CUET · MATHS · PYQ PAPER 2023
Match List-I with List-II
| LIST-I (Function \(f(x)\)) | LIST-II (Interval) |
| (A) \(f(x)=x|x|\) | (I) Decreases on (0, \(\infty\) ) |
| (B) \(f(x)=x^2+2 x-5\) | (II) Increases on ( \(3, \infty\) ) |
| (C) \(f(x)=x^2-6 x+9\) | (III) Decreases on \((-\infty,-1)\) |
| (D) \(f(x)=-x^2\) | (iv) Increases on \((-\infty, \infty)\) |
- A \((A)-(I I),(B)-(I I I),(C)-(I V),(D)-(I)\)
- B \((A)-(I V),(B)-(I I I),(C)-(I I),(D)-(I)\)
- C \((A)-(I I),(B)-(I V),(C)-(I I I),(D)-(I)\)
- D \((A)-(I I),(B)-(I I I),(C)-(I V),(D)-(I V)\)
Answer & Solution
Correct Answer
(B) \((A)-(I V),(B)-(I I I),(C)-(I I),(D)-(I)\)
Step-by-step Solution
Detailed explanation
(A) \(f(x)=x|x|\) \(f'(x) = \begin{cases} 2x & x \ge 0 \\ -2x & x \(f'(x) > 0\) for all \(x \neq 0\). Increases on \((-\infty, \infty)\). Match: (IV) (B) \(f(x)=x^2+2 x-5\) \(f'(x) = 2x+2\) \(f'(x) Decreases on \((-\infty, -1)\). Match: (III) (C) \(f(x)=x^2-6 x+9\)…
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