Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

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 value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is

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.

Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?

A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is

If ^n + 1C₃ = 2 · ⁿC₂ , then n =

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 number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

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?