Permutations and Combinations

JEE Main 2025 (Online) 22nd January Morning ShiftMCQEasy📈 Topic in 26% papers+4−1

Ques. 1JEE Main 2025, 22 January (Morning Shift)

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

6084
5148
14950
4356

Answer

(2) 5148

Solution

Alphabetical order fixes the arrangement, so only the choice of letters matters; M is the 13th letter.

M in the middle (3rd place) 2 letters from A–L (12 letters) and 2 from N–Z (13 letters)

12C2 13C2=66 78=5148

Answer: (2)

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Ques. 2JEE Main 2025, 22 January (Evening Shift)

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1 and B2 are not adjacent to each other, is :

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All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

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