An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant.

Question: An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure $\mathrm{P}$ and volume $\mathrm{V}$ is given by $\mathrm{PV}=$ constant, then $\mathrm{n}$ is given by (Here $\mathrm{C}_{\mathrm{P}}$ and $\mathrm{C}_{\mathrm{V}}$ are molar specific heat at constant pressure and constant volume, respectively) :- $\mathrm{n}=\frac{\mathrm{C}-\mathrm{C}_{\mathrm{V}}}{\mathrm{C}-\mathrm{C}_{\math...

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it.

Question: Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3 \%$ each, then error in the value of resistance of the wire is :-$3 \%$$6 \%$zero$1 \%$Correct Option: , 2 Solution:...

Choose the correct statement :

Question: Choose the correct statement :In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the frequency of the audio signal.In amplitude modulation the amplitude of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.In amplitude modulation the frequency of the high frequency carrier wave is made to vary in proportion to the amplitude of the audio signal.In frequency modulation the amplitude of...

The current in the primary circuit of a potentiometer is

Question: The current in the primary circuit of a potentiometer is $0.2 \mathrm{~A}$. The specific resistance and crosssection of the potentiometer wire are $4 \times 10^{-7} \mathrm{ohm}$ metre and $8 \times 10^{-7} \mathrm{~m}^{2}$ respectively. The potential gradient will be equal to :-$0.2 \mathrm{~V} / \mathrm{m}$$1 \mathrm{~V} / \mathrm{m}$$0.5 \mathrm{~V} / \mathrm{m}$$0.1 \mathrm{~V} / \mathrm{m}$Correct Option: , 4 Solution:...

Prove the following

Question: If $400 \Omega$ of resistance is made by adding four $100 \Omega$ resistance of tolerance $5 \%$, then the tolerance of the combination is :$20 \%$$5 \%$$10 \%$$15 \%$Correct Option: , 2 Solution:...

Solve the following

Question: A single of $5 \mathrm{kHz}$ frequency is amplitude modulated on a carrier wave of frequency $2 \mathrm{MHz}$. The frequencies of the resultant signal is/are -$2005 \mathrm{kHz}, 2000 \mathrm{kHz}$ and $1995 \mathrm{kHz}$$2000 \mathrm{kHz}$ and $1995 \mathrm{kHz}$$2 \mathrm{MHz}$ only$2005 \mathrm{kHz}$ and $1995 \mathrm{kHz}$Correct Option: 1 Solution:...

If a wire is stretched to make it 0.1 % longer its resistance will :-

Question: If a wire is stretched to make it $0.1 \%$ longer its resistance will :-decrease by $0.2 \%$decrease by $0.05 \%$increase by $0.05 \%$increase by $0.2 \%$Correct Option: , 4 Solution:...

Solve this following

Question: ' $n$ ' moles of an ideal gas undergoes a process $\mathrm{A} \rightarrow \mathrm{B}$ as shown in the figure. The maximum temperature of the gas during the process will be :$\frac{9 \mathrm{P}_{0} \mathrm{~V}_{0}}{\mathrm{nR}}$$\frac{9 \mathrm{P}_{0} \mathrm{~V}_{0}}{4 \mathrm{nR}}$$\frac{3 \mathrm{P}_{0} \mathrm{~V}_{0}}{2 \mathrm{nR}}$$\frac{9 \mathrm{P}_{0} \mathrm{~V}_{0}}{2 \mathrm{n} \mathrm{R}}$Correct Option: , 2 Solution:...

A diode detector is used to detect an amplitude modulated wave of

Question: A diode detector is used to detect an amplitude modulated wave of $60 \%$ modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.$10.62 \mathrm{kHz}$$5.31 \mathrm{MHz}$$5.31 \mathrm{kHz}$$10.62 \mathrm{MHz}$Correct Option: , 3 Solution:...

Two conductors have the same resistance at

Question: Two conductors have the same resistance at $0^{\circ} \mathrm{C}$ but their temperature coefficients of resistance are $\alpha_{1}$ and $\alpha_{2}$. The respective temperature coefficients of their series and parallel combinations are nearly:$\frac{\alpha_{1}+\alpha_{2}}{2}, \frac{\alpha_{1}+\alpha_{2}}{2}$$\frac{\alpha_{1}+\alpha_{2}}{2}, \alpha_{1}+\alpha_{2}$$\alpha_{1}+\alpha_{2}, \frac{\alpha_{1}+\alpha_{2}}{2}$$\alpha_{1}+\alpha_{2}, \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alph...

Seven identical circular planar

Question: Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is : $\frac{55}{2} \mathrm{MR}^{2}$$\frac{73}{2} \mathrm{MR}^{2}$$\frac{181}{2} \mathrm{MR}^{2}$$\frac{19}{2} \mathrm{MR}^{2}$Correct Option: , 3 Solution:...

From a uniform circular

Question: From a uniform circular disc of radius $\mathrm{R}$ and mass $9 \mathrm{M}$, a small disc of radius $\frac{\mathrm{R}}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of dise is : $\frac{40}{9} \mathrm{MR}^{2}$$10 \mathrm{MR}^{2}$$\frac{37}{9} \mathrm{MR}^{2}$$4 \mathrm{MR}^{2}$Correct Option: , 4 Solution:...

