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When an ideal gas expands, the temperature –

A Battery of emf $E$ (internal resistance = 0) is connected with $n$ resistors in parallel having equal resistance $R$, then $I$ vs $n$ graph is:

Two bodies $A$ and $B$ are travelling with constant velocities of $20\text{m/s}$ and $30\text{m/s}$ in the same positive direction. The relative velocity of $A$ with respect $B$ is

A ball is projected with a velocity of $\sqrt{17}m/s$ at an angle $\theta$ with the horizontal. Its horizontal range is equal to its maximum height. Velocity of the particle $0.1s$ after it is projected is (in $m/s$)
Take $g=10m/s^2$

Two ideal gases have the same valuve of $C_p/C_v=\gamma$. What will be the value of this ratio for a mixture of the two gases in the ratio 1 :2 ?

A boat which has a speed of $5km/hr$ in still water crosses a river of width $1km$ along the shortest possible path in $20min$. The velocity of the river water in $km/hr$ is

State and prove law of conservation of energy in case of freely falling body.

A circular disc is rotating with constant $\omega =2$ rad/sec, about an axis passing through its centre. An object is kept at a distance of ${}^{\prime }{r}_1=2c{m}^{\prime }$ from the centre and another object is kept at a distance of ${}^{\prime }{r}_2=1c{m}^{\prime }$. Find the ratio of their linear speeds.

The focal length of objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale 2 metre distant from it. The distance of objective lens from eye lens to see with relaxed eye is:

A closed tube filled with water is rotating about an axis as shown in figure. The pressure difference $P_A-P_C$ is

Find the percentage error in resistance if v= 100+-5. And I= 10+-2 ?

The number of photons of wavelength 540 nm emitted per second by an electric bulb of power 100W is (taking h = $h=6\times {10}^{-34}J-sec$ )

Cream gets separated out of milk when it is churned, it is due to

A solid cylinder of 200g and radius 10 cm has a moment of inertia (about its natural axis)

The magnetic field shown in the figure consist of the two magnetic fields.
If V is the velocity just required for a charge particle of mass $m$ and charge $-q$ to pass through the magnetic field. Particle is projected with velocity V perpendicular to the fields, then how much time does the charge spend in the magnetic field (W represent the radius of circular path traced by charge)

A convex lens of focal length $f_1$ is kept in contact with a concave lens of focal length $f_2$. Find the focal length of the combination.

A stone of mass $1\text{kg}$ tied to a light string of length $\frac{10}{3}\text{m}$ is whirled in a vertical circle. If the ratio of the maximum tension to minimum tension is 4 and $g=10{\text{m/s}}^2$, then the speed of the stone at the highest point of the circle is

Two wires A and B of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is $\frac{3}{2}$ times of that of wire B. The ratio of the forces produced in two wires will be

The area bounded by the curve $y=-4x+3$ and $y=0$ between $x=2$ and $x=4$ is

The Boolean equation for the circuit given in the figure:

A car is negotiating a curve of radius R = 20 m on a banked road with banking angle $\theta$ and coefficient of friction $\mu$. Take speed of car as v.

$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2}& & \text{Column 3}\\ \left(I\right)& v=10\sqrt{2}m/s& \left(i\right)& \mu =0.2& \left(p\right)& \theta ={30}^{\circ }\\ \left(II\right)& v=20m/s& \left(ii\right)& \mu =0.4& \left(Q\right)& \theta ={45}^{\circ }\\ \left(III\right)& v=50m/s& \left(iii\right)& \mu =0.6& \left(R\right)& \theta ={37}^{\circ }\\ \left(IV\right)& v=5m/s& \left(iv\right)& \mu =0.8& \left(S\right)& \theta ={60}^{\circ }\end{array}$

In which of the following cases, sliding occurs?

The position of the particle is given by $x=2t^2+6t+2$ in $\text{m}$. The instantaneous speed of the particle at $6\text{sec}$ is

The unit of momentum is

Two identical billiard balls are in contact on a smooth table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is

Find the dimensions of

(a) linear momentum,

(b) Frequency and

(c) pressure.

A dance competition takes place where participants take place in pairs. If during the performance they gradually form a group of four, six and nine persons, then the number of participants can be

Two containers of sand are arranged like the block as shown in figure. The containers alone have negligible mass; the sand in these containers has a total mass $M_{tot}$; the sand in the hanging container $H$ has mass $m$.
To measure the magnitude of the acceleration of the system, a large number of experiments have been carried out where $m$ varies from experiment to experiment but $M_{tot}$ does not; that is, sand is shifted between the containers before each trial.

Which of the curves in the graph correctly gives the acceleration magnitude as a function of the ratio $m/M_{tot}$ (vertical axis is for acceleration)?

A body is dropped freely from the window of a train. Will the time of the free fall be equal in all the following cases?

(1) the train is stationary,

(2) the train moves with constant velocity,

(3) the train moves with an acceleration.

A wave in the string is defined by the function $y={\sin }^2\omega t$, then the time period of this function is

In a hypothetical system a particle of mass m and charge - 3q is moving around a very heavy particle having charge q. Assuming Bohr's model to be true to this system, the orbital velocity of mass m when it is nearest to heavy particle is

The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times of its initial speed. If range of projectile is $p$ times the maximum height reached by it, then find the value of $p$.

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

If $\overrightarrow{a}=\hat{i}+\hat{j}+2\hat{k}\text{and}\overrightarrow{b}=2\hat{i}+\hat{j}+2\hat{k},$ then find the unit vector in the direction of 6 $\overrightarrow{b}$

The horizontal component of a force of $10N$ inclined at ${30}^o$ to vertical is

A wire of 15ohm is gradually stretched to twice it's original length it is then cut into two equal parts these parts are then connected in parallel a cross 3volt battery find current drawn from battery

Work required to rotate given square frame by ${180}^{\circ }$ can be given as

A system is shown in the figure. Find the moment of inertia about an axis passing through its $COM$ and perpendicular to the plane. (Assume masses are connected with light extensible strings)

A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\varphi$ $\left(Wb\right)$ linked with the coil varies with time $t$ (sec) as $\varphi =50t^2+4$, the current in the coil at $t=2sec$ is

A battle ship simultaneously fires two shells at enemy ships. Both are fired with the same speed but with different directions as shown. If the shells follow the parabolic trajectories shown, which ship gets hit first?

What will be the fraction of volume of a floating object of volume V and density d above the surface of a liquid of density D?

from the top of a tower of height 78. 4 metres to stones are projected horizontally with speed 10 metre per second and 15 M per second in opposite directions the distance of separation between them on reaching the ground is

A child sits stationary at one end of long trolley moving uniformly with speed v on a smooth horizontal floor. If the child gets up and runs about on the trolley in the forward direction with speed u. The centre of mass of the system (child + trolley) will move with speed