GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

x direction scalar of velocity field,
$\mathit{u}=\frac{\mathit{d}\mathit{x}}{\mathit{d}\mathit{t}}=-\mathit{k}{\mathit{x}}_{\mathit{o}}{\mathit{e}}^{-\mathit{k}\mathit{t}}=-\mathit{k}\mathit{x}$
y direction scalar of velocity field
$\mathit{v}=\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{t}}=\mathit{k}{\mathit{y}}_{\mathit{o}}{\mathit{e}}^{\mathit{k}\mathit{t}}=\mathit{k}\mathit{y}$
$\mathit{u}$ & $\mathit{v}$ are non zero scalar $\mathit{t}\ge 0$ so it is $2\mathit{D}$ flow.
Continuity equation for steady flow,
$\frac{\partial \mathit{u}}{\partial \mathit{x}}+\frac{\partial \mathit{V}}{\partial \mathit{y}}=0$
$\frac{\partial }{\partial \mathit{x}}\left(-\mathit{k}{\mathit{x}}_0{\mathit{e}}^{-\mathit{k}\mathit{t}}\right)+\frac{\partial }{\partial \mathit{y}}\left(\mathit{k}{\mathit{y}}_0{\mathit{e}}^{\mathit{k}\mathit{t}}\right)=0$
$0+0=0$ Continuity is satisfied.
Hence flow is $2\mathit{D}$ and steady.