Mathematics Mock Test - 6

There are two linear inequations represented by $x+2y\ge 3$ and $x-y\ge -3$. Which region based on color contains the solutions of these two inequations?

The per-unit profit of a product is given by $P=600-5x$, where $x$ is the number of units sold. What is the expression for marginal revenue?

Two events $A$ and $B$ are independent and equally likely. If $P(A\cup B)=3/4$, then $P(A)=$ ?

The probability density function for a continuous random variable $x$ is:$f(x)=\{\begin{array}{ll}\frac{x}{6},& 0\le x<2\\ \frac{1}{3},& 2\le x<4\\ -\frac{x}{6}+1,& 4\le x<6\end{array}$ The mean value of $x$ is:

In a box containing $100$ eggs, $10$ eggs are rotten. The probability that out of a sample of $5$ eggs none is rotten (if sampling is with replacement) is: