Mathematics Mock Test - 8

A fair die is tossed thrice. If the probabilities of zero, one, two, and three successes are $8/27,4/9,2/9,\text{ and }1/27$ respectively, find the mean of the number of successes.

Let $A=\{a,b,c,d\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of one-to-one functions from $A$ to $B$ is:

If $A=\{1,2,3,4,5\}$ and let $\ast$ is an operation on $A$ such that $a\ast b=\min \{a,b\}$. Which of the following is true?

Durgesh works in a restaurant preparing two types of dishes, A and B. Dish A takes 20 minutes to prepare and Dish B takes 30 minutes. He earns Rs 50 for dish A and Rs 70 for dish B. He works for 12 hours a day and needs 1 hour for personal activities. What will be the time constraint if formulated as a linear programming problem? Assume $x$ and $y$ are the packets of dishes A and B respectively.

The number of solutions in a linear programming model to maximize $5x+4y$ subject to $x-2y\ge 2$, $2x-4y\le -3$, and $x,y\ge 0$ will be: