Mathematics · 2023
JEE Main · 8 April 2023, Shift 1 · Q26
The largest natural number n such that 3^n divides 66! is ____.
The largest natural number $\displaystyle n$ such that $\displaystyle 3^n$ divides $\displaystyle 66$ ! is $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
31
More from Permutations and Combinations
- If all the six digit numbers x_1 x_2 x_3 x_4 x_5 x_6 with 0<x_1<x_2<x_3<x_4<x_5<x_6 are arranged in the increasing order, then the sum of the digits…2023
- The number of symmetric matrices of order 3, with all the entries from the set \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}, is2023
- The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is ____.2025
- The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is2024
- The number of square matrices of order 5 with entries from the set {0,1}, such that the sum of all the elements in each row is 1 and the sum of all…2023
- Let the set S={2,4,8,16, …, 512} be partitioned into 3 sets A, B, C with equal number of elements such that A ∪ B ∪ C=S and A ∩ B=B ∩ C=A ∩ C=φ. The…2024
- The number of strictly increasing functions f from the set \{1, 2, 3, 4, 5, 6\} to the set \{1, 2, 3,...., 9\} such that f(i) ≠ i for 1 ≤ i ≤ 6, is…2026
- Let S be the set of the first 11 natural numbers. Then the number of elements in A={B ⊆ S: n(B) ≥ 2 and the product of all elements of B is even } is…2026
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.