The binding energy per nucleon for ${\mathrm{C}}^{12}$ is $7.68\mathrm{MeV}$ and that for ${\mathrm{C}}^{13}$ is $7.47\mathrm{MeV}$. The energy required to remove a neutron from ${\mathrm{C}}^{13}$ is

The distance of closest approach when an alpha particle of kinetic energy $6.5\mathrm{MeV}$ strikes a nucleus of atomic number 50 is

A scooter moves with a speed of $7{\mathrm{ms}}^{-1}$, on a straight road and is stopped by applying the brakes. Before stopping, the scooter travels $10\mathrm{m}$. If the weight of the scooter is $\mathrm{W}$, then the total resistance to the motion of the scooter will be

In Young's double slit experiment light of wavelength $500\mathrm{nm}$ is used to form interference pattern. A uniform glass plate of refractive index 1.5 and thickness $0.1\mathrm{mm}$ is introduced in the path of one of the interfering beams. The number of fringes that will shift due to this is

Figure below shows a network of resistors, cells, and a capacitor at steady state.

What is the current through the resistance 4 $\mathrm{\Omega }$ ?

A cricketer of height $2.5\mathrm{m}$ throws a ball at an angle of ${30}^{\circ }$ with the horizontal such that it is received by another cricketer of same height standing at a distance of $50\mathrm{m}$ from the first one. The maximum height attained by the ball is ($\tan {30}^{\circ }=0.577$)

If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength $\lambda$. When it jumps from the second to the first orbit, the corresponding wavelength of the photon will be

A solid cylinder of mass $2\mathrm{kg}$ and radius $0.2\mathrm{m}$ is rotating about its own axis without friction with angular velocity $5\mathrm{rad}{\mathrm{s}}^{-1}$. A particle of mass $1\mathrm{kg}$ moving with a velocity of $5{\mathrm{ms}}^{-1}$ strikes the cylinder and sticks to it as shown in figure.

The angular velocity of the system after the particle sticks to it will be

A neutral water molecule is placed in an electric field $E=2.5\times {10}^4{\mathrm{NC}}^{-1}$. The work done to rotate it by ${180}^{\circ }$ is $5\times {10}^{-25}\mathrm{J}$. Find the approximate separation of centre of charges.

A telescope has an objective of focal length $60\mathrm{cm}$ and eyepiece of focal length $5\mathrm{cm}$. The telescope is focussed for least distance of distinct vision $300\mathrm{cm}$ away from the object. The magnification produced by the telescope at least distance of distinct vision is

A parallel plate capacitor having a dielectric constant 5 and dielectric strength ${10}^6\mathrm{V}{\mathrm{m}}^{-1}$ is to be designed with voltage rating of $2\mathrm{kV}$. The field should never exceed $10\mathrm{\%}$ of its dielectric strength. To have the capacitance of $60\mathrm{pF}$ the minimum area of the plates should be

The coefficient of volume expansion of glycerine is $49\times {10}^{-5}{\mathrm{K}}^{-1}$. The percentage change in its density for a ${50}^{\circ }\mathrm{C}$ rise in temperature is

A current I flows in an infinitely long wire with cross section in the form of semi-circular ring of radius $1\mathrm{m}$. The magnitude of the magnetic induction along its axis is

Three bulbs of $40\mathrm{W},60\mathrm{W}$, and $100\mathrm{W}$ are arranged in series with a $220\mathrm{V}$ source. The maximum light is obtained from

A photon emitted during the de-excitation of electron from a state $\mathrm{n}$ to the second excited state in a hydrogen atom, irradiates a metallic electrode of work function $0.5\mathrm{eV}$, in a photocell, with a stopping voltage of $0.47\mathrm{V}$. Obtain the value of quantum number of the state '$n$'.

