The angles of a triangle are in the ratio 1 : 3 : 5. Then the greatest angle is :

• $\frac{5\mathrm{\pi }}{9}$

• $\frac{2\mathrm{\pi }}{9}$

• $\frac{7\mathrm{\pi }}{9}$

• $\frac{11\mathrm{\pi }}{9}$

A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. Then angle subtended by the arc at the centre is:

• 50°

• 210°

• 100°

• 60°

The radius of the circle x² + y² + z² - 2y - 4z - 11 = 0 and x + 2y + 2z - 15 = 0 is :

• $\sqrt{3}$

• $\sqrt{5}$

• $\sqrt{7}$

• 3

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} = \overrightarrow{0}, \left|\overrightarrow{\mathrm{a}}\right| = 3, \left|\overrightarrow{\mathrm{b}}\right| = 5 \mathrm{and} \left|\overrightarrow{\mathrm{c}}\right| = 7$, then angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is :

• 0

• 30°

• 45°

• 60°

The points A (4, 5, 1), B (0, - 1, - 1), C(3, 9, 4) and D(- 4, 4, 4) are

• collinear

• coplanar

• non-coplanar

• non-collinear

If $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}} = \overrightarrow{0}, \left|\overrightarrow{\mathrm{a}}\right| = 3, \left|\overrightarrow{\mathrm{b}}\right| = 5 \mathrm{and} \left|\overrightarrow{\mathrm{c}}\right| = 7$, then the angle between $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$ is :

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• ${\cos }^{-1}\left(\frac{2}{225}\right)$

• $\frac{\mathrm{\pi }}{4}$

The shortest distance from the point (1, 2, - 1) to the surface of the sphere x² + y² + z² = 24 is :

• $3\sqrt{6}$ unit

• $\sqrt{6}$ unit

• $2\sqrt{6}$

• 2 sq unit

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is :

• x - y - z - 15 = 0

• x - y - z - 15 = 0

• x + y + z - 15 = 0

• x + y + z + 15 = 0

199.

A line makes acute angles of $\mathrm{\alpha }, \mathrm{\beta } \mathrm{and} \mathrm{\gamma }$ with the co-ordinate axes such that $\cos \left(\mathrm{\alpha }\right)\cos \left(\mathrm{\beta }\right) = \cos \left(\mathrm{\beta }\right)\cos \left(\mathrm{\gamma }\right) = \frac{2}{9} \mathrm{and} \cos \left(\mathrm{\gamma }\right)\cos \left(\mathrm{\alpha }\right) = \frac{4}{9}$, then $\cos \left(\mathrm{\alpha }\right) + \cos \left(\mathrm{\beta }\right) + \cos \left(\mathrm{\gamma }\right)$ is equal to :

• $\frac{25}{9}$

• $\frac{5}{9}$

• $\frac{5}{3}$

• $\frac{2}{3}$

The equation of the plane through the point (1, 2, 3), (- 1,  4, 2) and (3, 1, 1) is :

• 5x + y + 12z - 23 = 0

• 5x + 6y + 2z - 23 = 0

• x + 6y + 2z - 13 = 0

• x + y + z - 13 = 0