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A bullet of mass 20 g moving with a velocity of 100 m/s strikes a wooden block of mass 80 g and gets embedded into it. Calculate the velocity of the combined system.

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In which of the following, pressure exerted on the ground is the least?

${\int }_{-\pi /2}^{\pi /2}cosxdx$

Find the height by which the sphere rises when the wedge is moved to touch the wall. The distance between the wedge and the wall is $10\text{m}$ and the wedge is moved to the left until it touches the wall.

A ray of light travelling in air is incident at angle of ${30}^{\circ }$ on one surface of a slab in which refractive index varies with $y$. The light travels along the curve $y=4x^2$ ($y$ and $x$ are in metre) in the slab. If the refractive index of the slab at $y=\frac{1}{2}m$ in the slab is $\frac{15}{x_o}$, then $x_o$ is

A bead of mass $m$ stays at point $P(a,b)$ on a wire bent in the shape of a parabola $y=4C{x}^2$ and rotating with angular speed $\omega$ (see figure). The value of $\omega$ is (neglect friction)

What is the maximum intensity of interference of $n$ identical waves each of intensity $I_0$, if the sources are coherent and incoherent respectively.

The couple acting on a bar magnet of pole strength $4\text{Am}$, when placed in a uniform magnetic field of intensity $10\sqrt{3}{\text{Am}}^{-1}$, such that axis of the magnet makes an angle ${60}^{\circ }$ with the direction of the field is $80\times {10}^{-6}\text{Nm}$. Find the distance between the poles of the magnet is,

How much energy must a gamma ray photon have, if it is to materialize into a pair of electron and positron, with each particle having a $K.E$ of $1\text{MeV}$?

A car approaching a crossing at a speed of $50\text{m/s}$ blows a horn of frequency $500\text{Hz}$ when $30\text{m}$ away from the crossing. The speed of sound in air is $330\text{m/s}$. What frequency will be heard by an observer at rest at $40\text{m}$ from the crossing?

A point charge of 2 micro Coulomb is at the centre of a cubic Gaussian surface 9 cm on edge. What is the net electric flux through the surface?

For a particle moving along a straight line, the position $x$ depends on time $t$ as $x=A{t}^3+B{t}^2+Ct+D$. The ratio of its initial velocity to its initial acceleration will be

If the potential difference between the plates of a capacitor is increased by 20%, the energy stored in the capacitor increases by exactly

A system has two charges $q_A=2.5\times {10}^{-7}Cand{q}_B=-2.5\times {10}^{-7}C$ located at points A(0,0,-15cm) and B(0,0,+15cm), respectively. What are the total charge and electric dipole moment of the system?

Mean free path for molecules of a gas is $\lambda$. If diameter of molecules is kept constant and the number density is increased to two times of its initial value, then new mean free path will be

Let $x^k+y^k=a^k,(a,k>0)$ and $\frac{dy}{dx}+{\left(\frac{y}{x}\right)}^{\frac{1}{3}}=0$, then $k$ is

Question 36

Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to $\frac{1}{3}rd$ of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?

An electrical dipole of dipole moment ${}^{\prime }{p}^{\prime }$ is placed in an electric field of intensity ${}^{\prime }{E}^{\prime }$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with electric field. Assuming that the potential energy of the dipole to be zero when $\theta ={90}^{\circ }$, the torque on dipole and the potential energy of the dipole will be respectively

A dip needle vibrates in the vertical plane perpendicular to the magnetic meridian. The time period of vibration is found to be $2\text{sec}$. The same needle is then allowed to vibrate in the horizontal plane and the time period is again found to be $2\text{sec}$. Then the angle of dip is

Two transparent media $\text{A}$ & $\text{B}$ having refractive indices ${\mu }_A=1.5$ and ${\mu }_B=1.2$ respectively in an optical fibre are seperated by a plane boundary. The speed of light in medium $\text{A}$ is $2\times {10}^3\text{m/s}$ and in medium $B$ is $2.5\times {10}^3\text{m/s}$. The critical angle for which a ray of light going from $\text{A}$ to $\text{B}$ is totally internally reflected is :-

A square loop of side $22\text{cm}$ is changed into a circle in $0.4\text{sec}$, inside a uniform magnetic field of $0.2\text{T}$. The emf induced is,

The position of a block placed on a surface having co-efficient of friction $0.5$ is given by $y=\frac{x^2}{4}$. Find the maximum height at which block can stay still.

A sound source S emitting waves of frequency $100\text{Hz}$ and an observer O are located at some distance from each other. The source is moving with a speed, $V_S=19.4{\text{ms}}^{-1}$ at an angle of ${60}^{\circ }$ with line joining the source and the observer as shown in the figure. If the observer is at rest, the apparent frequency observed by the observer is

(Velocity of sound in air $330{\text{ms}}^{-1})$

The plate current in a diode is 20 mA when the plate voltage is 50 V or 60 V. What will be th ecurrent if the plate voltage is 70 V?

What is tension?

How does tension varies in a rope which has negligible mass?

When does tension become zero?