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Which of the following graphs correctly represents the variation of photo current with respect to energy of incident radiation?

Find the quadratic equation if the sum roots is $-\frac{8}{5}$ and the product of the roots is $\frac{7}{5}$.

The angular velocity is given by

A particle is executing simple harmonic motion with a time period $T$. At time $t=0,$ it is at its position of equilibrium. The kinetic energy$\left(KE\right)$-time $\left(t\right)$ graph of the particle will look like:

A flywheel has an intial rotational kinetic energy equal to $10\text{J}$. A constant torque is applied on the flywheel and work done by the torque is $25\text{J}$. Find the final rotational kinetic energy of the flywheel.

If $a=(3t^2+2t+1)m/s^2$ is the expression according to which the acceleration of a particle moving along a straight line varies, then find displacement of the particle 2 seconds after starting.

A parallel plate capacitor is charged to a potential difference of $50\text{Volts}$. It is then discharged through a resistance for $2\text{s}$ and its potential drops by $10\text{Volts}$. Calculate the fraction of energy stored in the capacitor.

Two equal charges ar eplaced at a separation of 1.0 m. What should be the magnitude of the charges so that the force between them equals the weight of a 50 kg person?

A body is suspended from a spring balance placed on a ground in the earth. The reading of the balance is $100g$. When the body is placed in a satellite which is revolving in a an orbit of radius $2R$, the reading is $W_1$. What is $W_1$? ($R$ is the radius of earth)

The density of water at the surface of the ocean is $\rho$. If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is $n{P}_0$, where $P_0$ is the atmospheric pressure?

A block of mass $m$ is projected on a smooth horizontal circular track with speed $v$. What is the average normal force (in Newtons) exerted by circular walls on the block during its motion from $A$ to $B$?

A car is going with constant speed on a circular path. If it starts from point A at t = 0 and reaches diametrically opposite point B after 2 sec then find its angular velocity.

The kinetic energy of a projectile at the highest point is half of the initial kinetic energy. What is the angle of projection with the horizontal?

The sphere shown in figure lies on a rough plane when a particle of mass 'm' traveling at a speed $v_0$ collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the angular speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the center of mass of the combined system is not appreciably shifted from the center of the sphere.

Comment on the correctness of the following two statements.

Statement I – Net Electric field strength on a Gaussian surface may change if the charges inside or outside move.

Statement II – Electric flux through a Gaussian surface will not change if the charges contained inside do not cross the boundary of the assumed Gaussian surface.

A particle is performing simple harmonic motion along x-axis with amplitude 4 cm and time period 1.2 sec. The minimum time taken by the particle to move from x =2 cm to x = + 4 cm and back again is given by

Two squares of size $(a\times a)$ each are removed from a bigger square of size $(2a\times 2a)$ as shown in the figure. Removed parts are unshaded in the figure given below. Find the coordinates of the $COM$ w.r.t the origin $\text{O}$.

The graph below shows the relationship between number of people and profits earned (in $).





The equation of the above graph is .

The balancing lengths of potentiometer wire are $l_1$ and $l_2$ when two cells of emf $E_1$ and $E_2$ are connected in the secondary circuit in series. first to support each other and next to oppose each other. Then the ratio of $\frac{E_1}{E_2}$ is equal to [if $E_1>E_2$]

At $0^{\circ }C$, the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At ${100}^{\circ }C$, this quotient is

A shell of mass 2m fired with a speed u at an angle $\theta$ to the horizontal explodes at the highest point of its motion into two fragments of mass m each. If one fragment, falls vertically, the distance at which the other fragment falls from the gun is given by

A black body is at rest at a temperature of $2880\text{K}$. The energy of radiation emitted by this object with wavelength between $499\text{n-m}$ and $500\text{n-m}$ is $U_1$, between $999$ and $1000\text{nm}$ is $U_2$ and between $1499\text{nm}$ and $1500\text{nm}$ is $U_3$. The Wien's constant $b=2.88\times {10}^6\text{nm-K}$. Then