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

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

Find the coefficient of x⁵ in (x + 3)⁸

Write the general term in the expansion of (x² – y)⁶

Write the general term in the expansion of (x² – yx)¹², x ≠ 0

Find the 4^th term in the expansion of (x – 2y)¹² .

Find the 13^th term in the expansion of `(9x - 1/(3sqrtx))^18 , x != 0`

Find the middle terms in the expansions of  `(3 - x^3/6)^7`

Find the middle terms in the expansions of `(x/3 + 9y)^10`

The coefficients of the (r – 1)^th, r^th and (r + 1)^th terms in the expansion of (x + 1)ⁿ are in the ratio 1:3:5. Find n and r.

Prove that the coefficient of xⁿ in the expansion of (1 + x)²ⁿ is twice the coefficient of xⁿ in the expansion of (1 + x)^2n–1 .

Find a positive value of m for which the coefficient of x² in the expansion

(1 + x)^m is 6

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of `(root4 2 + 1/ root4 3)^n " is " sqrt6 : 1`

Find the sum of odd integers from 1 to 2001.