An engine of a train, moving with uniform acceleration,
Question: An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:$\sqrt{\frac{\mathrm{v}^{2}+\mathrm{u}^{2}}{2}}$$\frac{\mathrm{v}-\mathrm{u}}{2}$$\frac{u+v}{2}$$\sqrt{\frac{\mathrm{v}^{2}-\mathrm{u}^{2}}{2}}$Correct Option: 1 Solution: $\left(\mathrm{v}^{\prime}\right)^{2}=\mathrm{u}^{2}+2 \mathrm{ad}$' $v^{2}=\left(v^{\prime}\right)^{2}...
Read More →Each side of a box made
Question: Each side of a box made of metal sheet in cubic shape is 'a' at room temperature ' $T$ ', the coefficient of linear expansion of the metal sheet is ' $\alpha$ '. The metal sheet is heated uniformly, by a small temperature $\Delta \mathrm{T}$, so that its new temperature is $\mathrm{T}+\Delta \mathrm{T}$. Calculate the increase in the volume of the metal box.$3 a^{3} \alpha \Delta T$$4 \mathrm{a}^{3} \alpha \Delta \mathrm{T}$$4 \pi a^{3} \alpha \Delta T$$\frac{4}{3} \pi \mathrm{a}^{3} \...
Read More →A particle is moving with uniform speed along the
Question: A particle is moving with uniform speed along the circumference of a circle of radius $\mathrm{R}$ under the action of a central fictitious force $\mathrm{F}$ which is inversely proportional to $\mathrm{R}^{3}$. Its time period of revolution will be given by :$\mathrm{T} \propto \mathrm{R}^{2}$$T \propto \mathrm{R}^{\frac{3}{2}}$$\mathrm{T} \propto \mathrm{R}^{\frac{5}{2}}$$\mathrm{T} \propto \mathrm{R}^{\frac{4}{3}}$Correct Option: 1 Solution: $F \propto \frac{1}{R^{3}}$ $\frac{\mathr...
Read More →A diatomic gas,
Question: A diatomic gas, having $C_{p}=\frac{7}{2} R$ and $C_{v}=\frac{5}{2} R$, is heated at constant pressure. The ratio $\mathrm{dU}: \mathrm{dQ}: \mathrm{dW}:$$5: 7: 3$$5: 7: 2$$3: 7: 2$$3: 5: 2$Correct Option: , 2 Solution: $\mathrm{dU}=\mathrm{nC}_{\mathrm{v}} \mathrm{dT}$ $\mathrm{dQ}=\mathrm{nC}_{\mathrm{p}} \mathrm{dT}$ $\mathrm{dW}=\mathrm{PdV}=\mathrm{nRdT}$ (isobaric process) $\mathrm{dU}: \mathrm{dQ}: \mathrm{dW}: \mathrm{C}_{\mathrm{v}}: \mathrm{C}_{\mathrm{p}}: \mathrm{R}$ $=\fra...
Read More →Match List-I with List-II :
Question: Match List-I with List-II : Choose the correct answer from the options given below :(a) $\rightarrow$ (i), (b) $\rightarrow$ (iii), (c) $\rightarrow$ (ii), (d) $\rightarrow$ (iv)(a) $\rightarrow$ (ii), (b) $\rightarrow$ (iii), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (i)(a) $\rightarrow$ (ii), (b) $\rightarrow$ (iv), (c) $\rightarrow$ (iii), (d) $\rightarrow$ (i)(a) $\rightarrow$ (iii), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (i), (d) $\rightarrow$ (iv)Correct Option: , 2 Solution: ...
Read More →The normal density of a material is
Question: The normal density of a material is $\rho$ and its bulk modulus of elasticity is $\mathrm{K}$. The magnitude of increase in density of material, when a pressure $P$ is applied uniformly on all sides, will be :$\frac{\rho \mathrm{K}}{\mathrm{P}}$$\frac{\rho P}{K}$$\frac{K}{\rho P}$$\frac{\mathrm{PK}}{\rho}$Correct Option: , 2 Solution: $\rho=\frac{M}{V}$ $\frac{\mathrm{d} \rho}{\rho}=-\frac{\mathrm{dV}}{\mathrm{V}}$ $\mathrm{k}=-\frac{\mathrm{P}}{\frac{\mathrm{dV}}{\mathrm{V}}}$ $-\frac...
Read More →An α particle and a proton are accelerated
Question: An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200 \mathrm{~V}$. After this, their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{\mathrm{p}}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_{\alpha}}$ is :$3.8$8$7.8$$2.8$Correct Option: , 4 Solution: $\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}$ $\frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{m_{a} q_{\alpha}}{m_{p} q_{p}}}=\sqrt{\frac{4 m...
Read More →If an emitter current is
Question: If an emitter current is changed by $4 \mathrm{~mA}$, the collector current changes by $3.5 \mathrm{~mA}$. The value of $\beta$ will be :70.50.8753.5Correct Option: 1 Solution: $\mathrm{I}_{\varepsilon}=\mathrm{I}_{\mathrm{C}}+\mathrm{I}_{\mathrm{B}}$ $\Rightarrow \Delta \mathrm{I}_{\varepsilon}=\Delta \mathrm{I}_{\mathrm{C}}+\Delta \mathrm{I}_{\mathrm{B}}$ $4 \mathrm{~mA}=3.5 \mathrm{~mA}+\Delta \mathrm{I}_{\mathrm{B}}$ $\Rightarrow \Delta \mathrm{I}_{\mathrm{B}}=0.5 \mathrm{~mA}$ $\R...
Read More →Two equal capacitors
Question: Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:$4: 1$$2: 1$$1: 4$$1: 2$Correct Option: , 3 Solution: For series combination For parallel combination $\mathrm{C}_{\mathrm{eq}_{2}}=\mathrm{C}+\mathrm{C} \Rightarrow \mathrm{C}_{\mathrm{eq}_{2}}=2 \mathrm{C}$ $\Rightarrow \frac{\mathrm{C}_{\mathrm{eq}_{1}}}{\mathrm{C}_{\mathrm{eq}_{2}}}=\frac{(\mathrm{C} / 2)}{2 \mathrm{C}}=\frac{1}{4}=1: 4$...
Read More →A 5V battery is connected across the points
Question: A $5 \mathrm{~V}$ battery is connected across the points $\mathrm{X}$ and $\mathrm{Y}$. Assume $\mathrm{D}_{1}$ and $\mathrm{D}_{2}$ to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point $X$. $\sim 0.5 \mathrm{~A}$$\sim 1.5 \mathrm{~A}$$\sim 0.86 \mathrm{~A}$$\sim 0.43 \mathrm{~A}$Correct Option: , 4 Solution: Here only $D_{1}$ will work and we know for silicon diode, potential drop on $\mathrm{D}_{1}$ will be $0....
Read More →An alternating current is given by the equation
Question: An alternating current is given by the equation $\mathrm{i}=\mathrm{i}_{1} \sin \omega \mathrm{t}+\mathrm{i}_{2} \cos \omega \mathrm{t}$. The rms current will be$\frac{1}{\sqrt{2}}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}$$\frac{1}{\sqrt{2}}\left(i_{1}+i_{2}\right)^{2}$$\frac{1}{2}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}$$\frac{1}{\sqrt{2}}\left(i_{1}+i_{2}\right)$Correct Option: 1 Solution: $\mathrm{i}=\mathrm{i}_{1} \sin \omega \mathrm{t}+\mathrm{i}_{2} \sin (\omega \mathr...
Read More →If the velocity-time graph
Question: If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ? Correct Option: , 2 Solution: Slope of v-t graph gives acceleration...
Read More →The pitch of the screw gauge is 1mm and
Question: The pitch of the screw gauge is $1 \mathrm{~mm}$ and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is$1.64 \mathrm{~mm}$$0.82 \mathrm{~mm}$$1.80 \mathrm{~mm}$$0.90 \mathrm{~...
Read More →Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance
Question: Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $(\mathrm{R} / 2)$ from the earth's centre, where ' $R$ ' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:$\frac{2 \pi R}{g}$$\frac{g}{2 \pi R}$$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{g}}{\mathrm{R}}}$$2 \pi \sqrt{\frac{\mathrm{R}}{\mathrm{g}}}$Correct Option: , 4 Solution: Force along ...
Read More →Four identical particles of
Question: Four identical particles of equal masses $1 \mathrm{~kg}$ made to move along the circumference of a circle of radius $1 \mathrm{~m}$ under the action of their own mutual gravitational attraction. The speed of each particle will be :$\sqrt{\frac{G}{2}(1+2 \sqrt{2})}$$\sqrt{G(1+2 \sqrt{2})}$$\sqrt{\frac{G}{2}(2 \sqrt{2}-1)}$$\sqrt{\frac{(1+2 \sqrt{2}) G}{2}}$Correct Option: , 4 Solution: $\mathrm{F}_{1}=\frac{\mathrm{Gmm}}{(2 \mathrm{R})^{2}}=\frac{\mathrm{Gm}^{2}}{4 \mathrm{R}^{2}}$ $\m...
