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A wire carrying a $10\text{A}$ current is bent to pass through various sides of a cube of side $10\text{cm}$ as shown in the figure. A magnetic field $\overrightarrow{B}=(2\hat{i}-3\hat{j}+\hat{k})\text{T}$ is present in the region. Find the magnetic moment vector of the loop.

If I is the moment of inertia of a ring having $\alpha$ coefficient of linear expansion, then the change in $I$ corresponding to a small change in temperature $\Delta T$ is

A dip needle lies initially in the magnetic meridian when it shows an angle of dip $\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip ${\theta }^{\prime }$. Then $\frac{\tan {\theta }^{\prime }}{\tan \theta }$ is

A force $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$ where $k$ is a positive constant acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point $(a,0)$ and then parallel to the y-axis to the point $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is

The wavelengths of $K_{\alpha }$ and $L_{\alpha }$ X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of $K_{\beta }$ X-ray of the material.

At ${27}^{\circ }C$ temperature the kinetic energy of an ideal gas is $E_1$ .If the temperature is increased to ${327}^{\circ }C$, then the kinetic energy will be

Dimensions of pressure gradient are

According to Einstein photoelectric effect equation, the graph between the kinetic energy of photoelectron ejected and the frequency ($\nu$) of incidented radiations is:

Pure Si at $300\text{K}$ has equal electron $\left(n_e\right)$ and hole $\left(n_h\right)$ concentrations of $1.5\times {10}^{16}{\text{m}}^{-3}$. Doping by indium increases $n_h$ to $4.5\times {10}^{22}{\text{m}}^{-3}$. Calculate $n_e$ in the doped Si.

10^-3 W of 5000⁰ALight is directed on a photoelectric cell. If the current in the cell is 0.16 μA, the percentage of incident photons which produce photoelectrons, is

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle α should be

The compressibility of water is $4\times {10}^{-5}$ per unit atmospheric pressure. The decrease in volume of $100c{m}^3$ of water under a pressure of 100 atmosphere will be

Two liquids of the same mass which are at temperatures ${20}^{\circ }\text{C}$ and ${40}^{\circ }\text{C}$ are mixed to form a composite liquid. If the final temperature of the mixture is ${32}^{\circ }\text{C}$, then the ratio of their specific heat capacities is

An impulse acts on a body of constant mass$\left(m\right)$ initially at rest. If it travels with constant velocity afterwards, which graph represents the variation of force$\left(F\right)$ with time during the time impulse was acting.

A wave travelling along the positive $x-$direction having maximum displacement along $y-$direction as $1\text{m}$, wavelength $2\pi \text{m}$ and frequency of $1/\pi \text{Hz}$ is represented by:

The capacitance between the adjacent plates shown in figure (31-E20) is 50 nF. A charge of $1.0\mu C$ is placed on the middle plate. (a) What will be the charge on the outer surface of the upper plate ? (b) Find the potential difference developed between the upper and the middle plates.

Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification $M_1$. When the set-up is kept in a medium of refractive index 7/6, the magnification becomes $M_2$. The magnitude $\left|\frac{M_2}{M_1}\right|$ is (give answer upto two decimal place)

If the linear mass density of a rod of length $2\text{m}$ varies as $\lambda =a+bx\text{kg/m}$, where $x$ is the distance (in metres) from its one end, then its centre of mass (in metres) is given by

Three plane mirrors are placed as shown in the figure. A light ray striking the first mirror at an angle of incidence ${60}^{\circ }$, after reflections at all the three mirrors, becomes opposite to the initial direction. Find the value of $\theta$.







Take angle of incidence to be equal at all the mirrors.

A rope of uniform mass $m$ and length $L$ is hanging from a support. A block of mass $M$ is attached to the rope at the lower end. If a transverse pulse is produced at the lower end, find the time taken by the pulse to reach the upper end.

Find the dipole moment of a system of charge $+q$ distributed uniformly on an arc of radius $R$ subtending an angle $\frac{\pi }{2}$ at its center where another charge $-q$ is placed.

The potential energy (in joule) of a body of mass 2 kg moving in the x-y plane is given by

U = 6x + 8y

where the position coordinates x and y are measured in metre. If the body is at rest at point (6 m, 4m) at time t = 0, it will cross the y-axis at time t equal to

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength ${\lambda }_0$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$. If the wave pulse of wavelength ${\lambda }_0$ is produced at point $A$ (Pulse 2) without disturbing the position of $M$ it takes time $T_{AO}$ to reach point $O$. Which of the following options is/arc correct?

A car has to negotiate a curve of radius $200\text{m}$. By how much should the outer side of the road be raised with respect to the inner side for a speed of $72\text{km/h}$. The width of the road is $1\text{m}$. $(g=10{\text{m/s}}^2)$

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}$ and $\overrightarrow{c}=\hat{i}-2\hat{j}+\hat{k}$, then a vector of magnitude $6$ units which is parallel to the vector $2\overrightarrow{a}-\overrightarrow{b}+3\overrightarrow{c}$ is

A spherical metal shell A of radius RA and a solid metal sphere B of radius RB(< RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

An ideal gas expands isothermally from volume $V_1$ to $V_2$ and is then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done by gas during the whole process is $W$. Then identify the correct statement.

Neglecting the air resistance, the time of flight of a projectile is determined by