CUET Mathematics Mock Test - 2

Consider the Linear Programming problem:Maximize: $7X_1+6X_2+4X_3$ subject to:$X_1+X_2+X_3\le 5$$2X_1+X_2+3X_3\le 10$$X_1,X_2,X_3\ge 0$ The number of basic solutions is:

A manufacturing firm has its variable cost given by $C(x)=x(12-x^3)$. The price per unit is $p(x)=6x-2$. Find the marginal revenue when $3$ units were in demand.

A solution of $100\text{L}$ contains $75\%$ water and the rest liquid sugar. How much liquid sugar must be added to make it a $50\%$ sugar solution?

A card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is either an Ace or a King?

The mean of the probability distribution function given by the following table will be:\begin{center}\begin{tabular}{|c|c|c|c|c|c|}\hline$x$ & 1 & 2 & 3 & 4 & 5 \ \hline$P(x)$ & 0.2 & 0.35 & 0.25 & 0.15 & 0.05 \ \hline\end{tabular}\end{center}