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JEE Advanced 2020 Concept Recapitulation Test 4 Paper 2

Answer the following by appropriately matching the list based on the information given in the paragraph.

Consider the following functions:

f(x)=\frac{32}{4+x^{2}+x^{4}}

g(x)=9+x^{2}

List-l: Contains new functions defined with the help of given functions
List-Il: Contains some information about them

List - I	List - II
(I) $p(x)=f(x)-g(x)$	(P) Is an odd function
(II) $q(x)=(f(x)+g(x)) x$	(Q) Is an even function
(III) $r(x)=f(x) ⋅ g(x)$	(R) Function never intersect $X$ -axis
(IV) $s(x)=\;{f(x)}/{g(x)}$	(S) Range is a subset of $(0, ∞)$
	(T) Range is a subset of $(-∞, 0)$
	(U) Function intersect $X$ -axis exactly once

Question : 47 of 54

Marks: +1, -0

Which of the following is the only correct combination?

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