Arun Sharma Solutions for Exercise 1: Level of Difficulty

At the Narora nuclear power plant, a technician is allowed a maximum shift of $100$ minutes. A timer with a bell rings at specific intervals of time, such that the minutes when the timer rings is not divisible by $2$, $3$, $5$, and $7$. How many times will the bell ring within these $100$ minutes?

The internal angles of a plane polygon are in AP. The smallest angle is $100°$, and the common difference is $10°$. Find the number of sides of the polygon.

If $\frac{{\mathrm{a}}^{\mathrm{n}+1}+{\mathrm{b}}^{\mathrm{n}+1}}{{\mathrm{a}}^{\mathrm{n}}+{\mathrm{b}}^{\mathrm{n}}}$ is the arithmetic mean of $\mathrm{a}$ and $\mathrm{b}$, then find the value of $\mathrm{n}$.

If $\frac{{\mathrm{a}}^{\mathrm{n}+1}+{\mathrm{b}}^{\mathrm{n}+1}}{{\mathrm{a}}^{\mathrm{n}}+{\mathrm{b}}^{\mathrm{n}}}$ is the harmonic mean of $\mathrm{a}$ and $\mathrm{b}$, then find the value of $\mathrm{n}$.

If $\mathrm{a}$ and $\mathrm{b}$ are two numbers such that $\mathrm{a}, \mathrm{b}>0$, and the harmonic mean of $\mathrm{a}$ and $\mathrm{b}$ is equal to the geometric mean of $\mathrm{a}$ and $\mathrm{b}$, then what can be said about the relationship between $\mathrm{a}$ and $\mathrm{b}$?

The product of $36$ positive integers is $1$. Their sum is greater than or equal to _____.

If the AM of two numbers $\mathrm{a}$ and $\mathrm{b}$ is $12$, while their HM is $3$, then find the value of $\mathrm{ab}$.

If $\mathrm{x}+\frac{1}{\mathrm{yz}}$, $\mathrm{y}+\frac{1}{\mathrm{zx}}$, and $\mathrm{z}+\frac{1}{\mathrm{xy}}$ are in AP, then $\mathrm{x}$, $\mathrm{y}$, and $\mathrm{z}$ are in _____.