CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer function, is continuous at \(x=\)
(A) 2.9
(B) 5
(C) -3
(D) 6.5
Choose the correct answer from the options given below:
- A (A), (B) and (C) only
- B (B), (C) and (D) only
- C (A) and (D) only
- D (C) and (D) only
Answer & Solution
Correct Answer
(C) (A) and (D) only
Step-by-step Solution
Detailed explanation
\(f(x) = [x]\) is continuous for \(x \notin \mathbb{Z}\). Checking options for continuity: (A) \(x=2.9\): Not an integer. Continuous. (B) \(x=5\): Integer. Discontinuous. (C) \(x=-3\): Integer. Discontinuous. (D) \(x=6.5\): Not an integer. Continuous. The function is continuous…
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