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(A) Step $1$: Find the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$. Multiplying the second equation by $3$,we get $9x +

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$5x + 3y + 8 = 0$

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(A) Step $1$: Find the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$. Multiplying the second equation by $3$,we get $9x + 6y + 15 = 0$. Adding this to the first equation: $(5x - 6y - 1) + (9x + 6y + 15) = 0$ $\Rightarrow 14x + 14 = 0$ $\Rightarrow x = -1$. Substituting $x = -1$ into $3x + 2y + 5 = 0$: $3(-1) + 2y + 5 = 0$ $\Rightarrow -3 + 2y + 5 = 0$ $\Rightarrow 2y = -2$ $\Rightarrow y = -1$. The point of intersection is $(-1, -1)$. Step $2$: Find the equation of the line perpendicular to $3x - 5y + 11 = 0$. The general form of a line perpendicular to $ax + by + c = 0$ is $bx - ay + k = 0$. Thus,the line is $5x + 3y + k = 0$. Step $3$: Since the line passes through $(-1, -1)$,substitute these coordinates into the equation: $5(-1) + 3(-1) + k = 0$ $\Rightarrow -5 - 3 + k = 0$ $\Rightarrow k = 8$. Therefore,the required equation is $5x + 3y + 8 = 0$.

The equation of the straight line passing through the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$ and perpendicular to the line $3x - 5y + 11 = 0$ is

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