Quantitative Aptitude - Arithmetic Ability Questions

If tan(A/2) = x, then the value of x is

Determine the value of a2+b2a3+b3 when a = 2+√3 and b = 2-√3.

The income of X is 60% more than Y’s income and the income of Y is 40% more than Z’s income. X’s income is how much percentage more than Z’s income?

If(x + y)2 = xy + 1 and x3 – y3 = 1, then what is the value of x – y?

The length of a string is 8 feet and 9 inches, which is divided into 3 equal parts. What is the length of each part in inches?

If 3 tan θ = cot θ where 0 < θ < π/2, then what is the value of θ ?

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

What is the value of Cot 60°- Sec 45°?