JEE Main 2025 Maths Important Question - PDF Download
JEE Mains & Advanced
JEE Main 2025 Maths Important Questions PDF Download - Introduction
eSaral provides study materials that are very much essential for you to excel JEE Main 2025 exam. One such form of study material is in the form of Important questions available in PDF format that can be downloaded without any hassle. JEE Main 2025 important questions are available in various formats like Multiple Choice Questions (MCQs). So that students can practice them and gain expertise in all subjects leaving no chance for defeat.
These important questions also include Previous Year’s Question papers and Sample question papers.
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Chapter-wise Important Questions for Maths
Here is a link to download Important Questions for Maths
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JEE Main 2025: Chapter-wise Links To Maths Important Questions PDF |
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Sets, Relations, and Functions Important Questions |
Differential Equations Important Questions |
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Complex Numbers and Quadratic Equations Important Questions |
Coordinate Geometry Important Questions |
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Matrices and Determinants Important Questions |
Three-Dimensional Geometry Important Questions |
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Permutations and Combinations Important Questions |
Vector Algebra Important Questions |
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Mathematical Induction Important Questions |
Statistics and Probability Important Questions |
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Binomial Theorem and Its Simple Applications Important Questions |
Trigonometry Important Questions |
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Sequences and Series Important Questions |
Integral Calculus Important Questions |
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Limit Continuity and Differentiability Important Questions |
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Important Formulas Covered in JEE Main
Trigonometry Formulas: Trigonometry is an essential topic in JEE mains Mathematics and involves a lot of formulas. Some of the critical formulas in Trigonometry are:
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${{\sin ^2}x + {\cos ^2}x = 1}$
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${\tan x = \dfrac{{\sin x}}{{\cos x}}}$
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${\sec x = \dfrac{1}{{\cos x}}}$
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${\cot x = \dfrac{{\cos x}}{{\sin x}}}$
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${\cos ecx = \dfrac{1}{{\sin x}}}$
Aspirants should first understand the concepts behind Trigonometry and then memorize these formulas. Regular practice and solving different types of problems will also help aspirants master Trigonometry.
Download Algebra Formulas as PDF
Algebra is another crucial topic in JEE Mathematics that involves several formulas. Some of the essential Algebra formulas are:
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${{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}}$
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${{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}}$
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${{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)}$
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${{\left( {a + b} \right)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}}$
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${{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}}$
Aspirants should first understand the basic concepts of Algebra and then memorize these formulas. Regular practice and solving different types of problems will also help aspirants master Algebra.
Download Calculus Formulas as a PDF
Calculus is an important topic in JEE mains Mathematics and involves several formulas. Some of the essential Calculus formulas are:
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${\dfrac{d}{{dx}}\left( a \right) = 0}$
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${\dfrac{d}{{dx}}\left( {ax} \right) = a}$
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${\dfrac{d}{{dx}}\left( {{x^n}} \right) = n{x^{n - 1}}}$
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${\dfrac{d}{{dx}}\left( {\sin x} \right) = \cos x}$
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${\dfrac{d}{{dx}}\left( {\cos x} \right) = - \sin x}$
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${\dfrac{d}{{dx}}\left( {\tan x} \right) = {\sec ^2}x}$
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${\dfrac{d}{{dx}}\left( {\cot x} \right) = - \cos e{c^2}x}$
Aspirants should first understand the basic concepts of Calculus and then memorize these formulas. Regular practice and solving different types of problems will also help aspirants master Calculus.
Download Probability Formulas as PDF
Probability Formulas: Probability is an important topic in JEE mains Mathematics and involves several formulas. Some of the essential Probability formulas are:
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${{{P}}\left( {{{A}} \cup {{B}}} \right) = {{P}}\left( {{A}} \right) + {{P}}\left( {{B}} \right) - {{P}}\left( {{{A}} \cap {{B}}} \right)}$
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${{{P}}\left( {{{A}} \cap {{B}}} \right) = {{P}}\left( {{A}} \right) \times {{P}}\left( {\dfrac{{{B}}}{{{A}}}} \right)}$
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${{{P}}\left( {\dfrac{{{A}}}{{{B}}}} \right) = \dfrac{{{{P}}\left( {{{A}} \cap {{B}}} \right)}}{{{{P}}\left( {{B}} \right)}}}$
Aspirants should first understand the basic concepts of Probability and then memorize these formulas. Regular practice and solving different types of problems will also help aspirants master Probability.
