}$Correct Option: 1 Solution: $\frac{50-40}{300}=\beta\left(\frac{50+40}{2}-20\right)$ $\frac{40-\mathrm{T}}{300}=\beta\left(\frac{40+\mathrm{T}}{2}-20\right)$ $\th...
Read More →Assuming the nitrogen molecule is moving with
Question: Assuming the nitrogen molecule is moving with r.m.s. velocity at $400 \mathrm{~K}$, the de-Broglie wavelength of nitrogen molecule is close to: (Given: nitrogen molecule weight : $4.64 \times 10^{-26} \mathrm{~kg}$, Boltzman constant : $1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$, Planck constant: $6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ )$0.34 A$0.24 A$0.20 A$0.44 ACorrect Option: , 2 Solution: $\mathrm{v}_{\text {rms }}=\sqrt{\frac{3 \mathrm{KT}}{\mathrm{m}}}$ $\mathrm{m} \...
Read More →Solve this following
Question: Identify the correct output signal $\mathrm{Y}$ in the given combination of gates (as shown) for the given inputs $\mathrm{A}$ and $\mathrm{B}$. Correct Option: , 3 Solution: $\mathrm{y}=\overline{\overline{\mathrm{A}} \cdot \overline{\mathrm{B}}}=\overline{\overline{\mathrm{A}}}+\overline{\overline{\mathrm{B}}}=\mathrm{A}+\mathrm{B}$...
Read More →The electric field of a plane electromagnetic wave
Question: The electric field of a plane electromagnetic wave propagating along the $x$ direction in vacuum is $\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx}) .$ The magnetic field $\overrightarrow{\mathrm{B}}$, at the moment $\mathrm{t}=0$ is :$\overrightarrow{\mathrm{B}}=\mathrm{E}_{0} \sqrt{\mu_{0} \in_{0}} \cos (\mathrm{kx}) \hat{\mathrm{j}}$$\overrightarrow{\mathrm{B}}=\frac{\mathrm{E}_{0}}{\sqrt{\mu_{0} \in_{0}}} \cos (\mathrm{kx}) \hat{\mat...
Read More →A driver in a car, approaching a vertical wall notices that the frequency
Question: A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440 \mathrm{~Hz}$ to $480 \mathrm{~Hz}$, when it gets reflected from the wall. If the speed of sound in air is $345 \mathrm{~m} / \mathrm{s}$, then the speed of the car is$36 \mathrm{~km} / \mathrm{hr}$$24 \mathrm{~km} / \mathrm{hr}$$18 \mathrm{~km} / \mathrm{hr}$$54 \mathrm{~km} / \mathrm{hr}$Correct Option: 4, Solution: $\mathrm{f}_{1}=$ frequency heard by wall $=\mathrm{f}_{\...
Read More →Solve this following
Question: You are given that Mass of ${ }_{3}^{7} \mathrm{Li}=7.0160 \mathrm{u}$, Mass of ${ }_{2}^{4} \mathrm{He}=4.0026 \mathrm{u}$ and Mass of ${ }_{1}^{1} \mathrm{H}=1.0079 \mathrm{u}$. When $20 \mathrm{~g}$ of ${ }_{3}^{7} \mathrm{Li}$ is converted into ${ }_{2}^{4} \mathrm{He}$ by proton capture, the energy liberated, (in $\mathrm{kWh}$ ), is: [Mass of nudeon $=1 \mathrm{GeV} / \mathrm{c}^{2}$ ] $8 \times 10^{6}$$1.33 \times 10^{6}$$6.82 \times 10^{5}$$4.5 \times 10^{5}$Correct Option: , 2...
Read More →A fluid is flowing through a horizontal pipe
Question: A fluid is flowing through a horizontal pipe of varying cross-section, with speed $\mathrm{v} \mathrm{ms}^{-1}$ at a point where the pressure is P Pascal. P At another point where pressure is $\frac{\mathrm{P}}{2}$ Pascal its speed is $\mathrm{V} \mathrm{ms}^{-1}$. If the density of the fluid is $\rho \mathrm{kg} \mathrm{m}^{-3}$ and the flow is streamline, then $\mathrm{V}$ is equal to :$\sqrt{\frac{\mathrm{P}}{2 \rho}+\mathrm{v}^{2}}$$\sqrt{\frac{\mathrm{P}}{\rho}+\mathrm{v}^{2}}$$\s...
Read More →Two light waves having the same wavelength
Question: Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a path $L_{1}$ through a medium of refractive index $\mathrm{n}_{1}$ while the second wave travels a path of length $\mathrm{L}_{2}$ through a medium of refractive index $\mathrm{n}_{2}$. After this the phase difference between the two waves is:$\frac{2 \pi}{\lambda}\left(\mathrm{n}_{1} \mathrm{~L}_{1}-\mathrm{n}_{2} \mathrm{~L}_{2}\right)$$\frac{2 \pi}{\lambda}\left(\frac...
Read More →A block of mass 1.9kg is at rest at the edge of a table,
Question: A block of mass $1.9 \mathrm{~kg}$ is at rest at the edge of a table, of height $1 \mathrm{~m}$. A bullet of mass $0.1 \mathrm{~kg}$ collides with the block and sticks to it. If the velocity of the bullet is $20 \mathrm{~m} / \mathrm{s}$ in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$. Assume there is no rotational motion and loss of energy after the collision i...
Read More →In a dilute gas at pressure
Question: In a dilute gas at pressure $P$ and temperature $T$, the mean time between successive collisions of a molecule varies with $T$ as :$\sqrt{\mathrm{T}}$$\frac{1}{T}$$\frac{1}{\sqrt{T}}$$\mathrm{T}$Correct Option: , 3 Solution: $\mathrm{v}_{\mathrm{avg}} \propto \sqrt{\mathrm{T}}$ $\mathrm{t}_{0}:$ mean time $\lambda:$ mean free path $\mathrm{t}_{0}=\frac{\lambda}{\mathrm{V}_{\mathrm{avg}}} \propto \frac{1}{\sqrt{\mathrm{T}}}$...
Read More →Four point masses, each of mass
Question: Four point masses, each of mass $m$, are fixed at the corners of a square of side $\ell$. The square is rotating with angular frequency $\omega$, about an axis passing through oneof the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is: $2 \mathrm{~m} \ell^{2} \omega$$3 \mathrm{~m} \ell^{2} \omega$$\mathrm{m} \ell^{2} \omega$$4 m \ell^{2} \omega$Correct Option: , 2 Solution: $\mathrm{I}=\mathrm{m}(0)^{2}+\m...
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