\begin{tabular}{|l|l|l|l|}
\hline & Column \( \mathbf{I} \) & & Column - II \\
\hline I. & \begin{tabular}{l}
Let \( \lambda \neq 0 \) be the real number. \\
Let \( \alpha, \beta \) be the roots of the \\
equation \( 14 x^{2}-31 x+3 \lambda=0 \) \\
and \( \alpha, \gamma \) be the roots of the \\
equation \( 35 x^{2}-53 x+4 \lambda=0 \). \\
Then \( \frac{3 \alpha}{\beta} \) and \( \frac{4 \alpha}{\gamma} \) are the roots \\
of the equation with sum of \\
roots as.
\end{tabular} & 0 \\
\hline
\end{tabular}
\begin{tabular}{|l|l|l|l|}
\hline II. & \begin{tabular}{l}
The number of real roots of the \\
equation \\
\( \left(x^{2}+\frac{1}{x^{2}}\right)-2\left(x+\frac{1}{x}\right)+5=0 \),
\end{tabular} & Q. & 1 \\
\hline iII. & \begin{tabular}{l}
The equation \( x^{2}-4 x+[x]+3= \) \\
\( x[x] \), where \( [x] \) denotes the \\
greatest integer function, has \\
solutions in R. (R stands for \\
real numbers)
\end{tabular} & R. & 5 \\
\hline
\end{tabular}
(1) I-P, II-R, III-Q
(2) I-Q, II-R, III-P
(3) I-P, II-Q, III-R
(4) I-R, II-P, III-Q
0