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

If ⁿC₁₂ = ⁿC₈ , then n =

If ⁿC_r + ⁿC_{r + 1} = ^n + 1C_x , then x =

If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =

⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ +⁵C₅ is equal to

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

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