PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is 

If the first term of a G.P. a₁, a₂, a₃, ... is unity such that 4 a₂ + 5 a₃ is least, then the common ratio of G.P. is

If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then P² is equal to

The fractional value of 2.357 is 

If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is

The value of 9^1/3 . 9^1/9 . 9^1/27 ... upto inf, is 

The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is 

If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is 

The n^th term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then its first term is ______.

If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is

If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then 

If A be one A.M. and p, q be two G.M.'s between two numbers, then 2 A is equal to 

If p, q be two A.M.'s and G be one G.M. between two numbers, then G² = 

If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]

If x = (4³) (4⁶) (4⁶) (4⁹) .... (4^3x) = (0.0625)⁻⁵⁴, the value of x is 

Given that x > 0, the sum \[\sum^\infty_{n = 1} \left( \frac{x}{x + 1} \right)^{n - 1}\] equals 

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

Let x be the A.M. and y, z be two G.M.s between two positive numbers. Then, \[\frac{y^3 + z^3}{xyz}\]  is equal to 

The product (32), (32)^1/6 (32)^1/36 ... to ∞ is equal to 

The two geometric means between the numbers 1 and 64 are