Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 2 hour, B was opened and after 4 hours from the start of A, C was also opened. Find the time in which the cistern is just full.

The coordinates of the incentre of the triangle whose sides are 3x – 4y = 0, 5x + 12y = 0 and y – 15 = 0, are

If cos²α + cos²β = 2, then the value of tan³ α + sin⁵ β is :

A shopkeeper has 11 books of same cost price. He sells the first book at certain price, then he sells second book at a price which is ₹ 1 less than the selling price of first book and then he sells third book at a price which is ₹1 less than the selling price of second book. Following this pattern, he sold all 11 books. If he sells sixth book at its cost price. Find the overall percent profit or loss on selling all 11 books. 

θθ then the value of θθ?

The average salary of all the staff in an office of a corporate house is Rs 5,000. The average salary of the officers is Rs 14,000 and that of the rest is Rs 4,000. If the total number of staff is 500, the number of officers is

Sudhir and Shyam can do a work in 12 days, while Shyam alone can complete it in 30 days. In how many days can Sudhir complete that work alone?

6 litres are drawn from a cask full of wine and it is then filled with water. 6 litres of the mixture are drawn and the cask is again filled with water. The quantity of wine now left in the cask is to that of the water in it as 121 : 23. How much does the cask hold?