If the equation $x^8 - kx^2 + 3 = 0$ has a real solution,then the least integral value of $k$ is-

If $\sum\limits_{r = 0}^{25} {\left( {^{50}{C_r} \cdot ^{50 - r}{C_{25 - r}}} \right) = K\left( {^{50}{C_{25}}} \right)}$,then $K$ is equal to

The sum of the first three terms of a $G.P.$ is $S$ and their product is $27$. Then all such $S$ lie in

If the sum of the first ten terms of the series ${\left( {1\frac{3}{5}} \right)^2} + {\left( {2\frac{2}{5}} \right)^2} + {\left( {3\frac{1}{5}} \right)^2} + {4^2} + \dots$ is $\frac{16}{5}m$,then $m$ is equal to:

Let $a_{1}, a_{2}, \ldots, a_{n}$ be a given $A.P.$ whose common difference is an integer and $S_{n} = a_{1} + a_{2} + \ldots + a_{n}$. If $a_{1} = 1$,$a_{n} = 300$ and $15 \leq n \leq 50$,then the ordered pair $(S_{n-4}, a_{n-4})$ is equal to

If the $5^{th}$ term of a $G.P.$ is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$,then the $4^{th}$ term will be