IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q3

Algebra Level 4

If \(\displaystyle (1+x)^n=C_0+C_1x+C_2x^2+...+C_nx^n\), then the sum of the products of the coefficients taken two at a time can be represented by \[\sum_{i=0}^n \sum_{j=i+1}^{n}C_iC_j = 2^a - \frac{b!}{c(d!)^2}\] Then which of the following are correct?

  • A: \(\ a=2n-1\)
  • B: \(\ b=2n\)
  • C: \(\ c=2\)
  • D: \(\ d=n\)

Enter your answer as a 4-digit string of 1s and 9s \(-\) 1 for correct option, 9 for wrong. For example, 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives.

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