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Velocity-time equation of a particle moving in a straight line is, $v=(10+2t+3t^2)$. Find displacement of particle from the origin at time $t=1\text{s}$, if it is given that displacement is $20\text{m}$ at time $t=0$

The horizontal and vertical components of the velocity of projection of a projectile are $10{\text{ms}}^{-1}$ and $20{\text{ms}}^{-1}$ respectively. Find the horizontal range of projectile. ($g=10{\text{ms}}^{-2}$).

An object of mass 5 kg is acted upon by a force that varies with position of the object as shown. If the object starts out from rest at a point x = 0, what is its speed at x = 50 m?

In a hydrogen atom, the electron makes the transition from an energy level with quantum number $n$ to another with quantum number $(n-1)$. If $n>>1$, the frequency of radiation emitted is proportional to

Question 20

Three 2 ~$\Omega$ resistors, A, B and C, are connected as shown in the figure. Each of them dissipates energy and can withstand a maximum power of 18 W without melting. Find the maximum current that can flow through the three resistors?

At what
angle should a ray of light be incident on the face of a prism of
refracting angle 60° so that it just suffers total internal
reflection at the other face? The refractive index of the material of
the prism is 1.524.

A current carrying hollow wire has inner radius $\frac{R}{2}$ and outer radius $R$ .Which of the following plots correctly represent variation of magnetic field with respect to distance from its axis.

Beams of red, green and violet light are falling on the refracting face of a thin prism, all at same angle of incidence. If their angles of deviation are ${\theta }_1,{\theta }_2$ and ${\theta }_3$ respectively, then

Two trains move towards each other with the same speed. Speed of sound is $340{\text{ms}}^{-1}$. If the pitch of the tone of the whistle of one when heard on the other changes by $\frac{9}{8}$ times, then the speed of each train is:

Find the capacitance of the infinite ladder between point $X\text{and}Y.$

Find the charges on the capacitor assembly shown in the figure below.

A solid sphere rests on a horizontal surface. A horizontal impluse $J$ is applied at height $h$ from center. The sphere starts pure rolling just after the application of the impluse. The ratio $\frac{h}{R}$ will be

A long cylindrical conductor of radius 'a' has two cylindrical cavities each of diameter 'a' through its entire length as shown in the figure. A current I is directed out of the page and is uniform throughout the cross-section of the conductor. The magnetic field at point $P_1$ is

An electron and a photon have same wavelength. It p is the momentum of electron and E the energy of photon. The magnitude of p/ E in S.I. unit is

Find the angular width between the first maxima on either sides of the central maxima. The double slit experiment is performed with light of wavelength $3\times {10}^{-6}\text{m}$ and the separation between the slits is $6\mu \text{m}$,

A person of mass $40\text{kg}$ is inside a lift of mass $960\text{kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration $2{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

Ratio of maximum to minimum intensity during interference of two waves is $25:1$. The amplitude ratio of these two waves is

A magnetic field of $2\times {10}^{-2}T$ acts at right angles to a coil of area $100c{m}^2$, with $50$ turns. The average e.m.f. induced in the coil is $0.1V$, when it is removed from the field in $t$ $sec$. The value of $t$ is

Water is allowed to come out of a hole $P$ in one of the walls at a depth $h_1$ below the surface of water. Express the horizontal distance covered by water jet in terms of $h_1$ and $h_2$.

Is initial speed is equal to Modula's of initial velocity???

How???

When a coil of copper is kept at a certain distance above a flame, the candle keeps burning, but when the coil is placed over the flame, it is extinguished. This happens because

A uniform ring of radius $R$ is given a back spin of angular velocity $\frac{V_0}{2R}$ and thrown on a horizontal rough surface with velocity of centre to be $V_0$. The velocity of the centre of the ring when it starts pure rolling will be

Two straight long conductors $\text{AOB}$ and $\text{COD}$ are perpendicular to each other and carries currents $i_1$ and $i_2$ respectively. The magnitude of magnetic induction at a point $\text{P}$ at a distance $a$ from the point $\text{O}$ in a direction perpendicular to the plane $\text{ACBD}$ is