CUET · MATHS · PYQ PAPER 2025
Match List-l with List-ll
| List-l | List-ll |
| (A) \(f(x)=x \cdot \sin x\) | (I) is not continuous at \(x=-3\) |
| (B) \(f(x)=\frac{|x|}{x}, x \neq 0\) and \(f(x)=1\) at \(x=0\) | (II) is continuous everywhere |
| (C) \(f(x)=x-[x],[x]\) denotes greatest integer function | (III) is not differentiable at \(x=1\) |
| (D) \(f(x)=e^{|x-1|}\) | (IV) is not continuous at \(x=0\) |
- A (A) (II), (B) - (IV), (C) - (III), (D) - (I)
- B (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
- C (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
- D (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
Answer & Solution
Correct Answer
(C) (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
Step-by-step Solution
Detailed explanation
(A) \(f(x)=x \cdot \sin x\) Product of continuous functions is continuous everywhere. (A) - (II) (B) \(f(x)=\frac{|x|}{x}, x \neq 0; f(x)=1, x=0\) \(\lim_{x \to 0^-} f(x) = \lim_{x \to 0^-} \frac{-x}{x} = -1\) \(\lim_{x \to 0^+} f(x) = \lim_{x \to 0^+} \frac{x}{x} = 1\) LHL…
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