The acceleration due to gravity at pole and equator can be related as

A bar magnet is held perpendicular to a uniform field. If the couple acting on the magnet is to be halved, by rotating it, the angle by which it is to be rotated is

A negative charge particle is moving upward in a magnetic field which is towards north. The particle is deflected towards

Two point charges $\mathrm{M}$ and $\mathrm{N}$ having charges $+q$ and $-q$ respectively are placed at a distance apart. Force acting between them is $\mathrm{F}$. If $30\mathrm{\%}$ of charge of $\mathrm{N}$ is transferred to $\mathrm{M}$, then the force between the charges becomes:

A conducting circular loop is placed in a uniform magnetic field $\mathrm{B}=0.125\mathrm{T}$ with its plane perpendicular to the loop. If the radius of the loop is made to shrink at a constant rate of $2\mathrm{mm}{\mathrm{s}}^{-1}$, then the induced emf when the radius is $4\mathrm{cm}$ is

Figure below shows a lens of refractive index, $\mu =1.4$. $C_1$ and $C_2$ are the centres of curvature of the two faces of the lens of radii of curvature $4\mathrm{cm}$ and $8\mathrm{cm}$ respectively.

The lens behaves as a

The temperature of a wire is doubled. The Young's modulus of elasticity

A wire of length $2\mathrm{m}$ carries a current of $1\mathrm{A}$ along the $\mathrm{x}$ axis. A magnetic field $B=B_0(i+j+k)$ tesla exists in space. The magnitude of magnetic force on the wire is

The dimension $[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}]$ is the physical quantity of

The resistance of a $10\mathrm{m}$ long wire is $10\mathrm{\Omega }$. Its length is increased by $25\mathrm{\%}$ by stretching the wire uniformly. The new resistance is

A body is executing SHM. When its displacements from the mean position are $4\mathrm{cm}$ and $5\mathrm{cm}$ it has velocity $10{\mathrm{cms}}^{-1}$ and $8{\mathrm{cms}}^{-1}$ respectively. Its periodic time $\mathrm{t}$ is

When water falls from a height of $80\mathrm{m}$ at the rate of $20\mathrm{kg}{\mathrm{s}}^{-1}$ to operate a turbine the losses due to frictional force are $20\mathrm{\%}$ of input energy. How much power is generated by the turbine?

An electron has a mass of $9.1\times {10}^{-31}\mathrm{kg}$. It revolves round the nucleus in a circular orbit of radius $0.529\times {10}^{-10}\mathrm{m}$ at a speed of $2.2\times {10}^6{\mathrm{ms}}^{-1}$. The magnitude of its angular momentum is

$\text{ If the nuclear radius of }{}^{27}\mathrm{Al}\text{ is }3.6\text{ fermi, the nuclear radius of }{}^{125}\mathrm{Fe}\text{ is }$

When an A.C. source is connected to a inductive circuit,

A satellite is revolving around the earth in a circular orbit with kinetic energy of $1.69\times {10}^{10}\mathrm{J}$. The additional kinetic energy required for just escaping into the outer space is

A ball is moving in a circular path of radius $5\mathrm{m}$. If tangential acceleration at any instant is $10{\mathrm{ms}}^{-2}$ and the net acceleration makes an angle of ${30}^{\circ }$ with the centripetal acceleration, then, the instantaneous speed is

If 216 drops of the same size are charged at $200\mathrm{V}$ each and they combine to form a bigger drop, the potential of the bigger drop will be

The conductivity of a semiconductor increases with increase in temperature because

A) number density of free current carriers increases

B) relaxation time increases

C) both number density of carriers and relaxation time increase

D) number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density

Four resistors, each of resistance R, are connected as shown in the figure below.

In the $\mathrm{A}.\mathrm{C}$. circuit given below, voltmeters ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ read $100\mathrm{V}$ each. Find the reading of the voltmeter ${\mathrm{V}}_3$ and the ammeter $\mathrm{A}$.

