If $a,\;b,\;c$ are in $A.P.$ as well as in $G.P.$, then

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

Let $a, b, c$ be the sides of a triangle. If $t$ denotes the expression $\frac{\left(a^2+b^2+c^2\right)}{(a b+b c+c a)}$, the set of all possible values of $t$ is

If the arithmetic, geometric and harmonic means between two positive real numbers be $A,\;G$ and $H$, then

Let $x, y, z$  be positive real numbers such that $x + y + z = 12$ and  $x^3y^4z^5 = (0. 1 ) (600)^3$. Then $x^3 + y^3 + z^3$ is equal to

If $a,\,b,\,c,\,d$ are positive real numbers such that $a + b + c + d$ $ = 2,$ then $M = (a + b)(c + d)$ satisfies the relation