Mathematics Mock Test - 6

The value of $C$ for which $P(x=K)=C{K}^2$ can serve as the probability function of a random variable $x$ that takes values $0,1,2,3,4$ is:

If $A=\{1,-1,i,-i\}$ and $\ast$ is an operation on $A$ such that $a\ast b=ab$ for all $a,b\in A$, find the identity element of $A$ with respect to $\ast$?

The index number for the price of diesel in $2015$ was $125$ and in $2016$ it was $140$, with $2011$ as the base year. What is the percent increase in the price of diesel from $2015$ to $2016$?

In a race of $200\text{m}$, $A$ beats $B$ by $45\text{m}$ or $9$ seconds. Find the time taken by $A$ to complete the race.

Joe and Jeff are partners in a business. Joe is an active partner and Jeff is a sleeping one. Joe invests \ 5000$andJeffinvests$ \$6000$. Joe receives $12.5\%$ ($25/2\%$) of the profit for managing the business and the rest is divided in proportion to their investment. What does each get out of a profit of \ 880$?