IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q5

Calculus Level 5

Let \[\int \frac{(x-1)e^x}{(x+1)^3}dx=f(x)+c\] and \[f(x)=\displaystyle\sum_{i=0}^n\frac{a_ie^x}{(x+1)^i}+d\] with all \(a_i=0\) for \(i\geq n\) and \(f(1)=\dfrac{e}{2}\). Then which of the following is/are correct options?

  • A: \(a_0=0\)
  • B: \(a_1=0\)
  • C: \(a_2=1\)
  • D: \(f(0)\) is irrational

Enter your answer as a 4 digit string of 1s and 9s, using 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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