If a straight line perpendicular to 2x - 3y + 7 = 0 forma triangle with the co-ordinate axes whose area is 3 sq. units, then the equation of the straight line is

• $3\mathrm{x} + 2\mathrm{y} = \pm 2$

• $3\mathrm{x} + 2\mathrm{y} = \pm 6$

• $3\mathrm{x} + 2\mathrm{y} = \pm 4$

• $3\mathrm{x} + 2\mathrm{y} = \pm 8$

If ( - 2, 6) is the image of the point (4, 2) with respect to the line L = 0, then L is equal to

• 6x - 4y - 7 = 0

• 2x + 3y - 5 = 0

• 3x - 2y + 5 = 0 

• 3x - 2y + 10 = 0

If the co-ordinate axes are the bisectors of the angles between the pair of lines ${\mathrm{ax}}^2 + 2\mathrm{hxy} + {\mathrm{by}}^2 = 0 \mathrm{where} {\mathrm{h}}^2 >\mathrm{ab} \mathrm{and} \mathrm{a} \ne \mathrm{b}, \mathrm{then}$

• a + b = 0 

• h = 0

• $\mathrm{h} \ne 0, \mathrm{a} + \mathrm{b} = 0$

• $\mathrm{a} + \mathrm{b} \ne 0$

If the angle 20 is acute, then the acute angle between the pair of straight lines ${\mathrm{x}}^2\left(\cos \left(\mathrm{\theta }\right) - \sin \left(\mathrm{\theta }\right)\right) + 2\mathrm{xycos}\left(\mathrm{\theta }\right) + {\mathrm{y}}^2\left(\cos \left(\mathrm{\theta }\right) + \sin \left(\mathrm{\theta }\right)\right) = 0$

• $2\mathrm{\theta }$

• $\frac{\mathrm{\theta }}{2}$

• $\frac{\mathrm{\theta }}{3}$

• $\mathrm{\theta }$

If the lines 4x + 3y - 1 = 0, x - y + 5 = 0 and kx + 5y - 3 are concurrent, then k is equal to

• 4

• 5

• 6

• 7

126.

If the pair of straight lines given by Ax² + 2Hxy + By² = 0 (H² > AB) forms an equilateral triangle with line ax + by + c = 0, then (A + 3B)(3A + B) is equal to :

• H²

• - H²

• 2H²

• 4H²

The area (in sq units) of the quadrilateral formed by two pairs of lines ${\mathrm{\lambda }}^2{\mathrm{x}}^2 - {\mathrm{m}}^2{\mathrm{y}}^2 - \mathrm{n}\left(\mathrm{\lambda x} + \mathrm{my}\right) = 0$ and ${\mathrm{\lambda }}^2{\mathrm{x}}^2 - {\mathrm{m}}^2{\mathrm{y}}^2 + \mathrm{n}\left(\mathrm{\lambda x} + \mathrm{my}\right) = 0$ is :

• $\frac{{\mathrm{n}}^2}{2\left|\mathrm{\lambda m}\right|}$

• $\frac{{\mathrm{n}}^2}{\left|\mathrm{\lambda m}\right|}$

• $\frac{\mathrm{n}}{2\left|\mathrm{\lambda m}\right|}$

• $\frac{{\mathrm{n}}^2}{4\left|\mathrm{\lambda m}\right|}$

Suppose A, B are two points on 2x - y + 3 = 0 and P (1, 2) is such that PA = PB. Then, the mid-point of AB is

• $\left(\frac{- 1}{5}, \frac{13}{5}\right)$

• $\left( \frac{- 7}{5}, \frac{9}{5}\right)$

• $\left( \frac{7}{5}, \frac{- 9}{5}\right)$

• $\left( \frac{- 7}{5}, \frac{- 9}{5}\right)$

The angle between the lines represented by

${\mathrm{y}}^2{\sin }^2\left(\mathrm{\theta }\right) - {\mathrm{xysin}}^2\left(\mathrm{\theta }\right) + {\mathrm{x}}^2\left({\cos }^2\left(\mathrm{\theta }\right) - 1\right) = 0 \mathrm{is}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

Area of the triangle formed by the lines 3x² + 4xy + y² = 0, 2x - y = 6 is

• 16 sq. units

• 25 sq. units

• 36 sq. units

• 49 sq. units