Quantitative Aptitude - Arithmetic Ability Questions

If 3x + [1/(5x)] = 7, then what is the value of 5x/(15x2+ 15x + 1)?

What is the value of cot 5π/3?

If x(2x + 3) = 90 and 7y-1/2+ 2y-1/2= y1/2 (x and y are positive numbers), then what is the value of x2+ y2?

Three bottles of equal capacity containing mixture of milk and water in ratio 2 : 5, 3 : 4 and 4 : 5 respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?

If each median of an equilateral triangle has a length of 12cm. Then what will be the value of in-radius (in cm) of the equilateral triangle?

∆PQR is right angled at Q. If sinP = 12/13, then what is the value of tanR?

If a + b = 11 and a2+ b2= 61, then value of ab is

In ∆ABC, ∠B=35°, ∠C=65° and the bisector of ∠BAC meets BC in D. Then ADB is