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

Prove that

Prove that

Show that one of the following progression is a G.P. Also, find the common ratio in case:

4, −2, 1, −1/2, ...

Show that one of the following progression is a G.P. Also, find the common ratio in case:

−2/3, −6, −54, ...

Show that one of the following progression is a G.P. Also, find the common ratio in case:

\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]

Show that one of the following progression is a G.P. Also, find the common ratio in case:1/2, 1/3, 2/9, 4/27, ...

Prove that:

Prove that:

Prove that:

Show that the sequence <a_n>, defined by a_n = \[\frac{2}{3^n}\], n ϵ N is a G.P.

Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].

Find:
the ninth term of the G.P. 1, 4, 16, 64, ...

Find:

the 10^th term of the G.P.

\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]

Find :

the 8^th term of the G.P. 0.3, 0.06, 0.012, ...

Find :

the 12th term of the G.P.

\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]

Find : 

nth term of the G.P.

\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]

 If \[\tan A = \frac{5}{6}\text{ and }\tan B = \frac{1}{11}\], prove that \[A + B = \frac{\pi}{4}\].

If \[\tan A = \frac{m}{m - 1}\text{ and }\tan B = \frac{1}{2m - 1}\], then prove that \[A - B = \frac{\pi}{4}\].

Find :

the 10^th term of the G.P.

\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, . . .\]

Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]