\begin{tabular}{|l|l|l|l|}
\hline & Column -I & & Column - II \\
\hline I. & \begin{tabular}{l}
Ramesh and Mahesh solve an \\
equation. In solving Ramesh \\
commits a mistake in \\
constant term and finds the \\
root 8 and 2. Mahesh \\
commits a mistake in the \\
coefficient of \( x \) and finds the \\
roots -9 and -1. Find the sum \\
of correct roots.
\end{tabular} & 7 \\
\hline II. & \begin{tabular}{l}
\( \alpha \& \beta \) are the roots of the \\
equation \( x^{2}-7 x-1=0 \), then \\
\( \alpha^{10}+\beta^{10}-\left(\alpha^{8}-\beta^{8}\right) \)
\end{tabular} & Q. & 114 \\
\hline \begin{tabular}{l}
\( \alpha^{\alpha+\beta+2}-\beta^{\alpha+\beta+2} \)
\end{tabular} \\
\hline III. & \begin{tabular}{l}
The minimum value of \\
\( (x-6)^{2}+(x+3)^{2}+(x-8)^{2}+ \) \\
\( (x+4)^{2}+(x-3)^{2} \) is
\end{tabular} & R. & 10 \\
\hline IV. & \begin{tabular}{l}
The number of integral values \\
of \( k \) for which the equation 3 \\
sin \( x+4 \) cos \( x=k+1 \) has a \\
solution, \( k \in R \) is
\end{tabular} & S. & 11 \\
\hline
\end{tabular}
\( \mathrm{P} \)
W
(1) I-P, II-S, III-R, IV-Q
(2) I-S, II-R, III-P, IV-Q
(3) I-R, II-P, III-Q, IV-S
(4) I-R, II-P, III-S, IV-Q
0