Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance \(R_p=1 \Omega\) as shown in the figure. An external resistance of \(R_e=2 \Omega\) is connected via the sliding contact. The electric current in the circuit is :

An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\)

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 :

Two cars are approaching each other at an equal speed of \(7.2\, km / hr\). When they see each other, both blow horns having frequency of \(676\, Hz\). The beat frequency heard by each driver will be \(.....\, Hz\). [Velocity of sound in air is \(340\,m / s .]\)

The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of the third orbit will be

The charged particle moving in a uniform magnetic field of \((3\hat{i} + 2\hat{j})\) T has an acceleration \(\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right)\) m/s\(^2\). The value of \(x\) is __________.

If earth has a mass nine times and radius twice to the of a planet \(P\). Then \(\frac{v_e}{3} \sqrt{x}\; ms ^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(P\), where \(v_e\) is escape velocity on earth. The value of \(x\) is

Given below are two statements: One is labelled as Assertion \((A)\) and other is labelled as Reason \((R)\). Assertion \((A)\) : Time period of oscillation of a liquid drop depends on surface tension \((S)\), if density of the liquid is \(p\) and radius of the drop is \(r\), then \(T = k \sqrt{ pr ^{3} / s ^{3 / 2}}\) is dimensionally correct, where \(K\) is dimensionless. Reason \((R)\): Using dimensional analysis we get \(R.H.S.\) having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.