Quantitative Aptitude - Arithmetic Ability Questions

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

A work can be completed by 18 boys in 24 days. If 6 boys leave after working for 12 days, then how many days will be needed to complete the remaining work?

2 ­- (cosA + sinA)2 is equal to

Coefficient of x in (x + 9)(8 - 5x) is

Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of areas of triangle APQ: triangle ABC is 16:25. Then the ratio of AP:PB is?

If Tan A = 15/8 and Tan B = 7/24, then Cos(A - B) = ?

129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30°. The height of this cliff is

Product of digits of a 2-digit number is 27. If we add 54 to the number, the new number obtained is a number formed by interchange of the digits. Find the number.