Here are 10 JEE maths questions in JEE Main style, each with the answer and full working. They mix algebra, circles, vectors, calculus and probability. Each answer names the trap in the wrong options and its mistake type. We wrote these JEE-style questions. They are not real past questions.
10 questions · 25 minutes
10 JEE maths questions: what this set covers
JEE Main maths has 25 questions: 20 in Section A with four options, and 5 in Section B where you type a whole number. Here, questions 1 to 8 have options and questions 9 and 10 need a number.
Algebra and geometry
|x| equations, a determinant, a sequence, a circle and a vector.
Calculus and counting
An integral, a limit, a bag of balls, a largest value and a binomial term.
NTA’s full maths topic list is on jeemain.nta.nic.in.
How to use these questions
Set a 25-minute timer. The target times on the questions add up to 25 minutes.
Use rough paper only. NTA does not allow calculators.
Leave a question blank if you cannot rule out any option.
Mark with +4, −1 and 0, and note the mistake type of each wrong answer.
The JEE Main marking scheme page explains the rules. The mistake types come from the Free BMI Maths Test. Questions you did not reach are ROT, ran out of time.
JEE-style maths questions 1 to 5
Question 1
How many real numbers x satisfy x² − 5|x| + 6 = 0?
- 2
- 3
- 4
- 6
Show answer to question 1
Answer: C, 4.
Working: x² = |x|², so let t = |x|. Then (t − 2)(t − 3) = 0, so |x| = 2 or 3. Each gives two values: x = ±2, ±3.
Trap A: counting only t = 2 and t = 3. BMI type: CNC, concept not clear. Trap B: picking 3, a root, when the question asks how many. BMI type: DRC, did not read carefully.
Question 2
The matrix with rows (1, 2, 3), (2, k, 1) and (3, 1, 2) has determinant 0. What is k?
- 3/7
- −3/7
- 7/3
- 1
Show answer to question 2
Answer: A, 3/7.
Working: Expand along row 1 with signs +, −, +: 1(2k − 1) − 2(4 − 3) + 3(2 − 3k) = 3 − 7k. So 3 − 7k = 0 and k = 3/7.
Trap D: a + sign on the middle term gives 7 − 7k = 0, so k = 1. BMI type: CMT, calculation mistake.
Question 3
In an arithmetic sequence, the 3rd term is 11 and the 8th term is 31. What is the sum of the first 20 terms?
- 800
- 820
- 860
- 1640
Show answer to question 3
Answer: B, 820.
Working: The 3rd to the 8th term is 5 steps, so 5d = 20 and d = 4. Then a = 11 − 8 = 3. Sum = (n/2)(2a + (n − 1)d) = 10 × (6 + 76) = 820.
Trap C: nd in place of (n − 1)d gives 860. BMI type: CNC. Trap D: not halving n gives 1640. BMI type: CMT.
Question 4
The line 3x + 4y = k touches the circle x² + y² − 6x + 8y − 11 = 0, and k is positive. What is k?
- 23
- 30
- 37
- 43
Show answer to question 4
Answer: A, 23.
Working: The centre is (3, −4), the opposite signs of −6/2 and 8/2. The radius is √(9 + 16 + 11) = 6. A tangent is 6 from the centre: |9 − 16 − k| ÷ 5 = 6. So |−7 − k| = 30, and k = 23 or −37. Positive: 23.
Trap C: a centre of (−3, 4) gives k = 37. BMI type: CNC.
Question 5
a = i + 2j − k and b = 2i − j + 2k. What is the projection of a on b?
- 2/3
- −2/3
- −2/√6
- −2/9
Show answer to question 5
Answer: B, −2/3.
Working: a · b = 2 − 2 − 2 = −2 and |b| = √9 = 3. Projection of a on b = (a · b) ÷ |b| = −2/3. A minus sign is fine: the angle is over 90°.
Trap C: dividing by |a| = √6 gives the projection of b on a. BMI type: DRC. Trap D: dividing by |b|² = 9. BMI type: CNC.
Free BMI Maths Test
Lost marks on the first five? Find the mistake type.
A sign slip and a gap in an idea need different fixes. The Free BMI Maths Test finds your child’s real maths level and sorts each mistake into one of 6 types.
