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Vector Algebra JEE Mains Previous Year Questions with Solutions, and Weightage

Sahaj Anand's profile photo

Sahaj Anand

Content Writer | Journalism Graduate | Updated 3+ months ago

Vector Algebra is an important and high-weightage topic that is asked both in the JEE Main and JEE Advanced Exam. The topics carry an approximate weightage of 5-7% and candidates can expect 2 to 3 questions from this section in the exam.

The vector algebra focuses on vector representation, their application in geometry and physics, and operations on vectors (addition and product).

The most asked topics in Vector Algebra are Dot product, Cross Product, Scalar Triple product, and vector equations of Lines and Planes.

Must Read Articles:

JEE Main Previous Year Question Vector Algebra

Below is the list of Vector Algebra questions with detailed solutions asked in JEE Main.

Question 1:

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Question 2:

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Question 3:

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Question 4:

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Question 5:

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Question 6:

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Question 7:

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Question 8:

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Question 9:

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Question 10:

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JEE Main Mathematics Paper Pattern

The NTA has updated the JEE Main Mathematics Exam Pattern for 2025. Earlier, section B allowed candidates to attempt only 5 out of 10 NVQs, but now all 5 are compulsory.

The detailed exam pattern for JEE Main Mathematics is given below:

Aspect Details
Mode of Exam Online Computer-Based Test (CBT)
Language of Exam English, Hindi, Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu
Types of Questions Section A: Multiple Choice Questions (MCQs)Section B: Numerical Value-Based Questions (NVQs)
Total Number of Questions 25 QuestionsSection A: 20 MCQsSection B: 5 NVQs (All mandatory)
Marking Scheme Correct Answer: +4 marksIncorrect Answer: -1 mark (applies to both MCQs and NVQs)Unanswered/Marked for Review: No marks deducted
Total Marks 100 Marks

JEE Main Mathematics Chapter-Wise Weightage

Calculus and algebra are the most important sections in the JEE Main Mathematics. These topics carry approximately 35 to 40% weightage in the exam.

The detailed chapter-wise weightage for mathematics is given in the table below for classes 11th and 12th.

Class 11 Mathematics High-weightage Topics:

Chapter Approximate Weightage
Sets, Relations & Functions 3.3%
Complex Numbers & Quadratic Equations 3.3%
Permutations & Combinations 3.3%
Binomial Theorem 3.3%
Sequences & Series 6.6%
Straight Lines 6.6%
Conic Sections (Parabola, Ellipse, Hyperbola) 9.9%
Trigonometric Equations 3.3%

Mathematics Chapter-wise Weightage for Class 12 Topics:

Chapter Approximate Weightage
Matrices & Determinants 6.6%
Limits, Continuity & Differentiability 3.3%
Integral Calculus (Definite & Indefinite Integrals) 6.6%
Differential Equations 3.3%
Vector Algebra 3.3%
Three-Dimensional Geometry 6.6%
Probability & Statistics 6.6%

JEE Main Last 5 Year Mathematics Papers Pdf

You can download the JEE Main last 5 years’ Mathematics pdf with solutions from the table given below:

JEE Main 2024 Mathematics Question Paper Session 1

Exam Date Question Paper Solution PDF
JEE Main 2024 Feb 1 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Feb 1 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 31 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 31 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 30 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 30 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 29 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 29 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 27 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 Jan 27 Shift 1 Mathematics Question Paper Download Check Solution

JEE Main 2024 Mathematics Question Paper Session 2

Exam Date and Shift Question Paper Solution PDF
JEE Main 2024 April 4 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 4 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 5 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 5 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 6 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 6 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 8 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 8 Shift 2 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 9 Shift 1 Mathematics Question Paper Download Check Solution
JEE Main 2024 April 9 Shift 2 Mathematics Question Paper Download Check Solution

JEE Main 2023 Mathematics Question Paper

Exam Date Mathematics Question Paper PDF
Mathematics 6 April Shift 1 Question Paper Check Here
Mathematics 6 April Shift 2 Question Paper Check Here
Mathematics 8 April Shift 1 Question Paper Check Here
Mathematics 8 April Shift 2 Question Paper Check Here
Mathematics 10 April Shift 1 Question Paper Check Here
Mathematics 10 April Shift 2 Question Paper Check Here
Mathematics 11 April Shift 1 Question Paper Check Here
Mathematics 11 April Shift 2 Question Paper Check Here
Mathematics 12 April Shift 1 Question Paper Check Here
Mathematics 13 April Shift 1 Question Paper Check Here
Mathematics 13 April Shift 2 Question Paper Check Here
Mathematics 15 April Shift 1 Question Paper Check Here

