If  tan²θ +cot²θ  = 2, then what is the value of  2^{secθ cosecθ}?

In the given figure ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?

Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3 : 5 ? 

A pipe of diameter d can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter 2d for doing the same job in: 

The profit percentage of P and Q is same on selling the articles at Rs. 1800 each but A calculates his profit on the selling price while Q calculates it correctly on the cost price which is equal to 20%. What is the difference in their profits?

The average of three consecutive odd numbers is 12 more than one third of the first of these numbers. What is the last of the three numbers?

During a month-long annual sale, a shopkeeper sells his goods at a discount of 50%. But in the last week, he offers an additional discount of 40%. If the original price of a shirt is ₹ x, then the price (in rupees) during the last week of the sale will be