If $\tan \,n\theta = \tan m\theta $, then the different values of $\theta $ will be in
$A.P.$
$G.P.$
$H.P.$
None of these
The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be
If the sum of $n$ terms of an $A.P.$ is $\left(p n+q n^{2}\right),$ where $p$ and $q$ are constants, find the common difference.
The sum of all natural numbers between $1$ and $100$ which are multiples of $3$ is
If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$ is
If ${\log _3}2,\;{\log _3}({2^x} - 5)$ and ${\log _3}\left( {{2^x} - \frac{7}{2}} \right)$ are in $A.P.$, then $x$ is equal to