31.

If line joining points A and B having position vectors 6a - 4b + 4c and - 4c respectively and the line joining the points C and 0 having position vectors - a - 2b - 3c and a + 2b - 5c intersect, then point of intersection is

• B

• C

• D

• A

Direction ratios of the line which is perpendicular to the lines with direction ratios - 1, 2, 2 and 0, 2, 1 are

• 1, 1, 2

• 2, - 1, 2

• - 2, 1, 2

• 2, 1, - 2

If $\mathrm{a} = \hat{\mathrm{i}} + \hat{\mathrm{j}} + \hat{\mathrm{k}}$, $\mathrm{b} = 2\hat{\mathrm{i}} + \mathrm{\lambda }\hat{\mathrm{j}} + \hat{\mathrm{k}}$, $\mathrm{c} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + 4\hat{\mathrm{k}}$ and $\mathrm{a} . \left(\mathrm{b} \times \mathrm{c}\right)$ = 10, then $\mathrm{\lambda }$ is equal to

• 6

• 7

• 9

• 10

If random variable $\mathrm{X} ~ \mathrm{B}\left(\mathrm{n} = 5, \mathrm{P} = \frac{1}{3}\right)$, then P(2 < X < 4) is equal to

• $\frac{80}{243}$

• $\frac{40}{243}$

• $\frac{40}{343}$

• $\frac{80}{343}$

The objective function Z = x₁ + x₂, subject to the constraints are  x₁ + x₂ $\le$ 10, - 2x₁ + 3x₂ $\le$ 15, x₁ $\le$ 6, x₁x₂ $\ge$ 0 has maximum value of _ the feasible region.

• at only one point

• at only two points

• at every point of the segment joining two points

• at every point of the line joining two points equivalent to