$2 \cos ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ is valid for all values of ' $x$ ' satisfying
Consider the following statements:
Statement (I): In a LPP, the objective function is always linear.
Statement (II): Ina LPP, the linear inequalities on variables are called constraints. Which of the following is correct?
The maximum value of $\mathrm{z}=3 \mathrm{x}+4 \mathrm{y}$, subject to the constraints $\mathrm{x}+\mathrm{y} \leq 40, \mathrm{x}+2 \mathrm{y} \leq 60$ and $\mathrm{x}, \mathrm{y} \geq 0$ is
Consider the following statements.
Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prime}$ are also independent.
Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.
Which of the following is correct?