Quantitative Aptitude - Arithmetic Ability Questions

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

The inradius of a equilateral triangle is 10 cm. What is the circum-radius (in cm) of the same triangle?

What is the simplified value of [(sec3x – tan3x)/(sec x – tan x)] – 2 tan2x – sec x tan x?

The average weight of 25 candles is 40 grams. If some candles of weight 50 grams each were removed, then average weight becomes 37.5 grams. How many candles of weight 50 grams each were removed? 

3 hrs after a goods train passed a station, another train travelling at a speed of 88 km/hr following that goods train passed through that station. If after passing the station the train overtakes the goods train in 8 hours. What is the speed of the goods train?

A man travels 401 kilometres in, partly by rail and partly by steamer. He spends 6 hours more time on steamer. If the velocity of the steamer is 21 km/hr and the velocity of rail is 56 km/hr, how much distance does he cover by steamer?

If Sin θ = 12/13, then what is the value of Cot θ?

If a - b = 2 and ab = 15, then what is the value of a3- b3?