Embibe Experts Solutions for Chapter: UPSC CDS (II) Previous Year Paper 2020, Exercise 1: Elementary Mathematics

The Euclidean algorithm is used to calculate the _____.

If $\mathrm{cosec} \mathrm{\theta }-\sin \mathrm{\theta }=\mathrm{m}$ and $\sec \mathrm{\theta }-\cos \mathrm{\theta }=\mathrm{n}$, then what is ${\mathrm{m}}^{\frac{4}{3}}{\mathrm{n}}^{\frac{2}{3}}+{\mathrm{m}}^{\frac{2}{3}}{\mathrm{n}}^{\frac{4}{3}}$ equal to?

If $\cos \mathrm{\theta }+\sec \mathrm{\theta }=\mathrm{k}$, then what is the value of ${\sin }^2\mathrm{\theta }-{\tan }^2\mathrm{\theta }$?

Consider the following statements:

$1. \sin a=x+\frac{1}{x}$ is possible for some real value of $x$.

$2. \cos a=x+\frac{1}{x}$ is possible for some real value of $x$.

Which of the above statements is/are correct?

When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance, and it takes $4 \mathrm{seconds}$ to fall $78.40 \mathrm{m}$. How long would it take to fall $122.50 \mathrm{m}$ ?

If $6^{3-4x}{4}^{x+5}=8$ ( Given ${\log }_{10}2=0.301 \text{and} {\log }_{10}3=0.477$), then which one of the following is correct?

If radius of a sphere is rational, then which of the following is/are correct ?

$1.$Its surface area is rational.

$2.$ Its volume is rational.

Select the correct answer using the code given below :

$ABC$ is a triangle inscribed in a semicircle of diameter $AB$. What is $\cos \left(A+B\right)+\sin \left(A+B\right)$ equal to?