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For $x\in R,x\ne 0$ if $y\left(x\right)$ is a differentiable function such that $x\underset{1}{\overset{x}{\int }}y\left(t\right)dt=(x+1)\underset{1}{\overset{x}{\int }}ty\left(t\right)dt,$ then $y\left(x\right)$ equals:

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Lines with direction ratios}(1,–c,–b),(–c,1,–a)\text{and}(–b,–a,1)& \text{(P)}& -1\\ & \text{are coplanar. Then}{a}^2+b^2+c^2+2abc\text{is}& & \\ \text{(B)}& \text{If the lines}x=ay+1,z=by+2\text{and}x=cy+3,z=dy+4& \text{(Q)}& 1\\ & \text{are perpendicular, then}ac+bd\text{is equal to}& & \\ \text{(C)}& \text{If}(a,b,c)\text{lies on a plane which forms}△ABC\text{with coordinate axes}& \text{(R)}& 3\\ & \text{whose centroid lies on}(\alpha ,\beta ,\gamma ),\text{then}\frac{a}{\alpha }+\frac{b}{\beta }+\frac{c}{\gamma }\text{is equal to}& & \\ \text{(D)}& \text{Let}\left[x\right]\text{denote the greatest integer less than or equal to}x.\text{Then}& \text{(S)}& 0\\ & f\left(x\right)=\left[x\sin \pi x\right]\text{is not differentiable when}x\text{is equal to}& & \\ & & \text{(T)}& 2\end{array}$



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