Column - 1		Column - 2
A)	Let  f(x)  be a non-constant thrice differential function defined on  $(-\infty ,\infty )$ such that  $f\left(\frac{x+13}{2}\right)=f\left(\frac{3-x}{2}\right)$  and $f^{\text{'}}\left(0\right)=f^{\text{'}}\left(\frac{1}{2}\right)=f^{\text{'}}\left(2\right)=f^{\text{'}}\left(3\right)=f^{\text{'}}\left(\frac{9}{2}\right)=0$ then the minimum number of zeroes of $h\left(x\right)={\left(f^{\text{'}\text{'}}\left(x\right)\right)}^2+f^{\text{'}}\left(x\right)f^{\text{'}\text{'}\text{'}}\left(x\right)$  in the interval  [0,9]  is  2 k  then  k  is equal to____	P)	10
B)	If the maximum value of  $|\sqrt{x^4-7x^2-4x+20}-\sqrt{x^4+9x^2+16}|$ is P , then the value of  [P] (where [.] denotes  GIF)	Q)	8
C)	Consider a function  $f\left(x\right)$ where $f:R^{+}\to R$  such that $f\left(2023\right)=1$ and $f\left(x\right)f\left(y\right)+f\left(\frac{2023}{x}\right)f\left(\frac{2023}{y}\right)=2f\left(xy\right),\forall x,y\in R^{+}$ then  $\frac{10f\left(2\right)}{f\left(1\right)+f\left(2\right)}=$	R)	5
D)	If  $\alpha$ and  $\beta (\alpha <\beta )$ are roots of equation  $\underset{t\to \infty }{\lim }{\cos }^{-1}\left[\sin \left({\tan }^{-1}\left(\frac{\sqrt{tx}}{\sqrt{t{x}^2-3tx+t-1}-x}\right)\right)\right]=\frac{\pi }{6}$   then the value of  $(8^{\alpha }+2^{\beta }-\alpha \beta )$	S)	9