JEE Main 2023 Mathematics Question Paper Session 1

Exam Date and Shift Mathematics Question Paper PDF
Mathematics 24 January Shift 1 Question Paper Check Here
Mathematics 24 January Shift 2 Question Paper Check Here
Mathematics 25 January Shift 1 Question Paper Check Here
Mathematics 25 January Shift 2 Question Paper Check Here
Mathematics 29 January Shift 1 Question Paper Check Here
Mathematics 29 January Shift 2 Question Paper Check Here
Mathematics 30 January Shift 1 Question Paper Check Here
Mathematics 30 January Shift 2 Question Paper Check Here
Mathematics 31 January Shift 1 Question Paper Check Here
Mathematics 31 January Shift 2 Question Paper Check Here
Mathematics 1 February Shift 1 Question Paper Check Here
Mathematics 1 February Shift 2 Question Paper Check Here

JEE Main 2022 Mathematics Question Paper with Solution PDF

Exam Date Shift/ Slot Question Paper PDF
July 25 Shift 1 Check Here
July 25 Shift 2 Check Here
July 26 Shift 1 Check Here
July 26 Shift 2 Check Here
July 27 Shift 1 Check Here
July 27 Shift 2 Check Here
July 28 Shift 1 Check Here
July 28 Shift 2 Check Here
July 29 Shift 1 Check Here
July 29 Shift 2 Check Here

JEE Main 2022 Mathematics Question Paper with Solution PDF- Phase 1

Exam Date Shift/ Slot Question Paper PDF
June 29 Shift 1 Check Here
June 29 Shift 2 Check Here
June 28 Shift 1 Check Here
June 28 Shift 2 Check Here
June 27 Shift 1 Check Here
June 27 Shift 2 Check Here
June 26 Shift 1 Check Here
June 26 Shift 2 Check Here
June 25 Shift 1 Check Here
June 25 Shift 2 Check Here
June 24 Shift 1 Check Here
June 24 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper- Download PDF

JEE Main 2021 Mathematics Question Paper with Solution (Session 4- August)- Download PDF

Exam Date Shift/ Slot Question Paper PDF
August 26 Shift 1 Check Here
August 26 Shift 2 Check Here
August 27 Shift 1 Check Here
August 27 Shift 2 Check Here
August 31 Shift 1 Check Here
August 31 Shift 2 Check Here
September 1 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session3- July)- Download PDF

Exam Date Shift/ Slot JEE Main Question Paper PDF
July 22 Shift 2 Check Here
July 25 Shift 1 Check Here
July 25 Shift 2 Check Here
July 27 Shift 1 Check Here
August 3 Shift 1 Check Here
August 3 Shift 2 Check Here
August 4 Shift 1 Check Here
August 4 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session 2- March)- Download PDF

Exam Date Shift/ Slot Question Paper PDF
March 16 Shift 1 Check Here
March 16 Shift 2 Check Here
March 17 Shift 1 Check Here
March 17 Shift 2 Check Here
March 18 Shift 1 Check Here
March 18 Shift 2 Check Here

JEE Main 2021 Mathematics Question Paper with Solution (Session 1- February)- Download PDF

Exam Date Shift/ Slot Question Paper PDF
February 24 Shift 1 Check Here
February 24 Shift 2 Check Here
February 25 Shift 1 Check Here
February 25 Shift 2 Check Here
February 26 Shift 1 Check Here
February 26 Shift 2 Check Here

JEE Main 2020 Mathematics Question Paper with Solutions- Download PDF

JEE Main 2020 Mathematics Question Paper with Solutions (Session 2- September)- Download PDF

Exam Date Shift/ Slot Question Paper PDF
September 2 Shift 1 Check Here
September 2 Shift 2 Check Here
September 3 Shift 1 Check Here
September 3 Shift 2 Check Here
September 4 Shift 1 Check Here
September 4 Shift 2 Check Here
September 5 Shift 1 Check Here
September 5 Shift 2 Check Here
September 6 Shift 1 Check Here
September 6 Shift 2 Check Here

JEE Main 2020 Mathematics Question Paper with Solutions (Session 1- January)- Download PDF

Exam Date Shift/ Slot JEE Main Question Paper PDF
January 8 Shift 1 Check Here
January 8 Shift 2 Check Here
January 9 Shift 1 Check Here
January 9 Shift 2 Check Here

Important Books for Mathematics:

Frequently Asked Questions

What are the advantages of vector algebra?

