A spherical liquid drop of radius \(R\) acquires the terminal velocity \(v_1\) when falls through a gas of viscosity \(\eta\). Now the drop is broken into \(64\) identical droplets and each droplet acquires terminal velocity \(v_2\) falling through the same gas. The ratio of terminal velocities \(v_1/v_2\) is ________.

A mass \(M\) hangs on a massless rod of length \(l\) which rotates at a constant angular frequency. The mass \(M\) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \(\omega .\) The angular momentum of \(M\) about point \(A\) is \(L _{ A }\) which lies in the positive \(z\) direction and the angular momentum of \(M\) about \(B\) is \(L _{ B }\). The correct statement for this system is

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.

The dimensions of angular momentum , latent heat and capacitance are, respectively.

A wire of length \(30\,cm\), stretched between rigid supports, has it's \(n^{\text {th}}\) and \((n+1)^{\text {th}}\) harmonics at \(400\,Hz\) and \(450\; Hz\), respectively. If tension in the string is \(2700\,N\), it's linear mass density is.........\(kg/m\).

The mass of proton, neutron and helium nucleus are respectively \(1.0073\,u , 1.0087\,u\) and \(4.0015\,u\). The binding energy of helium nucleus is \(.........\,MeV\)

A \(2\, W\) carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is .............. \(mA\)

A line charge of length \(\frac{\text { ' } a \text { ' }}{2}\) is kept at the center of an edge \(B C\) of a cube \(A B C D E F G H\) having edge length ' \(a\) ' as shown in the figure. If the density of line charge is \(\lambda\) C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, \(\epsilon_0\) as the free space permittivity)

The ratio of the coefficient of the middle term in the expansion of \((1+x)^{20}\) and the sum of the coefficients of two middle terms in expansion of \((1+x)^{19}\) is \(....\)

The area of cross-section of a railway track is \(0.01\, {m}^{2}\). The temperature variation is \(10^{\circ} {C}\). Coefficient of linear expansion of material of track is \(10^{-5} /{ }^{\circ} {C}\). The energy stored per meter in the track is ...... \({J} / {m} .\) (Young's modulus of material of track is \(10^{11} \,{Nm}^{-2}\) ))

If the plane \(2x -y + 2z + 3 = 0\) has the distances \(\frac {1}{3}\) and \(\frac {2}{3}\) units from the planes \(4x -2y + 4z + \lambda = 0\) and \(2x -y + 2z + \mu = 0,\) respectively, then the maximum value of \(\lambda + \mu \) us equal to

The number of ways of getting a sum \(16\) on throwing a dice four times is ....................