If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to
Show Hint
Correct Answer: 14
Solution and Explanation
Total 7 digit numbers = 9000000 7 digit numbers having sum of digits even
= 4500000 = \( 9.5 \cdot 10^5 \)
\( m = 9 \), \( n = 5 \) \( m + n = 14 \)
Top Questions on permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- A mother was asked how many gifts she had in the bag. She replied that there were dolls but six, cars but six, and all books but six. How many gifts had she in all?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- In a school, 120 boys have registered for a singles carrom tournament. Each match eliminates one player. How many matches are to be organized to determine the champion?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- A person needs to find the fastest two horses from 16 horses. Only a race of 4 horses can be conducted at a time. What is the minimum number of races to be conducted to determine the fastest two? (Assume that horses will not get tired at all and time cannot be measured)
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
Questions Asked in JEE Main exam
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to:
- JEE Main - 2025
- Integration
- Given below are two statements: Statement I: One mole of propyne reacts with excess of sodium to liberate half a mole of H₂ gas. Statement II: Four g of propyne reacts with NaNH₂ to liberate NH₃ gas which occupies 224 mL at STP. In the light of the above statements, choose the most appropriate answer from the options given below:
- JEE Main - 2025
- Organic Chemistry
- Given below are two statements about X-ray spectra of elements:
Statement (I):A plot of \(\sqrt {v}\) (v=frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II): A plot of v (v=frequency of X-rays emitted)} vs atomic number is a straight line.- JEE Main - 2025
- X-ray Spectra and Moseley's Law
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).
- JEE Main - 2025
- Organic Chemistry
- The ratio of the power of a light source \( S_1 \) to that of the light source \( S_2 \) is 2. \( S_1 \) is emitting \( 2 \times 10^{15} \) photons per second at 600 nm. If the wavelength of the source \( S_2 \) is 300 nm, then the number of photons per second emitted by \( S_2 \) is \_\_\_\_\_ \( \times 10^{14} \).
- JEE Main - 2025
- Units and measurement