People put me on the table and cut me but do not eat me. What am I?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

People are waiting in line to board a 100-seat aeroplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise, they will choose an open seat at random to sit in. The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

You can win me and lose me but never buy me
You can not eat me and never want to part with me
I can make you cry or bring you joy
I am not a machine and definitely not a toy
You keep me but i am not forever just yours
You might find me in a case or on a shelf next to a vase
I am hard and i am tall if you bump me i am sure to fall
I am made of different materials and am at many events
If your lucky and fight hard I might be yours
What am I ?

What is the next number?

77, 49, 36, 18 ?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.