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

If $0.\bar{7}=\frac{p}{q}0.\backslash bar7\; =\; \backslash frac\{p\}\{q\}$ then p + q = …………

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

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

$\underset{n\to \mathrm{\infty }}{\lim }[\frac{1}{n^2}+\frac{2}{n^2}+\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{.}+\frac{1}{n}]\backslash lim\backslash limits\_\{n\backslash to\; \backslash infty\}\backslash left[\backslash frac\{1\}\{n^2\}+\backslash frac\{2\}\{n^2\}+.......\; +\backslash frac\{1\}\{n\}\backslash right]$ = …………

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

If $\sqrt{15-x\sqrt{14}}=\sqrt{8}-\sqrt{7}\backslash sqrt\{15-x\backslash sqrt\{14\}\}=\backslash sqrt8-\backslash sqrt7$  then x = ……………

If $T=\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}T=\; \backslash frac\{1\}\{3-\backslash sqrt8\}-\backslash frac\{1\}\{\backslash sqrt8-\backslash sqrt7\}+\backslash frac\{1\}\{\backslash sqrt7-\backslash sqrt6\}-\backslash frac\{1\}\{\backslash sqrt6-\backslash sqrt5\}+\backslash frac\{1\}\{\backslash sqrt5-2\}$ then …………

$a^x=b^y=c^{z}a^x=b^y=c^z$ and  $b^{2}b^2$ = 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 …………