Equivalent resistance of the following network is _______ \(\Omega\).

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25 \%\) more charge from the battery. The dielectric constant of mica is ___________ .

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then:

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\)  nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is

The ratio of de Broglie wavelength of a deutron with kinetic energy \(E\) to that of an alpha particle with kinetic energy \(2 E\), is \(n: 1\). The value of \(n\) is ___________.
(Assume mass of proton = mass of neutron) :

A thermodynamic system is taken through the cyclic process ABC as shown in the figure (P-V graph : A(2, 100), B(5, 300), C(5, 100). The total work done by the system during the cycle ABC is ___________ J.

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is \( 32\times10^{18}/s \) then collision frequency in gas A is__________/s.

A particle executes \(S.H.M.,\) the graph of velocity as a function of displacement is :-

A body is dropped on ground from a height \(h_1\) and after hitting the ground, it rebounds to a height \(h _2\) If the ratio of velocities of the body just before and after hitting ground is \(4\), then percentage loss in kinetic energy of the body is \(\frac{x}{4}\). The value of \(x\) is \(.......\)

Potential energy as a function of \(r\) is given by \(U=\frac{ A }{ r ^{10}}-\frac{ B }{ r ^{5}}\), where \(r\) is the interatomic distance, \(A \) and \(B\) are positive constants. The equilibrium distance between the two atoms will be

Consider a circular coil of wire carrying constant current \(I\), forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by \(\phi_{i} .\) The magnetic flux through the area of the circular coil area is given by \(\phi_{0} .\) Which of the following option is correct?