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

Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 meters, in what time (in seconds) will they cross each other traveling in opposite direction? 

The simple interest on a certain sum for 2 years at a certain rate of interest is Rs.2000 and compound interest on the same sum, same time and same rate of interest is Rs.2050. Then find the ratio between CI for 2 years and CI for 3 years?

A merchant marks his goods at Rs. 900 and allows a discount of 25%. If he still gain 12.5%, then the cost price of the article 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. 

If a + b + c = 12, a² + b² + c² = 52, then what is ab + bc + ca equal to-

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?