JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

A

be a matrix of order

2\times2

, whose entries are from the set

\{0, 1, 2, 3, 4, 5\}

. If the sum of all the entries of

A

is a prime number

p

2<p<8

, then the number of such matrices

A

is ___________.

Official answer

180

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Distribution of Identical Objects

Same idea in other shifts

Asked 11× in all

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 2024, Shift 1 · Q23The number of ways of getting a sum 16 on throwing a dice four times is ________.MediumNumerical value
9 Apr 2024, Shift 2 · Q23The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is ______________.MediumNumerical value
1 Feb 2024, Shift 1 · Q24The number of elements in the set $S=\{(x,y,z): x,y,z\in\mathbb{Z}, x+2y+3z=42, x,y,z\geq0\}$ equals __________.MediumNumerical value
31 Jan 2024, Shift 2 · Q5The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, isEasySingle correct
11 Apr 2023, Shift 1 · Q4The number of triplets $(x, y, z)$ , where $x, y, z$ are distinct non negative integers satisfying $x + y + z = 15$ , isMediumSingle correct
28 Jun 2022, Shift 2 · Q3The number of ways to distribute 30 identical candies among four children $C_1, C_2, C_3$ and $C_4$ so that $C_2$ receives atleast 4 and…MediumSingle correct
25 Feb 2021, Shift 1 · Q78The total number of positive integral solutions $(x, y, z)$ such that $xyz = 24$ is :MediumSingle correct

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.