I am quite hot but become too cold if you remove the first two letters. What am I?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

Which is the rope you never skip with?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

Which is the smallest number that you can write using all the vowels exactly once?

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

If Rajina's daughter is my daughter's mom, who am I to Rajina?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

What is the word or phrase?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99