CUET Mathematics Mock Test - 2

Maximize $z=4x_1+3x_2$ subject to constraints:$2x_1+x_2\le 1000$$x_1+x_2\le 800$$x_1\le 400$$x_2\le 700$$x_1,x_2\ge 0$ Find the optimum units of $x_1$ and $x_2$ to be used.

Let $f(x)=x+x^{-1}$. Then which of the following is correct?

Rate of growth of bacteria is proportional to the number of bacteria present at time. If $x$ is the number of bacteria present at any instant $t$, then which one of the following is correct? (Let the proportional constant equal to $2$)

Find the condition on $k$, so that the system of equations: $x+3y=5$ and $2x+ky=8$ has a unique solution.

If $\theta$ is the acute angle between the diagonals of a cube, then which one of the following is correct?