Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Find the sixth term in the expansion of \( (2x + 5y/2)^9 \).
Options
A 124x^4 y^5
B 196875x^4 y^5
C 393750x^4 y^5
Correct Answer
D 2016x^4 y^5
Correct Answer

Option C is the correct answer.

Detailed Explanation

The general term is T_{r+1} = C(9, r) (2x)^{9-r} (5y/2)^r. For the sixth term, r=5. T_6 = C(9,5) (2x)^4 (5y/2)^5 = 126 * (16 x^4) * (3125 y^5 / 32) = 126 * 16 * 3125 / 32 * x^4 y^5 = 126 * (16/32) * 3125 * x^4 y^5 = 126 * (1/2) * 3125 * x^4 y^5 = 63 * 3125 * x^4 y^5 = 196875 x^4 y^5.

Hint

Apply the binomial theorem carefully, simplifying the coefficients and exponents.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 522 of 696
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