# 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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