In the given circuit all resistances are of value \(R\,ohm\) each. The equivalent resistance between \(A\) and \(B\) is 

The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\)

The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\)

The electric potential as a function of \(x, y\) is given by \(V = 5(x^2 - y^2)\) V. The electric field at a point \((2, 3)\) m is __________ V/m.

Thermodynamic process is shown below on a \(P-V\) diagram for one mole of an ideal gas. If \(V _{2}=2 V _{1}\) then the ratio of temperature \(T _{2} / T _{1}\) is ...... .

The number density of molecules of a gas depends on their distance \(r\) from the origin as, \(n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}\). Then the total number of molecules is proportional to

The half life of a radioactive substance is \(5\) years. After \(x\) years a given sample of the radioactive substance gest reduced to \(6.25 \%\) of its initial value of \(x\) is ...............

A direct current of \(4\,A\) and an alternating current of peak value \(4\,A\) flow through resistance of \(3\,\Omega\) and \(2\,\Omega\) respectively. The ratio of heat produced in the two resistances in same interval of time will be.