JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is ____________.

Official answer

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: The Gap Method

Same topic in other shifts

All Permutations and Combinations questions

2 Apr 2026, Shift 1 · Q6The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once,…MediumSingle correct
2 Apr 2026, Shift 2 · Q7Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$ -side regular polygon. If $p_{n+1} - p_n = 66$ ,…EasySingle correct
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.