Quantitative Aptitude - Arithmetic Ability Questions

If x + y = 3, then what is the value of x3 + y3 + 9xy?

For triangle PQR, what is the equation of altitude PS if co­ordinates of P, Q and R are (5,1), (0,­4) and (­2,3) respectively?

The third proportional of two numbers 24 and 36 is

The radii of two concentric circles are 68 cm and 22 cm. The area of the closed figure bounded by the boundaries of the circles 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 AP:PB is 2:5, and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?

The co-ordinates of the centroid of a triangle ABC are (1 , -4). What are the co-ordinates of vertex C if co-ordinates of A and B are (3 , -4) and (0 , 5) respectively?

The line passing through (­3,4) and (0,3) is perpendicular to the line passing through (5,7) and (4,x). What is the value of x?

The distance between the points (7,7) and (k,-5) is 13. Find k?