Cracking JEE maths comes down to one thing: solving a large number of varied problems until the methods become second nature. The trouble with past papers alone is that you run out of them, and you start remembering answers instead of working them out. Maths Daily Helper generates unlimited fresh JEE-style questions across every topic in the syllabus, so you always have something new to attempt, and every question comes with a complete worked solution so you can check your method, not just your final answer.
What the JEE maths syllabus covers
Your practice here spans the full JEE Main and Advanced maths syllabus:
- Calculus: limits, continuity, differentiation, applications of derivatives, definite and indefinite integration, differential equations, area under curves.
- Coordinate geometry: straight lines, circles, parabola, ellipse, hyperbola.
- Algebra: quadratic equations, sequences and series, binomial theorem, permutations and combinations, complex numbers, matrices and determinants.
- Trigonometry: identities, equations, inverse functions, heights and distances.
- Vectors and 3D geometry.
- Probability and statistics.
JEE Main and Advanced maths exam pattern
The two exams test the same syllabus very differently, so it pays to practise both formats:
| Exam | Format | Marking |
|---|---|---|
| JEE Main | 30 questions, 100 marks, 1 hour. Section A: 20 single-correct MCQs. Section B: 10 numerical value, attempt any 5. | MCQ +4/-1. Numerical +4/no negative marking. |
| JEE Advanced (Paper 1) | 3 sections, 3 hours. 6 single-correct MCQs, 8 multi-correct MCQs, 6 integer-type. | Single-correct +3/-1. Multi-correct +4 with partial marking/-2. Integer-type +3/no negative marking. |
JEE Main rewards speed and accuracy on moderate problems; JEE Advanced rewards deeper, multi-concept reasoning with less time pressure per mark. Practising both formats separately, not just "JEE-level" questions in general, builds the right instincts for each.
Try a few JEE-style problems
Attempt each one on paper first, then reveal the working.
Evaluate the limit: lim (x → 0) (1 − cos x) / x².
1. Use the identity 1 − cos x = 2 sin²(x/2), so the expression becomes 2 sin²(x/2) / x².
2. Rewrite as (1/2) · [ sin(x/2) / (x/2) ]², since x² = 4 · (x/2)².
3. As x → 0, sin(x/2)/(x/2) → 1, so the bracket → 1.
Answer: 1/2.
If z is a complex number satisfying |z − 3| = 2, find the maximum value of |z|.
1. |z − 3| = 2 describes a circle in the Argand plane, centred at 3 (i.e. the point (3, 0)) with radius 2.
2. |z| is the distance from the origin to a point z on that circle.
3. The maximum distance from the origin to a point on the circle is the distance to the centre plus the radius: 3 + 2.
Answer: 5.
Find the equation of the tangent to the parabola y² = 8x at the point (2, 4).
1. For y² = 4ax, here 4a = 8, so a = 2. The tangent at (x₁, y₁) is y·y₁ = 2a(x + x₁).
2. Substitute y₁ = 4, x₁ = 2, 2a = 4: 4y = 4(x + 2).
3. Simplify: y = x + 2, or x − y + 2 = 0.
Answer: x − y + 2 = 0.
Evaluate ∫ x·eˣ dx.
1. Use integration by parts: ∫ u dv = uv − ∫ v du. Let u = x and dv = eˣ dx.
2. Then du = dx and v = eˣ.
3. So ∫ x·eˣ dx = x·eˣ − ∫ eˣ dx = x·eˣ − eˣ + C.
Answer: eˣ(x − 1) + C.
If the roots of x² − px + 12 = 0 differ by 1, find the positive value of p.
1. Let the roots be α and α + 1. Sum = 2α + 1 = p; product = α(α + 1) = 12.
2. Solve α² + α − 12 = 0, which factors as (α + 4)(α − 3) = 0, so α = 3 or α = −4.
3. Taking α = 3 gives p = 2(3) + 1 = 7.
Answer: p = 7.
Two dice are rolled. What is the probability that the sum is 7?
1. Total outcomes when rolling two dice: 6 × 6 = 36.
2. Favourable outcomes summing to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), that is 6 outcomes.
3. Probability = 6/36 = 1/6.
Answer: 1/6.
Solve for x in [0, 2π): 2 sin x = 1.
1. sin x = 1/2.
2. In [0, 2π), sin x = 1/2 at x = π/6 and x = 5π/6 (first and second quadrants).
Answer: x = π/6 or 5π/6.
Find the angle between the vectors a = i + j and b = j + k.
1. Dot product: a·b = (1)(0) + (1)(1) + (0)(1) = 1.
2. Magnitudes: |a| = √2, |b| = √2, so |a||b| = 2.
3. cos θ = (a·b)/(|a||b|) = 1/2, so θ = 60°.
Answer: 60° (π/3).
Common mistakes JEE aspirants make in maths
- Ignoring negative marking when guessing. On JEE Main MCQs (+4/-1), a blind guess has negative expected value across four options; only guess once you've eliminated at least two.
- Forgetting the constant of integration. Indefinite integrals without "+ C" lose marks even when the method and final expression are otherwise correct.
- Not checking the domain in inverse trig and log problems. A numerically correct answer that falls outside the valid domain is wrong; always state the domain before solving.
- Rushing coordinate geometry sign conventions. Mixing up which point is (x₁, y₁) versus (x₂, y₂) in distance, section, or slope formulae is one of the most common silly errors under time pressure.
- Treating JEE Advanced multi-correct questions like single-correct ones. Stopping after finding one valid option costs partial marks; verify every option against the condition before moving on.
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Pick your topic and difficulty. The AI generates a fresh problem every time, with hints and full solutions.
Open Maths Daily Helper →How to use daily practice for JEE
Consistency beats cramming. Fifteen to twenty focused problems a day, spread across topics, keeps every method fresh through the long JEE preparation cycle. Use the hint feature when you are stuck rather than jumping straight to the solution, so you train the habit of finding the next step yourself. Reserve full worked solutions for checking and for the problems that genuinely defeat you. Over weeks, this turns the standard JEE techniques, substitution in integrals, parametric forms of conics, argument and modulus tricks for complex numbers, into reflexes.
Frequently asked questions
How can I practise IIT JEE maths for free?
Maths Daily Helper generates fresh JEE Main and Advanced maths questions across calculus, coordinate geometry, complex numbers and more, each with a full step-by-step solution. You can start for free with no card: 50 questions and 3 full papers a month.
Does it cover both JEE Main and JEE Advanced?
Yes. You can choose the difficulty level, from JEE Main style single-correct questions up to JEE Advanced multi-concept problems, and get worked solutions for every one.
Does it generate full-length JEE Main mock papers?
Yes. You can generate a realistic JEE Main Mathematics section (30 questions, 100 marks, 1 hour, with the real Section A/B split and marking scheme), attempt it under timed conditions, and get it graded automatically.
Does it explain the negative marking?
Every generated question follows the real JEE marking scheme (for example +4/-1 for MCQs in JEE Main), and full solutions show the working so you understand why an answer is correct, not just what it is.
Is it free?
Yes — you can start for free, with no card. The free plan gives you 50 practice questions and 3 full exam papers every month, with every feature unlocked. Paid plans start at ₹420 a month if you want a bigger allowance.
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