Suppose $\log _a b+\log _b a=c$. The smallest possible integer value of $c$ for all $a, b>1$ is
$4$
$3$
$2$
$1$
The reciprocal of the mean of the reciprocals of $n$ observations is their
Three numbers form a $G.P.$ If the ${3^{rd}}$ term is decreased by $64$, then the three numbers thus obtained will constitute an $A.P.$ If the second term of this $A.P.$ is decreased by $8$, a $G.P.$ will be formed again, then the numbers will be
If $a,\,b,\;c$ are in $A.P.$ and ${a^2},\;{b^2},\;{c^2}$ are in $H.P.$, then
If three unequal non-zero real numbers $a,\;b,\;c$ are in $G.P.$ and $b - c,\;c - a,\;a - b$ are in $H.P.$, then the value of $a + b + c$ is independent of
${2^{\sin \theta }} + {2^{\cos \theta }}$ is greater than