Let $a_1, a_2, a_3, \ldots$. be a $GP$ of increasing positive numbers. If the product of fourth and sixth terms is $9$ and the sum of fifth and seventh terms is $24 ,$ then $a_1 a_9+a_2 a_4 a_9+a_5+a_7$ is equal to $.........$.
$600$
$606$
$60$
$6$
Let $a, b, c, d$ and $p$ be any non zero distinct real numbers such that $\left(a^{2}+b^{2}+c^{2}\right) p^{2}-2(a b+b c+ cd ) p +\left( b ^{2}+ c ^{2}+ d ^{2}\right)=0 .$ Then
The sum of first two terms of a $G.P.$ is $1$ and every term of this series is twice of its previous term, then the first term will be
The number $111..............1$ ($91$ times) is a
The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$, is
$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $