Question
Let a_0, a_1, , a_ 23 be real numbers such that (1+ 2 5 x )^ 23 = _ i=0 ^ 23 a_i x^i for every real number x. let a_r be the largest among the numbers a_j for 0 j 23. The the value of r is ______
JEE Advanced
Mathematics
Binomial Theorem
2025
JEE Advanced 2025 (Paper 2)
JEE Advanced Mathematics Question (2025) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
For x =1 (1+ 2 5 )^ 23 =a_0+a_1+a_2+ +a_ 23 for numerically greatest term n+1 1+ | a b | = 23+1 1+ 5 2 = 48 7 [ 48 7 ]=6= m (where [.] greatest integer function) so, T _7 is numerical greatest term Hence r=6
Related: Mathematics — Binomial Theorem · All PYQ Banks