Question
The coefficient of x^n in the expansion of e^ 7 x +e^x e^ 3 x is
BITSAT
Mathematics
Binomial Theorem
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 4^ n-1 +(-2)^n n!
- B. 4^ n-1 +2^n n!
- C. 4^n+(-2)^n n!
- D. 4^ n-1 +(-2)^ n-1 n!
Answer
C. 4^n+(-2)^n n!
Step-by-step solution
Given, e^ 7 x +e^x e^ 3 x e^ 4 x +e^ -2 x Series of e^a=1+ a 1! + a^2 2! + a^3 3! aligned e^ 4 x + & e^ -2 x = (1+ 4 x 1! + (4 x)^2 2! + (4 x)^3 3! + ) \\ & + (1+ (-2 x) 1! + (-2 x)^2 2! + ) aligned Here, coefficient of aligned & x^2 4^2 2! + (-2)^2 2! \\ & x^3 4^3 3! + (-2)^3 3! \\ & \\ & x^n= 4^n n! + (-2)^n n! aligned
Related: Mathematics — Binomial Theorem · All PYQ Banks