(a) 2023: If \( y \propto x \) and \( y=5 \) when \( x=15 \), Find the value of \( x \) when \( y=3 \) (b) If \( y \) varies inversely with \( x^{2} \) and \( x=3 \) when \( y=4 \), Find: [1] The relation between \( y \) and \( x \) [2] The value of \( x \) when \( y=9 \) (C) If \( a, b, c \) and \( d \) are proportion quantities, then prove that : \( \frac{a}{b+2 c}=\frac{c-a}{d-b} \)

\( 8 x y \) is a monomial expression. Is the statement true or fause?

\( 1 \leftarrow \quad \begin{array}{l}\text { Solve the system of equations by the substitution method. } \\ \begin{aligned} 4 x+2 y & =-154 \\ x-5 y & =0\end{aligned}\end{array} \)

The cost price of a pen is Rs \( (3 x+5) \) and is selling price is \( \operatorname{Rs}(4 x+3) \) Write the formulato find protit.

/Evaluate \( :\left(\frac{4^{-8}}{8^{-4}}\right)^{3 / 4} \)

What is the value of one third the determinant of \( \left[\begin{array}{cccc}2 & 3 & 0 & 11 \\ 3 & 5 & -1 & 10 \\ 0 & -6 & 2 & 4 \\ 2 & 4 & 7 & -5\end{array}\right] \) ?