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

Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P² R³ : S³ is equal to ______.

In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.

If the p^th and q^th terms of a G.P. are q and p respectively, show that its (p + q)^th term is `(q^p/p^q)^(1/(p - q))`

If p^th, q^th, and r^th terms of an A.P. and G.P. are both a, b and c respectively, show that a^b–c . b^{c – a} . c^{a – b} = 1

The third term of G.P. is 4. The product of its first 5 terms is ______.

If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is ______.

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm³ and the total surface area is 252cm². The length of the longest edge is ______.

For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.

The third term of a G.P. is 4, the product of the first five terms is ______.

The sum or difference of two G.P.s, is again a G.P.

Find the distance between the lines 3x + 4y = 9 and 6x + 8y = 15.

Show that the locus of the mid-point of the distance between the axes of the variable line x cosα + y sinα = p is `1/x^2 + 1/y^2 = 4/p^2` where p is a constant.

The distance of the point P(1, – 3) from the line 2y – 3x = 4 is ______.

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.

Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10.

If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.

The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is ______.

The distance between the lines y = mx + c₁ and y = mx + c₂ is ______.

A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is ______.

The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is ______.