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A particle of mass $m$ with an initial velocity $u\hat{i}$ collides elastically with a mass $3m$ at rest. It moves with a velocity $v\hat{j}$ after collision, then, $v$ is given by :

Potentiometer wire $\text{PQ}$ of $1\text{m}$ length is connected to a standard cell $E_1$. Another cell $E_2$ of emf $1.02\text{V}$ is connected with a resistance $r$ and a switch $S$ as shown in circuit diagram. With switch $S$ open, null position is obtained at a distance of $51\text{cm}$ from $\text{P}$. Calculate the e.m.f. of cell $E_1$.

Two particles A and B are thrown vertically upward with velocity, 5m/s and 10 m/s respectively ($g=10m/s^2$). Find separation between them after one second.

The current (i) in the network is

A ball moving with speed $v$ in $x$ direction changes its direction and speed. Its speed reduces to $\frac{v}{2}$ in $y-$ direction. Find out the magnitude of the impulse on the ball while the ball changes its direction. [Given mass of the ball is $m$]

A bar magnet of length $10\text{cm}$ and pole strength $2\text{Am}$ makes an angle ${60}^{\circ }$ with a uniform magnetic field of induction $B=50\text{T}.$ The couple acting on it is-

A galvanometer of resistance $5\Omega$ has a scale divided into 100 equal divisions and has a current sensitivity of 10 divisions per milliampere. To convert it into an ammeter of range of 5 amp, the necessary shunt required is

A car is moving with an initial velocity of $10{\text{m s}}^{-1}$ and an acceleration of $5{\text{m s}}^{-2}$ for a time interval of $10\text{s}$. If the mass of the car is $20\text{kg}$, find the average power of the car.

A particle at a height '$h$' from the ground is projected with an angle ${30}^{\circ }$ from the horizontal. It strikes the ground making angles ${45}^{\circ }$ with horizontal. It is again projected from the same point with the same speed but with an angle of ${60}^{\circ }$ with horizontal. Find the angle it makes with the horizontal when it strikes the ground.

A body of mass 'm' starts from rest and slides down an inclined plane of height h, and angle $\theta$. The velocity of the body when it reaches the bottom if the incline is smooth is-

A ray of light is incident on a plane mirror along a vector $(\hat{i}+\hat{j}-\hat{k})$. The normal on the incident point is along $\left(\hat{k}\right)$. The unit vector along the reflected ray will be:

What minimum horizontal speed should be given to the bob of a simple pendulum of length l so that it describes a complete circle?

An object is displaced from point $A(1,0)m$ to a point $B(0,4)m$ under the influence of a force $\overrightarrow{F}=-2\hat{i}+5\hat{j}.$ The workdone by this force is

In the network given points one of potentials of $70\text{V},0\text{V}$ and $10\text{V}$ respectively. The ratio of current through AD, DB and DC is

Three charges are kept on a straight line as shown in figure. With $A$ and $B$ denoting arbitrary constants, the potential at a far-off point $(r>>a)$ on the axis is given by

Three charges $+4q,Q$ and $+q$ are placed in a straight line such that the charge $Q$ is equidistant from both the other charges. What should be the charge $Q$ in order to make the net force on $+q$ to be zero ?

A current 4 A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a 12 V ac source $(\Omega =50rad{s}^{-1})$ a current of 2.4 A flows in the circuit. The inductance of the coil is

A man weighing $60\text{kg}$ is standing on a flat boat having ends $A$ and $B$, such that he is at a distance of $10\text{m}$ from one end $\left(B\right)$. The boat weighs $20\text{kg}$ and there is no friction between it and the water. If the man walks $4\text{m}$ relative to the boat towards the end $\left(B\right)$ and stops, then how far is the man from the end $B$ ?

A smooth sphere of mass $m$ is moving on a horizontal plane with velocity $3\hat{i}+\hat{j}$. It collides with a vertical wall which is parallel to vector$\hat{j}$. If the coefficient of restitution is $0.5$, the angle of velocity of the ball with repect to the normal to the wall after impact will be

A $3\varphi$ SC occurs at BUS -4. The SC current flowing between buses 1 and 2 is ___

Assume that the pre fault voltage at all the buses is 1.0 Pu.



$Z_{bus}=j\left[\begin{array}{cccc}0.15& 0.08& 0.04& 0.07\\ 0.08& 0.15& 0.06& 0.09\\ 0.04& 0.06& 0.13& 0.05\\ 0.07& 0.09& 0.05& 0.12\end{array}\right]$

A person stands in contact against the wall of a cylindrical drum of radius $R$ rotating with an angular velocity $\omega$ . If the coefficient of friction between the wall and the person is $\mu$ , the minimum rotational speed of the cylinder which enables the person to remain stuck to the wall when the floor is suddenly removed is

Under the action of a force, a $2\text{kg}$ body moves such that its position $x$ as a function of time t is given by $x=\frac{t^3}{3}$, where $x$ is in meter and $t$ in second. The work done by the force in the first two seconds is

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at $t=0$), the car was at $x=0$, where, $x$ is the position of the car at any time ‘$t$’.



The displacement of the car from the starting position will be

A magnetic needle is free to rotate in vertical plane. Initially plane of rotation of needle is perpendicular to magnetic meridian and needle is in vertical position (i.e. angle of dip is ${90}^{\circ }$). Now if plane of rotation of needle is rotated by ${60}^{\circ }$ about a vertical axis and angle of dip measured in this position is found to be ${30}^{\circ }$, then true angle of dip at this place is

Some positive charge is spread uniformly over the surface of a thin spherical shell. Radius of sphere is $100cm$ and electric field on the surface is $90\times {10}^{3}N/C$. A point $A$ is at $50cm$ from the centre & point $B$ is at $150cm$ from the centre. Field at $A$ & $B$ are $E_A$ & $E_B$ respectively, then

The equation of a wave disturbance propagating in the positive Y-direction is given by $y=\frac{1}{1+x^2}$ at $t=0$ and $y=\frac{1}{[1+(x-1{)}^2]}$ at $t=2s$, where $x$ and $y$ are in $\text{metres}$. If the shape of the wave disturbance does not change during the propagation, what is the velocity of the wave?

If the separation between the two eyes of a man is d, what should be the minimum width of the mirror in which the man could see the full image of his face of width w, using both of his eyes.