If (√2 + √5 - √3) × k = -12, then what will be the value of k?

Answer: Option D

$$\begin{array}{rl}& \left(\sqrt{2}+\sqrt{5}-\sqrt{3}\right)\times \text{k}=-12\\ & \text{In these type of questions, we can go through option}\\ & \text{From option D}\\ & \Rightarrow \left(\sqrt{2}+\sqrt{5}-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{5}+\sqrt{3}\right)\left(2-\sqrt{10}\right)=-12\\ & \Rightarrow \left[{\left(\sqrt{2}+\sqrt{5}\right)}^2-{\left(\sqrt{3}\right)}^2\right]\left(2-\sqrt{10}\right)=-12\\ & \Rightarrow \left(2+5+2\sqrt{10}-3\right)\left(2-\sqrt{10}\right)=-12\\ & \Rightarrow 2\left(2+\sqrt{10}\right)\left(2-\sqrt{10}\right)=-12\\ & \Rightarrow 2\left[{\left(2\right)}^2-{\left(\sqrt{10}\right)}^2\right]=-12\\ & \Rightarrow 2\times \left[-6\right]=-12\\ & \Rightarrow -12=-12\left(\text{Satisfy}\right)\end{array}$$