If 21x = 79x, what is the value of x?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

I look at you, you look at me, I raise my right, you raise your left. What am I?

Why is it very easy to weigh a fish?

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

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 ?

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?

A man and his wife were doing missionary work near the city of Nairobi in the country of Kenya in eastern Africa. Their housing had not yet been completed, so the man, the woman, and their six year old daughter were spending a few nights in the jungle in three small pup tents. During their third night there, the woman was awakened by the call of a hyena passing by, so she got out of her tent to see if her young daughter had been frightened by the noise. As she peered into her daughter's tent she was surprised to see the dark figures of lion, a panther, and a cheetah which were curled up next to her daughter. Seeing her daughter was asleep and unharmed, the woman slowly and quietly withdrew from the tent, and simply returned to her own tent and went back to bed. How could this child's mother leave her daughter in such a dangerous situation, and simply ignore what she had just witnessed without intervening in some way? How can such emotional coldness ever be explained; or is there something here we are missing?

Make the seating arrangement of 10 children in such a way that there are 5 rows with 4 children in each row.

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?