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QUESTION 8 Which of the following is a coefficient of the term containing x' in the binomial expansion of (2x – 1)1? Select all that applies. O -128 O 128. - 128. O 42,240 128

QUESTION 8 Which of the following is a coefficient of the term containing x' in the binomial expansion of (2x – 1)1? Select all that applies. O -128 O 128. - 128. O 42,240 128

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### QUESTION 8 **Which of the following is a coefficient of the term containing \( x^7 \) in the binomial expansion of \( (2x - 1)^{11} \)?** *Select all that apply.* 1. □ \(-128\) 2. □ \(128 \cdot \binom{11}{4}\) 3. □ \(-128 \cdot \binom{11}{4}\) 4. □ \(42,240\) 5. □ \(-\binom{11}{7} \cdot 128\) #### Explanation of Binomial Coefficient Symbols: - \(\binom{n}{k}\) denotes the binomial coefficient, also known as "n choose k," which represents the number of ways to choose \(k\) elements from a set of \(n\) elements without regard to order. #### Options Explained: - **Option 1:** \(-128\) - **Option 2:** \(128 \cdot \binom{11}{4}\) - **Option 3:** \(-128 \cdot \binom{11}{4}\) - **Option 4:** \(42,240\) - **Option 5:** \(-\binom{11}{7} \cdot 128\) To determine which options are correct, one would typically expand the binomial expression \( (2x - 1)^{11} \) and identify the coefficient of the term containing \( x^7 \).
Transcribed Image Text:### QUESTION 8 **Which of the following is a coefficient of the term containing \( x^7 \) in the binomial expansion of \( (2x - 1)^{11} \)?** *Select all that apply.* 1. □ \(-128\) 2. □ \(128 \cdot \binom{11}{4}\) 3. □ \(-128 \cdot \binom{11}{4}\) 4. □ \(42,240\) 5. □ \(-\binom{11}{7} \cdot 128\) #### Explanation of Binomial Coefficient Symbols: - \(\binom{n}{k}\) denotes the binomial coefficient, also known as "n choose k," which represents the number of ways to choose \(k\) elements from a set of \(n\) elements without regard to order. #### Options Explained: - **Option 1:** \(-128\) - **Option 2:** \(128 \cdot \binom{11}{4}\) - **Option 3:** \(-128 \cdot \binom{11}{4}\) - **Option 4:** \(42,240\) - **Option 5:** \(-\binom{11}{7} \cdot 128\) To determine which options are correct, one would typically expand the binomial expression \( (2x - 1)^{11} \) and identify the coefficient of the term containing \( x^7 \).
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