The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively.

If $$x=e^t(\sin t-\cos t)$$ and $$y=e^t(\sin t+\cos t)$$, then $$\frac{d y}{d x}$$ at $$t=\frac{\pi}{3}$$ is

If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{K}$$ are

If $$\bar{a}=3 \hat{i}+\hat{j}-\hat{k}, \bar{b}=2 \hat{i}-\hat{j}+23 \hat{k}$$ and $$\bar{c}=7 \hat{i}-\hat{j}+23 \hat{k}$$, then which of the following is valid.