Mass of Mars is 6.42 × 10²⁹ kg and mass of the Sun is 1.99 × 10³⁰ kg. What is the total mass?

Long back in ancient times, a farmer saved the life of a king’s daughter. The king decided to reward the farmer with whatever he wished. The farmer, who was a chess champion, made an unusual request:

“I would like you to place 1 rupee on the first square of my chessboard,

2 rupees on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares.

Each square should have twice as many rupees as the previous square.” The king thought this to be too less and asked the farmer tothink of some better reward, but the farmer didn’t agree.

How much money has the farmer earned?

[Hint: The following table may help you. What is the first square on which the king will place at least Rs 10 lakh?]

The diameter of the Sun is 1.4 × 10⁹ m and the diameter of the Earth is 1.2756 × 10⁷ m. Compare their diameters by division.

The distance between the Sun and the Earth is 1.496 × 10¹¹ km and distance between the Earth and the Moon is 3.84 × 10⁸ m. During solar eclipse the Moon comes in between the Earth and the Sun. What is distance between the Moon and the Sun at that particular time? (Question given is wrong, corrected.)

A particular star is at a distance of about 8.1 × 10¹³ km from the Earth. Assuring that light travels at 3 × 10⁸ m per second, find how long does light takes from that star to reach the Earth.