The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $.....$

If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is

What is the sum of all two digit numbers which give a remainder of $4$ when divided by $6$ ?

If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$  is 

Find the sum of all natural numbers lying between $100$ and $1000,$ which are multiples of $5 .$

If three distinct number $a, b, c$ are in $G.P.$ and the equations $ax^2 + 2bc + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root, then which one of the following statements is correct?