IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q12

Calculus Level pending

For any real \(t\), \(x=\frac12(e^t+e^{-t}), \ y=\frac12(e^t-e^{-t})\) is a point on the hyperbola \(x^2-y^2=1\). The area bounded by the hyperbola and the lines joining the centre to the points corresponding to \(t_1\) and \(-t_1\) is \(A(t_1)\). Then which of the following is/are true?

  • (A) \(\lfloor A(\frac12ln2) \rfloor=0\)
  • (B) \(\lfloor A(ln4) \rfloor=2\)
  • (C) \(\lfloor A(3) \rfloor=3\)
  • (D) \(\lfloor A(4) \rfloor=2\)

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


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