Question:
How many natural numbers, when converted to base 5 are four- digit numbers ?
How many natural numbers, when converted to base 5 are four- digit numbers ?
Updated On: Aug 21, 2024
- 500
- 470
- 530
- 400
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The smallest and largest four-digit numbers in base 5 are 1000 and 4444, respectively.
Let’s convert the above numbers in base 10 :
(1000)5 = 1 × 53 + 0 × 52 + 0 × 51 + 0 × 50 = 125
(4444)5 = 4 × 53 + 4 × 5² + 4 × 51 + 4 × 50 = 624
Thus, desired number 125 to 624, i.e., 624 - 125 + 1 = 500
So, the correct option is (A) : 500.
Let’s convert the above numbers in base 10 :
(1000)5 = 1 × 53 + 0 × 52 + 0 × 51 + 0 × 50 = 125
(4444)5 = 4 × 53 + 4 × 5² + 4 × 51 + 4 × 50 = 624
Thus, desired number 125 to 624, i.e., 624 - 125 + 1 = 500
So, the correct option is (A) : 500.
Was this answer helpful?
0
0
Top Questions on Number Systems
- The greatest value of \( n \), where \( n \in \mathbb{N} \), such that \( 3^n \) divides \( 50! \) is:
- JEE Main - 2025
- Mathematics
- Number Systems
- The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _____.
- JEE Main - 2025
- Mathematics
- Number Systems
- Let \( A = \{1, 2, 3, \dots, 10\} \) and \( B = \left\{ \frac{m}{n} : m, n \in A, m <n \text{ and } \gcd(m, n) = 1 \right\} \). Then \( n(B) \) is equal to :
- JEE Main - 2025
- Mathematics
- Number Systems
- The remainder, when \(7^{98}\) is divided by 23, is equal to:
- JEE Main - 2025
- Mathematics
- Number Systems
- If \( \frac{1}{q + r}, \frac{1}{r + p}, \frac{1}{p + q} \) are in A.P., then:
- VITEEE - 2024
- Mathematics
- Number Systems
View More Questions
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- In September, the incomes of \(K\), \(A\), and \(V\) are in the ratio \(8:6:5\). They rent a house, contributing \(15\%\), \(12\%\), and \(18\%\) of their respective incomes. In October, the rent remains the same, but the salaries of \(K\), \(A\), and \(V\) increase by \(10\%\), \(12\%\), and \(15\%\), respectively. What percentage of their total income is paid as house rent in October? (Round to the nearest percentage.)
- CAT - 2024
- Percentages
- There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is
- CAT - 2024
- Averages
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Time and Work
View More Questions