51.

When a light enters a refracting medium, it is found that the magnitude of the angle of refraction is equal to half the angle of reflection. If µ is the refractive index of the medium, then the angle of incidence is

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

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

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

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

The fraction of atoms of radioactive element that decays in 6 days is 7 / 8. The fraction that decays in 10 days will be

• 77 / 80

• 71 / 80

• 31 / 32 

• 15 / 16

A compound microscope has a magnifying power of 100, when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. The
focal length of eye-piece is

• 4 cm

• 2 cm

• 6 cm

• 5.2 cm

In a single slit diffraction experiment, first minimum for λ₁  = 660 nm coincides with first maxima for wavelength λ₂  is

• 950 nm

• 610 nm

• 390 nm

• 440 nm

When a ray of light enters a glass lens surrounded by air, it slows down. As it  leaves the glass, does its speed increases, decreases or stay the same ? Choose the correct answer from the following.

1. Its speed decreases as the ray is propagating in a medium with higher refractive index.
2. Its speed increases as the refractive index of air is less than that of glass.
3. The speed will stay the same because the speed of light is a universal constant.

• Only I

• Only II

• Only III

• None of these

In a common emitter (CE) amplifier having a voltage gain G, the transistor used has transconductance 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance 0.02 mhoand current gain 20,  the voltage gain will be

• $\frac{5}{4}\mathrm{G}$

• $\frac{2}{3}\mathrm{G}$

• 1.5 G

• $\frac{1}{3}\mathrm{G}$

The photoelectric threshold wavelength of silver is 3520 x 10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light ofwavelength 2536 x 10^-10 m is (Given, h = 4.14 × 10^-15 eV , c = 3 × 10⁸ m/s)

• 0.3 × 10⁶ m/s

• 0.6 ×10⁵ m/s

• 0.6 × 10⁶ m/s

• 61 × 10³ m/s

A telescope consists of two thin lenses of focal lengths 0.3 m and 3 cm respectively. It is focused on moon which subtends an angle of 0.5° at the objective. Then, the angle subtended at the eye by the final image will be

• 5°

• 0.25°

• 0.5°

• 0.35°

Two cars A and B approach a stationary observer from opposite sides as shown in the figure hears no beats. If the frequency of the horn of the car B is 504 Hz, the  frequency of horn of the car A will be

• 529.2 Hz

• 295.2 Hz

• 440.5 Hz

• 259.2 Hz

An object is placed at a distance of 10 cm from a co-axial combination of two lenses A and B in contact. The combination forms a real image three times the  size of the object. If lens B is concave with focal length of 30 cm, the nature and focal length of lens A is

• convex, 12 cm

• concave, 12 cm

• convex, 6 cm

• convex, 18 cm