A thin prism \(\mathrm{P}_1\) with angle \(4^{\circ}\) made of glass having refractive index 1.54 , is combined with another thin prism \(\mathrm{P}_2\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \(P_2\) in degrees is _______.

If the potential difference between \(B\) and \(D\) is zero, the value of \(x\) is \(\frac{1}{n} \Omega\). The value of \(n\) is .......

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is \(30\,cm\) and refraction index of the material for both the lenses is \(1.75\). Both the lenses are placed at distance of \(40\,cm\) from each other. Due to the combination, the image of the object is formed at distance \(x =..........cm\), from concave lens.

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let \(r_{d}\) and \(r_{\alpha}\) be their respective radii of circular path. The value of \(\frac{r_{d}}{r_{\alpha}}\) is equal to

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \(\sqrt 3\) , then the angle of incidence....\(^o\)

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

A diatomic gas, having \(C_{p}=\frac{7}{2} R\) and \(C _{ v }=\frac{5}{2} R ,\) is heated at constant pressure. The ratio \(dU : dQ : dW :\)

A liquid column of height \(0.04 \mathrm{~cm}\) balances excess pressure of soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) and surface tension of soap solution is \(0.28 \mathrm{Nm}^{-1}\), then diameter of the soap bubble is _______ \(\mathrm{cm}\). \(\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }\)

Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be

A person driving car at a constant speed of \(15\,m / s\) is approaching a vertical wall. The person notices a change of \(40\,Hz\) in the frequency of his car's horn upon reflection from the wall. The frequency of horn is ............ \(Hz\). (Given : Speed of sound : \(330\,m / s\) )

A prism of refractive index \(n_{1}\) and another prism of refractive index \(n_{2}\) are stuck together (as shown in the figure). \(n_{1}\) and \(n_{2}\) depend on \(\lambda\), the wavelength of light, according to the relation \({n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text { and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}\) The wavelength for which rays incident at any angle on the interface \(B C\) pass through without bending at that interface will be \(....\,nm.\)