\(10\) resistors each of resistance \(10\,\Omega\) can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be \(..........\).

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

A uniform conducting wire of length is \(24 {a}\), and resistance \({R}\) is wound up as a current carrying coil in the shape of an equilateral triangle of side \('a'\) and then in the form of a square of side \('a'.\) The coil is connected to a voltage source \({V}_{0}\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is \(1: \sqrt{y}\) where \(y\) is ..... .

The rms value of conduction current in a parallel plate capacitor is \(6.9\,\mu\,A\). The capacity of this capacitor, if it is connected to \(230 V\) ac supply with an angular frequency of \(600\,rad / s\), will be \(....\,pF\)

The value of net resistance of the network as shown in the given figure is _______.

A small liquid drop of radius \(R\) is divided into \(27\) identical liquid drops. If the surface tension is \(\mathrm{T}\), then the work done in the process will be _______.

Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J .

Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\)  The intensity of emergent light is \(I/2.\)  If a third polarizer \(C\)  is placed between \(A\) and \(B,\)  the intensity of emergent light is reduced to \(I/3 .\)  The angle between the polarizers \(A\) and \(C\) is \(\theta \) . Then

Three charges \(+Q, q, +Q\) are placed respectively, at distance, \(0, \frac d2\) and \(d\) from the origin, on the \(x-\) axis. If the net force experienced by \(+Q\), placed at \(x = 0\), is zero, then value of \(q\) is

An electric dipole is placed on \({x}\)-axis in proximity to a line charge of linear charge density \(3.0 \times 10^{-6}\, {C} / {m}\). Line charge is placed on \(z-\)axis and positive and negative charge of dipole is at a distance of \(10\, {mm}\) and \(12\, {mm}\) from the origin respectively. If total force of \(4\, {N}\) is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\) Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason \(\mathrm{R}\) : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below

A body rotating with an angular speed of \(600\, {rpm}\) is uniformly accelerated to \(1800 \,{rpm}\) in \(10\; sec\). The number of rotations made in the process is ..... .