Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

I have branches, but no fruit, trunk or leaves. What am I?

Can you find out the remainder when 3^300 is divided by 5?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

I am an odd number. Take away a letter and I become even. What number am I?

It is always ahead of me yet I can never see it. What is it?