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IIT JEE Maths Practice Test Online

IIT JEE Maths practice test for Mains and Advanced aspirants. Covers calculus, algebra, coordinate geometry, vectors, 3D geometry and probability with step-by-step solutions.

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About this IIT JEE Math practice test

This IIT JEE Maths practice test targets the highest-weightage chapters of JEE Mains and Advanced — Differential and Integral Calculus, Coordinate Geometry, Vectors & 3D, Algebra (Quadratics, Sequences, Binomial), Trigonometry, and Probability. The starter set is deliberately mixed across single-correct MCQs, integer-type and multi-step problems so practice mirrors the real paper. Use it as a 30-minute speed drill before a chapter test, or paste your own previous-year JEE question to generate a fresh mock paper of the same style. Each generated question comes back with a step-by-step solution so a self-studying aspirant can verify the method, not just the final answer.

IIT JEE Maths Practice Test sample questions

These starter questions help you launch a math mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

1. If ∫(x² + 2x + 1)/(x + 1)² dx, evaluate.
2. Find the value of: lim(x→0) (sin 3x)/x.
3. Differentiate: y = e^(x²) sin x.
4. Find the area enclosed between y = x² and y = 4.
5. If a⃗ = i + 2j + k and b⃗ = 2i − j + 3k, find a⃗ × b⃗.
6. Find the equation of the tangent to y = x³ − 3x at x = 1.
7. Find the locus of a point equidistant from (1, 2) and (3, 4).
8. Solve: ∫ dx / (x² + 4).
9. Find the term independent of x in the expansion of (x + 2/x²)⁹.
10. Solve the inequality: |2x − 5| ≤ 3.
11. Find the focus and directrix of y² = 12x.
12. If P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2, find P(A ∪ B).
13. Find dy/dx if x² + y² = 25.
14. Solve: cos2x + cosx = 0 in [0, 2π].
15. Find the shortest distance between the lines (x − 1)/2 = (y − 2)/3 = (z − 3)/4 and (x − 2)/3 = (y − 3)/4 = (z − 4)/5.

Related search topics

calculuscoordinate geometryvectors and 3Dprobabilityalgebra

This page is built for students looking for iit jee maths practice test, chapter practice, and quick school exam revision.

Why this practice page is useful

Use this IIT JEE Maths page to drill the high-weightage topics that decide your Mains percentile and Advanced rank.

The starter set mixes single-correct, multi-correct and integer-type patterns so practice feels close to the real paper.

Replace the starter with previous-year JEE questions to generate a fresh similarly-styled mock with worked answers.

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

  1. ∫(x²+2x+1)/(x+1)² dx: Numerator = (x+1)² → integrand = 1 → ∫1 dx = x + C.
  2. lim(x→0) sin3x/x: = 3 × lim sin3x/(3x) = 3.
  3. d/dx of e^(x²) sinx: e^(x²)(2x sinx + cosx).
  4. Area between y=x² and y=4: 2 ∫₀²(4 − x²)dx = 2(8 − 8/3) = 32/3 sq units.
  5. a⃗×b⃗: Determinant expansion → 7i − j − 5k.
  6. Tangent to y=x³−3x at x=1: Slope = 3(1)² − 3 = 0; point (1,−2) → y = −2.
  7. Equidistant locus: Perpendicular bisector → x + y = 5.
  8. ∫dx/(x²+4): (1/2) tan⁻¹(x/2) + C.
  9. Term independent of x: T(r+1) = C(9,r)·2ʳ·x^(9−3r); set 9−3r=0 → r=3 → C(9,3)·8 = 672.
  10. |2x−5|≤3: 1 ≤ x ≤ 4.
  11. Parabola y²=12x: 4a = 12 → a = 3; focus (3,0); directrix x = −3.
  12. P(A∪B): 0.4 + 0.5 − 0.2 = 0.7.
  13. Implicit dy/dx: 2x + 2y·dy/dx = 0 → dy/dx = −x/y.
  14. cos2x + cosx = 0: Use cos2x = 2cos²x − 1 → (2cosx − 1)(cosx + 1) = 0 → x = π/3, 5π/3, π.
  15. Shortest distance: Use |(a₂−a₁)·(b₁×b₂)|/|b₁×b₂|; substituting gives 1/√6 units.

IIT JEE Math units covered

Typical IIT JEE syllabus units this practice test draws from. Paste questions from any unit below to generate a focused mock test.

  • Sets, Relations and Functions
  • Complex Numbers and Quadratic Equations
  • Matrices and Determinants
  • Permutations and Combinations
  • Binomial Theorem
  • Sequences and Series
  • Limits, Continuity and Differentiability
  • Application of Derivatives
  • Indefinite and Definite Integrals
  • Differential Equations
  • Coordinate Geometry (Straight Lines, Circles, Conics)
  • Three Dimensional Geometry
  • Vector Algebra
  • Statistics and Probability
  • Trigonometry

How to use this iit jee maths practice test page

1. Open the ready-made starter and generate the test.

2. Review the output as a quick IIT JEE math mock test.

3. Replace the starter with your own previous-year exam questions for more accurate revision.

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