21.

A resistor R and 2 μF capacitor in series connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after  the switch has been closed. (log₁₀ 2.5 = 0.4)

• 1.7 x 10⁵ Ω

• 2.7 x 10⁶ Ω

• 3.3 x 10⁷ Ω

• 3.3 x 10⁷ Ω

If a wire is stretched to make it 0.1% longer, its resistance will

• increase by 0.2%

• decreases by 0.2%

• decrease by 0.05 %

• decrease by 0.05 %

The electrostatic potential inside a charged spherical ball is given by Φ = ar² + b where r is the distance from the centre; a,b are constants. Then the charge density inside the ball is

• -6aε₀r

• -24πaε₀

• -6aε₀

• -6aε₀

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements. 
Statement 1 - Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals.
Statement 2- The state of ionosphere varies from hour to hour, day to day and season to season.

•  Statement 1 is true, statement 2 is false. 

• Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

•  Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

•  Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

This question has Statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements :
Statement 1 :
A metallic surface is irradiated by a monochromatic light of frequency v > v₀ (the threshold frequency). The maximum kinetic energy and the stopping potentials are K_max and V₀ respectively. If the frequency incident on the surface is doubled, both the Kmax and V₀ are also doubled.
Statement 2 :
The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

• Statement 1 is true, statement2 is false.

• Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

The half life of a radioactive substance is 20 minutes. The approximate time interval (t₂ - t₁) between the time t₂ when 2/3 of it has decayed and time t₁ when 1/3 of it had decayed is

• 14 min

• 20 min

• 28 min

• 28 min

Energy required for the electron excitation in Li⁺⁺ from the first to the third Bohr orbit is

• 36.3 eV

• 108.8 eV

• 122.4 eV

• 122.4 eV

The question has a paragraph followed by two statements, Statement 1 and Statement 2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement 1 :
When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of π
Statement 2 :
The centre of the interference pattern is dark.

• Statement 1 is true, statement 2 is false. 

• Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

• Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

Let the xz-plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of √2 and medium 2 with z<0 has a refractive index of √3. A ray of light in medium 1 given by the vector is incident on the plane of separation. The angle of refraction in medium 2 is

• 45° 

• 60° 

• 75° 

• 75° 

A car is fitted with a convex sideñview mirror of focal length 20 cm.Asecond car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is

• 1/15 m/s

• 10 m/s

• 15 m/s

• 15 m/s