In the question, it is given that the equation ∣x+a∣+∣x−1∣=2 has an infinite number of solutions for any value of x This is possible when x in ∣x+a∣ and x in ∣x−1∣ cancels out. Case 1:x+a<0,x−1≥0−a−x+x−1=2a=−3Case 2:x+a≥0 and x−1<0x+a−x+1=2a=1 Largest value of a is 1. The answer is option C.