A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as the shortest. What is the possible length for the shortest piece?

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

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

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

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

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

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