The given figure shows the strain?stress curve for a given material. What are
(a) Young?s modulus and (b) approximate yield strength for this material?

Yield strength, Y, is the ratio of stress to strain. within the elastic limits
It is the slope of the linear portion of the curve
Looking into the graph it can be seen that the curve passes a stress value of 150 N/m2 at a strain value of 0.002. 
Y=1500.002=75000 N/m2
Yield strength of the material is the point where the stress strain curve deviates from its linear pattern.
Looking into the graph, the stress value where the curve deviates from proportionality, i.e., the Yield strength value is slightly less than 300 N/m2 which is approximately 295 N/m2

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