Match the LIST-I with LIST-II, LIST-I, LIST-II, A., y = x^2, I., decreasing on (0, ∞), B., y = -x^2, II., increasing on (0, ∞), C., y = x, III., decreasing on (-∞, ∞), D., y = -x, IV., increasing on (-∞, ∞), Choose the correct answer from the options given below: Option 1: A-IV, B-I, C-II, D-III Option 2: A-III, B-IV, C-I, D-II Option 3: A-II, B-III, C-IV, D-I Option 4: A-II, B-I, C-IV, D-III

Answer: A-II, B-I, C-IV, D-III. Solution: For y=x^2, y'=2x>0 on (0,∞) (II). For y=-x^2, y'=-2x 0 everywhere (IV). For y=-x, y'=-1<0 everywhere (III).

Calculus

Application of Derivatives

Easy

applied

Match the LIST-I with LIST-II

LIST-I LIST-II
A. $y = x^2$ I. decreasing on $(0, \infty)$
B. $y = -x^2$ II. increasing on $(0, \infty)$
C. $y = x$ III. decreasing on $(-\infty, \infty)$
D. $y = -x$ IV. increasing on $(-\infty, \infty)$

Choose the correct answer from the options given below:

	LIST-I		LIST-II
A.	$y = x^2$	I.	decreasing on $(0, \infty)$
B.	$y = -x^2$	II.	increasing on $(0, \infty)$
C.	$y = x$	III.	decreasing on $(-\infty, \infty)$
D.	$y = -x$	IV.	increasing on $(-\infty, \infty)$

A-IV, B-I, C-II, D-III

A-III, B-IV, C-I, D-II

A-II, B-III, C-IV, D-I

A-II, B-I, C-IV, D-III

✅ Correct Option: 4

For $y=x^2$ , $y'=2x>0$ on $(0,\infty)$ (II). For $y=-x^2$ , $y'=-2x<0$ there (I). For $y=x$ , $y'=1>0$ everywhere (IV). For $y=-x$ , $y'=-1<0$ everywhere (III).

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