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

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 

In a G.P. if the (m + n)^th term is p and (m − n)^th term is q, then its m^th term is 

Mark the correct alternative in the following question: 

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 p²R³ : S³ is equal to 

Find the maximum and minimum values of each of the following trigonometrical expression:

 12 sin x − 5 cos x 

Find the maximum and minimum values of each of the following trigonometrical expression: 

12 cos x + 5 sin x + 4 

Find the maximum and minimum values of each of the following trigonometrical expression: 

\[5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4\]

Find the maximum and minimum values of each of the following trigonometrical expression:

sin x − cos x + 1