An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is

When two displacements represented by $y_1 = a\sin(\omega t)$ and $y_2 = b\cos(\omega t)$ are superimposed, the motion is

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to: $v(x) = \beta x^{-2n}$ where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by

If radius of the $^{27}_{13}Al$ nucleus is taken to be $R_{Al}$ then the radius of $^{125}_{53}Te$ nucleus is nearly

In a double-slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining 10 maxima of double slit within the central maxima of single slit pattern?

For a parallel beam of monochromatic light of wavelength $\lambda,$ diffraction is produced by a single slit whose width $a$ is of the order of the wavelength of the light. If $D$ is the distance of the screen from the slit, the width of the central maxima will be

Across a metallic conductor of the non-uniform cross section, a constant potential difference is applied. The quantity which remains constant along the conductor is

On observing light from three different stars P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum of Q. If $T_P, T_Q,$ and $T_R$ are the respective absolute temperatures of P, Q and R, then it can be concluded from the above observation that

A potentiometer wire has length 4 m and resistance 8 $\Omega.$ The resistance that must be connected in series with the wire and an accumulator of emf 2 V, so as to get a potential gradient 1 mV per cm on the wire is

Consider third orbit of He$^+$ (Helium), using non-relativistic approach, the speed of electron in this orbit will be $[K = 9 \times 10^9, Z = 2$ and $h = 6.63 \times 10^{-34} Js]$

A wire carrying current $I$ has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to the x-axis while a semi-circular portion of radius $R$ is lying in a $yz$ plane. Magnetic field at point $O$ is

Which of the following figure represents the variation of particle momentum and the associated de Broglie wavelength?

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

The refracting angle of a prism is $A,$ and the refractive index of the material of the prism is $\cot(A/2).$ The angle of minimum deviation is

Which logic gate is represented by the following combination of logic gates?

A Carnot engine, having an efficiency of $\eta = \frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

A certain metallic surface is illuminated with monochromatic light of wavelength, $\lambda.$ The stopping potential for photoelectric current for this light is $3V_0.$ If the same surface is illuminated with light of wavelength $2\lambda,$ the stopping potential is $V_0.$ The threshold wavelength for this surface for photoelectric effect is

A radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is $(c =$velocity of light$)$

A mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_0$ at a radius $R_0.$ The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally $m$ moves in a circle of radius $\frac{R_0}{2}.$ The final value of the kinetic energy is

Two identical thin plano-convex glass lenses (refractive index $1.5)$ each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index $1.7.$ The focal length of the combination is

A block A of mass $m_1$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end another block B of mass $m_2$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu_k.$ When the block A is sliding on the table, the tension in the string is

A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2,$ respectively. Its time period is

A ship A is moving westwards with a speed of $10$ km h$^{-1}$ and a ship B 100 km south of A, is moving northwards with a speed of $10$ km h$^{-1}.$ The time after which the distance between them becomes shortest, is

A rod of weight $W$ is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at distance $x$ from A. The normal reaction on A is

The approximate depth of an ocean is $2700$ m$.$ The compressibility of water is $45.4 \times 10^{-11}$ Pa$^{-1}$ and density of water is $10^3$ kg m$^{-3}.$ What fractional compression of water will be obtained at the bottom of the ocean?

Two particles of masses $m_1, m_2$ move with initial velocities $u_1$ and $u_2.$ On collision, one of the particles gets excited to a higher level, after absorbing energy $\varepsilon.$ If final velocities of the particles be $v_1$ and $v_2$ then we must have:

Kepler’s third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet, that is, $T^2 = K r^3,$ here $K$ is constant.$$If the masses of sun and planet are $M$ and $m,$ respectively then as per Newton’s law of gravitation force of attraction between them is$\\F = \frac{G M m}{r^2},$ here $G$ is gravitational constant.$\\$The relation between $G$ and $K$ is described as

A block of mass $10$ kg, moving in $x$ direction with a constant speed of $10$ ms$^{-1},$ is subjected to a retarding force $F = 0.1 \times J$ m$^{-1}$ during its travel from $x = 20$ to $30$ m. Its final K.E. will be

A wind with speed $40$ ms$^{-1}$ blows parallel to the roof of a house. The area of the roof is $250$ m$^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $(\rho_{air} = 1.2$ kg m$^{-3})$

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R.$ If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

A resistance $R$ draws power $P$ when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes $Z,$ the power drawn will be

The ratio of the specific heat $\frac{C_P}{C_V} = \gamma$ in terms of degrees of freedom $(n)$ is given by

The figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, $400$ J of heat is added to the system and in process BC, $100$ J of heat is added to the system. The heat absorbed by the system in the process AC will be

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

If in a p-n junction, a square input signal of 10 V is applied as shown, then the output across $R_L$ will be:

Three blocks A, B and C of masses 4, 2 and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied onto the 4 kg block, then the contact force between A and B is

A, B and C are voltmeters of resistance R, 1.5 R and 3R, respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are $V_A, V_B$ and $V_C,$ respectively. Then,

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $XX^{\prime}$ which is touching to two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about$XX^{\prime}$axis is

The electric field in a certain region is acting radially outward and is given by $E = A r.$ A charge contained in a sphere of radius $a$ centred at the origin of the field, will be given by

The two ends of a metal rod are maintained at temperatures $100^{\circ}C$ and $110^{\circ}C.$ The rate of heat flow in the rod is found to be $4.0$ Js$^{-1}.$ If the ends are maintained at temperatures $200^{\circ}C$ and $210^{\circ}C,$ the rate of heat flow will be

Two similar springs P and Q have spring constants $K_P$ and $K_Q,$ such that $K_P > K_Q.$ They are stretched, first by the same amount (case a,) then by the same force (case b). The work done by the springs $W_P$ and $W_Q$ are related as, in case (a) and case (b), respectively

A conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $V.$ The emf induced in the frame will be proportional to

A particle of mass $m$ is driven by a machine that delivers a constant power $k$ watt. If the particle starts from rest, the force on the particle at time $t$ is