Question
The middle term in the expansion of ( 10 x + x 10 )^ 10 is
BITSAT
Mathematics
Binomial Theorem
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. ^ 10 C _5
- B. ^ 10 C _6
- C. ^ 10 C _5 1 x^ 10
- D. ^ 10 C _5 x ^ 10
Answer
A. ^ 10 C _5
Step-by-step solution
General term =T_ r+1 = ^ 10 C _r ( 10 x )^ 10-r ( x 10 )^r Here n=10, which is an even number. Now, [ 10 2 +1 ]^ th term i.e. 6^ th term is the middle term. Hence, middle term =T_6 T _ 5+1 = ^ 10 C _5 ( 10 x )^ 10-5 ( x 10 )^5 = ^ 10 C _5 ( 10 x )^5 ( x 10 )^5= ^ 10 C _5.
Related: Mathematics — Binomial Theorem · All PYQ Banks