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Light rays of wavelengths $6000\mathring{A}$ and of Photon intensity $39.6{\text{W m}}^2$ is incident on a metal surface. If only one percent of photons incident on the surface, emit photo electrons, then the number of electrons emitted per second per unit area from the surface will be-

[Use $h=6.64\times {10}^{-34}\text{J s}$]

A disc which is at rest started to spin about a stationary axis. The angular acceleration of the disc is given by $\alpha =2\theta rad/s$, where $\theta$ is the angle of rotation of disc from its initial position. Which of the following graphs correctly represents the variation of angular velocity with respect to '$\theta$' ?

In case of projectile motion if two projectiles A and B are projected with same speed at angles ${15}^{\circ }$ and ${75}^{\circ }$ respectively to the horizontal then:

Heat generated in the given circuit will be maximum when r is

One mole of an ideal gas undergoes a process :
$P=\frac{P_0}{1+(V_0/V{)}^2}$
Here $P_0$ and $V_0$ are constants. Change in temparature of the gas when volume is changed from $V=V_0$ to $V=2V_0$ is

An ideal spring with spring constant $k$ is hung from the ceiling and a block of mass $m$ is attached to its lower end. The mass is released with the spring initially unstretched. The maximum extension in the spring is

Two stereo speakers $S_1$ and $S_2$ are separated by a distance of $2.40\text{m}$. A person $\left(P\right)$ is at a distance of $3.20\text{m}$ directly in front of one of the speakers as shown in the figure. The frequency in the audible range$(20–20000\text{Hz})$ for which the listener can hear minimum sound intensity is (Take speed of sound in air as $320\text{m/s}$)

A particle describes a circular motion in horizontal plane in a conical funnel with speed v, the height of plane of circle from bottom is 40 cm, find v.

The relation between internal energy $U$, pressure $P$ and volume $V$ of a gas in an adiabatic process is $U=a+bPV$, where $a$ and $b$ are constants. What is the effective value of adiabatic constant $\gamma$?

A heat source at $T={10}^3\text{K}$ is connected to another heat reservoir at $T={10}^2\text{K}$ by a copper slab which is $1\text{m}$ thick. Given that the thermal conductivity of copper is $0.1{\text{WK}}^{-1}{\text{m}}^{-1}$, the energy flux through it in the steady state is:

Which of the following nuclei shown in the graph is light and stable?

A solenoid 4cm in diameter and 20 cm in length has 250 turns and carries a current of 15A. Calculate the flux through the surface of a disc of 10 cm radius that is positioned perpendicular to and centered on the axis of the solenoid.

In an oscillating $L-C$ circuit in which $C=4\mu \text{F}$, the maximum potential difference across the capacitor during the oscillations is $1.5\text{V}$ and the maximum current through the inductor is $50\text{mA}$. What is the frequency of the oscillations?

Three balloons are filled with different amounts of an ideal gas. One balloon is filled with 3 moles of the gas, filling the balloon to 30 L. The second balloon contains 2 moles of gas.

The third balloon occupies a volume of 45 L.

(i) What volume will the second balloon occupy?

(ii) How many moles of the gas does the third balloon contain?

A radio station emits radiations of $400\text{kHz}$. The metre band of the station is:

The Young’s modulus of steel is twice as that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of ${45}^{\circ }$ with the vertical, the escape velocity will be

Which of the following curve represents the variation of gravitational potential of a hollow sphere of radius $R$ with radial distance $\left(r\right)$?

A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density $\frac{\text{mass}}{\text{length}}\rho$ of the rod varies with the distance x from the origin as $\rho$ = a +bx.

(a) Find the SI units of a. and b.

(b) Find the mass of the rod in terms of a, b and L.

If the voltage of a source in an AC circuit is represented by the equation, $E=220\sqrt{2}\sin \left(314t\right)$. Calculate the average voltage of the signal for full cycle.

A bob of a simple pendulum of mass $40\text{g}$ with a positive charge of $4\times {10}^{-6}\text{C}$ is oscillating with time period $T_1$. An electric field of intensity $3.6\times {10}^4\text{N/C}$ is applied vertically upwards, now the time period is $T_2$. The value of $\frac{T_2}{T_1}$ is



$(g=10\text{m}/{\text{s}}^2)$

An electron and a proton are at a distance of $1\dot{A}$. The dipole moment will be $(C\times m)$

A satellite under the influence of the gravitational field of a massive planet at point $P$ moves along a parabolic path $y=x^2$ as shown. At point $O$, the satellite moves with a speed $v$. What is the time taken by satellite to move from point $O$ to $B?$

Dhoni and Raina are standing in the field at point $a=(3,4)$ and $b=(6,8)$ respectively. The shortest distance (in units) between them is

A car starts from rest and moves with uniform acceleration$a$ on a straight road from time$t=0tot=T$. After that, a constant deceleration brings it to rest. In this process the average speed of the car is

A radioactive substance of half life 69.3 days is kept in a container. The time in which 80% of the substance will disintegrate will be [take ln(5) = 1.61]

A positive point charge $q$ is located inside a neutral hollow spherical conducting shell. The shell has inner radius $a$ and outer radius $b$; ($b-a$ is not negligible). The shell is centered on the origin. Which of the following graphs correctly represent the variation of electric field $\text{vs}$ radius distance $X$ or electric potential $\text{vs}$ radial distance $X$. The point charge can be located anywhere inside shell on $X-axis$

Three bodies of mass $1\text{kg},2\text{kg}$ & $4\text{kg}$ have position vectors $3\hat{i},2\hat{i}-\hat{j},2\hat{i}+\hat{j}$ respectively. Then, centre of mass of this system has a position vector :

The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36%. The % change in its radius of gyration is

A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ acts in the same direction on the moving particle during time interval $T$, so that its momentum changes from $p$ to $3p$. Here, $k$ is a constant. The value of $T$ is

The rate at which the velocity of a freely falling body increases is called

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_1$ and $r_2(r_1=1.5r_2)$ through $1\text{K}$ are in the ratio