Read More →If the time period of a two meter long simple pendulum
Question: If the time period of a two meter long simple pendulum is $2 \mathrm{~s}$, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :$\pi^{2} \mathrm{~ms}^{-2}$$9.8 \mathrm{~ms}^{-2}$$2 \pi^{2} \mathrm{~ms}^{-2}$$16 \mathrm{~m} / \mathrm{s}^{2}$Correct Option: , 3 Solution: $\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$ $2=2 \pi \sqrt{\frac{2}{g}}$ $\Rightarrow \mathrm{g}=2 \pi^{2}$...
Read More →In the given figure
Question: In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked $A, B, C, D$ and $E$. The transitions $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ respectively represent : The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.The first member of the Lyman series, third member of Balmer series and second member of Paschen series.The series limit of Lyman series, third member of Balmer series and se...
Read More →Given below are two statement :
Question: Given below are two statement : Statement-I: A speech signal of $2 \mathrm{kHz}$ is used to modulate a carrier signal of $1 \mathrm{MHz}$. The band width requirement for the signal is $4 \mathrm{kHz}$. Statement-II : The side band frequencies are $1002 \mathrm{kHz}$. and $998 \mathrm{kHz}$. In the light of the above statements, choose the correct answer from the options given below:Statement I is true but Statement II is falseStatement I is false but Statement II is trueBoth Statement ...
Read More →A short straight object of height
Question: A short straight object of height $100 \mathrm{~cm}$ lies before the central axis of a spherical mirror whose focal length has absolute value $|f|=40 \mathrm{~cm}$. The image of object produced by the mirror is of height $25 \mathrm{~cm}$ and has the same orientation of the object. One may conclude from the information:Image is real, same side of concave mirror.Image is virtual, opposite side of concave mirror.Image is real, same side of convex mirror.Image is virtual, opposite side of...
Read More →If Y, K and
Question: If $\mathrm{Y}, \mathrm{K}$ and $\eta$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.$\mathrm{Y}=\frac{9 \mathrm{~K} \eta}{3 \mathrm{~K}-\eta} \mathrm{N} / \mathrm{m}^{2}$$\eta=\frac{3 Y K}{9 K+Y} N / m^{2}$$\mathrm{Y}=\frac{9 \mathrm{~K} \eta}{2 \eta+3 \mathrm{~K}} \mathrm{~N} / \mathrm{m}^{2}$$\mathrm{K}=\frac{\mathrm{Y} \eta}{9 \eta-3 \mathrm{Y}} \mathrm{N} / \mathrm{m}^{2}$Corre...
Read More →A proton, a deuteron and an
Question: A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is_________ and their speed is_________ in the ratio.$1: 2: 4$ and $2: 1: 1$$2: 1: 1$ and $4: 2: 1$$4: 2: 1$ and $2: 1: 1$$1: 2: 4$ and $1: 1: 2$Correct Option: , 2 Solution: $\mathrm{F}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}})=\frac{\mathrm{q}}{\mathrm{m}}(\overrightarrow{\mathrm{P}} \times \overrightarro...
Read More →Solve this following
Question: If $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $\lambda_{1}: \lambda_{2}$ is:$1: 9$$7: 108$$7: 135$$1: 3$Correct Option: , 3 Solution: $\frac{1}{\lambda_{1}}=\mathrm{R}\left[\frac{1}{1^{2}}-\frac{1}{4^{2}}\right]$ $\frac{1}{\lambda_{2}}=\mathrm{R}\left[\frac{1}{3^{2}}-\frac{1}{4^{2}}\right]$ $\frac{\lambda_{1}}{\lambda_{2}}=\frac{\left[\frac{1}{9}-\frac{1}{16}\right]}{\left[1-\fr...
Read More →The angular frequency of alternating current in a L-C-R circuit
Question: The angular frequency of alternating current in a L-C-R circuit is $100 \mathrm{rad} / \mathrm{s}$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser. $0.8 \mathrm{H}$ and $150 \mu \mathrm{F}$$0.8 \mathrm{H}$ and $250 \mu \mathrm{F}$$1.33 \mathrm{H}$ and $250 \mu \mathrm{F}$$1.33 \mathrm{H}$ and $150 \mu \mathrm{F}$Correct Option: , 2 Solution: Current through $60 \Omega$ resistance $=\frac{15}{60}=\frac{1}{4} \mathrm{~...
Read More →In the given figure,
Question: In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period $T$ and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be : $A \sqrt{\frac{M-m}{M}}$$A \sqrt{\frac{M}{M+m}}$$A \sqrt{\frac{M+m}{M}}$$A \sqrt{\frac{M}{M-m}}$Correct O...
Read More →Given below are two statements:
Question: Given below are two statements: Statement-I : Two photons having equal linear momenta have equal wavelengths. Statement-II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.Both Statement I and Statement II are trueStatement I is false but Statement II is trueBoth Statement I and Statement II are falseStatement $\mathrm{I}$ is true but Stat...
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