JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 28 July 2022, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

Let 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\}

or a number from

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

with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from

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

\alpha\times5^6

, then

\alpha

is equal to __________.

Official answer

7073

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 4× 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
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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.