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Jee Main 2025 — Medium JEE math MCQ

Let \( X = \mathbb{R} \times \mathbb{R} \). Define a relation \( R \) on \( X \) as: \((a_1, b_1)R(a_2, b_2) \iff b_1 = b_2 \) Statement I : \( R \) is an equivalence relation. Statement II : For some \((a, b) \in X\), the set \( S = \{(x, y) \in X : (x, y)R(a, b)\} \) represents a line parallel to \( y = x \). In the light of the above statements, choose the correct answer from the options given below
  1. A. Both Statement I and Statement II are false
  2. B. Statement I is true but Statement II is false
  3. C. Both Statement I and Statement II are true
  4. D. Statement I is false but Statement II is true

Solution

The correct option is **B**. (B. Statement I is true but Statement II is false)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let X=R×R X = \mathbb{R} \times \mathbb{R} . Define a relation R R on X X as: (a1,b1)R(a2,b2)  ⟺  b1=b2(a_1, b_1)R(a_2, b_2) \iff b_1 = b_2 Statement I : R R is an equivalence relation. Statement II : For some (a,b)∈X(a, b) \in X, the set S={(x,y)∈X:(x,y)R(a,b)} S = \{(x, y) \in X : (x, y)R(a, b)\} represents a line parallel to y=x y = x . In the light of the above statements, choose the correct answer from the options given below
AI hints
Ask for a nudge. Keep it specific.