
- (5, 0)
- (6, 5)
- (6, 8)
- (4, 10)

Solution:
| Corner points | Corresponding value of Z = 3x - 4y |
| (0, 0) (5, 0) (6, 5) (6, 8) (4, 10) (0, 8) | 0 15 (Maxmimum) -2 -14 -28 -32 |
Hence, maximum of Z occurs at (5, 0) and its maximum value is 27.
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Eight coins are tossed together. The probability of getting exactly 3 heads is:
Statement $-I$ : Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$ and $\vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Then the vector $\vec{r}$ satisfying $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{r}}=0$ is of magnitude $\sqrt{10}$.
Statement $-II$ : In a triangle $A B C, \cos 2 A+\cos 2 B$ $+\cos 2 \mathrm{C} \geq-\frac{3}{2}$