Real Number Quiz 8

$a^x = b^y = c^z$ and abc = 1 then $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ = ……………

If $0.\bar7 = \frac{p}{q}$ then p + q = …………

For what values of $x,2^x\times5^x$ ends with 8 or 5 ?

If $7^{x+3}=5^{x+3}$ then the value of ‘x’ is …………

$\lim\limits_{n\to \infty}\left[\frac{1}{n^2}+\frac{2}{n^2}+....... +\frac{1}{n}\right]$ = …………

If a + b + c = 1 and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=3$. where a, b, c are non zero real numbers. Then the value of ab(a + b) + bc (b + c) + ca (a + c) is ……………

If $\sqrt{15-x\sqrt{14}}=\sqrt8-\sqrt7$  then x = ……………

If $T= \frac{1}{3-\sqrt8}-\frac{1}{\sqrt8-\sqrt7}+\frac{1}{\sqrt7-\sqrt6}-\frac{1}{\sqrt6-\sqrt5}+\frac{1}{\sqrt5-2}$ then …………

$a^x=b^y=c^z$ and  $b^2$ = ac then y = …………

If the ratio of the ages of Mona and Sona is 4:5 and twelve years hence their ages will be in the ratio of 5 : 6, then the age of Sona after 6 years will be …………