JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let

S

be the set containing all

3 \times 3

matrices with entries from

\{-1, 0, 1\}

. The total number of matrices

A \in S

such that the sum of all the diagonal elements of

A^{\mathrm{T}}A

is 6 is ________.

Official answer

5376

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Fundamental Counting Principle

Same idea in other shifts

Asked 13× in all

3 Apr 2025, Shift 1 · Q21If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n$ ;…MediumNumerical value
8 Apr 2024, Shift 1 · Q23The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not…MediumNumerical value
1 Feb 2024, Shift 2 · Q22The lines $L_1, L_2, \ldots, L_{20}$ are distinct. For $n=1,2,3,\ldots,10$ all the lines $L_{2n-1}$ are parallel to each other and all the…MediumNumerical value
13 Apr 2023, Shift 2 · Q22Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______MediumNumerical value
26 Jul 2022, Shift 2 · Q23Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of…MediumNumerical value
28 Jul 2022, Shift 1 · Q21Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $\{A,B,C,D,E\}$ …MediumNumerical value
25 Jun 2022, Shift 1 · Q22The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is __________.HardNumerical value
25 Jun 2022, Shift 1 · Q29Let A be a $3\times3$ matrix having entries from the set $\{-1,0,1\}$ . The number of all such matrices A having sum of all the entries…HardNumerical 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.