Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the distance between parallel lines:

15x + 8y – 34 = 0 and 15x + 8y + 31 = 0

Find the distance between parallel lines  l (x + y) + p = 0 and l (x + y) – r = 0

What are the points on the y-axis whose distance from the line  `x/3 + y/4 = 1` is 4 units.

Find perpendicular distance from the origin to the line joining the points (cosΘ, sin Θ) and (cosΦ, sin Φ).

Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.

Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y+ 7 = 0 is always 10. Show that P must move on a line.

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

Find `lim_(x -> 5) f(x)`, where f(x)  = |x| - 5

Suppose f(x)  = `{(a+bx, x < 1),(4, x = 1),(b-ax, x > 1):}`  and if `lim_(x -> 1) f(x) = f(1)` what are possible values of a and b?

Rewrite the following statement with “if-then” in five different ways conveying the same meaning.

If a natural number is odd, then its square is also odd.

Write the contrapositive and converse of the following statements.

If x is a prime number, then x is odd

Write the contrapositive and converse of the following statements.

It the two lines are parallel, then they do not intersect in the same plane.

Write the contrapositive and converse of the following statements.

Something is cold implies that it has low temperature.

Write the contrapositive and converse of the following statements.

You cannot comprehend geometry if you do not know how to reason deductively.

Write the contrapositive and converse of the following statements.

x is an even number implies that x is divisible by 4

Write each of the following statement in the form “if-then”.

You get a job implies that your credentials are good.

Write each of the following statement in the form “if-then”.

The Banana trees will bloom if it stays warm for a month.

Write each of the following statement in the form “if-then”.

A quadrilateral is a parallelogram if its diagonals bisect each other.