Statement-1 : The temperature dependence of resistance is usually given as $

Question: Statement-1 : The temperature dependence of resistance is usually given as $\mathrm{R}=\mathrm{R}_{0}(1+\alpha \Delta \mathrm{t})$. The resistance of a wire changes from $100 \Omega$ to $150 \Omega$ when its temperature is increased from $27^{\circ} \mathrm{C}$ to $227^{\circ} \mathrm{C}$. This implies that $\alpha=2.5 \times 10^{-3} /{ }^{\circ} \mathrm{C}$. Statement $-2: R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta \mathrm{T}$ is small and $\D...

A radar has a power of

Question: A radar has a power of $1 \mathrm{~kW}$ and is operating at a frequency of $10 \mathrm{GHz}$. It is located on a mountain top of height $500 \mathrm{~m}$. The maximum distance up to which it can detect object located on the surface of the earth (Radius of earth $=6.4 \times 10^{6} \mathrm{~m}$ ) is :$40 \mathrm{~km}$64$80 \mathrm{~km}$$16 \mathrm{~km}$Correct Option: , 3 Solution:...

Consider a spherical shell of radius

Question: Consider a spherical shell of radius $\mathrm{R}$ at temperature $\mathrm{T}$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $\mathrm{u}=\frac{\mathrm{U}}{\mathrm{V}} \propto \mathrm{T}^{4}$ and pressure $\mathrm{p}=\frac{1}{3}\left(\frac{\mathrm{U}}{\mathrm{V}}\right)$. If the shell now undergoes an adiabatic expansion the relation between $\mathrm{T}$ and $\mathrm{R}$ is - $T \propto \frac{1}{R}$$\mathrm{T} \propt...

A slender uniform rod of mass

Question: A slender uniform rod of mass $\mathrm{M}$ and length $\ell$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is : $\frac{3 g}{2 \ell} \cos \theta$$\frac{2 g}{3 \ell} \cos \theta$$\frac{3 \mathrm{~g}}{2 \ell} \sin \theta$$\frac{2 \mathrm{~g}}{3 \ell} \sin \theta$Co...

This questions has Statement-1 and Statement-2. Of the four choice given after the statements,

Question: This questions has Statement-1 and Statement-2. Of the four choice given after the statements, choose the one that best describes the two statements. Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement- 2 : The state of ionosphere varies from hour to hour, day to day and season to season.Statement-1 is true, Statement-2 is true, Statement- 2 is the correct explanation of statement-1...

The moment of inertia of a uniform

Question: The moment of inertia of a uniform cylinder of length $\ell$ and radius $\mathrm{R}$ about its perpendicular bisector is I. What is the ratio $\ell / R$ such that the moment of inertia is minimum ?1$\frac{3}{\sqrt{2}}$$\sqrt{\frac{3}{2}}$$\frac{\sqrt{3}}{2}$Correct Option: , 3 Solution:...

One mole of diatomic ideal gas undergoes a cyclic process

Question: One mole of diatomic ideal gas undergoes a cyclic process $\mathrm{ABC}$ as shown in figure. The process $\mathrm{BC}$ is adiabatic. The temperatures at $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $400 \mathrm{~K}, 800 \mathrm{~K}$ and $600 \mathrm{~K}$ respectively. Choose the correct statement : The change in internal energy in the process $\mathrm{AB}$ is $-350 \mathrm{R}$.The change in internal energy in the process $B C$ is $-500 R$The change in internal energy in whole cyclic p...

A roller is made by joining

Question: A roller is made by joining together two cones at their vertices $\mathrm{O}$. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre $\mathrm{O}$ at the centre of line joining $\mathrm{AB}$ and $\mathrm{CD}$ (see figure). It is given a light push so that it starts rolling with its centre $\mathrm{O}$ moving parallel to $\mathrm{CD}$ in the direction shown. As it moves, the roller will tend to :- turn left and ri...

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M.

Question: An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $\mathrm{V}_{0}$ and its pressure is $\mathrm{P}_{0}$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency. $...

In a coil of resistance

Question: In a coil of resistance $100 \Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :- $250 \mathrm{~Wb}$$275 \mathrm{~Wb}$$200 \mathrm{~Wb}$$225 \mathrm{~Wb}$Correct Option: 1 Solution:...

Question: In a coil of resistance $100 \Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :- $250 \mathrm{~Wb}$$275 \mathrm{~Wb}$$200 \mathrm{~Wb}$$225 \mathrm{~Wb}$Correct Option: 1 Solution:...

An electron beam is accelerated by a potential difference

Question: An electron beam is accelerated by a potential difference $\mathrm{V}$ to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays.If $\lambda_{\min }$ is the smallest possible wavelength of $X$-ray in the spectrum, the variation of $\log \lambda_{\min }$ with $\log \mathrm{V}$ is correctly represented in :Correct Option: , 3 Solution:...

An inductor L =0.03 H and a resistor

Question: An inductor $(\mathrm{L}=0.03 \mathrm{H})$ and a resistor $(\mathrm{R}=0.15 \mathrm{k} \Omega)$ are connected in series to a battery of $15 \mathrm{~V}$ EMF in a circuit shown below. The key $\mathrm{K}_{1}$ has been kept closed for a long time. Then at $\mathrm{t}=0, \mathrm{~K}_{1}$ is opened and key $\mathrm{K}_{2}$ is closed simultaneously. At $\mathrm{t}=1 \mathrm{~ms}$, the current in the circuit will be $\left(\mathrm{e}^{5} \cong 150\right):-$ $6.7 \mathrm{~mA}$$0.67 \mathrm{~m...