Find the roots of the following quadratic equation by factorisation:
$2x^{2} - x + \frac{1}{8} = 0$

Solve the following equation using the method of factorization and write its solution set: $\frac{x}{x+1} + \frac{x+1}{x} = \frac{41}{20}$

The roots of a quadratic equation $6 x^{2}-13 x+6=0$ are .... .

$A$ cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was $3$ more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ $90,$ find the number of articles produced and the cost of each article.

The sum of two natural numbers is $5$ and the sum of their reciprocals is $\frac{5}{6}$. Find those numbers.

Hypotenuse of a right triangle is $25 \, cm$ and out of the remaining two sides,one is longer than the other by $5 \, cm$. Find the lengths of the other two sides.