41.

The area of the region bounded by the curve y = x² and the line y = 16

• $\frac{256}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{128}{3} \mathrm{sq} \mathrm{unit}$

Two events A and B will be independent if

• $\mathrm{P}\left(\mathrm{A}\text{'} \cap \mathrm{B}\text{'}\right) = \left(1 - \mathrm{P}\left(\mathrm{A}\right)\right)\left(1 - \mathrm{P}\left(\mathrm{B}\right)\right)$

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) = 1$

• $\mathrm{P}\left(\mathrm{A}\right) = \mathrm{P}\left(\mathrm{B}\right)$

• A and B are mutually exclusive

Area of the region bounded by the curve y = cos(x), x = 0 and x = $\mathrm{\pi }$ is

• 4 sq unit

• 3 sq units

• 1 sq units

• 2 sq units

The distance of the point (- 2, 4, - 5) from the line $\frac{\mathrm{x} + 3}{3} = \frac{\mathrm{y} - 4}{5} = \frac{\mathrm{z} + 8}{6}$ is

• $\sqrt{\frac{37}{10}}$

• $\frac{37}{10}$

• $\frac{\sqrt{37}}{10}$

• $\frac{37}{\sqrt{10}}$