Can you find a five letter word that is left with only two letters if one is removed?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?

I have no life, but I can die. What am I?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

What does man love more than life, hate more than death or mortal strife; That which contented men desire; the poor have, the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

There is a hypothetical state between the USA and Mexico border 'Tango'.
Here 70 percent of the population have defective eyesight, 75 percent are hard of hearing, 80 percent have Nose trouble and 85 percent suffer from allergies, what percentage (at a minimum) suffer from all four ailments?

What can you catch but never throw?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?