The correct option is B (10,∞)
Let f(x)=x2−(a−3)x+a
Case 1: Both the roots lie in the interval (1,2)
(i) f(1)>0 and f(2)>0
⇒a<10 ⋯(1)
(ii) 1<−b2a<2
⇒1<−a−32<2
⇒5<a<7 ⋯(2)
(iii) D≥0 ⇒D=(a−3)2−4a≥0
⇒a2−10a+9≥0⇒(a−1)(a−9)≥0⇒a∈(−∞,1]∪[9,∞) ⋯(3)
∴(1)∩(2)∩(3)⇒a∈ϕ ⋯(4)
Case 2: Exactly one root lies in the interval (1,2)
f(1)f(2)<0
⇒4(10−a)<0
⇒a>10 ⋯(5)
∴(4)∪(5)⇒a∈(10,∞)