Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202312 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
12 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2023 · 12 April · Morning Shift · Mathematics · Permutation and Combination

The number of five-digit numbers, greater than 40000 and divisible...

The number of five-digit numbers, greater than 4000040000 and divisible by 55, which can be formed using the digits 0,1,3,5,70, 1, 3, 5, 7 and 99 without repetition, is equal toThe number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,

Options

  1. A132132
  2. B120120
  3. C7272
  4. D9696

Correct answer

B. 120120

Step-by-step solution

We need to find the number of 55 digit numbers greater than 4000040000 and divisible by 55.

Case I : Numbers start with 55.

Here if the number starts with 55 it should end with 00 to be divisible by 55.

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,

Case II : Number starts with 77 and the last digit can have 00 or 55.

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,

Case III : The number starts with 99 and the last digit should have 00 or 55.

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3,

Total numbers =120= 120.

Hence this is the correct option.

Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list Permutation and Combination JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs