51.

The value of $\mathrm{\lambda }$. for which the lines 3x + 4y = 5, 2x + 3y = 4and $\mathrm{\lambda }$x + 4y = 6 meet at a point, is :

• 2

• 1

• 4

• 3

Three vertices of a parallelogram taken in order are (- 1, -  6), (2, - 5) and (7, 2). The fourth vertex is :

• (1, 4)

• (1, 1)

• (4, 4)

• (4, 1)

The orthocentre of the triangle whose vertices are (5, - 2), - 1, 2) and (1, 4), is :

• $\left(- \frac{1}{5}, \frac{16}{5}\right)$

• $\left(\frac{14}{5}, \frac{1}{5}\right)$

• $\left(\frac{1}{5}, \frac{1}{5}\right)$

• $\left(\frac{14}{5}, \frac{14}{5}\right)$

Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is :

• $\frac{35}{\sqrt{34}}$

• $\frac{1}{3\sqrt{34}}$

• $\frac{35}{3\sqrt{34}}$

• $\frac{35}{2\sqrt{34}}$

If the equation 2x² + 7 xy + 3y² - 9 x - 7y + k = 0 represents a pair of lines, then k is equal to

• 4

• 2

• 1

• - 4

The angle between the lines 2x - y + 3 = 0 and x + 2y + 3 = 0 is :

• 90°

• 60°

• 45°

• 30°

Distance between the pair of lines represented by the equation x² - 6xy + 9y² + 3 - 9y - 4 = 0 is:

• $\frac{15}{\sqrt{10}}$

• $\frac{1}{2}$

• $\sqrt{\frac{5}{2}}$

• $\frac{1}{\sqrt{10}}$

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°