Let $y=y(x)$ be the solution of the differential equation $x^4 \mathrm{~d} y+\left(4 x^3 y+2 \sin x\right) \mathrm{d} x=0, x>0, y\left(\frac{\pi}{2}\right)=0$.

Then $\pi^4 y\left(\frac{\pi}{3}\right)$ is equal to :

Let $\mathrm{A}=\{-2,-1,0,1,2,3,4\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $2 x+y \leqslant 2$. Let $l$ be the number of elements in R . Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then $\mathrm{l}+\mathrm{m}+\mathrm{n}$ is equal to :

Let $f(x)= \begin{cases}\frac{\mathrm{a} x^2+2 \mathrm{a} x+3}{4 x^2+4 x-3} & , x \neq-\frac{3}{2}, \frac{1}{2} \\ \mathrm{~b} & , x=-\frac{3}{2}, \frac{1}{2}\end{cases}$ be continuous at $x=-\frac{3}{2}$. If $f \circ f(x)=\frac{7}{5}$, then $x$ is equal to:

Let $|\mathrm{A}|=6$, where A is a $3 \times 3$ matrix. If $\left|\operatorname{adj}\left(3\operatorname{adj}\left(\mathrm{A}^2 \cdot \operatorname{adj}(2 \mathrm{~A})\right)\right)\right|=2^{\mathrm{m}} \cdot 3^{\mathrm{n}}, \mathrm{m}, \mathrm{n} \in \mathbf{N}$, then $\mathrm{m}+\mathrm{n}$ is equal to

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