What is both possible and impossible at the same time?

Find the combined weight of the Cat, Dog and Rabbit in the given picture.

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

During which month do people sleep the least?

In a school, 280 students studied chemistry, 254 students studied physics and 280 students studied biology.

97 students studied chemistry as well as physics, 138 students studied physics as well as biology and 152 students studied chemistry as well as biology.

73 students studied all the three branches.

Can you find out the total number of students?

using four eights (8) and a one (1) and one mathematical symbol , create the number 100

In an interview, a boy was asked an unusual question 'How two persons sitting with a table in between them can't see each other?' He was unable to reply. Can you?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?