March 2021

Find the product of roots of $\dfrac{x^{2002} + 4x^{2001}}{4x^{2000}} = 8$.

Calculate $\sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$

The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. Find the area of the smallest circle.

A rectangle ABCD which measures 18 by 24 units is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

A circle with radius 6 has half its area removed by cutting off a border of uniform width. Find the width of the border.

Three forces 20 N, 30 N, and 40 N are in equilibrium. Find the angle between the 20 N and 40 N forces.

The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.

Determine the equation of an open upward parabola with (2, 1) and (-4, 1) as ends of latus rectum.

Find the distance between foci of the conic 8x² + 9y² = 288.

Find the point in the parabola y² = 4x at which the rate of change of the ordinate and abscissa are equal.