List of top Mathematics Questions on Pair of Linear Equations in Two Variables asked in JEE Main

Let \( f : \mathbb{R} - \{0\} \to \mathbb{R} \) be a function such that \[ f(x) - 6f\left(\frac{1}{x}\right) = \frac{35}{3x} - \frac{5}{2}. \] If \( \lim_{x \to 0} \left( \frac{1}{\alpha x} + f(x) \right) = \beta \), then \( \alpha, \beta \in \mathbb{R} \), and \( \alpha + 2\beta \) is equal to:
Two equal sides of an isosceles triangle are along \( -x + 2y = 4 \) and \( x + y = 4 \). If \( m \) is the slope of its third side, then the sum of all possible distinct values of \( m \) is:
\(f(x) =   \begin{cases}     \frac{sin(x-|x|)}{x-|x|}       & \quad {x \in(-2,-1) } \\     max{2x,3[|x|]},  & \quad \text{|x|<1}\\1 & \quad \text{,otherwise}  \end{cases}\) Where [t] denotes greatest integer t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is