Question
If the domain of the function f(x)= _ (10 x^ 2 -17 x+7 ) (18 x^ 2 -11 x+1 ) is (- , a) (b, c) (d, )-\ e\ , then 90(a+b+c+d+e) equals:
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 170
- B. 307
- C. 316
- D. 177
Answer
C. 316
Step-by-step solution
For f(x) = _ (10x^2-17x+7) (18x^2-11x+1), we need: Base > 0: 10x^2-17x+7 > 0 10(x-1)(x-7/10) > 0 x 1 Base 1: 10x^2-17x+6 = 0 x = 1/2 or x = 6/5 Argument > 0: 18x^2-11x+1 > 0 18(x-1/2)(x-1/9) > 0 x 1/2 Intersecting conditions 1 and 3: (- , 1/9) (1/2, 7/10) (1, ) Removing base = 1 points: x = 1/2 is already excluded; x = 6/5 (1, ) must be removed. Domain: (- , 1/9) (1/2, 7/10) (1, ) - \ 6/5\ So a = 1/9,\; b = 1/2,\; c = 7/10,\; d = 1,\; e = 6/5. 90(a+b+c+d+e) = 90 ( 1 9 + 1 2 + 7 10 +1+ 6 5 ) = 10+45+63+90+108 = 316
Related: Mathematics — Functions · All PYQ Banks