A block of mass \(200\, g\) is kept stationary on a smooth inclined plane by applying a minimum horizontal force \(F =\sqrt{ x }N\) as shown in figure. The value of \(x =.....\)

An object moves with speed \(v_1, v_2\), and \(v_3\) along a line segment \(A B, B C\) and \(C D\) respectively as shown in figure. Where \(AB = BC\) and \(AD =3 AB\), then average speed of the object will be :

A uniform chain of \(6\, m\) length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is \(0.5\), the maximum length of the chain hanging from the table is.......\(m.\)

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

Given below are two statements: Statements \(I:\) The temperature of a gas is \(-73^{\circ}\,C\). When the gas is heated to \(527^{\circ}\,C\), the root mean square speed of the molecules is doubled. Statement \(II:\) The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below :

Two ideal polyatomic gases at temperatures \(T _{1}\) and \(T _{2}\) are mixed so that there is no loss of energy. If \(F _{1}\) and \(F _{2}, m _{1}\) and \(m _{2}, n _{1}\) and \(n _{2}\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is

Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below.

The logic operations performed by the given digital circuit is equivalent to:

The frequency of a car horn encountered a change from \(400\, {Hz}\) to \(500\, {Hz}\), when the car approaches a vertical wall. If the speed of sound is \(330\, {m} / {s}\). Then the speed of car is \(.....\,{km} / {h} .\)

Given below are two statements :
Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.

An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.