Let ${\left( {1 - 2x + 3{x^2}} \right)^{10x}} = {a_0} + {a_1}x + {a_2}{x^2} + .....+{a_n}{x^n},{a_n} \ne 0$, then the arithmetic mean of $a_0,a_1,a_2,...a_n$ is
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=a_{2}=2, a_{n}=a_{n-1}-1, n\,>\,2$
The sum of all two digit numbers which, when divided by $4$, yield unity as a remainder is
Three numbers are in $A.P.$ whose sum is $33$ and product is $792$, then the smallest number from these numbers is
If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $