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

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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