Which of the following pairs of displacements cannot be added to give a resultant displacement of 2m?

1. 1m+1m

2. 1m+2m

3. 1m+3m

4. 1m+4m

1 m and 4 m cannot be added to give result 2 m.
Applying vector addition for 1 m and 4 m
$$\begin{gathered} R=\sqrt{1^2+4^2+2\times 1\times 4\cos \left(\theta \right)} \\ 2=\sqrt{1^2+4^2+2\times 1\times 4\cos \left(\theta \right)} \\ squaring \\ 4=17+8\cos \left(\theta \right) \\ \cos \left(\theta \right)=\frac{-13}{8} \end{gathered}$$
There is no angle which can satisfy this equation.


For other option there is value of angle which gives result 2 m.