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An object is placed in front of a concave mirror of focal length $f$. A virtual image is formed with a magnification of 2. To obtain a real image of same magnification, the object has to moved by a distance

Suppose we have a box filled with gas and a piston is also attached at the top of the box. What are the ways of changing the state of gas (and hence its internal energy)? Answer could be more than one choice.

The approximate depth of an ocean is $2700\text{m}$. The compressibility of water is $45.4\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. Fractional compression of water will be:
[Take $g=10{\text{m/s}}^2$]

Assuming potential energy at infinite separation is zero, what is the Potential Energy of a two charge system if the charges are both +10C and are separated by 10m?

A free hydrogen atom after absorbing a photon of wavelength ${\lambda }_a$ gets excited from the state $n=1$ to the state $n=4$. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength ${\lambda }_e$. Let the change in momentum of atom due to the absorption and the emission are $\Delta P_a$ and $\Delta P_e$ respectively. If ${\lambda }_a/{\lambda }_e=1/5$, which of the option (s) is/are correct ?

[Use $hc=1242eV$ nm ; $1nm={10}^{-9}m$, h and c are Plank's constant and speed of light, respectively]

A 10000kg engine pulls a metro train of 6 wagons wiegning 2000kg each. If engine exerted a force of 50000N and track offer a frictional force 5000N then calculate (1) Acceleration (2) the force by wagon 1 on wagon 2

If $97.52$ is divided by $2.54$, the correct result in terms of significant figures is

Given two continuous time signal x(t) $=e^{-t}andy\left(t\right)=e^{-2t}$ which exists for t> 0 then the convolution $z\left(t\right)=x\left(t\right)\ast y\left(t\right)$ is

The value of $\underset{-1}{\overset{3}{\int }}({\tan }^{-1}\frac{x}{x^2+1}+{\tan }^{-1}\frac{x^2+1}{x})dx$ is equal to

A capacitive type displacement transducer consists of two triangular plates, placed side by side, with negligible gap in between them and a rectangular plate moving laterally with an uniform air gap of 1 mm between the fixed plates and the moving plate. The schematic diagram is shown below with appropriate dimension.







With the position of the moving plate shown in the figure above, the values of the capacitances $C_{1}and{C}_2$ thus formed are

A metallic ball, dropped from a height undergoes _______________.

The velocity of the centre of mass of a system changes from $\overrightarrow{v_1}=4\hat{i}\text{m/s}$ to $\overrightarrow{v_2}=3\hat{j}\text{m/s}$ during time $\Delta t=2\text{s}$. If the mass of the system is $m=10\text{kg}$, the magnitude of constant force acting on the system is

A car has a headlight which can illuminate a horizontal straight road in front upto a distance of $10\text{m}$. If the coefficient of friction between tyre and road is $0.5$, the maximum safe speed of the car during a night drive is

[Neglect the reaction time of the driver and take $g=10{\text{m/s}}^2$]

Two protons A and B are placed in between the two plates of a parallel plate capacitor charged to a potential difference V as shown in the figure. The forces on the protons due to capcitor plates are

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In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[E\right]$ and [𝐵] stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[L\right]$ and $\left[T\right]$ are dimensions of length and time respectively. All the quantities are given in SI units.





The relation between [𝐸] and [𝐵] is

An electric current has the ability to produce magnetic field___

What is the reading of spring balance $D$ ?
(All the springs are ideal and identical)

When pressure of a gas (at ${20}^{\circ }\text{C}$ temperature) is changed from $P_1=1.01\times {10}^5\text{Pa}$ to $P_2=1.165\times {10}^5\text{Pa}$, the volume changes by $10$%. Then the bulk modulus of the gas is

A long cylindrical wire have linear density $+2\times {10}^{-8}\text{C/m}$. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron.

The ends of a stretched wire of length $L$ are fixed at $x=0$ and $x=L$. If in an experiment, the displacement of the wire is $y_1=A\sin \left(\frac{\pi x}{L}\right)\sin \omega t$ and energy is $E_1$ and in another experiment, its displacement is $y_2=A\sin \left(\frac{2\pi x}{L}\right)\sin 2\omega t$ and energy is $E_2$, then

[Assume, there is no energy loss at the ends of the stretched wire]

An infinite current carrying wire is bent making angle of ${60}^{\circ }$ at its center. The current of $0.5\text{A}$ is flowing through it. Calculate the strength of the magnetic field at a point which lies on it's angle bisector and at a distance of $2\text{cm}$ from the center.

The velocity at the maximum height of a projectile is half of its initial velocity of projection u. Its range on the horizontal plane is

The region between two concentric spheres of radii '$a$' and '$b$', respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is

If the wavelength of incident radiation is $248\text{nm}$, calculate the momentum associated with the photon.

Two waves are represented by the equations, $y_1=a\sin (\omega t-kx+{\varphi }_1)$ and $y_2=a\sin (\omega t-kx+{\varphi }_2)$. If the amplitude of the resultant wave remains equal to that of superimposing waves, then the phase difference between the original waves is

A railway carriage of mass $8000\text{kg}$ is moving with the speed of $54\text{km/hr}$ and collides with the another stationary carriage of same mass. Find the loss in kinetic energy in this process.