For $x \in \mathbb{R}$,the minimum value of $\frac{x^2+2x+5}{x^2+4x+10}$ is

Let $a, b, c$ and $d$ be any four real numbers. Then $a^{n} + b^{n} = c^{n} + d^{n}$ holds for any natural number $n$ if:

The diagram shows the graph of $y = ax^2 + bx + c$. Then:

If $\tan \alpha$ equals the integral solution of the inequality $4x^2 - 16x + 15 < 0$ and $\cos \beta$ equals the slope of the bisector of the first quadrant,then $\sin(\alpha + \beta)\sin(\alpha - \beta)$ is equal to

Let $\lambda \in R$ and let the equation $E$ be $|x|^2 - 2|x| + |\lambda - 3| = 0$. Then the largest element in the set $S = \{x + \lambda : x \text{ is an integer solution of } E\}$ is $..........$

The sum of all the roots of the equation $|x^2-8x+15|-2x+7=0$ is: