Let ABCD be a square of side length 2 units. $\mathrm{C}_2$ is the circle through vertices $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{C}_1$ is the circle touching all the sides of the square ABCD . L is a line through A.

A line $M$ through $A$ is drawn parallel to $B D$. Point $S$ moves such that its distances from

the line BD and the vertex A are equal. If locus of S cuts M at $\mathrm{T}_2$ and $\mathrm{T}_3$ and AC at $\mathrm{T}_1$, then area of $\Delta T_1 T_2 T_3$ is :

Comprehension IV

$\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$, if $\mathrm{U}_1, \mathrm{U}_2$ and $\mathrm{U}_3$ are columns matrices satisfying. $\mathrm{AU}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{AU}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AU}_3=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$ and U is $3 \times 3$ matrix whose columns are $\mathrm{U}_1, \mathrm{U}_2, \mathrm{U}_3$ then answer the following questions

The sum of the elements of $\mathrm{U}^{-1}$ is:

$\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$, if $\mathrm{U}_1, \mathrm{U}_2$ and $\mathrm{U}_3$ are columns matrices satisfying. $\mathrm{AU}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{AU}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AU}_3=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$ and U is $3 \times 3$ matrix whose columns are $\mathrm{U}_1, \mathrm{U}_2, \mathrm{U}_3$ then answer the following questions

The value of $\left[\begin{array}{lll}3 & 2 & 0\end{array}\right] U\left[\begin{array}{l}3 \\ 2 \\ 0\end{array}\right]$ is :

If roots of the equation $x^2-10 c x-11 d=0$ are $a, b$ and those of $x^2-10 a x-11 b=0$ are $c, d$, then the value of $a+b+c+d$ is $(a, b, c$ and $d$ are distinct numbers)