Mathematics Mock Test - 8

The maximum value of the objective function $Z=4x+3y$ subject to $4x+2y\le 12$, $2x+4y\ge 6$, $x\ge 0,y\ge 0$ is:

If $O(A)=2\times 3$, $O(B)=3\times 2$ and $O(C)=3\times 3$, which one of the following is not defined?

In the following table, $x$ is the discrete random variable and $p(x)$ is the probability density function. The standard deviation of $x$ is:| $x$ | $1$ | $2$ | $3$ | $4$ ||---|---|---|---|---|| $p(x)$ | $0.2$ | $0.4$ | $0.3$ | $0.1$ |

If $a\ne 6$, $b,c$ satisfy
$$\left|\begin{array}{ccc}a& 2b& 2c\\ 3& b& c\\ 4& a& b\end{array}\right|=0$$
then $abc=$

Let the function $f:[-7,0]\to \mathbb{R}$ be continuous on $[-7,0]$ and differentiable on $(-7,0)$. If $f(-7)=-3$ and $f^{\prime }(x)\le 2$ for all $x\in (-7,0)$, then for all such functions $f$, $f(-1)+f(0)$ lies in the interval: