If $a,\;b,\;c$ are in $A.P.$, then $\frac{1}{{bc}},\;\frac{1}{{ca}},\;\frac{1}{{ab}}$ will be in
$A.P.$
$G.P.$
$H.P.$
None of these
If $f(x + y,x - y) = xy\,,$ then the arithmetic mean of $f(x,y)$ and $f(y,x)$ is
If $\alpha ,\;\beta ,\;\gamma $ are the geometric means between $ca,\;ab;\;ab,\;bc;\;bc,\;ca$ respectively where $a,\;b,\;c$ are in A.P., then ${\alpha ^2},\;{\beta ^2},\;{\gamma ^2}$ are in
If the sum of three numbers of a arithmetic sequence is $15$ and the sum of their squares is $83$, then the numbers are
If ${\log _5}2,\,{\log _5}({2^x} - 3)$ and ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ are in $A.P.$ then the value of $x$ is :-
If in the equation $a{x^2} + bx + c = 0,$ the sum of roots is equal to sum of square of their reciprocals, then $\frac{c}{a},\frac{a}{b},\frac{b}{c}$ are in