Embibe Experts Solutions for Chapter: UPSC CDS (I) Previous Year Paper 2018, Exercise 1: Elementary Mathematics

$ABC$ is a right angled triangle with base $BC$ and height $AB$. The hypotenuse $AC$ is four times the length of the perpendicular drawn to it from the opposite vertex. What is $\tan C$ equal to?

$ABC$ is a triangle right angled at $C$ with $BC = a$ and $AC = b$. If $p$ is the length of the perpendicular from $C$ on $AB$, then which one of the following is correct?

The locus of a point equidistant from two intersecting lines is:

In the figure given below, $\mathrm{XA}$ and $\mathrm{XB}$ are two tangents to a circle, If $\angle AXB = {50}^{\circ }$ and $\mathrm{AC}$ is parallel to$\mathrm{XB}$, then what is $\angle \mathrm{ACB}$ equal to?

In the figure given below$, p, q, r$ are parallel lines; $l$ and $m$ are two transversals.

Consider the following:

1. $AB:AC=DE:DF$

2. $AB\times EF=BC\times DE$

Which of the above is/are correct?

In the equilateral triangle $ABC$ given below, $AD=DB$ and $AE=EC$. If $l$ is the length of a side of the triangle, then what is the area of the shaded region?

In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If $\angle QPT =\alpha$, then what is $\angle POQ$ equal to?

In the figure given below, two equal chords cut at point $\mathrm{P}$. If $\mathrm{AB}=\mathrm{CD}=10 \mathrm{cm}$, $\mathrm{OC}=13 \mathrm{cm}$ ($O$ is the centre of the circle) and $\mathrm{PB}=3 \mathrm{cm}$, then what is the length of $\mathrm{OP}$?