JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

The number of bijective functions

f:\{1,3,5,7,\ldots,99\}\rightarrow\{2,4,6,8,\ldots.,100\}

, such that

f(3)\geq f(9)\geq f(15)\geq f(21)\geq\ldots.\geq f(99)

, is ________.

(1) ${}^{50}P_{17}$
(2) ${}^{50}P_{33}$ Official answer
(3) $33!\times17!$
(4) $\frac{50!}{2}$

Official answer

Option 2

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Permutations with Fixed Relative Order

Same topic in other shifts

All Permutations and Combinations questions

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4 Apr 2026, Shift 1 · Q4The number of functions $f:\{1,2,3,4\}\to\{a,b,c\}$ , which are not onto, is:EasySingle correct
4 Apr 2026, Shift 1 · Q8The number of ways, of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:EasySingle correct
4 Apr 2026, Shift 2 · Q17Let $A=\{(a,b,c):a,b,c$ are non-negative integers and $a+b+2c=22\}$ . Then $n(A)$ is equal to:MediumSingle correct
5 Apr 2026, Shift 1 · Q21Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f: A \to A$ such that $f(1) \geq 3$ , $f(3) \leq 4$ and $f(2) + f(3) = 5$ ,…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.