Question:
The number of natural numbers less than $7,000$ which can be formed by using the digits $0,1,3,7,9$ (repitition of digits allowed) is equal to :
The number of natural numbers less than $7,000$ which can be formed by using the digits $0,1,3,7,9$ (repitition of digits allowed) is equal to :
Updated On: Apr 24, 2025
- 250
- 374
- 372
- 375
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Number of numbers = $2 \times 5^3$
Required number = $5^3 + 2 \times 5^3 - 1$
= 374
Required number = $5^3 + 2 \times 5^3 - 1$
= 374
Was this answer helpful?
20
9
Top Questions on Permutations
- The number of numbers greater than $5000$, less than $9000$ and divisible by $3$, that can be formed using the digits $0,1,2,5,9$, if repetition of digits is allowed, is
- JEE Main - 2026
- Mathematics
- Permutations
- The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is
- JEE Main - 2026
- Mathematics
- Permutations
- In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is:
- JEE Main - 2025
- Mathematics
- Permutations
- In how many ways can 5 people be arranged in a row?
- MHT CET - 2025
- Mathematics
- Permutations
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
- BITSAT - 2025
- Mathematics
- Permutations
View More Questions
Questions Asked in JEE Main exam
- Identify the correct statements: The presence of –NO\(_2\) group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring towards electrophilic substitutions. C. activates the ring towards nucleophilic substitutions. D. deactivates the ring towards nucleophilic substitutions. Choose the correct answer from the options given below:
- JEE Main - 2026
- General Chemistry
- If the distances of the point \( (1,2,a) \) from the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] along the lines \[ L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b} \quad \text{and} \quad L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c} \] are equal, then \( a+b+c \) is equal to:
- JEE Main - 2026
- Three Dimensional Geometry
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
- JEE Main - 2026
- Rotational motion
- In an experiment, a set of readings are obtained as follows: \[ 1.24~\text{mm},\ 1.25~\text{mm},\ 1.23~\text{mm},\ 1.21~\text{mm}. \] The expected least count of the instrument used in recording these readings is _______ mm.
- JEE Main - 2026
- General Physics
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
View More Questions
Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects