Logo
Jeeify
MCQMediumJEE 2023Sets & Operations

JEE Mathematics 2023 Question with Solution

Let AA = {x∈R:∣x+3∣+∣x+4∣≤3}\{x \in \mathbb{R} : |x+3| + |x+4| \le 3\}, BB = {x∈R:3⋅∑r=13x−310−r<3−[x]}\{x \in \mathbb{R}: 3 \cdot \sum_{r=1}^{3x-3}10^{-r} < 3^{-[x]}\} where [x][x] denotes the greatest integer function. Then,

  • A

    A⊂B,A≠BA \subset B, A \ne B

  • B

    A∩B=∅A \cap B = \varnothing

  • C

    A=BA = B

  • D

    B⊂A,A≠BB \subset A, A \ne B

Answer

Correct answer:C

Step-by-step solution

the solution unavailable

Given: A={x∈R:∣x+3∣+∣x+4∣≤3}A = \{x \in \mathbb{R} : |x+3| + |x+4| \le 3\} and B={x∈R:3⋅∑r=13x−310−r<3−[x]}B = \{x \in \mathbb{R}: 3 \cdot \sum_{r=1}^{3x-3}10^{-r} < 3^{-[x]}\}.

Find: The correct relation between AA and BB.

The solution does not match this question, so the working could not be extracted from the solution.

From the provided correct answer field, the correct option is C, so the required conclusion is A=BA = B.

Therefore, the correct option is C.

Common mistakes

  • Treating the raw source numbering incorrectly. The source options are numbered (1),(2),(3),(4)(1),(2),(3),(4), which must be mapped to A,B,C,DA,B,C,D respectively. Since the correct answer says (3)  A=B(3)\; A=B, the correct mapped answer is C, not A.

  • Ignoring that [x][x] denotes the greatest integer function. Replacing it with ordinary brackets or assuming it means nearest integer changes the set BB completely. Always interpret [x][x] as the floor function here.

  • Using the mismatched the solution as if it belonged to this question. The provided solution discusses a different domain-based problem, so extracting mathematical steps from it would be wrong. Use only the grounded information available from the question and the correct answer field.

Practice more Sets & Operations questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Sets & Operations

Related questions