MCQ
$\int_1^e {\frac{1}{x}\,dx} $ is equals to
- A$\infty $
- B$0$
- ✓$1$
- D$\log (1 + e)$
$ = [\log x]_1^e = {\log _e}e - \log 1 = 1$.
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$(A)$ $\cos \beta > 0$ $(B)$ $\sin \beta < 0$ $(C)$ $\cos (\alpha+\beta) > 0$ $(D)$ $\cos \alpha < 0$
Minimize $z=2 x+3 y$ the coordinates of the corner points of the bounded feasible region are $A\,(3,3), B\,(20,3),$ $\mathrm{C}\,(20,10), \mathrm{D}\,(18,12)$ and $\mathrm{E}\,(12,12) .$ The minimum value of $z$ is $\ldots \ldots$