11.

If w is an imaginary root of unity, then the $\left|\begin{array}{ccc}\mathrm{a}& {\mathrm{bw}}^2& \mathrm{aw}\\ \mathrm{bw}& \mathrm{c}& {\mathrm{bw}}^2\\ {\mathrm{cw}}^2& \mathrm{aw}& \mathrm{c}\end{array}\right|$ is :

• a³ + b³ + c³

• a²b - b²c

• 0

• a³ + b³ + c³ - 3abc

If A = {x, y}, then the power set of A is :

• {x^y, y^x}

• $\left\{\mathrm{\varphi }, \mathrm{x}, \mathrm{y}\right\}$

• $\left\{\mathrm{\varphi }, \left\{\mathrm{x}\right\}, \left\{2\mathrm{y}\right\}\right\}$

• $\left\{\mathrm{\varphi }\left\{\mathrm{x}\right\}, \left\{\mathrm{y}\right\}, \left\{\mathrm{x}, \mathrm{y}\right\}\right\}$

The differential equation of system of concentric circles with centre (1, 2) is :

• $\left(\mathrm{x} - 2\right) + \left(\mathrm{y} - 1\right)\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

• $\left(\mathrm{x} - 1\right) + \left(\mathrm{y} - 2\right)\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

• $\left(\mathrm{x} + 1\right)\frac{\mathrm{dy}}{\mathrm{dx}} + \left(\mathrm{y} - 2\right) = 0$

• $\left(\mathrm{x} + 2\right)\frac{\mathrm{dy}}{\mathrm{dx}} + \left(\mathrm{y} - 1\right) = 0$

The equation of line of intersection of planes 4x + 4y - 5z = 12, 8x + 12y - 13z = 32can be written as :

• $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} + 2}{- 3} = \frac{\mathrm{z}}{4}$

• $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} + 2}{3} = \frac{\mathrm{z}}{4}$

• $\frac{\mathrm{x}}{2} = \frac{\mathrm{y} + 1}{3} = \frac{\mathrm{z} - 2}{4}$

• $\frac{\mathrm{x}}{2} = \frac{\mathrm{y}}{3} = \frac{\mathrm{z} - 2}{4}$

The equation of the plane, which makes with co-ordinate axes, a triangle with its centroid $\left(\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }\right)$ is :

• $\mathrm{\alpha x} + \mathrm{\beta y} + \mathrm{\gamma z} = 3$

• $\mathrm{\alpha x} + \mathrm{\beta y} + \mathrm{\gamma z} = 1$

• $\frac{\mathrm{x}}{\mathrm{\alpha }} + \frac{\mathrm{y}}{\mathrm{\beta }} + \frac{\mathrm{z}}{\mathrm{\gamma }} = 3$

• $\frac{\mathrm{x}}{\mathrm{\alpha }} + \frac{\mathrm{y}}{\mathrm{\beta }} + \frac{\mathrm{z}}{\mathrm{\gamma }} = 1$

A variable plane moves so that sum of the reciprocals of its intercepts on the co-ordinate axes is 1/2. Then the plane passes through :

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

• (- 1, 1, 1)

• (2, 2, 2)

• (0, 0, 0)

The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is :

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• 0

The value of $\left[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} \overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}}\right]$ is :

• $\left[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}\right]$

• 0

• $2\left[\overrightarrow{\mathrm{a}} \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}\right]$

• $\overrightarrow{\mathrm{a}} \times \left(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}\right)$

The area of the triangle having vertices as $\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$, $- 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - \hat{\mathrm{k}}$, $4\hat{\mathrm{i}} - 7\hat{\mathrm{j}} + 7\hat{\mathrm{k}}$ is :

• 36 sq unit

• 0  sq unit

• 39 sq unit

• 11 sq unit

The figure formed by the four points $\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$, $2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}$, $5\hat{\mathrm{j}} - \hat{\mathrm{k}} \mathrm{and} \hat{\mathrm{k}} - \hat{\mathrm{j}}$ is :

• trapezium

• rectangle

• parallelogram

• None of these