Teachoo Quiz

Assertion Reasoning Quiz

Chapter 7 Class 11 Binomial Theorem | 7 questions | about 6 minutes

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Question 1 of 7
Question 1 of 7
Assertion (A): In the expansion of \((2x+3y)^5\), the sum of the powers of \(x\) and \(y\) in every term is exactly 5.
Reason (R): In the expansion of \((a+b)^n\), the sum of the indices of \(a\) and \(b\) is \(n\) in every term of the expansion.
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Question 2 of 7
Assertion: The sum of all numerical coefficients in the expansion of \((2x+3y)^5\) is \(3125\).
Reason: Substituting \(x=1\) and \(y=1\) gives \[ (2+3)^5=5^5=3125. \]
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Question 3 of 7
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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Question 4 of 7
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 7
Assertion (A): The number of terms in the expansion of \((x+y)^{10}\) is 11.
Reason (R): The total number of terms in the expansion of \((a+b)^n\) is \(n+1\).
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Question 6 of 7
Assertion (A): The value of \((1.01)^{1000000}\) is strictly greater than 10,000.
Reason (R): \((1+x)^n = 1 + nx + \text{other positive terms}\) for any positive real \(x\) and positive integer \(n\).
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Question 7 of 7
Assertion: The coefficient of \(x^4\) in \((2x-1)^6\) is positive.
Reason: The required term contains \((-1)^2\), which is positive.
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