If $p,\;q,\;r$ are in $A.P.$ and are positive, the roots of the quadratic equation $p{x^2} + qx + r = 0$ are all real for
$\left| {\,\frac{r}{p} - 7\;} \right|\; \ge 4\sqrt 3 $
$\left| {\;\frac{p}{r} - 7\;} \right|\; < 4\sqrt 3 $
All $p$ and $r$
No $p$ and $r$
There are $15$ terms in an arithmetic progression. Its first term is $5$ and their sum is $390$. The middle term is
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq\, 2$
The sum of all the elements of the set $\{\alpha \in\{1,2, \ldots, 100\}: \operatorname{HCF}(\alpha, 24)=1\}$ is
If $^n{C_4},{\,^n}{C_5},$ and ${\,^n}{C_6},$ are in $A.P.,$ then $n$ can be
The first term of an $A.P. $ is $2$ and common difference is $4$. The sum of its $40$ terms will be