In a hydrogen atom the electron makes a transition from
Question: In a hydrogen atom the electron makes a transition from $(n+1)^{\text {th }}$ level to the $n^{\text {th }}$ level. If $n1$, the frequency of radiation emitted is proportional to : $\frac{1}{n^{4}}$$\frac{1}{n^{3}}$$\frac{1}{n^{2}}$$\frac{1}{n}$Correct Option: , 2 Solution: In hydrogen atom, $E_{n}=\frac{-E_{0}}{n^{2}}$ Where $\mathrm{E}_{0}$ is Ionisation Energy of $\mathrm{H}$. $\rightarrow$ For transition from $(\mathrm{n}+1)$ to $\mathrm{n}$, the energy of emitted radiation is equa...
Read More →In a Young's double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength
Question: In a Young's double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength $700 \mathrm{~nm}$ is used. If the wavelength of light is changed to $400 \mathrm{~nm}$, the number of fringes observed in the same segment of the screen would be : 28241830Correct Option: Solution: Let the length of segment is " $\ell^{\prime \prime}$ Let $\mathrm{N}$ is the no. of fringes in " $\ell^{\prime \prime}$ and $\mathrm{w}$ is fringe width. $\rightarrow$ W...
Read More →A heat engine is involved with exchange of heat of
Question: A heat engine is involved with exchange of heat of $1915 \mathrm{~J},-40 \mathrm{~J},+125 \mathrm{~J}$ and $\mathrm{QJ}$, during one cycle achieving an efficiency of $50.0 \%$. The value of $Q$ is: $640 \mathrm{~J}$$400 \mathrm{~J}$$980 \mathrm{~J}$$40 \mathrm{~J}$Correct Option: , 3 Solution: $\eta=\frac{\text { Work done }}{\text { Heat supplied }}$ $\frac{1}{2}=\eta=\frac{1915-40+125-Q}{1915+125}$ $\frac{1}{2}=\frac{2000-\mathrm{Q}}{2040}$ $2040=4000-2 Q$ $2 Q=1960$ $Q=980 \mathrm{~...
Read More →A potentiometer wire PQ of
Question: A potentiometer wire PQ of $1 \mathrm{~m}$ length is connected to a standard cell $\mathrm{E}_{1}$. Another cell $\mathrm{E}_{2}$ of emf $1.02 \mathrm{~V}$ is connected with a resistance 'r' and switch S (as shown in figure). With switch $S$ open, the null position is obtained at a distance of $49 \mathrm{~cm}$ from Q. The potential gradient in the potentiometer wire is: $0.02 \mathrm{~V} / \mathrm{cm}$$0.04 \mathrm{~V} / \mathrm{cm}$$0.01 \mathrm{~V} / \mathrm{cm}$$0.03 \mathrm{~V} / ...
Read More →A wire carrying current I is bent in the shape ABCDEFA
Question: A wire carrying current $I$ is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and $b$, then the magnitude and direction of magnetic moment of the loop $\mathrm{ABCDEFA}$ is : $\sqrt{2}$ abI, along $\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}\right)$$\sqrt{2}$ abI, along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{5}}+\frac{2 \hat{\mathrm{k}}}{\sqrt{5}}\right)$abI, along $\left(\fr...
Read More →The displacement time graph of a particle executing S.H.M. is given in figure
Question: The displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale) Which of the following statements is/are true for this motion ? (A) The force is zero $\mathrm{t}=\frac{3 \mathrm{~T}}{4}$ (B) The acceleration is maximum at $\mathrm{t}=\mathrm{T}$ (C) The speed is maximum at $\mathrm{t}=\frac{\mathrm{T}}{4}$ (D) The P.E. is equal to $\mathrm{K}$.E. of the oscillation at $\mathrm{t}=\frac{\mathrm{T}}{2}$ (A), (B) and (D)$(\mathrm{B}),...
