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A closed container is filled with $20\text{moles}$ of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to it, the temperature remains constant, but $8\text{moles}$ of the gas dissociate into atoms. The heat energy supplied to the gas is

For a nucleus to be stable, the correct relation between neutron number N and Proton number Z is

Statement 1: In order to make a body rotate, the net external force applied can be zero.

Statement 2: A body can even rotate in absence of any external force.

A glass surface is coated by an oil film of uniform thickness $1.00\times {10}^{-4}$ cm. The index of refraction of the oil is 1.25 and that of the glass is 1.50 . Find the wavelengths of light in the visible region (400 nm - 750 nm) which are completelyi transmitted by the oil film under normal infcidnece.

Suppose
that the electric field part of an electromagnetic wave in vacuum is
E =
{(3.1 N/C) cos [(1.8 rad/m) y +
(5.4 × 10⁶
rad/s)t]}
.

(a)
What is the direction of
propagation?

(b)
What is the wavelength λ?

(c)
What is the frequency ν?

(d)
What is the amplitude of the
magnetic field part of the wave?

(e)
Write an expression for the
magnetic field part of the wave.

Initially the circuit is in steady state. When the switch S is closed, the heat generated in the circuit will be:

A light of intensity $8{\text{kWm}}^{-2}$ falls on a plane mirror with reflection coefficient $r=0.95$. The angle of incidence is ${60}^{\circ }.$ The pressure exerted by the light on the mirror is

1. Dynamo
2. Electric motor

Consider the following statements

The correct option regarding an isotope is

Plot the corresponding reference circle for each of the following
simple harmonic motions. Indicate the initial (t = 0) position
of the particle, the radius of the circle, and the angular speed of
the rotating particle. For simplicity, the sense of rotation may be
fixed to be anticlockwise in every case: (x is in cm and t
is in s).

(a) x = –2 sin (3t + π/3)

(b) x = cos (π/6 – t)

(c) x = 3 sin (2πt + π/4)

(d) x = 2 cos πt

The ratio of the weight of a man in a stationary lift and when it is accelerating downward with uniform acceleration $a$ is $3:2$. The value of $a$ is (Acceleration due to gravity is $g$ )

A copper wire of length $2\text{m}$ is placed in the magnetic field, $\overrightarrow{B}=(2\hat{i}+4\hat{j})\text{T}$ along $z-$axis. It moves with velocity, $\overrightarrow{v}=(4\hat{i}+6\hat{j}+8\hat{k})\text{m/s}$. Calculate the dynamic emf across its ends.

A transverse sinusoidal wave moves along a string in the positive $x-$direction at a speed of $10\text{cm/s}$. The wavelength of the wave is $0.5m$ and its amplitude is $10cm$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $0.05m$ is

The value of $\underset{-\pi /2}{\overset{\pi /2}{\int }}\frac{{\cos }^{2}x}{1+3^x}dx$ is :

In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

Light of wavelength $6000\stackrel{\circ }{A}$ is incident normally on a slit of width $24\times {10}^{-5}\text{cm}$. What is the angular position of second minimum from central maximum?

The plane $2x-3y+6z-11=0$ makes an angle $si{n}^{-1}\left(k\right)$ with X-axis. Then the value of ‘k’ is

You live on a busy street, but as a music lover, you want to reduce the traffic noise. If you install special sound-reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity $\left(in\frac{w}{m^2}\right)$?

In Young's double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance d (d>> b) from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

[IIT 1984; AIIMS 1995]

A loop of wire is placed in a magnetic field $\overrightarrow{B}=0.3\hat{j}\text{T}$. Find the flux through the loop, if the area vector is $\overrightarrow{A}=(2\hat{i}+5\hat{j}-3\hat{k}){\text{m}}^2$

How high does the ball go?

The de-Broglie wavelength of a proton moving with a velocity $v$, is $\lambda$. If an alpha particle is moving with a velocity $\frac{v}{2}$ then, what would be its de-Broglie wavelength ?

1. -100

The rate of heat radiation from two patches of skin of equal area on a patient's chest differs by $2\%$. If one of the patches is at $300K$ and both the patches is assumed to be blackbody, the temperature of other patch will be