SENAPREP
Permutation Questions
Chapter: Algebra | Total Available: 26 Real Questions
Let A = {1, 2, 3, 4, 5} and B = {6, 7}. What is the number of onto functions from A to B?
n(A) = 5 and n(B) = 2
Number of onto functions = 25 – 2C1(2 – 1)5 =
32 – 2 = 30
In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?
The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?
How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?
In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?
Explanation: Number of arrangements = 3!2! = 12
Let y = x! and z = (2x)!. If (z/y) = 120, then what is the value of (3x)!?
How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?
Explanation: Last two digit of number which is divisible by 4 are 12, 24, 32
No. of number whose last two digits is 12 = 2!
No. of number whose last two digits is 24 = 2!
No. of nubmer whose last two digits is 32 = 2!
Total number = 2! + 2! + 2! = 6
How many numbers greater than 1000 can be formed using the digits 0, 1, 2 and 3 (repetition of digits is not allowed)?
Solution
Option (b) is correct.
Explanation:
To determine how many numbers greater than 1000 can be formed using the digits 0, 1, 2, and 3 without repeating any digits, follow these steps: - The first digit (thousands place) must be among {1, 2, 3} (3 choices). - The second digit can be any of the remaining 3 digits. - The third digit can be any of the remaining 2 digits. - The fourth digit can be the last remaining digit. Using the multiplication principle: \[ \text{Total Numbers} = (\text{Choices for the first digit}) \times (\text{Choices for the second digit}) \times (\text{Choices for the third digit}) \times (\text{Choices for the fourth digit}) \] This can be expressed as: \[ \text{Total Numbers} = 3 \times 3 \times 2 \times 1 \] Calculating this:- Counting principle (multiplication principle).
- Permutations of digits without repetition.
A flow diagram showing choices for first, second, third, and fourth digits with branching paths can illustrate the counting process clearly.
Verified against NCERT Class IX Mathematics, Chapter on Permutations and Combinations.
How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?
