Teachoo Quiz

10 Question MCQ (including Assertion)

Chapter 7 Class 11 Binomial Theorem | 5 questions | about 4 minutes

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Question 1 of 5
Question 1 of 5
Assertion (A): The expansion of \((a+b)^4\) requires calculating \({}^4C_0\), \({}^4C_1\), \({}^4C_2\), \({}^4C_3\), and \({}^4C_4\), which map directly to the numbers 1, 4, 6, 4, 1.
Reason (R): The addition of elements in Pascal's triangle row for index \(n\) generates the row for index \(n+1\) using the property \({}^nC_r + {}^nC_{r-1} = {}^{n+1}C_r\).
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Question 2 of 5
Assertion: For every positive integer \(n\), \[ {}^{n}C_0-{}^{n}C_1+{}^{n}C_2-\cdots+(-1)^n{}^{n}C_n=0. \]
Reason: Substituting \(x=-1\) in the expansion of \((1+x)^n\) gives \((1-1)^n=0\).
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Question 3 of 5
Assertion (A): The sum \(\sum_{r=0}^{n} 3^r \cdot {}^nC_r\) is equal to \(4^n\).
Reason (R): The general expression \((1+a)^n\) is equal to \(\sum_{r=0}^{n} {}^nC_r a^r\).
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Question 4 of 5
Assertion (A): The expansion of \((x + \frac{1}{x})^5\) has exactly one term that is independent of \(x\).
Reason (R): A term is independent of \(x\) if the sum of the powers of \(x\) evaluates to zero.
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Question 5 of 5
Assertion (A): The value of \({}^7C_3\) is equal to the value of \({}^7C_4\).
Reason (R): In Pascal's triangle, the elements are symmetric because \({}^nC_r = {}^nC_{n-r}\).
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