Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

if `(a+ bx)/(a - bx) = (b +cx)/(b - cx) = (c + dx)/(c- dx) (x != 0)` then show that a, b, c and d are in G.P.

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 the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

x² = 6y

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.

y² = – 8x