\begin{tabular}{l|l|l|}
\hline \multicolumn{1}{|c|}{ Column I } & Column II \\
\hline A. In \( \Delta X Y Z \), let \( a, b \) and \( c \) be the lengths of the sides opposite to the angles \( X, Y \) and \( Z \), & \( p \). \\
despectively. \\
If \( 2\left(a^{2}-b^{2}\right)=c^{2} \) and \( \lambda=\frac{\sin (X-Y)}{\sin Z} \) then possible value(s) of \( n \) tor which \( \cos (n \pi \lambda)=0 \), \\
is/are \\
\hline B. In \( \Delta X Y Z \), let \( a, b \) and \( c \) be the lengths of the sides opposite to the angles \( X, Y \) and \( Z \), respectively. & q. \\
If \( 1+\cos 2 X-2 \cos 2 Y=2 \sin X \sin Y \), then possible value(s) of \( \frac{a}{b} \) is/are
\end{tabular}
C. \( \quad \ln R^{2} \), let \( \sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j} \) and \( \beta \hat{i}+(1-\beta) \hat{j} \) be the position vectors of \( X, Y \) and \( Z \) with respect \( \quad \) r. 3 to the origin \( O \), respectiveily. If the distance of \( Z \) from the bisector of the acute angle of \( O X \) with \( O Y \) is \( \frac{3}{\sqrt{2}} \), then possible value(s) of \( |\beta| \) is/are
D. Suppose that \( F(\alpha) \) denotes the area of the region bounded by \( x=0, x=2, y^{2}=4 x \) and
s. 5 \( y=|\alpha x-1|+|\alpha x-2|+\alpha x \), where \( \alpha \in\{0,1\} \). Then, the value(s) of \( F(\alpha)+\frac{8}{3} \sqrt{2} \), when \( \alpha=0 \) and \( \alpha=1 \), is/are
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