Quantitative Aptitude - Arithmetic Ability Questions

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 16000 for 2 years at 10% per annum. The sum placed on simple interest is:

If θ be positive acute angle and 5cosθ + 12sinθ = 13, then the value of cosθ is

If a + a2 + a3 – 1 = 0, then what is the value ofa3 + (1/a)?

If 169 is subtracted from the square of a number, then the result obtained is 7056. What is the number?

Ram's father is twice as old as Ram is. Eight years ago the age of Ram's father was 2.5 times his age. What is Ram's current age?

If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812, then what is the value of P – Q?

What is the value of (cosec30 - 1/√3)?