Embibe Experts Solutions for Chapter: UPSC CDS (I) Previous Year Paper 2019, Exercise 1: Elementary Mathematics

A race has three parts. The speed and time required to complete the individual Parts for a runner is displayed on the following chart:

What is the average speed of this runner?

If $\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$, then which one of the following statements is correct?

The number $3^{521}$ is divided by $8$. What is the remainder?

A $12$m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

The angles of a triangle are in the ratio $1:1:4$. If the perimeter of the triangle is K times its largest side, then what is the value of K?

The hypotenuse of a right angles triangle is $10$cm and its area is $24$cm^$2$. If the shorter side is halved and the longer side is doubled, the new hypotenuse becomes

In a circle of radius $8$cm, AB and AC are two chords such that AB=AC=$12$cm. What is the length of chord BC?

Consider the following statements:

1. An isosceles trapezium is always cyclic.
2. Any cyclic parallel is a rectangle.

Which of the above statements is/are correct?