Science (English Medium) Class 11 - CBSE Question Bank Solutions

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P²Rⁿ = Sⁿ

If a, b, c, d are in G.P, prove that (aⁿ + bⁿ), (bⁿ + cⁿ), (cⁿ + dⁿ) are in G.P.

If a and b are the roots of are roots of x² – 3x + p = 0 , and c, d are roots of x² – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.

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.