Read More →The figure shows a region of length
Question: The figure shows a region of length ' $l$ ' with a uniform magnetic field of $0.3 \mathrm{~T}$ in it and a proton entering the region with velocity $4 \times 10^{5} \mathrm{~ms}^{-1}$ making an angle $60^{\circ}$ with the field. If the proton completes 10 revolution by the time it cross the region shown, $l^{\prime}$ ' is close to (mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$, charge of the proton $\left.=1.6 \times 10^{-19} \mathrm{C}\right)$ $0.11 \mathrm{~m}$$0.22 \mathrm{~m}...
Read More →A satellite is moving in a low nearly circular
Question: A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_{e}$. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become $\sqrt{\frac{3}{2}}$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is $R$, value of $R$ is :$4 \mathrm{R}_{\mathrm{e}}$$3 \mathrm{R}_{\mathrm{e}}$$2 \mathrm{R}_{\mathrm{e}}...
Read More →Solve this following
Question: When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength $3 \lambda$, the stopping potential is $\frac{\mathrm{V}}{4}$. If the threshold wavelength for the metallic surface is $n \lambda$ then value of $\mathrm{n}$ will be Solution: $\frac{\mathrm{hc}}{\lambda}=\frac{\mathrm{hc}}{\lambda_{0}}+\mathrm{eV}$ ............(I) $\frac{\mathrm{hc}}{3 \lambda}=\frac{\mathrm{hc}...
Read More →Pressure inside two soap bubbles are 1.01
Question: Pressure inside two soap bubbles are $1.01$ and $1.02$ atmosphere, respectively. The ratio of their volumes is :$8: 1$$0.8: 1$$2: 1$$4: 1$Correct Option: 1 Solution: $\mathrm{P}_{1}=0.01=4 \mathrm{~T} / \mathrm{R}_{1}$............(1) $\mathrm{P}_{2}=0.02=4 \mathrm{~T} / \mathrm{R}_{2}$..........(2) Equation (1) . (2) $\frac{1}{2}=\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}$ $\mathrm{R}_{1}=2 \mathrm{R}_{2}$ $\frac{V_{1}}{V_{2}}=\frac{R_{1}^{3}}{R_{2}^{3}}=\frac{8 R_{2}^{3}}{R_{2}^{3}}=8$...
Read More →A balloon filled with helium (32 degree C and 1.7 atm.) bursts
Question: A balloon filled with helium $\left(32^{\circ} \mathrm{C}\right.$ and $1.7 \mathrm{~atm}$.) bursts. Immediately afterwards the expansion of helium can be considered as :Irreversible isothermalIrreversible adiabaticReversible adiabaticReversible isothermalCorrect Option: , 2 Solution: Bursting of helium balloon is irreversible \ adiabatic....
Read More →Solve this following
Question: A small block starts slipping down from a point $\mathrm{B}$ on an inclined plane $\mathrm{AB}$, which is making an angle $\theta$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $\mu$. It is found that the block comes to rest as it reaches the bottom (point $\mathrm{A}$ ) of the inclined plane. If $\mathrm{BC}=2 \mathrm{AC}$, the coefficient of friction is given by $\mu=\mathrm{k} \tan \theta$ ). The value of $\mathrm{k}$ i...
Read More →In a radioactive material, fraction of active material remaining after time
Question: In a radioactive material, fraction of active material remaining after time $t$ is $9 / 16$. The fraction that was remaining after $\mathrm{t} / 2$ is :$\frac{3}{4}$$\frac{7}{8}$$\frac{4}{5}$$\frac{3}{5}$Correct Option: 1 Solution: First order decay $\mathrm{N}(\mathrm{t})=\mathrm{N}_{0} \mathrm{e}^{-\mathrm{i} \mathrm{t}}$ Given $\mathrm{N}(\mathrm{t}) / \mathrm{N}_{0}=9 / 16=\mathrm{e}^{-\lambda \mathrm{t}}$ Now, $\mathrm{N}(\mathrm{t} / 2)=\mathrm{N}_{0} \mathrm{e}^{-2 \mathrm{t} / ...
