Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

Match List-I with List-II

List-I Function

List-II Increasing on the interval

(A) $f(x)=-x^2-2x+1$

(I) $(-∞,-1)$

(B) $f(x) = x^2+1$

(II) $(1,∞)$

(C) $f(x) = x^2-2x+3$

(III) $(-∞,0)$

(D) $f(x) = -x^2$

(IV) $(0,∞)$

Choose the correct answer from the options given below.

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (1) → (A)-(I), (B)-(IV), (C)-(II), (D)-(III) **

List-I Function

List-II Increasing on the interval

(A) $f(x)=-x^2-2x+1$

(I) $(-∞,-1)$

(B) $f(x) = x^2+1$

(IV) $(0,∞)$

(C) $f(x) = x^2-2x+3$

(II) $(1,∞)$

(D) $f(x) = -x^2$

(III) $(-∞,0)$

(A) $f(x)=-x^2-2x+1$

$f'(x)= -2x - 2$

Increasing when $-2x-2>0 \Rightarrow x<-1$

Matches (I)

(B) $f(x)=x^2+1$

$f'(x)=2x$

Increasing when $x>0$

Matches (IV)

(C) $f(x)=x^2-2x+3$

$f'(x)=2x-2$

Increasing when $x>1$

Matches (II)

(D) $f(x)=-x^2$

$f'(x)=-2x$

Increasing when $x<0$

Matches (III)