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

In a factory, the salary of each worker is increased in the ratio 22 : 25 but the number of workers is decreased by $$ 26{2\over3}\% $$. The net effect on the salary is: 

A moving train crosses a man standing on a platform and a bridge 640 metres long in 15 seconds and 35 seconds respectively. What will be the time taken by the train to cross a platform 1280 meters long?

In a business A and B gained some amount in a certain ratio. B and C received the profit in the ratio as that of A and B. If A received ₹ 6,400 and C received ₹ 10,000. Find the share of B 

The average of 21 consecutive natural numbers is 53. What is the value of the smallest of these 21 numbers?

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?

If the cost of pins reduces by Rs . 4 per dozen, 12 more pins can be purchased for Rs. 48. The cost of pins per dozen after reduction is: