If Zeba were younger by $5\, \text{years}$ than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now? (in $\text{years}$)

An express train takes $1\, hour$ less than a passenger train to travel $132\, km$ between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $11\, km/h$ more than that of the passenger train,find the average speed of the two trains. (in $km/h$)

Solve the following equation using the method of factorization and write its solution set: $\frac{9}{x-1} - \frac{2}{x-3} = \frac{5}{x+1}$

Find the roots of the following quadratic equation by factorisation:
$2x^{2} + x - 6 = 0$

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.

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