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If a particle has velocity $v\left(t\right)=t^2-5t+6$, the average velocity in $5\text{sec}$ is

An ideal gas is taken through a cycle ABCA as shown in P – V diagram. The work done during the cycle is

A radio wave has a maximum magnetic field of ${10}^{-4}T$ on arriving at a receiving antenna. The maximum electric field intensity of such a wave is

The cross-sectional area of a horizontal tube increases linearly along its length, as we move in the direction of flow. The variation of pressure, as we move along its length in the direction of flow (positive x-direction) is best represented by which of the following graphs?

Find the acceleration of the particle at $x=2\text{m}$.

give two factors on which self inductance of a long solenoid depends.

If a particle is projected from origin and it follows the trajectory $y=x-\frac{1}{4}{x}^2$, then the time of flight is ($g$ = acceleration due to gravity)

What is the average velocity during time interval $t=2\text{s}$ to $t=5\text{s}$, in the following position time curve?

At some instant $\overrightarrow{v}=4\hat{i}-3\hat{j}\text{m/s}$ and $\overrightarrow{a}=2\hat{i}+\hat{j}{\text{m/s}}^2$. Find the radius of curvature at that instant.

A gas undergoes a cyclic process $a\to b\to c\to a$ which is as shown in the $PV$ diagram. The process $a\to b$ is isothermal , $b\to c$ is adiabatic and $c\to a$ is a straight line on the $P-V$ diagram. Work done in process $ab$ and $bc$ is $5\text{J}$ and $4\text{J}$ respectively. Calculate the efficiency of the cycle, if the area enclosed by the diagram $\text{abca}$ in the figure is $3\text{J}$.

Current density in a cylindrical wire of radius $R$ is given as
$J=\{\begin{array}{c}{J}_0(\frac{x}{R}-1)\text{for}0\le x<\frac{R}{2}\\ J_0\frac{x}{R}\text{for}\frac{R}{2}\le x\le R\end{array}$.
The current flowing in the wire is

Three blocks $A$, $B$ and $C$ weighing $1$, $8$ and $27\text{kg}$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. $T_1$ is equal to $2\text{N}$. Then $T_3$ is

A particle performs S.H.M of amplitude A along a straight line. When it is at a distance $\frac{\sqrt{3}}{2}A$ from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega }^2{A}^2$ due to an impulsive force. Then its new amplitude becomes

Explain Bernoulli's Principle.

In photoelectric effect, electrons are emitted

(1) At a rate that is independent of emitter.

(2) At a rate that is proportional to the square of amplitude of incident radiation

(3) With a maximum velocity proportional to the frequency of incident radiation

(4) Only if frequency of the incident radiation is above a threshold value

Note: Please explain all the options...

Air streams flows horizontally past an air plane. The speed over the top surface is $50\text{m/s}$ and that under the bottom surface is $40\text{m/s}$. If the density of air is $1.2{\text{kg/m}}^3$, then the difference in pressure across the plane is

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of 2 m/s. At what angle $\alpha$ with the vertical should the screen be placed so that the rain drops falling downwards with velocity 6 m/s strike the windscreen perpendicularly?

A wire of mass $5\text{kg}$ and length $3.5\text{m}$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is

A machine gun is mounted on a $2000\text{kg}$ car on a horizontal frictionless surface. At some instant the gun fires bullets of mass $10\text{gm}$ with a velocity of $500\text{m/sec}$ with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is

A person moves 50m in northern direction, 40 m in east and after that 20m in southern direction. The magnitude of net displacement of the person will be,

The internal resistance of an accumulator battery of emf 6 V is 10 $\Omega$ when it is fully discharged. As the battery gets charged up, its internal resistance decreases to 1 $\Omega$. The battery in its completely discharged state is connected to a charger which maintains a constant potential difference of 9 V. Find the current through the battery (a) just after the connections are made and (b) after a long time when it is completely charged.

A person travels along a straight road for the first half of the time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then the mean velocity $\overline{v}$ is given by

A mass of 100 kg is resting on a rough inclined plane of 60^o. If the coefficient of friction is 0.5, then the least force acting parallel to the plane to keep the mass in equilibrium is

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation $I=i_{m}sin\omega twhere{i}_m=10Aand\omega =100\pi rad{s}^{-1}$ . The maximum value of the emf induced in the second coil is

The electric current in a charging R-C circuit is given is given by $i=i_o{e}^{\frac{-t}{RC}}$ where io, R and C are constant parameter of the circuit and t is time. Find the rate of change of current at (x)t=0, (y)t=RC, (z)t=10 RC

$\left(i\right)\frac{-i_o}{RC}\left(ii\right)0\left(iii\right)\frac{-i_o}{R{C}_e}\left(iv\right)\frac{-i_o}{R{C}_e^{10}}\left(v\right)\frac{-i_o{e}^{10}}{RC}$

The velocity-time graph of a moving train is depicted as shown in figure. The average velocity in time interval $OD$ is

A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height, bith occuring at the same time. The correct statement is

Statement I A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
Statement II For every action there is an equal and opposite reaction.

The wavelength of de-Broglie wave is $2\mu m$, then its momentum is $(h=6.63\times {10}^{-34}J-s)$

A block of mass $m$ is at rest with respect to a rough inclined plane kept in an elevator moving up with an acceleration $‘a^{\prime }$. Which of the following statements is correct?

In the figure shown there are two semicircles of radii $r_1$ and $r_2$ in which a current i is flowing. The magnetic induction at the centre O will be

The angle between two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. Vector $\overrightarrow{R}$ is the resultant of these two vectors. If $\overrightarrow{R}$ makes an angle $\frac{\theta }{2}$ with $\overrightarrow{A}$, then

A uniform bar of negligible cross sectional area of length 6a and mass 8m lies on a horizontal frictionless table. Two point masses m and 2m moving in opposite directions but in the same horizontal plane with speeds 2v and v respectively strike the bar at a distance a and 2a from one end and stick to the bar after the collision. Then, after the collision

In the figure, the potentiometer wire AB of length L & resistance 9r is joined to the cell D of emf E & internal resistance r. The emf of the cell C is E / 2 & its internal resistance is 2r. The galvanometer G will show no deflection when the length AM is

Of the following quantities, which one has dimensions different from the remaining three ?

A coil of Cu wire (radius-r, self inductance-L) is bent in two concentric turns each having radius $\frac{r}{2}$. The self inductance now is

Ship $A$ is sailing towards north-east with velocity $\overrightarrow{v}=30\hat{i}+50\hat{j}km/h$, where $\hat{i}$ points east and $\hat{j}$ points north. Ship $B$ at a distance of $80km$ east and $150km$ north of ship $A$ is sailing towards the west at $10km/h$. $A$ will be at minimum distance from $B$ in

If the ratio of diameters, lengths and Young’s moduli of steel and brass wires shown in the figure are p, q and r respectively. Then the corresponding ratio of increase in their lengths would be

A liquid $X$ of density $4.2{\text{g/cm}}^3$ is poured upto a height of $12\text{cm}$ in the right limb of an U-tube which contains mercury. Another liquid $Y$ is poured in the left arm with height $10\text{cm}$. If upper level of $X$ and $Y$ are same, then find the density of liquid $Y$. (Take density of mercury ${\rho }_{Hg}=13.6{\text{g/cm}}^3$)

A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After the collision, their final velocities are $V$ and $v$ respectively. The value of $v$ is: