Exams › JEE Main › Maths
The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:
- 372
- 375
- 250
- 374
Correct answer: 374
Solution
To find the total number of natural numbers less than 7,000 using the digits 0, 1, 3, 7, and 9, we consider the cases based on the number of digits. For 1-digit numbers, we have 4 options (1, 3, 7, 9). For 2-digit numbers, the first digit has 4 options (1, 3, 7, 9) and the second digit has 5 options (including 0). For 3-digit numbers, the first digit again has 4 options, while the other two digits have 5 options each. For 4-digit numbers, the first digit can only be 1, 3, or 6 (to keep it under 7,000), giving us 3 options, and the remaining three digits can be any of the 5 digits. Adding all these cases together gives a total of 374 valid numbers.
Related JEE Main Maths questions
- ABCD is a convex quadrilateral. Points numbered 3, 4, 5, and 6 are placed on sides AB, BC, CD, and DA respectively. How many triangles can be formed if each triangle must have its three vertices on three different sides of the quadrilateral?
- Let Tₙ represent the count of triangles that can be formed from the vertices of a regular polygon with n sides. If Tₙ₊₁ - Tₙ = 28, then the value of n is
- Let a be the number of permutations of x + 2 objects taken all at once, b be the number of permutations of x objects taken 11 at a time, and c be the number of permutations of x − 11 objects taken all at once. If a = 182bc, then what is the value of x?
- Five line segments have lengths 2, 3, 4, 5, and 6 units. How many triangles can be formed by choosing any three of these segments and joining them as sides?
- Three parallel lines lie in the same plane. If each line contains n marked points, what is the greatest possible number of triangles that can be formed using these points as vertices?
- Five speakers A, B, C, D and E are to speak at a meeting. How many different orders are possible if B is not allowed to come before A, whether directly or at any earlier position?
⚔️ Practice JEE Main Maths free + battle 1v1 →