CUET Mathematics Mock Test - 2

Maximize $z=5x_1+3x_2$ subject to the following constraints:$x_1+x_2\ge 3$$x_1-x_2\le 2$ and the solution is in the first quadrant ($x_1,x_2\ge 0$). What can be said about the solution of this LPP?

If $f$ and $g$ are differentiable functions in $(0,1)$ satisfying $f(0)=2=g(1)$, $g(0)=0$ and $f(1)=6$, then for some $c\in (0,1)$:

Given that $x$ is a random variable in the range $[0,\infty )$ with a probability density function $f(x)=\frac{e^{-x/2}}{K}$, the value of the constant $K$ is:

Find the present value of a sequence of payments of $Rs.432$ made at the end of each $5$ months and continuing forever if money is worth $5\%$ compounded at the end of each $5$ months.

A cricket bat manufacturing firm assesses its variable cost to be $2x(x-40)$, where $x$ is the number of bats produced, and the fixed cost incurred on storage is $Rs.1200$. How many bats should be manufactured for the minimum total cost?