Quantitative Aptitude - Arithmetic Ability Questions

In an alloy of German silver the ratio of copper to zinc was 17:7 while that of nickel to zinc was 4 :3. The ratio of copper to zinc to nickel in the alloy was

What is the value of 2sec2A?

If secA + tanA = x, then find the value of x.

If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?

If x+1x = 4, then what is the value of x6+1x6 ?

If 4x - 5y = -37 and 7x + y = -16, then x - y = ______

A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity and during the fifth hour it was only one -third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?

If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?