The sum of a two-digit number and the number obtained by interchanging the digits is always divisible by $\ldots \ldots \ldots \ldots$

For what value$(s)$ of $k$ does the pair of equations $kx + 3y = k - 3$ and $12x + ky = k$ have no solution?

For eliminating $y$ from the equations $3x - 2y = 1$ and $5x + y = 6$,the second equation should be multiplied by

If $\frac{5}{x}-\frac{4}{y}=4$ and $\frac{4}{x}-\frac{5}{y}=5,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Solve the following pair of linear equations: $\frac{8}{a} - \frac{9}{b} = 1$ and $\frac{10}{a} + \frac{6}{b} = 7$.

The length of a rectangle is five less than thrice its breadth. The perimeter of a rectangle is $110$. If we take $l$ as length and $b$ as breadth,then which of the following equations represents the relationship between length and breadth?