## Speed of the car

A wheel of car of radius 21 cm is rotating at 600 RPM. What is the speed of car in km/hr?

## The number of his ancestors

A person has 2 parents 4 grandparents, 8 great-grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.

## the sum of squares of the roots of the equation

Find the value of ‘a’ such that the sum of squares of the roots of the equation x^2 – (a – 2)x – (a + 1) = 0 is least?

## In drilling world’s deepest hole

In drilling world’s deepest hole, it was found that the temperature T in degree Celsius, x km below the surface of Earth, was given by T = 30 + 25(x – 3) , 3 < x < 15. At what depth will the temperature be between 2000C and 3000C?

## The integral value of ‘k’

What is the integral value of ‘k’ for which the quadratic equation x^2 – 6 x + k = 0 have real and distinct roots?

## Distance of the foot of the ladder from the building

A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.

## Find the value of ‘θ’

If sin 5θ = cos 4θ, where 5 θ and 4 θ are acute angles, find the value of ‘θ’.