The position of how many alphabets will remain unchanged

Determine the co-ordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY- plane?

Find the equation of the line passing through the points (1, 2) and (3, 8).

If P(A) = 0.7, P(B) = 0.5 and P (B/A) = 0.3, find (i) P(A/B) (ii) P(A ∪ B)?

The equation of a line is 2x - 3y = 12. Find the perpendicular distance of the point (4, 5) from this line.

The minute hand of a watch is 2 cm long. How far does its tip move in 45 minutes? (use π = 3.14)

Find the area of the triangle formed by the points A(2, 3), B(-1, -4), and C(5, -2).

A line passes through the point (4, 3) and is perpendicular to the line 3x + 4y = 12. Find the equation of the new line.

Find the co-ordinate of a point which divides the join of (3,2) and (3,2) internally in the ratio of 2:3?

Find the equation of the circle passing through the points (1, 2) and (2, -1), and whose center lies on the line x - 2y + 3 = 0.