If $f(x) = (x^2 - 1)^7$,then $f^{(14)}(x)$ is equal to

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in

The function $f(x) = \frac{x}{2} + \frac{2}{x}$ has a local minimum at $x = $ ..........

An achromatic combination of lenses produces

In algae with a haplontic life cycle,which of the following processes involves mitosis?

If $N$ denotes the set of all positive integers and if $f: N \rightarrow N$ is defined by $f(n) =$ the sum of positive divisors of $n$,then $f(2^k \cdot 3)$,where $k$ is a positive integer,is