A ray of light passes from vacuum into a medium of refractive index, the angle of incidence is found to be twice the angle of refractlon. Then the angle of incidence is

• ${\cos }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

• $2 {\cos }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

• $2 {\sin }^{-1} \left(\mathrm{\mu }\right)$

• $2 {\sin }^{-1} \left(\frac{\mathrm{\mu }}{2}\right)$

If α and β are the current gain in the CB and CE configurations respectively of the transistor circuit, then $\frac{\mathrm{\beta } - \mathrm{\alpha }}{\mathrm{\alpha \beta }}$

• infinite

• 1

• 2

• 0.5

The apparent frequency of the whistle of an engine changes in the ratio 9 : 8 as the engine passes a stationary observer. If the velocity of the sound is 340 ms^-1, then the velocity of the engine is 

• 40 ms^-1

• 20 ms^-1

• 340 ms^-1

• 180 ms^-1

The width of a single slit if the first minimum is observed at an angle 2° with a light of wavelength 6980 $\stackrel{\circ }{\mathrm{A}}$

• 0.2 mm

• 2 × 10^-5 mm

• 2 × 10⁵ mm

• 2 mm

A silicon specimen is made into a p-type semiconductor by doping, on an average, one indium atom per 5 x 10⁷ silicon atoms. If the number density of atoms in the silicon specimen is 5 x 10²⁸ atom/m³, then the number of acceptor atoms in silicon per cubic centimetre will be

• 2.5 × 10³⁰ atom/cm³

• 2.5 × 10³⁵ atom/cm³

• 1 × 10¹³ atom/cm³

• 1 × 10¹⁵ atom/cm³

In a photoelectric effect measurement, the stopping potential for a given metal is found to be V volt when radiation ofwavelength λ₀ is used. If radiation of wavelength 2λ₀ is used with the same metal then the stopping potential (in volt) will be

• $\frac{{\mathrm{V}}_0}{2}$

• 2V₀

• ${\mathrm{V}}_0 + \frac{\mathrm{hc}}{2 {\mathrm{e\lambda }}_0}$

• ${\mathrm{V}}_0 - \frac{\mathrm{hc}}{2 {\mathrm{e\lambda }}_0}$

67.

In artificial radioactivity, 1.414 x 10⁶ nuclei are disintegrated into 10⁶ nuclei in 10 min. The half-life in minutes must be 

• 5

• 20

• 15

• 30

If ε₀ and µ₀ are the electric permittivity and magnetic permeability of free space and ε and µ are the corresponding quantities in the medium, the index of refraction of the medium in terms of above parameter is

• $\frac{\mathrm{\epsilon \mu }}{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}$

• ${\left(\frac{\mathrm{\epsilon \mu }}{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}\right)}^{1/2}$

• $\left(\frac{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\mathrm{\epsilon \mu }}\right)$

• ${\left(\frac{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\mathrm{\epsilon \mu }}\right)}^{1/2}$

A light ray of 5895 $\stackrel{\circ }{\mathrm{A}}$ wavelength travelling in vacuum enters a medium of refractive index 1.5. The speed of light m the medium is

• 3 × 10⁸ m/s

• 2 × 10⁸ m/s

• 1.5 × 10⁸ m/s

• 6 × 10⁸ m/s

The half-life of radon is 3.8 days. How many radon will be left out of 1024 mg after 38 days

• 1 mg

• 2 mg

• 3 mg

• 4 mg