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Short Quiz

Chapter 2 Class 11 Relations and Functions | 5 questions | about 4 minutes

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Question 1 of 5
Question 1 of 5
Assertion (A): The domain of the real-valued function \(f(x) = \sqrt{16 - x^2}\) is \([-4, 4]\).

Reason (R): For a square root function \(\sqrt{g(x)}\) to yield real values, the expression inside the root must be non-negative (\(g(x) \ge 0\)).
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Question 2 of 5
Assertion (A): The rule \[ h(x)=\begin{cases} x^2, & 0\le x\le2,\\ 2x, & 2\le x\le5 \end{cases} \] is not a function because \(x=2\) belongs to both intervals.
Reason (R): At \(x=2\), both formulas give the same value, namely \(4\).
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Question 3 of 5
Assertion (A): If \((x+1,\,y-2)=(3,1)\), then \(x=2\) and \(y=3\).
Reason (R): In general, \(A\times B\neq B\times A\).
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Question 4 of 5
Assertion (A): The domain of the rational function \(f(x) = \frac{1}{x - 2}\) is \(\mathbb{R} - \{2\}\).

Reason (R): A rational function of the form \(\frac{p(x)}{q(x)}\) is defined for all real numbers except those where the denominator \(q(x) = 0\).
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Question 5 of 5
Assertion (A): If a set \(A\) has 3 elements and set \(B\) has 2 elements, the total number of relations from \(A\) to \(B\) is 64.

Reason (R): The total number of relations from a set with \(p\) elements to a set with \(q\) elements is \(2^{pq}\).
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