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

If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?

In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.

Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`

Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.

Find the number of permutations of n different things taken r at a time such that two specific things occur together.

Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.

The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together

There are 10 persons named P₁, P₂, P₃, ... P₁₀. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements.

In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?

A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.

The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.

The total number of 9 digit numbers which have all different digits is ______.

The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.

The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.

The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.

In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.

Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:

Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find