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Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their accelerations are $0.3m/s^{2}and0.2m/s^2$ respectively, then the time they take to pass each other will be

An infinite number of identical capacitors each of capacitance $4\mu \text{F}$ are connected as in the adjoining figure. If a battery of $10\text{V}$ is connected across $\text{AB}$, what is the charge flown through the battery?

Ionisation energy of He⁺ is 19.6×10^-18 J atom^-1. The energy of the first stationary state(n=1) of Li²⁺ is:

A fan is rotating with angular velocity 100 $\frac{rev}{sec}$. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution made before it stops. (Assume uniform angular retardation) (ii)) Find the value of angular retardation (iii) Find the average angular velocity during this interval.

A parallel plate capacitor has rectangular plates of 400 cm^2 area and are separated by a distance of 2 mm with air as the medium. What charge will appear on the plates if a 200-volt potential difference is applied across the capacitor?

A simple microscope is rated $5X$ for a normal relaxed eye. What will be its magnifying power for a relaxed farsighted eye whose near point is $40cm$?

The equivalent resistance between points $A$ and $B$ is:

The percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

Have you ever had any curious experience which others find hard to believe?

A ball is dropped from a height of $20\text{m}$ above the surface of water in a lake. The refractive index of water is $\frac{4}{3}$. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8\text{m}$ above the water surface, the fish sees the speed of ball as

Figure shows an imaginary cube of side $a$. A uniformly charged rod of length $a$ moves towards right at a constant speed $v$. At $t=0$, the right end of the rod just touches the left face of the cube. Which of the following represents the correct graph between electric flux passing through the cube with time?

A particle which is constrained to move along $x-$axis is subjected to a force in the same direction which varies with distance $x$ of the particle from the origin as $F\left(x\right)=-kx+a{x}^3$. Here, $k$ and $a$ are positive constant. For $x\ge 0$, the functional form of the potential energy $U\left(X\right)$ of the particle is

Which one of the following graphs represents the behaviour of an ideal gas?

A satellite of mass m is revolving round the earth at a height R above the surface of earth. If g is gravitational acceleration at surface of earth and R is radius of earth then magnitude of momentum of satellite is

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the center of the disc and perpendicular to its plane is.

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60{\text{kmh}}^{-1}$ and at a height of $490\text{m}$. At the time of dropping the bomb, how far the aeroplane should be from the enemy post so that the bomb may directly hit the target?

In the given reaction

${}_z{X}^A{\to }_{z+1}{Y}^A{\to }_{z-1}{K}^{A-4}{\to }_{z-1}{K}^{A-4}$
Radioactive radiations are emitted in the sequence of

The ratio of the wavelengths of the last line of Balmer series and the last line of Lyman series is -



Assume same element.

Light in certain cases may be considered as a stream of particles called photons.Each photon has a linear momentum $\frac{h}{\lambda }$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength (\lambda ) is incident on a plane mirror at an angle of incidence $\theta$.Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.

The position of a particle moving along the $x$-axis varies with time $t$ as $x=4t-t^2+1$. Find the time interval(s) during which the particle is moving along positive $x$- direction.

Let $y=\{x{\}}^{\left[x\right]}$ where $\left\{x\right\}$ denotes the fractional part of $x$ and $\left[x\right]$ denotes the greatest integer less than or equal to $x.$ Then $\underset{0}{\overset{3}{\int }}ydx$ is

The displacement of a particle in string stretched in X direction is represented by y. Among the following expressions for y, those describing wave motions are

A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{R}{2}$ from the earth’s centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with X (distance of the particle from the centre) according to:

Two perfect gases at absolute temperatures $T_1$ and $T_2$ are mixed.Assuming that there is no loss of energy.Find the temperature T of the mixture if the masses of the molecules are $m_1$ and $m_1$ and the number of molecules in the gases are $n_1$ and $n_2$.

A wire of area of cross section 3.0 $m{m}^2$and natural length 50 cm is fixed at one end and a mass of 2.1 kg is hung from the other end. Find the elastic potential energy stored in the wire in steady state. Young's modulus of the material of the wire = $1.9\times {10}^{11}N{m}^{-2}.Takeg=10m{s}^{-2}$

The capacity of a condenser is 4x10^-6 farad and its potential is100 volts. The energy released on discharging it fully will be

If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is

A particle performs simple harmonic motion with amplitude $A$. Its speed is tripled at the instant it is at a distance $\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is

A particle is moving along a circular path, tangential acceleration and angular acceleration are same in magnitude. Then distance covered by the particle in one complete round is