JEE Advanced 2025 Paper 2 · Mathematics · Permutations and Combinations · hard

Which of the following statements is(are) correct?

One or more options correct

A. The number of $4$ -digit even numbers with distinct digits that can be formed from the digits $1,2,3,4,5,6$ is $180$
B. The number of $4$ -digit numbers with distinct digits formed from $0,1,2,3,4,5,6$ that are divisible by $3$ is $252$
C. The number of distinct arrangements of all letters of the word LEVEL is $20$
D. The number of distinct arrangements of all letters of LEVEL in which the two E's are not adjacent is $12$

Show answer and solution

Answer: A

(A) True: units digit from

\{2,4,6\}

3

ways, remaining three places from the other

5

digits in

5\cdot4\cdot3=60

ways:

3\cdot60=180

. (B) False: enumerating digit sets with sum divisible by

3

(with non-zero leading digit) gives

264

, not

252

. (C) False:

\frac{5!}{2!\,2!}=30

. (D) False: glue the two E's:

4!/2!=12

arrangements with E's together, so

30-12=18

have them apart, not

12

. Only A is correct.

Original question written in the JEE Advanced 2025 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake