Permutations and Combinations

JEE Main 2025 (Online) 23rd January Evening ShiftNumericalMedium📈 Topic in 8% papers+4

Ques. 1JEE Main 2025, 23 January (Evening Shift)

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is .

Answer

17280

Solution

The two cases cannot overlap (if all boys are together, two of them are adjacent).

[figure]

Case I: block + 4 girls = 5 units: 5! 5!=14400

Case II: girls first 4!, boys in the 5 gaps 5!: 24 120=2880

Total = 14400+2880=17280

Answer: 17280

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Ques. 2JEE 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

Ques. 3JEE 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

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)