The interior angles of a polygon are AP. The smallest angle is 120° and the common difference is 5°. The number of sides of the polygon is :

• 9

• 10

• 16

• 5

The direction cosines of the line 4x - 4 = 1 - 3y = 2 - 1 are :

• $\frac{3}{\sqrt{56}}, \frac{{\displaystyle - 4}}{{\displaystyle \sqrt{56}}}, \frac{{\displaystyle 6}}{{\displaystyle \sqrt{56}}}$

• $\frac{3}{\sqrt{29}}, \frac{{\displaystyle - 4}}{{\displaystyle \sqrt{29}}}, \frac{{\displaystyle 6}}{{\displaystyle \sqrt{29}}}$

• $\frac{3}{\sqrt{61}}, \frac{{\displaystyle - 4}}{{\displaystyle \sqrt{61}}}, \frac{{\displaystyle 6}}{{\displaystyle \sqrt{61}}}$

• 4, - 3, 2

The centre of the sphere passing through the origin and through the intersection pomts of the plane$\frac{\mathrm{x}}{\mathrm{a}} + \frac{\mathrm{y}}{\mathrm{b}} + \frac{\mathrm{z}}{\mathrm{c}} = 1$ with axes is :

• $\left(\frac{\mathrm{a}}{2}, 0, 0\right)$

• $\left(0, \frac{\mathrm{a}}{2}, 0\right)$

• $\left(0, 0, \frac{\mathrm{a}}{2}\right)$

• $\left(\frac{\mathrm{a}}{2}, \frac{\mathrm{b}}{2}, \frac{\mathrm{c}}{2}\right)$

214.

The line 2x - y = 1 bisects angle between two lines. If equation of one line is y = x, then the equation of the other line is :

• 7x - y - 6 = 0

• x - 2y + 1 = 0

• 3x - 2y - 1 = 0

• x - 7y + 6 = 0

The angle between the lines $\sqrt{3}\mathrm{x} - \mathrm{y} - 2 = 0$ and x - $\sqrt{3}\mathrm{y} + 1 = 0$ is :

• 90°

• 60°

• 45°

• 30°

A force of magnitude $\sqrt{6}$ acting along the line joining the points A(2, - 1, 1) and B (3, 1, 2) displaces a particle from A to B. The work done by the force is :

• 6

• $6\sqrt{6}$

• $\sqrt{6}$

• 12

Equation of the plane parallel to the planes x + 2y + 3z - 5 = 0, x + 2y + 3z - 7 = 0 and equidistant from them is :

• x + 2y + 3z - 6 = 0

• x + 2y + 3z - 1 = 0

• x + 2y + 3z - 8 = 0

• x + 2y + 3z - 3 = 0

If the plane 2x - y + z = 0 is parallel to the line $\frac{2\mathrm{x} - 1}{2} = \frac{2 - \mathrm{y}}{2} = \frac{\mathrm{z} + 1}{\mathrm{a}}$, then the value of a is :

• 4

• - 4

• 2

• - 2

The shortest distance between the line y = x and the curve
y² = x - 2 is

• $\frac{11}{4\sqrt{2}}$

• $\frac{7}{8}$

• 2

• $\frac{7}{4\sqrt{2}}$

The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1 , 1, 0) is :

• x - 3y - 2z = - 2

• x - y - z = 0

• 2x - z = 2

• x + 3y + z = 4