We get $2$ litres of kerosene less in Rs. $360$ if the price of kerosene increases by Rs. $2$ per litre. Find the original price of kerosene per litre.

Find the roots of the quadratic equation by using the quadratic formula:
$\frac{1}{2} x^{2}-\sqrt{11} x+1=0$

Solve the following equation using the method of factorization: $x - \frac{1}{x} = \frac{45}{14} \quad (x \neq 0)$

State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has exactly one root.
$(ii)$ Every quadratic equation has at least one real root.

If both the roots of $25x^{2} - x(m - 2) - 1 = 0$ are opposite,then $m = \ldots$