If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
$0$
$1$
$2$
$3$
If $a, b, c$ are distinct positive numbers, each different from $1$, such that $[{\log _b}a{\log _c}a - {\log _a}a] + [{\log _a}b{\log _c}b - {\log _b}b]$ $ + [{\log _a}c{\log _b}c - {\log _c}c] = 0,$ then $abc =$
The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
If ${\log _{12}}27 = a,$ then ${\log _6}16 = $
$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $