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

If two lines $AB \text{and} CD$ intersect at $O$ such that $\angle AOC=5\angle AOD$, then the four angles at $O$ are______.

If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is.______.

The area of the region bounded externally by a square of side $2a \mathrm{cm}$ and internally by the circle touching the four sides of the square is_____.

In the figure given below, $ABC$ is a right-angled triangle where $\angle A=90°, AB=p \mathrm{cm} \text{and} AC=q \mathrm{cm}$. On the three sides as diameters semicircles are drawn in the figure. The area of the shaded portion, in square cm, is______.

In the figure given below, the radius of the circle is $6 \mathrm{cm} \mathrm{and} \mathrm{AT}=4 \mathrm{cm}$. The length of tangent $\mathrm{PT}$ is______.

In the figure given below, $ABCD$ is the diameter of a circle of radius $9 \mathrm{cm}$. The lengths $AB, BC \text{and} CD$ are equal. Semicircles are drawn on $AB\text{ and} BD$ as diameters as shown in the figure. What is the area of the shaded region ?

In the figure given below, what is $\angle BCD$ equal to?

In the figure given below, $AB$ is the diameter of the circle whose centre is at $O$. Given that $\angle ECD=\angle EDC=32°$, then $\angle CEF \text{and} \angle COF$ Respectively are______.