Read More →An engine takes in 5 moles of air at
Question: An engine takes in 5 moles of air at $20^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$, and compresses it adiabaticaly to $1 / 10^{\mathrm{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $\mathrm{X} \mathrm{kJ}$. The value of $\mathrm{X}$ to the nearest integer is Solution: Diatomic : $\mathrm{f}=5$ $\gamma=7 / 5$ $\mathrm{~T}_{\mathrm{i}}=\mathrm{T}=273+20=293 \mathrm{~K...
Read More →A 750Hz. 20V (rms) source is connected to a resistance of 100 om,
Question: A $750 \mathrm{~Hz}, 20 \mathrm{~V}(\mathrm{rms})$ source is connected to a resistance of $100_{\Omega}$, an inductance of $0.1803 \mathrm{H}$ and a capacitance of $10_{\mu} \mathrm{F}$ all in series. The time in which the resistance (heat capacity $2 \mathrm{~J} /{ }^{\circ} \mathrm{C}$ ) will get heated by $10^{\circ} \mathrm{C}$. (assume no loss of heat to the surroundings) is close to :$418 \mathrm{~s}$$245 \mathrm{~s}$$348 \mathrm{~s}$$365 \mathrm{~s}$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: A $5 \mu \mathrm{F}$ capacitor is charged fully by a $220 \mathrm{~V}$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5 \mu \mathrm{F}$ capacitor. If the energy change during the charge redistribution is $\frac{\mathrm{X}}{100} \mathrm{~J}$ then value of $\mathrm{X}$ to the nearest integer is Solution: $\mathrm{u}_{\mathrm{i}}=\frac{1}{2} \times 5 \times 10^{-6}(220)^{2}$ Final common potential $\mathrm{v}=\frac{220 \times 5+0 \times ...
Read More →When the wavelength of radiation falling on a metal
Question: When the wavelength of radiation falling on a metal is changed from $500 \mathrm{~nm}$ to $200 \mathrm{~nm}$, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :$0.61 \mathrm{eV}$$0.52 \mathrm{eV}$$0.81 \mathrm{eV}$$1.02 \mathrm{eV}$Correct Option: 1 Solution: $\frac{3}{1}=\frac{\frac{h c}{200 \mathrm{~nm}}-\phi}{\frac{h c}{500 \mathrm{~nm}}-\phi}, h c=1240 \mathrm{eV}-\mathrm{nm}$ On solving $\phi=0.61 \mathrm{eV}$...
Read More →Two identical strings
Question: Two identical strings $X$ and $Z$ made of same material have tension $\mathrm{T}_{\mathrm{X}}$ and $\mathrm{T}_{\mathrm{Z}}$ in them. It their fundamental frequencies are $450 \mathrm{~Hz}$ and $300 \mathrm{~Hz}$, respectively, then the ratio $\mathrm{T}_{\mathrm{X}} / \mathrm{T}_{\mathrm{Z}}$ is : $0.44$$1.5$$2.25$$1.25$Correct Option: , 3 Solution: $\mathrm{f}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mu}}$ For identical string $l$ and $\mu$ will be same $f \propto \sqrt{T}$ $\frac{4...
Read More →A charged particle carrying charge
Question: A charged particle carrying charge $1 \mu \mathrm{C}$ is moving with velocity $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mathrm{ms}^{-1}$. If an external magnetic field of $(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}) \times 10^{-3} \mathrm{~T}$ exists in the region where the particle is moving then the force on the particle is $\overrightarrow{\mathrm{F}} \times 10^{-9} \mathrm{~N}$. The vector $\vec{F}$ is :$-0.30 \hat{\mathrm{i}}+0.32 \hat{\mathrm{j}}...
