Sets & RelationseasyPYQ · JEE Main · 2 Apr 2026 · Shift 2 (Afternoon)Free

Relation on A×A with Divisibility and Order: 120 Elements | JEE 2026

JEE Maths question with a full step-by-step solution.

Question
Let A={2,3,4,5,6}A=\{2,3,4,5,6\}. Let RR be a relation on the set A×AA\times A given by (x,y)R(z,w)(x,y)R(z,w) if and only if xx divides zz and y≤wy\le w. Then the number of elements in RR is
Solution
Answer: 120 (± 0.01)
Step 1: Count ordered pairs (x,z)(x,z) with x∣zx\mid z (both in AA):
x=2: z=2,4,6 (3);x=3: z=3,6 (2);x=2:\ z=2,4,6\ (3);\quad x=3:\ z=3,6\ (2);
x=4: z=4 (1);x=5: z=5 (1);x=6: z=6 (1).\quad x=4:\ z=4\ (1);\quad x=5:\ z=5\ (1);\quad x=6:\ z=6\ (1).
 Total =3+2+1+1+1=8=3+2+1+1+1=8. Step 2: Count ordered pairs (y,w)(y,w) with y≤wy\le w (both in AA):
1+2+3+4+5=15.1+2+3+4+5=15.
 Step 3: The two conditions are independent, so
∣R∣=8×15=120.|R|=8\times15=120.
 Correct answer: 120
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