MCQ
Consider the objective function Z = 40x + 50y The minimum number of constraints that are required to maximize Z are:
- A4
- B2
- C3
- D1
Solution:
Since in the given function Z = 40x + 50y, two variables are used.
So, the two constraints will be $\text{x}\geq0,\text{y}\geq0$ and the third one will be of the type
$\text{ax}+\text{by}\geq\text{c}.$
Hence, at least 3 constraints are required.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right) \text {, where } x \in\left[0, \frac{\pi}{2}\right] \text {, }$
consider the following two statements :
($I$) $\mathrm{f}$ is increasing in $\left(0, \frac{\pi}{2}\right)$.
($II$) $\mathrm{f}^{\prime}$ is decreasing in $\left(0, \frac{\pi}{2}\right)$.
Between the above two statements,
$\frac{\pi}{12}+\log\big(2\sqrt{2}\big)$
$\frac{\pi}{2}+\log\big(2\sqrt{2}\big)$
$\frac{\pi}{6}+\log\big(2\sqrt{2}\big)$
$\frac{\pi}{3}+\log\big(2\sqrt{2}\big)$
$\text{x}_{1} + \text{x}_{2}, \text{y}_{1} +\text{ y}_{2}, \text{z}_{1} + \text{z}_{2}$
$ (\text{x}_{1}-\text{x}_{2})^2+(\text{y}_{1}-\text{y}_{2})^2+(\text{z}_{1}+\text{z}_{2})^2$
$\frac{\text{x}_{1}+\text{x}_{2}}{2}, \frac{\text{y}_{1}+\text{y}_{2}}{2}, \frac{\text{z}_{1}+\text{z}_{2}}{2}$
$\text{x}_{2} - \text{x}_{1}, \text{y}_{2} - \text{y}_{1}, \text{z}_{2} -\text{ z}_{1}$