The distance of the point (1, 3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4, is

• $\frac{5}{\sqrt{13}}$units

• $\frac{3}{\sqrt{17}}$units

• $\sqrt{17}$ units

• $\frac{\sqrt{17}}{2}\mathrm{units}$

The equation of a straight line .which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle 120° with positive direction of x-axis is :

• $\mathrm{y} + \sqrt{3}\mathrm{x} + 5 = 0$

• $\mathrm{y} - \sqrt{3}\mathrm{x} + 5 = 0$

• $\mathrm{y} + \sqrt{3}\mathrm{x} - 5 = 0$

• $\mathrm{y} - \sqrt{3}\mathrm{x} - 5 = 0$

The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x - 3y + 7 = 0 and 7x + 4y + 2 = 0 is :

• 21x + 46y - 180 = 0

• 21x - 46y + 96 = 0

• 46x + 21y - 155 = 0

• 46x - 21y - 29 = 0

A straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ ?

• 12 square units

• 15 square units

• 20 square units

• 30  square units

Consider the lines

y = 3x, y = 6x and y = 9

What is the area of the triangle formed by these lines ?

• $\frac{27}{4}$ square units

• $\frac{27}{2}$ square units

• $\frac{19}{4}$ square units

• $\frac{19}{2}$ square units

Consider the lines

y = 3x, y = 6x and y = 9

The centroid of the triangle is at which one of the following points ?

• (3, 6)

• $\left(\frac{3}{2}, 6\right)$

• (3, 3)

• $\left(\frac{3}{2}, 9\right)$

Consider the two lines

x + y + 1 = 0 and 3x + 2y + 1 = 0

What is the equation of the line passing through the point of intersection of the given lines and parallel to x -axis ?

• y + 1 = 0

• y - 1 = 0

• y - 2 = 0

• y + 2 = 0 

Consider the two lines

x + y + 1 = 0 and 3x + 2y + 1 = 0

What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis

• x + 1 = 0

• x - 1 = 0

• x - 2 = 0

• x + 2 = 0

49.

Consider the equation

$\mathrm{ksin}\left(\mathrm{x}\right) + \cos \left(2\mathrm{x}\right) = 2\mathrm{k} - 7$

If the equation possesses solution, then what is the minimum value of k ?

• 1

• 2

• 4

• 6

Consider a parallelogram whose vertices are A(1, 2), B(4, y), C(x, 6) and D(3, 5) taken in order

What is the value of AC² - BD² ?

• 25

• 30

• 36

• 40