If the solution of $$\frac{d y}{d x}-y \log _e 0.5=0, y(0)=1$$, and $$y(x) \rightarrow k$$, as $$x \rightarrow \infty$$, then $$k=$$

At any point $$(x, y)$$ on a curve if the length of the subnormal is $$(x-1)$$ and the curve passes through $$(1,2)$$, then the curve is a conic. A vertex of the curve is

$$y=A e^x+B e^{-2 x}$$ satisfies which of the following differential equations?

If $$N_A, N_B$$ and $$N_C$$ are the number of significant figures in $$A=0.001204 \mathrm{~m}, B=43120000 \mathrm{~m}$$ and $$C=1.200 \mathrm{~m}$$ respectively, then