31.

Equation of the plane perpendicular to the line $\frac{\mathrm{x}}{1} = \frac{\mathrm{y}}{2} = \frac{\mathrm{z}}{3}$ and passing through the point (2, 3, 4) is

• 2x + 3y + z = 17

• x + 2y + 3z = 9

• 3x + 2y + z = 16

• x + 2y + 3z = 20

The line $\frac{\mathrm{x} - 2}{3} = \frac{\mathrm{y} - 3}{4} = \frac{\mathrm{z} - 4}{5}$ is parallel to the plane

• 2x + 3y + 4z = 0

• 3x + 4y + 5z = 7

• 2x + y - 2z = 0

• x + y + z = 2

Te angle between two diagonals of a cube is

• ${\cos }^{-1}\left(\frac{1}{3}\right)$

• $30°$

• ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

• $45°$

Lines $\frac{\mathrm{x} - 2}{1} = \frac{\mathrm{y} - 3}{1} = \frac{\mathrm{z} - 4}{- \mathrm{k}}$ and $\frac{\mathrm{x} - 1}{\mathrm{k}} = \frac{\mathrm{y} - 4}{2} = \frac{\mathrm{z} - 5}{1}$ are coplanar, if

• k = 2

• k = 0

• k = 3

• k = - 1

If the events A and B are independent, if P(A') = $\frac{2}{3}$ and P(B') = $\frac{2}{7}$, then $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$ is equal to

• $\frac{4}{21}$

• $\frac{5}{21}$

• $\frac{1}{21}$

• $\frac{3}{21}$

The area ofthe parallelogram whose adjacent sides are $\hat{\mathrm{i}} + \hat{\mathrm{k}} \mathrm{and} 2\hat{\mathrm{i}} + \hat{\mathrm{j}} + \hat{\mathrm{k}}$ is

• 3

• $\sqrt{2}$

• 4

• $\sqrt{3}$

If a and b are two unit vectors mclined at an angle $\frac{\mathrm{\pi }}{3}$ then the value of $\left|\mathrm{a} + \mathrm{b}\right|$ is

• equal to

• greater than 1

• equal to 0

• less than 1

If x + y $\le 2, \mathrm{x} \ge 0, \mathrm{y} \ge 0$ the point at which maximum value of 3x + 2y attained will be

• (0, 2)

• (0, 0)

• (2, 0)

• $\left(\frac{1}{2}, \frac{1}{2}\right)$

The value of [(a - b)(b - c)(c - a)] is equal to

• 0

• 1

• 2[a b c]

• 2