Explain with a suitable diagram, why the sample frequency should be at least double than the signal frequency.

State with reasons whether the following statements are True or False.

i) Sound wave (longitudinal wave) propagation is the most preferred mode in modern communication systems.

ii) Scanning format at TV transmitter and receiver end need not be the same.

iii) Skin depth increases with frequency.

iv) Modulation can be used to reduce noise present in the input signal.

v) Interleaving of messages helps in reducing hum noise in a signal.

vi) Splicing involves soldering.

vii) CCD camera requires electron gun for scanning.

viii) Image frequency can be rejected by tuned IF amplifier.

ix) Centronic port of a computer is a serial port.

x) Blue tooth works only for mobile devices.

What do you understand by cosmic distance ladder? Explain how it is used to estimate distance of stars.

What is an active galaxy? What is the source of its activity? Under what conditions does an active galaxy emit synchrotron radiation?

Distinguish between elliptical, spiral and lenticular galaxies and give one example of each type of galaxy.

How long will a 5M, star burn hydrogen as fuel, given that the Sun will do so for about 10¹⁰ years?

A white dwarf star has a mass of 10³⁰kg. Its luminosity is 10²⁴ Js^-1. Calculate how long it can survive with its present luminosity if its internal temperature is 10⁷ K.

Derive an expression for Jeans mass and discuss its significance in the formation of stars.

Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds.

Derive the expression for the mean temperature in a star:

A star has surface temperature of 25000 K. Which lines would be prominent in its spectrum and why?

The mean distance of Mars from the Earth is 0.5 A.U. and its orbital period is 687 days. Calculate the orbital period of Jupiter given that its mean distance from the Earth is 4 A.U.

Explain how sunspots survive for so long even though they are surrounded by hotter matter.

A main sequence star has mass 2x10³¹ kg and radius 3x10⁹ m. Obtain an estimate of the average temperature throughout the star.

Explain the following terms with the help of a diagram, wherever needed: celestial sphere, zenith, circumpolar stars, diumal circle, resolving power of a telescope.

After about 1 billion year, the radius of a star is expected to increase by 100 times its present radius. If its temperature becomes half of what it is today, determine the change in its absolute magnitude.

The distance modulus of a star is-0.1. At what distance is it from the earth?

Using Rodrigue’s formula, obtain the expression for L₃ (x).

Using the following expression for a Bessel function of order m:

show that

i) 

ii) 

Obtain the first three terms in the expansion of the following function in a series of the form  :