JEE Main free practice questions with answers
Read question 1 and its full worked answer from paper 1 of our 20-paper JEE Main set, then download the 4-page PDF. These are original practice questions, not official past papers. Page updated 3 November 2026.
The number of relations on a set containing 4 elements that are both reflexive and symmetric is
A 16
B 64
C 4096
D 65536
Correct answer: B — 64
- A relation on a set A is a subset of A × A, which has 4 × 4 = 16 ordered pairs.
- Reflexive forces the diagonal pairs in. The n(n−1)/2 off-diagonal pairs of pairs are free, each in or out:
2^(n(n−1)/2).
- For n = 4 the exponent is 6, so the number is 2^6 = 64.
- Why the other options are wrong:
- A (16): Only the diagonal choices were counted.
- C (4096): Forgot that a symmetric pair is chosen together.
- D (65536): That counts all relations without the condition.
Count a relation by deciding in or out for each ordered pair, then apply the condition to reduce the free pairs.
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What is in the JEE Main free sample?
The first 3 questions from paper 1 of the set, in the real exam layout, followed by the step-by-step worked answers. It is a 4-page PDF; this page shows question 1 with its answer.
How many full JEE Main papers are there?
20 original papers for students in India preparing for JEE Main (B.E./B.Tech., Paper 1). Each is 75 questions in 180 minutes (Mathematics, Physics and Chemistry, 25 each): 20 multiple-choice (A to D) and 5 integer-answer questions per subject, +4 for a correct answer and −1 for a wrong one, no calculator, with a worked solution for every question. Papers start at A$11.99 and download instantly as a PDF.
Are these official past papers?
No. The sample is taken from our own original practice paper and is not an official past paper or affiliated with any exam authority.