CUET Mathematics 2026 14th May Shift 2 PYQs

For the function $f(x) = -2|\log_e|x||$, which of the following is true?

For what value of $\alpha$, the function $f$ defined by $f(x) = \begin{cases} \alpha(x^2 - 2x + 1), & \text{if } x \leq 0 \\ 2x + 1, & \text{if } x > 0 \end{cases}$ is continuous at $x = 0$?

If $e^x + e^y = e^{x+y}$, then $\frac{dy}{dx}$ =