What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y=5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10 ?

• 4x + 3y + 2 = 0

• 4x - y + 2 = 0

• 4x - 3y - 2 = 0

• 4x - 3y + 2 = 0

If (a, b) is at unit distance from the line 8x + 6y + 1 = 0, then which of the following conditions are correct ?

1. 3a - 4b - 4 = 0

2. 8a + 6b + 11 = 0

3. 8a + 6b - 9 = 0

Select the correct answer using the code given below : 

• 1 and 2 only

• 2 and 3 only

• 1 and 3 only

• 1, 2 and 3

A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point ( - 3, 5). What is the foot of the perpendicular drawn from the point (3, 3) on this line

• (1, 3)

• (2, 0)

• (0, 2)

• (1, 1)

If the point (x, y, - 3), (2, 0, - 1) and (4, 2, 3) lie on a straight line, then what are the values of x and y respectively ?

• 1, - 1

• - 1, 1

• 0, 2

• 3, 4

An equilateral triangle has one vertex at (- 1, - 1) and another vertex at $\left( - \sqrt{3}, \sqrt{3}\right)$. The third vertex may lie on

• $\left( - \sqrt{2}, \sqrt{2}\right)$

• $\left(\sqrt{2}, - \sqrt{2}\right)$

• (1, 1)

• (1, - 1)

What is the distance between the points P(m.cos2α, m.sin2α) and Q(m.cos2β, m.sin2β) ?

• $\left|2\mathrm{msin}\left(\mathrm{\alpha } - \mathrm{\beta }\right)\right|$

• $\left|2\mathrm{mcos}\left(\mathrm{\alpha } - \mathrm{\beta }\right)\right|$

• $\left|2\mathrm{msin}\left(\left(2\mathrm{\alpha } - 2\mathrm{\beta }\right)\right)\right|$

• $\left|\mathrm{msin}\left(2\mathrm{\alpha } - 2\mathrm{\beta }\right)\right|$

What is the angle between the lines xcos(α) + ysin(α) = α and xsin(β) – ycos(β) = α ?

• $\mathrm{\beta } - \mathrm{\alpha }$

• $\mathrm{\pi } + \mathrm{\beta } - \mathrm{\alpha }$

• $\frac{\left(\mathrm{\pi } + 2\mathrm{\beta } + 2\mathrm{\alpha }\right)}{2}$

• $\frac{\left(\mathrm{\pi } - 2\mathrm{\beta } + 2\mathrm{\alpha }\right)}{2}$

68.

The equation ax + by + c = 0 represents a straight line

• for all real numbers a, b and c

• only when a ≠ 0

• only when b ≠ 0

• only when at least one of a and b is non-zero

A ladder 9 m long reaches a point 9 m below the top of a vertical flag staff. From the foot of the ladder, the elevation of the flag staff is 60^o. What is the height of the flag staff ?

• 9m

• 10.5m

• 13.5m

• 15m

What is the area of the region enclosed between the curve y² = 2x and the straight line y = x ?

• $\frac{2}{3}$ Square units

• $\frac{4}{3}$ Square units

• $\frac{1}{3}$ Square units

• 1 Square units