Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

Trying to tease Birbal, Akbar gave him one gold coin and ask him to buy
* something for him to eat
* something for him to drink.
* something to feed the cows
* something to plant in the garden
and most important you need to buy only one thing.

What must Birbal buy to silence Akbar?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

A plane crashed between the border of Mexico and America. Where do you bury the survivors?

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?

Let's play a word game. Following are some meaningless words that can be completed by adding random letters on either side of the word.

For example, the word "rdo" can be formed into "pardon".

Using the same technique, can you complete the given words?
ecalc
airb
rinci
tibac
uidel
gorit
igna
eyho

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?