A particle P starts from the point $\mathrm{Z}_0=1+2 \mathrm{i}$ where $\mathrm{i}=\sqrt{-1}$. It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive Y -axis by 3 units to reach a point $Z_1$. From $Z_1$ the particle moves $\sqrt{2}$ units in the direction of vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin to reach at point $Z_2$, then $Z_2=$

$$ \mathop {\lim }\limits_{x \to 0} \frac{63^x-9^x-7^x+1}{\sqrt{2}-\sqrt{1+\cos x}}=\ldots \ldots $$

Consider the following three statements

(A) If $3+2=7$ then $4+3=8$.

(B) If $5+2=7$ then earth is flat.

(C) If both (A) and (B) are true then $5+6=11$. Which of the following statements is correct?

If $\mathrm{A}=\left[\begin{array}{cc}5 \mathrm{a} & -\mathrm{b} \\ 3 & 2\end{array}\right]$ and A .adj $\mathrm{A}=\mathrm{AA}^{\mathrm{T}}$, then $5 \mathrm{a}+\mathrm{b}=$