Quantitative Aptitude - Arithmetic Ability Questions

What is the value of [2 cot × (p – A)/2]/[1 + tan2× (2p – A)/2]?

What is the area (in square units) of the figure enclosed by the x-axis, the y-axis and the line x + 2y = 6 ?

(secA - 1)/(secA + 1) is equal to?

P and Q together can make a door in 12 days. They started the work together but after 8 days P left the work. The remaining work is completed by Q alone in 7 more days. In how many days can P alone complete the entire work?

What is the average of first 19 odd numbers?

If R019 is divisible by 11, find the value of the smallest natural number R?

Which of the following will yield a recurring decimal?

A thief is stopped by a policeman from a distance of 200 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed
of the thief as 8 km/hr and that of police man as 10 km/hr. How far the thief would have run, before he is over ­taken?