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(A) If the sum of first 84 terms of the series
\( P \) \( \frac{4+\sqrt{3}}{1+\sqrt{3}}+\frac{8+\sqrt{15}}{\sqrt{3}+\sqrt{5}}+\frac{12+\sqrt{35}}{\sqrt{5}+\sqrt{7}}+\ldots \). is \( 549 \mathrm{k} \), then \( k \) is equal to
(B) If \( x, y \in R, x^{2}+y^{2}-6 x+8 y+24=0 \), the greatest (Q) 2 value of \( \frac{16}{5} \cos ^{2}\left(\sqrt{x^{2}+y^{2}}\right)-\frac{24}{5} \sin \left(\sqrt{x^{2}+y^{2}}\right) \) is
(C) If \( (\sqrt{3}+1)^{6}+(\sqrt{3}-1)^{6}=416 \), if \( x y z=\left[(\sqrt{3}+1)^{6}\right] \),
(R)
5 \( x, y, z \in N \), (where [.] denotes the greatest integer function), then the number of ordered triplets \( (x, y, z) \) is
(D) If \( (1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \ldots\left(1+x^{128}\right)=\sum_{r=0}^{n} x^{r} \), then
(S)
9 \( \frac{n}{85} \) is equal to
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