Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2023 · Mathematics · Basics of Mathematics

Consider the following statements: 1. (25)!+1 is divisible by 26 2....

Consider the following statements: 1. (25)!+1(25)!+1 is divisible by 26 2. (6)! +1 is divisible by 7 Which of the above statement is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

1. 25!+1∵25!+1\because for any n>2,n!n > 2, n! is even (divisible by 2 ) ∴25!+1\therefore \quad 25!+1 is odd hence can't be divided by 2. ∴25!+1\therefore \quad 25!+1 also can not be divided by 26 as 26=13×22.6!+1=720+1=72126=13 \times 2 2. 6!+1=720+1=721. Clearly 721 is divisible by 7. ∴2\therefore 2 only is correct.
Practice Basics of Mathematics on Quantrex Academy →

More from Basics of Mathematics

All Basics of Mathematics questions Full Basics of Mathematics list Basics of Mathematics JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs