Quantitative Aptitude - Arithmetic Ability Questions

2sin[(C+D)/2].sin[(D­-C)/2] is equal to

If (7x -­ 13) ­ (12x + 3) = 14, then the value of x is ______ .

If x tan 60° + cos 45° = sec 45° then the value of x2 + 1 is

If cosθ = x2-y2x2+y2, then the value of cotθ is

If √x ­- √y = 1 , √x + √y = 17 then √xy = ?

A and B can complete a task in 20 days, B and C can complete it in 30 days while C and A can do the same task together in 24 days. How many days will each of and C take to complete the task individually? 

Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centers is 14 cm. The radius of the bigger circle is

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is: