Step-by-step Solution:

Given total students: \[ N = 400 \] From the table, the total number of students studying each subject includes those studying multiple subjects. Step 1: Finding Students Studying Only One Subject - Mathematics only: \[ M_{\text{only}} = \text{Total Mathematics} - (\text{Students studying multiple subjects with Mathematics}) \] \[ = 250 - (100 + 60 + 30) = 250 - 190 = 60 \] Since given statement (a) says 100, it is incorrect. - Physics only: \[ P_{\text{only}} = 150 - (100 + 40 + 30) = 150 - 170 = 40 \] This matches statement (b), so (b) is correct. - Chemistry only: \[ C_{\text{only}} = 100 - (60 + 40 + 30) = 100 - 130 = -30 \] Since negative is not possible, there is an error in statement (c), making it incorrect. Step 2: Finding Students Not Studying Any Subject Total students studying at least one subject: \[ M + P + C - (\text{overlap terms}) = 250 + 150 + 100 - (100 + 60 + 40 + 30) = 310 \] Thus, students not studying any subject: \[ N - \text{Students studying at least one subject} = 400 - 310 = 70 \] This matches statement (d), so (d) is correct. Final Answer: Since (b) and (d) are correct, the correct option is: \[ \boxed{\text{A) B and D only.}} \]