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A particle has position vector ( 3i - j + 2k) metre at t=0. It moves with constant velocity (-i + j - 3k) m/s. The position vector after 3s

A battery consists of a variable number $n$ of identical cells (having internal resistance $r$ each) which are connected in series. The terminal of the battery are short circuited and the current $I$ is measured. Which of the graph shows the correct relationship between $I$ and $n?$

A cylinder of mass(M), radius (R) is resting on a horizontal platform (which is parallel to (X-Y) plane) with its axis fixed along the (y) axis and free to rotate about its axis. The platform is given a motion in (X) direction given by: ($x=Acoswt$ ). There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is:

A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of same mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres $\frac{v_1}{v_2}$ after collision will be

In pure inductive circuit, the curves between frequency f and reciprocal of inductive reactance 1/X_L is

The magnetic field normal to the plane of a circular coil of $n$ turns and radius $r$ which carries a current $i$ is measured on the axis of coil at a very small distance $h$ from the centre of coil. The measured field is smaller than the magnetic field at centre by a fraction

An aeroplane is travelling horizontally at a height of $2000\text{m}$ from the ground. The aeroplane, when at a point $\text{P}$, drops a bomb to hit a stationary target $Q$ on the ground. In order that the bomb hits the target, what angle $\theta$ must the line $\text{PQ}$ make with the vertical ?

$[g=10{\text{m/s}}^2]$

A wire $\text{PQ}$ of mass $10\text{g}$ is at rest on two parallel metal rails. The separation between the rails is $4.9\text{cm}$. A magnetic field of $0.80\text{T}$ is applied perpendicular to the plane of rails, directed downwards. The net resistance of the entire circuit is slowly decreased by decreasing the resistance of a variable resistor. When the resistance decreases to below $20\Omega$, the wire $\text{PQ}$ just begins to slide on rails. The coefficient of friction between wire and rails will be:

A force exerts an impulse $I$ on a particle changing its velocity from initial velocity $u\text{m/s}$ to final velocity $-2u\text{m/s}$. If the applied force and initial velocity are oppositely oriented along the same line, find the work done by force.

The variation of translational kinetic energy of one mole of a monoatomic gas with temperature is shown in the graph. Find $\tan \theta$.

Seven capacitors each of capacity 2μFare to be so connected to have a total

capacity 10/11 μF. Which will be the necessary figure as shown

Equation of a plane progressive wave is given by $y=A_1\text{sin}\pi (t-\frac{x}{3})$. After reflecting from a rarer medium amplitude of reflected wave becomes $A_2$. The equation of the reflected wave can be

Particle displacements (in $\text{cm}$) in a standing wave are given by $y(x,t)=2\sin \left(0.1\pi x\right)\cos \left(100\pi t\right)$. The distance between a node and the next antinode is

A police car moving at 22 m/s chases a motorcyclist. The police man sounds his horn of frequency 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of motorcyclist if it is given that he does not hear any beat (speed of sound in air is 330 m/s)

The surface tension of a liquid is $5\text{N/m}$ . If a film of this liquid is held on a ring of area $0.02{\text{m}}^2$, it's surface energy is about

A ball is thrown downwards from the top of a tower of height ${}^{\prime }{h}^{\prime }$ with a velocity ${}^{\prime }{v}^{\prime }$. Find the relation between ${}^{\prime }{v}^{\prime }$ and ${}^{\prime }{h}^{\prime }$ if the ball hits the ground with ${}^{\prime }3v^{\prime }$.

A star initially has ${10}^{40}$ deuterons. It produces energy via the processes

${}_1{\text{H}}^2{+}_1{\text{H}}^2{\to }_1{\text{H}}^3+p\text{and}{}_1{\text{H}}^2{+}_1{\text{H}}^3{\to }_2{\text{He}}^4+n$. If the average power radiated by the star is ${10}^{16}\text{W}$, the deuteron supply of the star is exhausted in a time of the order of $11.6\times {10}^x\text{s}$. Then the value of $x$ is -



$\text{Take}m{(}_1{\text{H}}^2)=2.0141u,m{(}_2{\text{He}}^4)=4.0026u,m{(}_1{p}^1)=1.0078u,m{(}_0{n}^1)=1.0086u1u{c}^2=931.5\text{MeV}$

A tank cart is filled with water as shown in the figure. The initial mass of the cart with water is $m_0=100\text{kg}$. At time $t=0$, a hole is made in the left wall of the cart and water starts spilling out from the cart, with a constant velocity of $v_r=10\text{m/s}$ with respect to the cart. The rate of ejection of water is $r=2\text{kg/s}$. Find the acceleration of the cart after time $t=5\text{s}$.

A uniform cable of mass ${}^{\prime }{M}^{\prime }$ and length ${}^{\prime }{L}^{\prime }$ is placed on a horizontal surface such that its ${\left(\frac{1}{n}\right)}^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

A uniform rod of length $l$ lies on a frictionless horizontal surface on which it is pivoted about its centre. A ball moving with speed $v$ as shown in figure collides with the rod at one of the ends. After hitting, the ball sticks to the rod. There is a similar uniform rod of length $l$, pivoted at one of its ends and a similar ball with same speed strikes the other end of the rod and sticks to it. The ratio of final angular momentum in both cases is:

1. 8

Indium antimonide has a band gap of 0.23 eV between the valence and the conduction band. Find the temperature at which kT equals the band gap.

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If $a_0$ is the radius of the ground state orbit, m is the mass and e is charge of the electron and ${ϵ}_0$ is the vacuum permittivity, the speed of the electron is

What is the relationship between the three forces?

The torque about the point $3\hat{i}-\hat{j}+3\hat{k}$ of a force $4\hat{i}+2\hat{j}+\hat{k}$ through the point $5\hat{i}+2\hat{j}+4\hat{k}$, is

The variation of pressure in a medium due to propagation of sound is represented as



Which of the following graph correctly represents the displacement of particles of the medium?

1. 2.8

The moment of inertia of a uniform rectangular plate of length l and width b about diagonal axis as shown in figure is ________. (Mass of plate is M)