List of top Questions asked in MHT CET

If $f(1) = 3,\; f'(1) = 2$, then $\dfrac{d}{dx}\left\{\log\left[f\left(e^x + 2x\right)\right]\right\}$ at $x = 0$ is ______.

The line $L$ is passing through $(1, 2, 3)$. The distance of any point on the line $L$ from the line $\vec{r} = (3\lambda - 1)\hat{i} + (-2\lambda + 3)\hat{j} + (4 + \lambda)\hat{k}$ is constant. Then the line $L$ does not pass through the point ______.