PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

If angle \[\theta\]  is divided into two parts such that the tangents of one part is \[\lambda\] times the tangent of other, and \[\phi\] is their difference, then show that\[\sin\theta = \frac{\lambda + 1}{\lambda - 1}\sin\phi\]

The sum of first three terms of a G.P. is \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.

If \[\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}\] , then show that \[\sin\alpha + \cos\alpha = \sqrt{2}\cos\theta\].

The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.

Find the sum of the following geometric progression:

2, 6, 18, ... to 7 terms;

Find the sum of the following geometric progression:

1, 3, 9, 27, ... to 8 terms;

Find the sum of the following geometric progression:

1, −1/2, 1/4, −1/8, ... to 9 terms;

Find the sum of the following geometric progression:

(a² − b²), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;

Find the sum of the following geometric progression:

4, 2, 1, 1/2 ... to 10 terms.

Find the sum of the following geometric series:

 0.15 + 0.015 + 0.0015 + ... to 8 terms;

Find the sum of the following geometric series:

\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8  terms };\]

Find the sum of the following geometric series:

\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]

Find the sum of the following geometric series:

(x +y) + (x² + xy + y²) + (x³ + x²y + xy² + y³) + ... to n terms;

Find the sum of the following geometric series:

`3/5 + 4/5^2 + 3/5^3 + 4/5^4 + ....` to 2n terms;

Find the sum of the following geometric series:

\[\frac{a}{1 + i} + \frac{a}{(1 + i )^2} + \frac{a}{(1 + i )^3} + . . . + \frac{a}{(1 + i )^n} .\]

Find the sum of the following geometric series:

1, −a, a², −a³, ....to n terms (a ≠ 1)