If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$ is
$0$
$20$
$21$
$23$
The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be
Let ${S_1},{S_2},......,{S_{101}}$ be the consecutive terms of an $A.P$ . If $\frac{1}{{{S_1}{S_2}}} + \frac{1}{{{S_2}{S_3}}} + .... + \frac{1}{{{S_{100}}{S_{101}}}} = \frac{1}{6}$ and ${S_1} + {S_{101}} = 50$ , then $\left| {{S_1} - {S_{101}}} \right|$ is equal to
If the first, second and last terms of an $A.P.$ be $a,\;b,\;2a$ respectively, then its sum will be
The income of a person is $Rs. \,3,00,000,$ in the first year and he receives an increase of $Rs.\,10,000$ to his income per year for the next $19$ years. Find the total amount, he received in $20$ years.
Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is