Count the number of triangles in the below picture?

What can go up a chimney down, but can’t go down a chimney up?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

Spot 5 differences in two Christmas tree below:

He loves to dance, twist and prance, he shakes his tail, and as a way he sails, wingless he flies into the sky. What is he?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

A mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?