PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

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

Reduce each of the following expressions to the sine and cosine of a single expression: 

\[\sqrt{3} \sin x - \cos x\] 

Reduce each of the following expressions to the sine and cosine of a single expression: 

cos x − sin x