The value of k for which the lines 7x - 8y + 5 = 0, 3x - 4y + 5 = 0 and 4x + 5y + k = 0 are concurrent, is given by

• - 45

• 44

• 54

• - 54

The angle between the straight lines x - y$\sqrt{3}$ = 5 and $\sqrt{3}$x + y = 7, is

• $0°$

• $90°$

• $120°$

• $30°$

93.

Orthocentre of the triangle formed by the points (0, 0), (3, 4), (4,0) is

• $\left(3, \frac{5}{4}\right)$

• (3, 12)

• $\left(3, \frac{3}{4}\right)$

• (3, 9)

Equation of straight line passing through intersection of x + 5y + 7 = 0, 3x + 2y - 5 = 0 and perpendicularto 7x + 2y - 5 = 0, is

• 2x - 7y - 20 = 0

• 2x + 7y - 20 = 0

• - 2x + 7y - 20 = 0

• 2x + 7y + 20 = 0

The points situated on the line x + y = 4 whose distance fromthe line 4x + 3y = 10 is unity, are

• (3, 1), (- 7, 11)

• (3, 1), (7, 11)

• (- 3, 11), (- 7, 11)

• (1, 3), (- 7, 11)

Lines represented by the pair ofstraight lines ab (x² - y²) +(a² - b²)y = 0, are

• ax - by = 0, bx + ay = 0

• ax - by = 0, bx - ay = 0

• ax + by = 0, bx + ay = 0

• ax + by = 0, bx - ay = 0

Angle between the pair of straight lines (x² + y²) sin²($\mathrm{\alpha }$) = $\left(\mathrm{xcos}\left(\mathrm{\theta }\right) - \mathrm{ysin}\left(\mathrm{\theta }\right)\right)$² is

• $\mathrm{\alpha }$

• $2\mathrm{\alpha }$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

The pair of straight lines joining the origin to the points of intersection of the line y = $2\sqrt{2}$x + c and the circle x² + y² = 2, are at right angles, if

• c² - 4 = 0

• c² - 8 = 0

• c² - 9 = 0

• c² - 10 = 0

If the ratio of gradients ofthe lines represented by ax² + 2hxy + by = 0 is 1 : 3, then the value of  the ratio h² : ab is

• 1 : 3

• (1, 1)

• 4 : 3

• 1 : 1

If the equations of the opposite sides of a parallelogram are x² - 7x + 6 = 0 and y² - 14y + 40 = 0, then the equation of one of its diagonal will be

• 6x + 5y + 14 = 0

• 6x - 5y + 14 = 0

• 5x + 6y + 14 = 0

• 5x - 6y - 14 = 0