Minimum integral value of $\alpha$ for which graph of $f(x) = ||x -2| -\alpha|-5$ has exactly four $x-$intercepts-

A real valued function $f(x)$ satisfies the function equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$ where a is a given constant and $f(0) = 1$, $f(2a - x)$ is equal to

The range of the polynomial $P(x)=4 x^3-3 x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is

The period of the function $f(x) = e^{x -[x]+|cos\, \pi x|+|cos\, 2\pi x|+....+|cos\, n\pi x|}$ (where $[.]$ denotes greatest integer function); is:-

The sentence, What is your Name ? is

Let $A=\{a, b, c\}$ and $B=\{1,2,3,4\}$ Then the number of elements in the set $C =\{ f : A \rightarrow B \mid 2 \in f ( A )$ and $f$ is not one-one $\}$ is