\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column....
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & \begin{tabular}{l}
If \\
\( P\left(1+\frac{t}{\sqrt{2}}, 2+\frac{t}{\sqrt{2}}\right) \) \\
be any point on \\
a line then value \\
of \( t \) for which \\
the point \( P \) lies \\
between \\
parallel lines \( x+ \) \\
\( 2 y=1 \) and \( 2 x+ \) \\
\( 4 y=15 \) is
\end{tabular} & & \( (1,2) \) \\
\hline (B) & \begin{tabular}{l}
If the point \( \left(x_{1}+\right. \) \\
\( t\left(x_{2}-x_{1}\right), y_{1}+ \) \\
\( t\left(y_{2}-y_{1}\right) \) divides \\
the join of \( \left(x_{1}\right. \), \\
\( \left.y_{1}\right) \) and \( \left(x_{2}, y_{2}\right) \) \\
internally in the \\
ratio \( t: 1-t \), \\
then \( t \quad \) lies \\
between
\end{tabular} & & \\
\hline
\end{tabular}
\begin{tabular}{|c|c|c|c|}
\hline (C) & \begin{tabular}{l}
If the point \( (1, t) \) \\
always remains \\
in the interior of \\
the triangle \\
formed by the \\
lines \( y=x, y=0 \) \\
and \( x+y=4 \), \\
then
\end{tabular} & (R) & \( \left(\frac{-4 \sqrt{2}}{3}, \frac{5 \sqrt{2}}{6}\right) \) \\
\hline (D) & \begin{tabular}{l}
Set of values of \\
' \( t \) ' for which the \\
point \( P\left(t, t^{2}-2\right) \) \\
lies inside the \\
triangle formed \\
by lines \( x+y= \) \\
\( 1, y=x+1 \) and \\
\( y=-1 \) is
\end{tabular} & (S) & \( (0,1) \) \\
\hline
\end{tabular}
(1) (A) \( \rightarrow \) (P), (B) \( \rightarrow \) (Q), (C) \( \rightarrow \) (R), (D) \( \rightarrow \) (S)
(2) (A) \( \rightarrow \) (R), (B) \( \rightarrow \) (P), (C) \( \rightarrow \) (S), (D) \( \rightarrow \) (Q)
(3) (A) \( \rightarrow \) (R), (B) \( \rightarrow \) (S), (C) \( \rightarrow \) (S), (D) \( \rightarrow \) (Q)
(4) (A) \( \rightarrow \) (Q), (B) \( \rightarrow \) (P), (C) \( \rightarrow \) (R), (D) \( \rightarrow \) (S)
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