Read More →Train A and train B are running on parallel tracks in the opposite directions with speeds
Question: Train A and train B are running on parallel tracks in the opposite directions with speeds of $36 \mathrm{~km} /$ hour and $72 \mathrm{~km} /$ hour, respectively. A person is walking in train $\mathrm{A}$ in the direction opposite to its motion with a speed of $1.8 \mathrm{~km} / \mathrm{hr}$. Speed (in $\mathrm{ms}^{-1}$ ) of this person as observed from train B will be close to : (take the distance between the tracks as negligible) $30.5 \mathrm{~ms}^{-1}$$29.5 \mathrm{~ms}^{-1}$$31.5...
Read More →The magnetic field of a plane electromagnetic wave is
Question: The magnetic field of a plane electromagnetic wave is $\vec{B}=3 \times 10^{-8} \sin [200 \pi(y+c t)] \hat{i} \mathrm{~T}$ Where $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ is the speed of light. The corresponding electric field is :$\overrightarrow{\mathrm{E}}=-10^{-6} \sin [200 \pi(\mathrm{y}+\mathrm{ct})] \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}$$\overrightarrow{\mathrm{E}}=-9 \sin [200 \pi(\mathrm{y}+\mathrm{ct})] \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}$$\overrightarrow{\mathrm...
Read More →Moment of inertia of a cylinder of mass M,
Question: Moment of inertia of a cylinder of mass M, length $\mathrm{L}$ and radius $\mathrm{R}$ about an axis passing through its centre and perpendicular to the axis of the cylinder is $\mathrm{I}=\mathrm{M}\left(\frac{\mathrm{R}^{2}}{4}+\frac{\mathrm{L}^{2}}{12}\right)$. If such a cylinder is to be made for a given mass of material, the ratio $\mathrm{L} / \mathrm{R}$ for it to have minimum possible I is :-$\sqrt{\frac{2}{3}}$$\frac{3}{2}$$\sqrt{\frac{3}{2}}$$\frac{2}{3}$Correct Option: , 3 S...
Read More →Model a torch battery of length l to be made up of a thin cylindrical bar
Question: Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius ' $a$ ' and a concentric thin cylindrical shell of radius 'b' filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $\mathrm{R}$ will take place for:- $\mathrm{R}=\frac{2 \rho}{\pi l} l \mathrm{n}\left(\frac{\mathrm{b}}{\mathrm{a}}\right)$$\mathrm{R}=\frac{\rho}{\pi l} \ln \left(\frac{\mathrm{b}}...
Read More →Using screw gauge of pitch 0.1cm and 50 divisions on its circular scale,
Question: Using screw gauge of pitch $0.1 \mathrm{~cm}$ and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as:$2.123 \mathrm{~cm}$$2.125 \mathrm{~cm}$$2.121 \mathrm{~cm}$$2.124 \mathrm{~cm}$Correct Option: , 4 Solution: $\mathrm{LC}=\frac{\text { pitch }}{\text { CSD }}=\frac{0.1 \mathrm{~cm}}{50}=0.002 \mathrm{~cm}$ So any measurement will be integral Multiple of LC. So ans. will be $2.124 \mathrm{~cm}$...
Read More →An amplitude modulated wave is represented by the expression
Question: An amplitude modulated wave is represented by the expression $\mathrm{v}_{\mathrm{m}}=5(1+0.6 \cos 6280 \mathrm{t})$ $\sin \left(211 \times 10^{4} \mathrm{t}\right)$ volts. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively : $5 \mathrm{~V}, 8 \mathrm{~V}$$\frac{3}{2} \mathrm{~V}, 5 \mathrm{~V}$$\frac{5}{2} \mathrm{~V}, 8 \mathrm{~V}$$3 \mathrm{~V}, 5 \mathrm{~V}$Correct Option: , 3 Solution: $\mathrm{V}_{\mathrm{m}}=5(1+0.6 \cos 6280 \mathrm{t}) \sin ...
Read More →