PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Write the solution of the inequation\[\frac{x^2}{x - 2} > 0\]

A sequence is defined by a_n = n³ − 6n² + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.

Let < a_n > be a sequence defined by a₁ = 3 and, a_n = 3a_{n − 1} + 2, for all n > 1
Find the first four terms of the sequence.

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = 1, a_n = a_{n − 1} + 2, n ≥ 2

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = 1 = a₂, a_n = a_{n − 1} + a_{n − 2}, n > 2

Let < a_n > be a sequence. Write the first five term in the following:

a₁ = a₂ = 2, a_n = a_{n − 1} − 1, n > 2

The Fibonacci sequence is defined by a₁ = 1 = a₂, a_n = a_{n − 1} + a_{n − 2} for n > 2

Find `(""^an +1)/(""^an")` for n = 1, 2, 3, 4, 5.

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

 3, −1, −5, −9 ...

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

−1, 1/4, 3/2, 11/4, ...

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]

Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case. 

9, 7, 5, 3, ...

The n^th term of a sequence is given by a_n = 2n² + n + 1. Show that it is not an A.P.

Find:

 10th term of the A.P. 1, 4, 7, 10, ...

Find: 

18th term of the A.P.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]

Find:

nth term of the A.P. 13, 8, 3, −2, ...

If the sequence < a_n > is an A.P., show that a_m +n +a_m − n = 2a_m.

Which term of the A.P. 3, 8, 13, ... is 248?

Which term of the A.P. 84, 80, 76, ... is 0?