The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

• (2, - 1)

• (- 2, 1)

• (1, 1)

• (1, 2)

The line which is parallel to x - axis and crosses the curve y = $\sqrt{\mathrm{x}}$ at an angle 45°, is

• y = $\frac{1}{4}$

• $\mathrm{y} = \frac{1}{2}$

• y = 1

• y = 4

The distance between the lines 5x - 12y + 65 = 0 and 5x - 12y - 39 = 0 is

• 4

• 16

• 2

• 8

A particle is projected vertically upwards and is at a height h after t₁ seconds and again after t₂ seconds, then

• h = gt₁t₂

• h = $\frac{1}{2}{\mathrm{gt}}_1{\mathrm{t}}_2$

• $\mathrm{h} = \frac{2}{\mathrm{g}}{\mathrm{t}}_1{\mathrm{t}}_2$

• h = $\sqrt{{\mathrm{gt}}_1{\mathrm{t}}_2}$

65.

The equation of bisectors of the angles between the lines $\left|\mathrm{x}\right| = \left|\mathrm{y}\right|$ are

• $\mathrm{y} = \pm \mathrm{x} \mathrm{and} \mathrm{x} = 0$

• $\mathrm{x} = \frac{1}{2} \mathrm{and} \mathrm{y} = \frac{1}{2}$

• y = 0 and x = 0

• None of the above

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y²- 6x - 4y -12 = 0 is

• y² - 4y - 21 = 0

• y² + 4y - 21 = 0

• y² - 4y + 21 = 0

• y² + 4y + 21 = 0

If the foot of the perpendicular from the origin to a straight line is at the point (3 - 4). Then, the equation of the line is

• 3x - 4y = 25

• 3x - 4y + 25 = 0

• 4x + 3y - 25 = 0

• 4x - 3y + 25 = 0

The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x² + 4yx - 4x + 1= 0 is

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

The equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is

• 99x - 27y - 81 = 0

• 11x - 3y + 9 = 0

• 21x + 77y - 101 = 0

• 21x + 77y + 101 = 0

The angle between the straight lines

$\mathrm{x} - \mathrm{y}\sqrt{3} = 5 \mathrm{and} \sqrt{3}\mathrm{x} + \mathrm{y} = 7$ is

• 90$°$

• $60°$

• $75°$

• $30°$