What is both possible and impossible at the same time?

What is the word or phrase?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

In particular commonwealth games, a female participant won silver and gold medals for a single event.

How can this be possible?

What is next number in the pattern below:

131 517 192 123 ?

_ _ _ IE _ _
_ _ _ IE _
_ _ IE _ _
_ _ IE _
_ _ _ _ IE

Like you see, some letters have gone missing from these words that contain the IE pair at some or the other place. The letters that will be used to fill the blanks are given below. Use them and form meaningful words. Can you do that?

A, C, D, F, H, K, L, M, N, N, O, R, R, S, S, S, T, T, Y and Y.

You are a thief and you are being punished for your crime. People have tied your head down on a tree with a rope that has been anchored in the ground. A candle is burning below the rope which is slowly burning it away. Just below your head, a Lion has been left loose and is waiting for you to drop down on the ground so he can have you as his lunch.

You have to survive the scenario. How will you do it?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

Divide 110 into two parts so that one will be 150 per cent of the other. What are the 2 numbers?

You see me once in June, twice in November, and not at all in May. What am I?