Quantitative Aptitude - Arithmetic Ability Questions

The sum of a fraction and 7 times its reciprocal is 11/2. What is the fraction?

If the sum of ten different positive integers is 100, then what is the greatest possible number among these 10 numbers?

If α and β are roots of the equation 3x2 – 13x + 14 = 0, then what is the value of (α/β) + (β/α)?

If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2 )?

If cosec θ + sinθ = 5/2 then the value of cosecθ - sinθ is

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

What is the value of 232 ?

Find the maximum area of a rectangular field which is surrounded by a rope of 100 meters?