A charge of \(4\,\mu C\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be.

Time \((T)\), velocity \((C)\) and angular momentum \((h)\) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

The maximum rated power of the LED is \(2\) mW and it is used in the circuit with input voltage of \(5\) V as shown in the figure below. The current through resistance \(R_S\) is \(0.5\) mA. The minimum value of the resistance of \(R_S\), to ensure that the LED is not damaged is _______ k\(\Omega\).

The dimensional formula of latent heat is _______.

A ball is thrown vertically upward with an initial velocity of \(150\,m / s\). The ratio of velocity after \(3\,s\) and \(5\,s\) is \(\frac{x+1}{x}\). The value of \(x\) is \(...........\) Take \(\left(g=10\,m / s ^2\right)\)

Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

The height \({ }^{\prime} h ^{\prime}\) at which the weight of a body will be the same as that at the same depth \('h'\) from the surface of the earth is (Radius of the earth is \(R\) and effect of the rotation of the earth is neglected):

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between \(A\) and \(B\) is \(.......\Omega\).