Teachoo MCQ Test

10 Question MCQ (including Assertion)

Chapter 7 Class 11 Binomial Theorem | 5 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 480
Question 1 of 5
Question 1 of 5
Assertion (A): For distinct integers \(a\) and \(b\), \((a-b)\) is a factor of \(a^n - b^n\) for every positive integer \(n\).
Reason (R): \(a^n\) can be written as \(((a-b) + b)^n\), and upon expansion using the Binomial Theorem, every term except the last one contains \((a-b)\) as a factor.
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Question 2 of 5
Assertion: \[ 98^5<100^5. \]
Reason: In the binomial expansion of \((100-2)^5\), every term after \(100^5\) is negative.
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Question 3 of 5
The simplified form of \((a+b)^4-(a-b)^4\) is
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Question 4 of 5
The coefficient of \(x^3y^2\) in \((2x-3y)^5\) is
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Question 5 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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