Quantitative Aptitude - Arithmetic Ability Questions

If  tan2θ + cot2θ = 2, then what is the value of 2sec θ cosec θ?

If a + b = 10 and ab = 24, then what is the value of a3 + b3?

If x - 1/x = 1 then what is the value of 1x1x-1-1x+1+1x2+1-1x2-1?

By increasing the price of entry ticket to a fair in the ratio 7:17, the number of visitors to the fair has decreased in the ratio 9:5. In what ratio has the total collection increased or decreased?

A miner sells a diamond to a trader at a profit of 40% and the trader sells it to a customer at a profit of 25%. If the customer pays Rs 56 lakhs to buy the diamond, what had it cost the miner (in Rs lakhs)?

A train has to cover a distance of 900 km in 25 hours. What should be its average speed in meters/second?

The sum of a fraction and 3 times its reciprocal is 19/4. What is the fraction?

The product of the ages of Swati and Aparna is 120. If thrice the age of Aparna is more than Swati's age by 2 years, find the age of Swati.