Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

Match List-I with List-II

List-I

List-II

(A) The maximum value of $f(x)=\sin(3x) + 6$

(I) 2

(B) The maximum value of $f(x) = -|x+2|+4$

(II) 5

(C) The minimum value of $f(x) = (3x+1)^2+5$

(III) 7

(D) The minimum value of $f(x) = 2\cos x+4$

(IV) 4

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (2) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

List-I

List-II

(A) The maximum value of $f(x)=\sin(3x) + 6$

(III) 7

(B) The maximum value of $f(x) = -|x+2|+4$

(IV) 4

(C) The minimum value of $f(x) = (3x+1)^2+5$

(II) 5

(D) The minimum value of $f(x) = 2\cos x+4$

(I) 2

Matching List-I with List-II:

(A) The maximum value of \( f(x) = \sin(3x) + 6 \)

The maximum value of \( \sin(3x) \) is 1, so maximum value of \( f(x) = 1 + 6 = \mathbf{7} \)
⇒ (A) → (III)

(B) The maximum value of \( f(x) = -|x + 2| + 4 \)

The minimum value of \( |x + 2| \) is 0 (when \( x = -2 \)), so maximum of \( f(x) = -0 + 4 = \mathbf{4} \)
⇒ (B) → (IV)

(C) The minimum value of \( f(x) = (3x + 1)^2 + 5 \)

The minimum value of a square is 0, so minimum of \( f(x) = 0 + 5 = \mathbf{5} \)
⇒ (C) → (II)

(D) The minimum value of \( f(x) = 2\cos x + 4 \)

Minimum of \( \cos x \) is -1, so minimum of \( f(x) = 2(-1) + 4 = \mathbf{2} \)
⇒ (D) → (I)