A wave is travelling along a string. At an instant, shape of the string is as shown in figure. At this instant, point A is moving upwards

(i) The wave is travelling to the right
(ii) Displacement amplitude of the wave is equal to displacement of B at this instant
(iii) At this instant velocity of C is also directed upwards
(iv) Phase difference between A and C may be equal to $\frac{\mathrm{\pi }}{2}$
Which of the following statements are correct?

Since A is moving upwards, therefore, after an elemental time interval the wave will be as shown dotted in following figure. It means, the wave is travelling leftward. Therefore, (a) is wrong. Displacement amplitude of  the wave means maximum possible displacement of medium particles due to propagation of the wave, which is equal to the displacement at B at the instant shown in figure
Hence (b) is correct.
From figure, it is clear that C is moving downwards at this instant. Hence (c) is wrong.
The phase difference between two points will be equal to $\frac{\mathrm{\pi }}{2}$ if distance between them is equal to $\frac{\mathrm{\lambda }}{4}$ . Between A and C, the distance is less than $\frac{\lambda }{2}$ It may be equal to $\frac{\mathrm{\lambda }}{4}$. Hence, phase difference between these two points may be equal to $\frac{\pi }{2}$