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 Critical Thinking

  • question_answer
     In the polynomial \[(x-1)(x-2)(x-3).............(x-100),\]the coefficient of \[{{x}^{99}}\] is [AMU 2002]

    A) 5050

    B) - 5050

    C) 100

    D) 99

    Correct Answer: B

    Solution :

    \[(x-1)(x-2)(x-3)....(x-100)\] Number of terms = 100;   \  Coefficient of x99 = \[(x-1)(x-2)(x-3)...(x-100)\]  = \[(-1-2-3-......-100)\] = \[-(1+2+.....+100)\] = \[-\frac{100\times 101}{2}\] = - 5050.


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