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In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is ${\frac{1}{8}}^{\text{th}}$ of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

What is the force
between two small charged spheres having charges of 2 × 10⁻⁷
C and 3 × 10⁻⁷ C placed 30 cm apart in air?

In the circuit shown in the figure, reading of voltmeter is $V_1$ when only $S_1$ is closed, $V_2$ when only $S_2$ is closed and $V_3$ when both $S_1$ and $S_2$ are closed. Choose the correct relation between $V_1$, $V_2$ and $V_3$.

Waves in a medium are represented by y=0.2 sin$\pi$ (x-4t) where x and y are in metres and t is in seconds. The displacement at a point x=50 cm and t=2.5 sec is?

In a hydrogen atom, the electron makes $6.6\times {10}^{15}\text{revolutions per second}$ around the nucleus in an orbit of radius $0.5\times {10}^{-10}\text{m}$. It is equivalent to a current nearly

A spherical conductor of radius $10\text{cm}$ has a charge of $3.2\times {10}^{-7}\text{C}$ distributed uniformly. What is the magnitude of electric field at a point $5\text{cm}$ from the surface of the sphere?

A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q, inclined at an angle $\theta$ to the vertical upwards. The block will remain in equilibrium, if minimum coefficient of friction between it and the surface is

Magnetic field of light ray is given by $\overrightarrow{B}=(3\hat{i}+4\hat{j})\times {10}^{-4}sin(kz+\omega t)$ & electric field is given by $\overrightarrow{E}=(\alpha \hat{i}+\beta \hat{j})\times {10}^{4}sin(kz+\omega t)$, then what is the relation between $\alpha \&\beta$

Three equal resistors connected in series across a source of emf together dissipate $10\text{W}$ of power. What would be the power dissipated if the same resistors are connected in parallel across the same source of emf?

An object of mass $\text{10 kg}$ is sliding with a constant velocity of $\text{2 m/s}$ on a frictionless horizontal table. What is the force required to keep the object moving with the same velocity?

A uniform metre scale balances horizontally on a knife edge placed at $55\text{cm}$ mark when a mass of $25\text{g}$ is suspended from one end, then mass of the scale is

The adiabatic bulk modulus of a diatomic gas at atmospheric pressure is

An object of mass $m$ is tied to a string of length $l$ and a variable force $F$ is applied on it which brings the string gradually to angle $\theta$ with the vertical. Find the work done by the force $F$. ( Assume initial and final kinetic energy to be zero)

Where does the mirror needs to be placed in a medium having refractive index $4/3$ (i.e. $x$), if image is to be formed at same place as object $O$?

A body is moving down into a well through a rope passing over a fixed pulley of radius $20\text{cm}$. Assume that there is no slipping between the rope and pulley. Calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of $40\text{cm/s}$ and has an acceleration of $4{\text{m/s}}^2$?

The thickness at the centre of a planoconvex lens is $3\text{mm}$ and the diameter is $6\text{cm}$. If the speed of light in the material of the lens is $2\times {10}^8{\text{ms}}^{-1}$, the focal length of the lens kept in air is :

A pulse is travelling on a stretched string fixed at one end with velocity $2\text{cm/s}$ as shown in the figure. At $t=0\text{s}$, center of pulse is $4\text{cm}$ apart from the fixed end. The shape of string at $t=2\text{s}$ is

Choose the correct statement:

Two ends of a rod of non-uniform area of cross-section are maintained at temperature $T_1$ and $T_2(T_1>T_2)$ as shown in the figure. If $I$ is the heat current through the cross - section of the conductor at distance $x$ from its left face then the variation of $I$ with time $t$ is best represented by

If $40\text{\%}$ energy released during fission would be converted into electrical energy, then the number of fission in a second in a nuclear reactor of $6.4\text{MW}$ output is

$[\text{Energy per fission}=200\text{MeV}]$

An expression for the magnetic field strength B at the point between the capacitor plates indicates in figure express B in terms of the rate of change of the electric field strength ie, $\frac{dE}{dt}$ between the plates

If $ABCD$ is a quadrilateral such that $\overrightarrow{AB}=\hat{i}+2\hat{j}$ and $\overrightarrow{AD}=\hat{j}+2\hat{k}$ and $\overrightarrow{AC}=2(\hat{i}+2\hat{j})+3(\hat{j}+2\hat{k}).$ Then area of quadrilateral $ABCD$ in sq. units is

Under electrostatic conditions electric field inside a conductor is zero but in electrodynamic condition the field is not equal to zero,how field develop inside a conductor in electrodynamic condition.

A plane wavefront travelling in a straight line in a vacuum encounters a medium of refractive index $\mu$. At $P$, the shape of the wavefront is :