Let f ( x ) = x 2 + 7 x + 14 x 2 + 4 x + 3 and g ( x ) = x 2 + 5 x + 20 x 2 − 5 x + 10 , then List - I List - II (I) Greatest value of f ( x ) g ( x ) is 5 (P) 3 (II) Greatest value of ( g ( x ) )

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Let f ( x ) = x 2 + 7 x + 14 x 2 + 4 x + 3 ​ and g ( x ) = x 2 + 5 x + 20 x 2 − 5 x + 10 ​ , then List - I List - II (I) Greatest value of f ( x ) g ( x ) is 5 (P) 3 (II) Greatest value of ( g ( x ) ) f ( x ) is 9 (Q) 4 (III) No. of points of discontinuity for y = [ f ( x )] where [ ] = GIF (R) 5 (IV) No. of points of discontinuity of y = [ g ( x )] where [ ] = GIF (S) 6 (T) 9

TestHub · Accepted Answer

f ( x ) = x 2 + 7 x + 14 x 2 + 4 x + 3 ​ f ′ ( x ) = x 2 + 7 x + 4 ( 3 x + 7 ) ( x + 5 ) ​ − 5 − 7/3 f ( x ) max ​ = 2 at x = − 5 f ( x ) min ​ = 7 − 2 ​ at x = 3 − 7 ​ Graph of y = f ( x ) g ( x ) = x 2 + 5 x + 20 x 2 − 5 x + 10 ​ ( x 2 + 5 x + 20 ) 2 10 ( x + 5 ) ( x − 3 ) ​ g ( x ) max. ​ = 3 at x = − 5 g ( x ) min ​ = 11 1 ​ at x = 3 Graph of y = g ( x )

List - I	List - II
(I) Greatest value of $f (x) g (x)$ is 5	(P) 3
(II) Greatest value of $(g (x))^{f (x)}$ is 9	(Q) 4
(III) No. of points of discontinuity for $y = [f (x)]$ where [ ] = GIF	(R) 5
(IV) No. of points of discontinuity of $y = [g (x)]$ where [ ] = GIF	(S) 6
	(T) 9

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JEE Advanced (2028)