k) \( 75 a^{2} b^{2}-27 x^{2} y^{2} \)

Solve for \( f \) in the proportion. \[ \begin{array}{l}\frac{8}{13}=\frac{f}{15.6} \\ f=\square\end{array} \]

\( \left(I^{\text {st }}\right. \) Session 2022) If the ratio between the fourth term from the beginning to the fourth term from the end in the expansion of \( \left(\frac{a}{x}+\frac{x}{a}\right)^{2 n} \) equals \( a^{4}: x^{4} \) , then \( n=\cdots \cdots \) \( \begin{array}{llll}\text { (a) } 2 & \text { (b) } 4 & \left.\text { (where } x \in \mathbb{R}^{*}, a \in \mathbb{R}^{*}\right)\end{array} \)

Determine the values of \( x \) and \( y \), in the equation: \( \frac{x-1}{3+i}+\frac{y-1}{3-i}=i \). Solve the following equations: i) \( 2^{2 x+1}=3^{2 x-5} \quad \) ii) \( \log _{2} x-\log _{2} y=2 \) \( \log _{2}(x-2 y)=3 \) In a senior secondary school, 80 students play hockey or football. The number that plays football is 5 more than twice the number that play hockey. If 15 students play both games and every student in the schoo plays at least one game, find the number of students that play football.

Exercice 1 1) Compléter avec l'un des symboles : \( \epsilon ; \notin ; \subset \) ou \( \notin \) \( \{0 ;-7 ; 12\} \ldots \ldots \mathbb{N}^{*} ; \frac{5 \pi-\pi}{2 \pi-\pi} \ldots . \mathbb{Q} ;\left\{-1 ; \frac{18}{6} ; \sqrt{36} ;-7\right\} \ldots . \mathbb{Z} ; \frac{7}{3} \ldots \ldots \) ID 2) donner l'écriture scientifique : \( A=\frac{4 \times 300^{2} \times\left(2 \times 10^{-6}\right)^{-2}}{(0.01)^{-3}} \)

Rationalize the denominator of \( \frac{7}{2 + \sqrt{3}} \).