If 21x = 79x, what is the value of x?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

I have branches, but no fruit, trunk or leaves. What am I?

What kind of tree can you carry in your hand?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

Kareena is older than Katrina and younger than Karishma. Isabelle is younger than Bipasha and Karishma. Bipasha is older than Karishma. If Kareena and Isabelle are the same age, who's the youngest?

If an electric train is travelling south, then which way is the smoke going?