Mathematics Mock Test - 6

$A$ can row $15\text{km/h}$ in still water. It takes him twice as long to row upstream as to row downstream. Find the rate downstream.

$300\text{gm}$ of sugar solution has $40\%$ sugar. How much sugar should be added to make it $50\%$ in the solution?

When $67$ is divided by a number $x$, a remainder of $3$ is obtained. If $x<50$, then the largest value of $x$ is:

If $X=\{a,b,c\}$ and $R$ is a relation on $X$ such that $R=\{(a,a),(b,b),(c,c)\}$, then $R$ is:

Which of the following is an empty set?