A rational function $\dfrac{P(x)}{Q(x)}$ is called proper when
Adegree of $P(x)$ is less than degree of $Q(x)$
Bdegree of $P(x)$ equals degree of $Q(x)$
Cdegree of $P(x)$ is greater than degree of $Q(x)$
D$Q(x)$ is a constant polynomial
Answer & Solution
Correct answer: A. degree of $P(x)$ is less than degree of $Q(x)$
1. By definition a proper rational function has numerator degree below denominator degree.
2. If not, it is improper and is first reduced by long division.
3. Hence option A is correct.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.315_
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