The domain of the function, $f(x)=\sqrt{\log _{10}\left(\frac{5 x-x^2}{4}\right)}$ is

Let the greatest common divisor of $m, n$ be 1 . If $\frac{1}{1 \cdot 7}+\frac{1}{7 \cdot 13}+\frac{1}{13 \cdot 19}+\ldots \ldots$. upto 20 terms $=\frac{m}{n}$, then $5 m+2 n=$

If $A, B$ are two non singular matrices of order $3,|B|=k$, a positive integer, then match the items of list-I with the items of list-II.

$$ \text { The correct match is } $$

All the real values of $p, q$ so that the system of equations

$$ 2 x+p y+6 z=8, x+2 y+q z=5 $$

and $\quad x+y+3 z=4$

may have no solution are