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.

$$ {Cos^4θ +Sin^4θ}={2 \over3} $$ then the value of $$ {Cos^2θ -Sin^2θ+1}$$?

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

Two places P and Q are 92 km apart. A train leaves P for Q and at the same time another train leaves Q for P. Both the trains meet 4 hrs after they start moving. If the train travelling from P to Q travels 7 km/hr faster than the other train, find the speed of the two trains.

The MRP of a watch is Rs.4750. The shop sells it at 12% discount. If the shopkeeper had purchased the watch for Rs. 3,850, what is his gain? 

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