Question
If _ x 0 e ^ ( a -1) x +2 ~b x+( c -2) e ^ -x x x- _ e (1+x) =2, then a ^ 2 + b ^ 2 + c ^ 2 is equal to :
JEE Main
Mathematics
Limits
2026
JEE Main 2026 (22 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 5
- B. 9
- C. 3
- D. 7
Answer
D. 7
Step-by-step solution
_ x 0 (1+(a-1) x+ (a-1)^2 x^2 2! )+2 (1- b^2 x^2 2! )+(c-2) (1-x+ x^2 2! ) x (1- x^2 2! )- (x- x^2 2 ) =2 _ x 0 (1+2+c-2)+x(a-1-c+2)+x^2 ( (a-1)^2 2 -b^2+ ( c-2 2 ) ) x^2 2 - x^3 2! + =2 For which c+1=0 c=-1 a-c=-1 a=-2 (a-1)^2 2 -b^2+ ( c-2 2 )=1 9 2 -b^2- 3 2 =1 b^2=2 a^2+b^2+c^2=4+2+1=7
Related: Mathematics — Limits · All PYQ Banks