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

Let $x_1,x_2,x_3 \in R-\{0\} $ ,$x_1 + x_2 + x_3\neq 0$ and $\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}=\frac{1}{x_1+x_2+x_3}$, then  $\frac{1}{{x^n}_1+{x^n}_2+{x^n}_3} =\frac{1}{{x^n}_1}+\frac{1}{{x^n}_2}+\frac{1}{{x^n}_3}$ holds good for

Let $\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$

If $8 x^{2}+b x+c=0$ is a quadratic equation whose roots are $\alpha^{1 / 5}$ and $\beta^{1 / 5}$, then the value of $c-b$ is equal to:

The number of cubic polynomials $P(x)$ satisfying $P(1)=2, P(2)=4, P(3)=6, P(4)=8$ is

Let $y = \sqrt {\frac{{(x + 1)(x - 3)}}{{(x - 2)}}} $, then all real values of $x$ for which $y$ takes real values, are

Let $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4$ be the solution of the equation $4 x^4+8 x^3-17 x^2-12 x+9=0$ and $\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m$. Then the value of $\mathrm{m}$ is..........