Mathematics Mock Test - 7

If $g(x)=x\lfloor \frac{1}{x}\rfloor$, where $\lfloor \cdot \rfloor$ is the greatest integer function, find the value of ${\int }_{1/3}^{1}g(x)dx$.

The marginal cost is much less than the marginal revenue for a product. The company selling the product should:

If an event $E$ has only one sample point of a sample space, it is called a ______:

A player tosses three coins. If the first toss is a Head, find the probability that there are two consecutive Heads among the three coins.

A $10\text{km}$ race is organized on an $800\text{m}$ circular racecourse. $P$ and $Q$ are contestants. The ratio of their speeds is $5:4$, and the difference between their speeds is $1\text{m/s}$. How many times will the winner overtake the loser?