Exams › JEE Main › Maths

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

1. 216
2. 192
3. 120
4. 72

Correct answer: 192

Solution

To find the number of integers greater than 6,000 using the digits 3, 5, 6, 7, and 8 without repetition, we first consider the thousands place. The valid digits for the thousands place are 6, 7, and 8. For each choice of the thousands digit, we can fill the remaining three places with the remaining digits, leading to a total of 192 combinations.

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 →