If \( p=\{2,3,5,7,11\} \) and \( Q=\{1,3,5,11\} \) Rationalise the denominator of \( \frac{5+\sqrt{3}}{5-\sqrt{3}} \)

\( k+9, k-6 \) र 4 एउटा गुणोत्तर अनुक्रमका \( k+9, k-6 \) and 4 are the three terms of a geometric progression (i) \( k \) को मान पत्ता लगाउनुहोस् । (Find the value of \( k \).) (ii) समान अनुपात पत्ता लगाउनुहोस् । (Find the common ratio.) (iii) चौथो पद पत्ता लगाउनुहोस् । (Find the value of fourth term.) odel 3 Problems based on finding the position of a given term i)

\( \left. \begin{array} { l } { ( x + y ) ^ { 3 } = z } \\ { ( y + z ) ^ { 3 } = x } \\ { ( z + x ) ^ { 3 } = y } \end{array} \right. \)

\( \left. \begin{array} { l } { x ^ { 2 } - y ^ { 2 } + y } \\ { = 3 x ^ { 2 } y - y ^ { 3 } + x y } \end{array} \right. \)

Three quantities \( t, x \) and \( y \) are such that \( t \) varies directly as \( x \) and invisely as the square root of \( y \). Find the percentage decrease in \( t \) if \( x \) decreases by \( 44 \% \).

Calcula \( X \) tal que \( X-B^{2}=A \cdot B \), siendo que: \[ A=\left(\begin{array}{lll}1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 0 & 2\end{array}\right), \quad B=\left(\begin{array}{ccc}1 & 0 & -1 \\ 1 & 1 & 1 \\ 0 & 0 & 1\end{array}\right) \]