Question
If the 17^ th and the 18^ th terms in the expansion of (2+a)^ 50 are equal, then the coefficient of x^ 35 in the expansion of (a+x)^ -2 is
BITSAT
Mathematics
Binomial Theorem
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. -35
- B. 3
- C. 36
- D. -36
Answer
D. -36
Step-by-step solution
Given, 17^ th and 18^ th terms in the expansion (2+a)^ 50 are equal T_ 17 =T_ 18 ^ 50 C_ 16 (2)^ 34 (a)^ 16 = ^ 50 C_ 17 (2)^ 33 (a)^ 17 a= ^ 50 C_ 16 ^ 50 C_ 17 2=1 Now, coefficient of x^ 35 in the expansion (1+x)^ -2 =-36 Coefficient of x^r is (r+1) in (1-x)^ -2 .
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