Vector algebra is a useful concept of mathematics that helps represent quantities that have both magnitude and direction. Vectors have many advantages as they help simplify complex problems , they are used in computer graphics and animation, vectors are also useful in application and navigation system.

2. Who is the father of vector algebra?

Josiah Willard Gibbs is considered as the father of vector algebra. He discovered the concept of vectors in the late 19th century. He is credited for the development of vector analysis, and concepts such as dot product, cross product, and vector differentiation.

His work was based on advanced mathematics and physics, mainly in thermodynamics and electromagnetism.

3. What is the main purpose of vector algebra?

The main purpose of the vector is to represent and analyze quantities that have both magnitude and direction. It is mainly used to solve problems related to motion, force, and displacements. The main purpose is to simplify the calculation related to 3D geometry, physics, and engineering.

4. What is vector algebra based on?

Vector algebra is based on the mathematical study of quantities that have both magnitude and direction. The main foundation of vector is mainly based on:

  1. Geometric Interpretation in a coordinate plane or 3D space.
  2. Algebraic operations for vector addition, subtraction, and scalar multiplication.
  3. Coordinate system representation in unit vectors in 2D or 3D space for precise calculation.
  4. Dot and cross-product operations for calculating angles, projections, and determining perpendicularity.

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JEE Main Questions

  • 1.

    Given below are two statements I and II. 
    Statement I: Dumas method is used for estimation of "Nitrogen" in an organic compound. 
    Statement II: Dumas method involves the formation of ammonium sulfate by heating the organic compound with concentrated H\(_2\)SO\(_4\). In the light of the above statements, choose the correct answer from the options given below:

      • Both Statement I and Statement II are true
      • Statement I is false but Statement II is true
      • Both Statement I and Statement II are false
      • Statement I is true but Statement II is false
      View Solution

    • 2.
      Let \( f: \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 \). If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of \( 28 \sum_{i=1}^5 f(i) \) is:

        • 715
        • 675
        • 545
        • 735
        View Solution

      • 3.

          View Solution

        • 4.

          A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity): 

            • \( \sqrt{\frac{3Rg + kR^2}{m}} \)
            • \( \sqrt{\frac{2Rg + kR^2}{m}} \)
            • \( \sqrt{\frac{2gR + kR^2}{m}} \)
            • \( \sqrt{\frac{2Rg + 4kR^2}{m}} \)
            View Solution

          • 5.
            An infinite wire has a circular bend of radius \( a \), and carrying a current \( I \) as shown in the figure. The magnitude of the magnetic field at the origin \( O \) of the arc is given by:
            An infinite wire has a circular bend of radius

              • \( \frac{\mu_0 I}{4 \pi a} \left( \frac{3\pi}{2} + 2 \right) \)
              • \( \frac{\mu_0 I}{2 \pi a} \left( \frac{\pi}{2} + 2 \right) \)
              • \( \frac{\mu_0 I}{4 \pi a} \left( \frac{3\pi}{2} \right) \)
              • \( \frac{\mu_0 I}{2 \pi a} \left( \frac{3\pi}{2} + 1 \right) \)
              View Solution

            • 6.

              Choose the correct set of reagents for the following conversion:

                • \( \text{Cl}_2/\text{Fe}; \text{Br}_2/\text{anhy.} \text{AlCl}_3; \text{aq. KOH} \)
                • \( \text{Br}_2/\text{Fe}; \text{Cl}_2, \Delta; \text{alc. KOH} \)
                • \( \text{Cl}_2/\text{anhy.} \text{AlCl}_3; \text{Br}_2/\text{Fe}; \text{alc. KOH} \)
                • \( \text{Br}_2/\text{anhy.} \text{AlCl}_3; \text{Cl}_2, \Delta; \text{aq. KOH} \)
                View Solution
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