JEE-style maths questions 6 to 10
Question 6
What is the value of ∫ x(1 − x)⁹ dx from x = 0 to x = 1?
- 1/90
- 1/110
- 1/11
- 1/10
Show answer to question 6
Answer: B, 1/110.
Working: Do not expand. Put t = 1 − x. The sign of dx = −dt swaps the limits back. You get ∫ (t⁹ − t¹⁰) dt from 0 to 1 = 1/10 − 1/11.
Trap A: dividing by the old powers: 1/9 − 1/10 = 1/90. BMI type: CMT. Trap D: dropping the x in front gives 1/10. BMI type: CWV, copied a wrong value.
Question 7
What is the limit of (sin 3x)/x as x tends to 0?
- 0
- 1
- 1/3
- 3
Show answer to question 7
Answer: D, 3.
Working: (sin u)/u tends to 1 only when the angle and the bottom match. So write 3 × (sin 3x)/(3x), which tends to 3 × 1 = 3.
Trap B or C: using the rule without matching 3x, or putting the 3 below. BMI type: CNC.
Question 8
A bag has 4 red balls and 6 blue balls. Two balls are taken out, one after the other, and the first is not put back. What is the chance that the second ball is red?
- 1/3
- 4/15
- 2/5
- 2/15
Show answer to question 8
Answer: C, 2/5.
Working: Add both paths. Red then red: (4/10)(3/9) = 12/90. Blue then red: (6/10)(4/9) = 24/90. Total 36/90 = 2/5. Fast check: nobody saw the first ball, so the chance stays 4 in 10.
Traps: A assumes the first ball was red. B counts only blue then red. D is the chance that both are red. BMI type: CNC.
Question 9
f(x) = 2x³ − 9x² + 12x + 5. Find the largest value of f(x) for x from 0 to 3, end points included.
Show answer to question 9
Answer: 14. Type 14 on the number pad.
Working: f′(x) = 6(x − 1)(x − 2). Test x = 1, x = 2 and both ends: f(0) = 5, f(1) = 10, f(2) = 9, f(3) = 14.
Trap: typing 10, the local maximum, and skipping the ends. BMI type: CNC.
Question 10
Find the term that does not contain x in the expansion of (x² + 2/x)⁶.
Show answer to question 10
Answer: 240. Type 240.
Working: The general term is ⁶Cᵣ 2ʳ x¹²⁻³ʳ. No x means r = 4, so the term is 15 × 16 = 240.
Trap: copying 2/x as 1/x gives 15. BMI type: CWV. Typing r = 4 as the answer is DRC.
Score yourself out of 40
Marks = 4 × right − 1 × wrong. So 8 right and 2 wrong is 30.
| Your marks | What it means | What to do next |
|---|---|---|
| 30 to 40 in 25 minutes | The main units are in good shape. | Practise full 25-question sets on a timer. |
| 20 to 29, or over time | A weak unit, or slow pace. | Fix the mistake type that comes up twice. |
| 19 or less | The cause matters more than the score. | Book the Free BMI Maths Test to find the cause. |
Count wrong answers too. Six right and four wrong is 20. Five right, one wrong and four blank is 19.
19 or less? Book the Free BMI Maths Test to find the cause.
Which traps caught you?
The Free BMI Maths Test shows your child’s real maths level and the reason for each wrong answer.
Questions people ask about JEE maths questions
Are these real JEE Main questions?
No. We wrote all 10 in JEE Main style, with the real format and marking. None comes from a past paper.
How long should 10 JEE maths questions take?
About 25 minutes. The full paper gives 180 minutes for 75 questions: 2.4 minutes each, or 24 minutes for 10.
Where can I find official past papers?
The 2027 bulletin does not mention a public set of past papers. It says NTA shows each candidate their own question paper and recorded answers on jeemain.nta.nic.in before the result, for two to three days. Download your response sheet then. NTA will not give it later.
How is a number-answer question marked?
Like an option question: +4, −1 or 0. Round your answer to the nearest whole number.
Sources
Facts checked on 11 November 2026. Every answer and wrong option was checked in Python.
- NTA, JEE (Main) 2027 Information Bulletin: paper pattern, marking, section 11.2, sample test, calculators.
- NTA, jeemain.nta.nic.in: maths topic list and public notices.
