If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle x^2-x-6=0$, then the value of $\displaystyle \alpha^3+\beta^3+\alpha^2+\beta^2+\alpha+\beta$ is equal to

If $\displaystyle \sqrt{\frac{1}{25}} = 1 + \frac{x}{144}$, then $\displaystyle x$ is

If $\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1$ and $\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3}$ then $\displaystyle (x, y)$ is:

$\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5$, find $\displaystyle x$

Find value of $\displaystyle x^2 - 10x + 1$ if $\displaystyle x = \frac{1}{5-2\sqrt{6}}$

In a multiple choice question paper consisting of $\displaystyle 100$ questions of $\displaystyle 1$ mark each, a candidate gets $\displaystyle 60\%$ marks. If the candidate attempted all questions and there was a penalty of $\displaystyle 0.25$ marks for wrong answers is:

The solution of the following system of linear eqs. $\displaystyle 2x - 5y + 4 = 0$ and $\displaystyle 2x + y - 8 = 0$ will be: