Sarvesh K Verma Solutions for Chapter: Number System, Exercise 14: Introductory Exercise

If $\mathrm{a}=24, \mathrm{b}=26, \mathrm{c}=28$, then the value of ${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2-\mathrm{ab}-\mathrm{bc}-\mathrm{ca}$ will be

Among the expression $(1-3\mathrm{p}), \left[1-(3\mathrm{p}{)}^2\right], \left[1-(3\mathrm{p}{)}^3\right]$ and $\left[1-(3\mathrm{p}{)}^4\right]$, the number of factors of $\left(1-81{\mathrm{p}}^4\right)$ is:

The sum of two numbers is $9$and the sum of their squares is $41$. The numbers are:

The square root of
$\frac{{\left(3\frac{1}{4}\right)}^4-{\left(4\frac{1}{3}\right)}^4}{{\left(3\frac{1}{4}\right)}^2-{\left(4\frac{1}{3}\right)}^2}$ _____.

The value of $\frac{(119{)}^2+(119\left)\right(111)+(111{)}^2}{(119{)}^3-(111{)}^3}$ is:

The expression $(\mathrm{a}-\mathrm{b}{)}^3+(\mathrm{b}-\mathrm{c}{)}^3+(\mathrm{c}-\mathrm{a}{)}^3=0$ if:

If $a+b+c=11$, $a^2+b^2+c^2=51$. What is the value of $ab+bc+ac$ ?

If $\left(x+y+z\right)=0$, then the value of $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ is