Question:
Match List-I with List-II
List-I List-II (A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \) (I) 4 (B) The maximum value of \( f(x) = -|x + 1| + 4 \) (II) 10 (C) The minimum value of \( f(x) = \sin(2x) + 6 \) (III) 3 (D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \) (IV) 5
Choose the correct answer from the options given below:
Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) The minimum value of \( f(x) = (2x - 1)^2 + 3 \) | (I) 4 |
| (B) The maximum value of \( f(x) = -|x + 1| + 4 \) | (II) 10 |
| (C) The minimum value of \( f(x) = \sin(2x) + 6 \) | (III) 3 |
| (D) The maximum value of \( f(x) = -(x - 1)^2 + 10 \) | (IV) 5 |
Choose the correct answer from the options given below:
Show Hint
To find the max/min of simple quadratic and absolute value functions, find the value that makes the squared or absolute part zero. For trigonometric functions, use their known range (e.g., [-1, 1] for sine and cosine).
Updated On: Mar 27, 2026
- (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
- (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
- (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
- (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
We need to find the minimum or maximum value for each function in List-I by analyzing their properties. This involves understanding the range of basic functions like squares, absolute values, and trigonometric functions.
Step 3: Detailed Explanation:
(A) f(x) = $(2x - 1)^2 + 3$: The term $(2x - 1)^2$ is a square, so its minimum value is 0. This occurs when $2x - 1 = 0$.
Therefore, the minimum value of the entire function is $0 + 3 = 3$. This matches with (III).
(B) f(x) = $-|x + 1| + 4$: (Assuming a typo in the OCR, which likely missed the negative sign before the absolute value).
The term $|x + 1|$ is always greater than or equal to 0. Its minimum value is 0.
Therefore, the term $-|x + 1|$ has a maximum value of 0.
The maximum value of the entire function is $0 + 4 = 4$. This matches with (I).
(C) f(x) = sin(2x) + 6: The range of the sine function, sin(2x), is [-1, 1].
The minimum value of sin(2x) is -1.
Therefore, the minimum value of the entire function is $-1 + 6 = 5$. This matches with (IV).
(D) f(x) = $-(x - 1)^2 + 10$: The term $(x - 1)^2$ has a minimum value of 0.
Therefore, the term $-(x - 1)^2$ has a maximum value of 0.
The maximum value of the entire function is $0 + 10 = 10$. This matches with (II).
Step 4: Final Answer:
The correct matching is (A) - (III), (B) - (I), (C) - (IV), (D) - (II). This corresponds to option (3).
We need to find the minimum or maximum value for each function in List-I by analyzing their properties. This involves understanding the range of basic functions like squares, absolute values, and trigonometric functions.
Step 3: Detailed Explanation:
(A) f(x) = $(2x - 1)^2 + 3$: The term $(2x - 1)^2$ is a square, so its minimum value is 0. This occurs when $2x - 1 = 0$.
Therefore, the minimum value of the entire function is $0 + 3 = 3$. This matches with (III).
(B) f(x) = $-|x + 1| + 4$: (Assuming a typo in the OCR, which likely missed the negative sign before the absolute value).
The term $|x + 1|$ is always greater than or equal to 0. Its minimum value is 0.
Therefore, the term $-|x + 1|$ has a maximum value of 0.
The maximum value of the entire function is $0 + 4 = 4$. This matches with (I).
(C) f(x) = sin(2x) + 6: The range of the sine function, sin(2x), is [-1, 1].
The minimum value of sin(2x) is -1.
Therefore, the minimum value of the entire function is $-1 + 6 = 5$. This matches with (IV).
(D) f(x) = $-(x - 1)^2 + 10$: The term $(x - 1)^2$ has a minimum value of 0.
Therefore, the term $-(x - 1)^2$ has a maximum value of 0.
The maximum value of the entire function is $0 + 10 = 10$. This matches with (II).
Step 4: Final Answer:
The correct matching is (A) - (III), (B) - (I), (C) - (IV), (D) - (II). This corresponds to option (3).
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