When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

Let $2 \sin^2 x + 3 \sin x - 2 > 0$ and $x^2 - x - 2 < 0$. ($x$ is measured in radians). The $x$ lies in the interval

The events $A$ and $B$ have probabilities $0.25$ and $0.50$,respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then,the probability that neither $A$ nor $B$ occurs is:

The negation of the statement ''If $I$ become a teacher,then $I$ will open a school'',is

$\int_{-2}^2 |[x]| \, dx$ is equal to

If in a $\triangle ABC$,$\frac{1}{a+c} + \frac{1}{b+c} = \frac{3}{a+b+c}$,then $\angle C$ is equal to (in $^{\circ}$)