2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Binomial Theorem and Mathematical Induction

JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Self Evaluation Test - Principle of Mathematical Induction

  • question_answer
    If m, n are any two odd positive integers with \[n<m\], then the largest positive integer which divides all the numbers of the type \[{{m}^{2}}-{{n}^{2}}\] is

    A) 4

    B) 6

    C) 8

    D) 9

    Correct Answer: C

    Solution :

    [c] Let \[m=2k+1,\,\,\,n=2k-1(k\in N)\] \[\therefore \,\,\,\,{{m}^{2}}-{{n}^{2}}=4{{k}^{2}}+1+4k-4{{k}^{2}}+4k-1=8k\] Hence, all the numbers of the form \[{{m}^{2}}-{{n}^{2}}\] are always divisible by 8.


You need to login to perform this action.
You will be redirected in 3 sec spinner