The minimum value of $|x| + |x + \frac{1}{2}| + |x - 3| + |x - \frac{5}{2}|$ is

Statement $-1$: Any function $f(x)$ is an even function if $f(-x) = f(x)$ for all $x$ in its domain.
Statement $-2$: The function $f(x) = \frac{1}{\sqrt{1 - x^2}} + \left[ \frac{x^2 + x + 1}{4} \right]$,where $[.]$ denotes the greatest integer function,is an even function.

The equation $6^{x}+8^{x}=10^{x}$ has

Let $f(n) = 2^{n+1}$ and $g(n) = 1 + (n+1)2^n$ for all $n \in N$. Then:

If $\alpha_1 < \alpha_2 < \alpha_3 < \alpha_4 < \alpha_5 < \alpha_6$,then the equation $(x-\alpha_1)(x-\alpha_3)(x-\alpha_5) + 3(x-\alpha_2)(x-\alpha_4)(x-\alpha_6) = 0$ has :-

The number of elements in the set $\{x \in R : (|x|-3)|x+4|=6\}$ is equal to