Quantitative Aptitude - Arithmetic Ability Questions

What is the value of equation a3+b3+c3-3abc if a2+b2+c2=ab+bc+ca+4 and a+b+c = 4.

What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are 60 cm² and 5 cm respectively?

If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is

α and β are the roots of quadratic equation. If α + β = 8 and α – β = 2√5, then which of the following equation will have roots α4 and β4?

What is the area (in sq cm) of an equilateral triangle of side 14 cm?

A train 100 m long is running at a speed of 120 kms/hr. The time taken to pass a person standing near the line is

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1⁄2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

The distance between two cities X and Y is 270 km. First train starts from X at 7:00 a.m. and travels towards Y at 40 km/hr. Second train starts from Y at 8:30 a.m. and travels towards X at 30 km/hr. At what time (in a.m.) will both the trains meet?