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?

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

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?

A and B can complete a task in 1.5 days. However, A had to leave a few days before the task wascompleted and hence it took 2 days in all to complete the task. If A alone could complete the work in2.625 days, how many days before the work getting over did A leave?

A can do a work in 36 days and B in 12 days. If they work on it together, then in how many days will they be able to do the work?

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