\[\LARGE {\color {red}{Questions\ from\ Unit-I,\ Unit-II,\ Unit-III,\ Unit-IV,\ and\ Unit-V}}\]
\[Date:\ 13-12-2021\ \hspace{10cm}\ Max\ Marks:\ 5\ ×\ 4\ =\ 20m\]
\[\color {black} {1.}\ Solve\ the\ following\ equations\ using\ Cramers\ Rule\ \hspace{20cm}\]\[x\ +\ y\ +\ z\ =\ 3,\ 2\ x\ -\ y\ +\ z\ =\ 2\ and\ 3\ x\ +\ 2\ y\ -\ 2\ z\ =\ 3\ \hspace{10cm}\]
\[2.\ Solve\ x^6 + 1\ =\ 0\ \hspace{18cm}\]
\[3.\ Prove\ that\ \frac{Cos^3\ A\ -\ Cos\ 3\ A}{Cos\ A}\ +\ \frac{Sin^3\ A\ +\ Sin\ 3\ A}{Sin\ A}\ =\ 3\ \hspace{15cm}\]
\[4.\ Find\ \frac{dy}{dx}\ (i)\ if\ y\ =\ Sin^{-1}\ (\sqrt{x}),\ \hspace{2cm}\ (ii)\ if\ a\ x^2\ +\ 2\ h\ x\ y\ +\ b\ y^2\ +\ 2\ g\ x\ +\ 2\ f\ y\ +\ c\ =\ 0\ \hspace{7cm}\]
\[5.\ If\ y\ =\ x^2\ Cos\ x,\ prove\ that\ x^2\ y_2\ -\ 4\ x\ y_1\ +\ (x^2\ +\ 6)y\ =\ 0\ \hspace{15cm}\]
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