Joule second is the unit of

When a biconvex lens of glass of refractive index 1.5 is dipped in a liquid, it acts like a plane sheet of paper. This means the refractive index of the liquid is

The latent heat of vaporisation of water is $2240\mathrm{J}$. If the work done in the process of vaporisation of $1\mathrm{g}$ is $168\mathrm{J}$, the increase in internal energy is

A particle of mass $2\mathrm{mg}$ has the same wavelength as a neutron moving with a velocity of $3\times {10}^5{\mathrm{ms}}^{-1}$. The velocity of the particle is (mass of neutron is $1.67\times {10}^{-27}\mathrm{Kg}$)

Two narrow parallel slits illuminated by a coherent monochromatic light produces an interference pattern on a screen placed at a distance $\mathrm{D}$ from the slits. The separation between the dark lines of the interference pattern can be increased by

Three point charges are located on a circular arc at $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ as shown in the figure below. The total electric field at the centre of the $\mathrm{arc}(\mathrm{C})$ is

A voltmeter of resistance $1000\mathrm{\Omega }.0.5\mathrm{V}/$ div is to be converted into a voltmeter to make it to read $=1\mathrm{V}/\mathrm{div}$. The value of high resistance to be connected in series with it is

Column - I lists the waves of the electromagnetic spectrum. Column - II gives approximate frequency range of these waves. Match Column - I and Column - II and choose the correct match from the given choices.

A monochromatic light of wavelength $800\mathrm{nm}$ is incident normally on a single slit of width $0.020\mathrm{mm}$ to produce a diffraction pattern on a screen placed $1\mathrm{m}$ away. Estimate the number of fringes obtained in Young's double slit experiment with slit separation $0.20\mathrm{mm}$, which can be accommodated within the range of total angular spread of the central maximum due to single slit.

Internal energy of ${\mathrm{n}}_1$ moles of hydrogen at temperature T is equal to internal energy of ${\mathrm{m}}_2$ moles of helium at temperature 2T. The ratio $\frac{n_1}{n_2}$ is

A body initially at rest undergoes rectilinear motion. The forcetime (F-t) graph for the motion of the body is given below. Find the linear momentum gained by the body in $2\mathrm{s}$.

Incident light of wavelength $\lambda =800\mathrm{nm}$ produces a diffraction pattern on a screen $1.5\mathrm{m}$ away when it passes through a single slit of width $0.5\mathrm{mm}$. The distance between the first dark fringes on either side of the central bright fringe is

A transformer of $100\mathrm{\%}$ efficiency has 200 turns in the primary and 40000 turns in the secondary. It is connected to a $220\mathrm{V}$ main supply and secondary feeds to a $100\mathrm{K}\mathrm{\Omega }$ resistance. The potential difference per turn is

Action and reaction can never balance out because

The current in a coil changes steadily from $3\mathrm{A}$ to $5\mathrm{A}$ in $0.2\mathrm{s}$ when an emf of $2\mu \mathrm{V}$ is induced in it. The self-inductance of the coil is

The output of the given circuit is

A. Negatively rectified half wave

B. Positively rectified half wave

C. Negatively rectified full wave

D. Zero all times

For a paramagnetic material, the dependence of the magnetic susceptibility $\chi$ on the absolute temperature is given as

The magnetic flux linked with a coil is given by the equation: $\varphi =8t^2+t+10$. The e.m.f. induced in the coil in the $3^{\text{rd }}$ second will be

A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by ${20}^{\circ }\mathrm{C}$ ? ($R=8.31\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$)

A hollow prism is filled with water and placed in air. It will deviate the incident rays

The number of possible natural oscillations of air column in a pipe closed at one end of length $85\mathrm{cm}$ whose frequencies lie below $1250\mathrm{Hz}$ are (velocity of sound $=340{\mathrm{ms}}^{-1}$)

The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 $\mu$F capacitor.

What is the relation obeyed by the angles of contact ${\theta }_1,{\theta }_2$ and ${\theta }_3$ of 3 liquids of different densities $P_1,P_2$ and $P_3$ respectively $({\mathrm{P}}_1<{\mathrm{P}}_2<{\mathrm{P}}_3$) when they rise to the same capillary height in 3 identical capillaries and having nearly same surface tension $\mathrm{T}$ ?

The following are the graphs of potential barrier versus width of the depletion region for a p-n junction diode.

Which of the following is correct?