Quantitative Aptitude - Arithmetic Ability Questions

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 16000 for 2 years at 10% per annum. The sum placed on simple interest is:

If the angle subtended by the radius of the circle and vertex B of the triangle ABC is 400. Then calculate the value of ∠BAC

What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?

If x + 1/x = √13, then 3x(x2-1) equal to

In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5:3. The number of girls to be added in the union, so that the number of boys to girls in 6:5 is

What is the slope of the line parallel to the line passing through the points (4,-2) and (-3,5)?

Two circles touch each other at point X. A common tangent touch them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA= 16 cm, then what is the value (in cm) of YZ?

Speeds of a boat along the current and against the current are 14 km/hr and 7 km/hr respectively. What is the speed of boat (in km/hr) in still water?