Question
If x^ 18 occurs in the rth term in the expansion of (x^4+ 1 x^3 )^ 15 , then what is the value of r ?
BITSAT
Mathematics
Binomial Theorem
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. 3
- B. 5
- C. 7
- D. 9
Answer
C. 7
Step-by-step solution
In the expansion of (x^4+ 1 x^3 )^ 15 , let T_r is the r^ th term aligned T_r & = ^ 15 C_ r-1 (x^4 )^ 15-r+1 ( 1 x^3 )^ r-1 \\ & = ^ 15 C_ r-1 x^ 64-4 r-3 r+3 =15_ C_ r-1 x^ 67-7 r aligned x ^ 18 occurs in this term 18=67-7 r 7 r=49 r=7 .
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