Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is

There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?

If C₀ + C₁ + C₂ + ... + C_n = 256, then ²ⁿC₂ is equal to

The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is

Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120

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.

If ⁴³C_{r − 6} = ⁴³C_{3r + 1} , then the value of r is

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.

The number of diagonals that can be drawn by joining the vertices of an octagon is

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 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?