R. D. Sharma Solutions for Chapter: Real Numbers, Exercise 8: MULTIPLE CHOICE QUESTIONS (MCQs)

${\mathrm{n}}^2-1$ is divisible by $8$, if $\mathrm{n}$ is

The decimal expansion of the rational number $\frac{33}{2^2\times 5}$ will terminate after

If two positive integers $a$ and $b$ are written as $a=x^3{y}^2$ and $b=x{y}^3, x, y$ are prime numbers, then, $\text{HCF}\left(a, b\right)$ is

The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is

The largest number which divides $70$ and$125$, leaving remainders $5$ and $8$, respectively, is

If the $\mathrm{HCF}$ of $65$ and $117$ is expressible in the form $65\mathrm{m}-117$, then the value of $\mathrm{m}$ is

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after:

Euclid's division lemma states that for two positive integers $a$ and $b$, there exist unique integers $q$ and $r$, such that $a=bq+r$, where $r$ must satisfy: