What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

A maths symbol is hidden in the below Bar Graph. Can you decipher it?

As you can see that fifteen matches have been used to form an arrangement. What you have to do is remove any six of them to make them ten.

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

The centre of the third figure is empty. What digit should fit inside?

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?

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?

Joseph buys three kinds of chocolates for 100 rupees. The first one is priced at 5 rupees, second one at 3 rupees and third one at 0.5 rupees.

If he bought 100 chocolates in total, how many pieces do you think he bought each chocolate?

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