A ball will a speed of \(9\, m / s\) collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of \(30^{\circ}\) with the original direction. The ratio of velocities of the balls after collision is \(x : y\) where \(x\) is........

A convex lens of focal length \(20\, cm\) produces images of the same magnification \(2\) when an object is kept at two distances \(x_1\) and \(x_2\) \((x_1 > x_2)\) from the lens. The ratio of \(x_1\) and \(x_2\) is

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws \(n\) balls per second, the maximum height the balls can reach is

The dimensions of angular momentum , latent heat and capacitance are, respectively.

In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : The nuclear density of nuclides \({ }_5^{10} B ,{ }_3^6 Li ,{ }_{26}^{56} Fe ,{ }_{10}^{20} Ne\) and \({ }_{83}^{209} Bi\) can be arranged as \(\rho_{ Bi }^{ N }>\rho_{ Fe }^{ N }>\rho_{ Ne }^{ N }>\rho_{ B }^{ N }>\rho_{ Li }^{ N }\). Reason \(R\) : The radius \(R\) of nucleus is related to its mass number \(A\) as \(R=R_0 A^{1 / 3}\), where \(R_0\) is a constant. In the light of the above statement, choose the correct answer from the options given below :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
Reason (R): There is no mass associated with the electromagnetic waves.
In the light of the above statements, choose the correct answer from the options given below :

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.