For the given cyclic process \(CAB\) as shown for a gas, the work done is ..... \(J\)

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 _______.

A sphere of capacitance \(100\) pF is charged to a potential of \(100\) V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7}\) J. The value of \(\alpha\) is __________. (combined capacitance of spheres is \(200\) pF)

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face \(PQ\) of a right angled prism PQR as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are \(1.27, 1.42\) and \(1.49\) respectively. The colour of the ray(s) emerging out of the face \(PR\) is:

A submarine \((A)\) travelling at \(18\, km/hr\) is being chased along the line of its velocity by another submarine \((B)\) travelling at \(27\, km/hr\). \(B\) sends a sonar signal of \(500\, Hz\) to detect \(A\) and receives a reflected sound of frequency \(v\). The value of \(v\) is close to ... \(Hz\) (Speed of sound in water \(= 1500\, ms^{-1}\))

The half-life of a radioactive element \(A\) is the same as the mean-life of another radioactive element \(B.\) Initially both substances have the same number of atoms, then

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

There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)

The co-ordinates of a particle moving in \(x-y\) plane are given by :  \(\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .\) The motion of the particle is _______.

Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)

At steady state the charge on the capacitor, as shown in the circuit below, is _________ \(\mu \mathrm{C}\).

What will be the magnitude of electric field at point \(O\) as shown in figure ? Each side of the figure is \(I\) and perpendicular to each other.