Download Geometry Formulas as PDF
Geometry Formulas: Geometry is an important topic in JEEmains Mathematics and involves several formulas. Some of the essential Geometry formulas are:
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Area of a Triangle = $\left(\dfrac{1}{2}\right) { \times }$ base ${ \times }$ height
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Perimeter of a Square = 4 ${ \times }$ side
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Perimeter of a Rectangle = 2 ${ \times }$ (length + breadth)
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Area of a Circle = ${\pi {r^2}}$
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Circumference of a Circle = ${2\pi r}$
Aspirants should first understand the basic concepts of Geometry and then memorize these formulas. Regular practice
Basic Integration Formulas: The basic integration formulas are the ones that are used to find the integral of a function. Some of the essential basic integration formulas are:
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${\int dx = x + c}$
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${\int {x^n}dx = \dfrac{{\left( {{x^{\left( {n + 1} \right)}}} \right)}}{{\left( {n + 1} \right)}} + C}$
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${\int {e^x}dx = {e^x} + C}$
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${\int \sin xdx = - \cos x + C}$
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${\int \cos xdx = \sin x + C}$
Download Integration Formulas as PDF
Integration by Substitution: Integration by substitution is a common technique for solving integrals. This technique involves substituting a part of the integral with a new variable. The formula for Integration by substitution is:
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${\int f\left( {g\left( x \right)} \right)g'\left( x \right)dx = \int f\left( u \right)du}$
Integration by Parts: Integration by parts is another technique for solving integrals. This technique involves selecting two integral parts and applying a specific formula. The formula for Integration by Parts is:
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$\int udv = uv - \int vdu$
Download Straight Line Formulas as PDF
Equation of a Straight Line: The equation of a straight line is y = mx + c, where m is the slope of the line, and c is the y-intercept. The slope of a line is given by:
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${m = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}}$
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Point-Slope Form: The Point-Slope Form of a straight line is $y - y_1 = m(x - x_1)$. This form is used to find the equation of a straight line when the slope and one point on the line are given.
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Intercept Form: The Intercept Form of a straight line is ${\dfrac{x}{a} + \dfrac{y}{b} = 1}$, where a and b are the x-intercept and y-intercept, respectively. This form is used to find the equation of a straight line when the intercepts are given.
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Slope-Intercept Form: The Slope-Intercept Form of a straight line is $y = mx + c$. This form is used to find the equation of a straight line when the slope and y-intercept are given.
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Two-Point Form: The Two-Point Form of a straight line is ${\dfrac{{\left( {y - {y_1}} \right)}}{{\left( {{y_2} - {y_1}} \right)}} = \dfrac{{\left( {x - {x_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}}$. This form is used to find the equation of a straight line when two points on the line are given.
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Perpendicular Distance Formula: The Perpendicular Distance Formula is used to find the perpendicular distance between a point and a line. The formula is:
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Distance = {\dfrac{{\left| {ax + by + c} \right|}}{{\sqrt {\left( {{a^2} + {b^2}} \right)} }}}
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Distance Formula: The Distance Formula is used to find the distance between two points. The formula is:
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Distance = ${\sqrt {\left[ {{{\left( {x2 - x1} \right)}^2} + {{\left( {y2 - y1} \right)}^2}} \right]} }$
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A Parabola is a U-shaped curve that is symmetric around a line called the axis of the parabola. The standard equation of a parabola is ${{y^2} = 4ax}$, where a is a constant and the axis of the parabola is parallel to the x-axis.
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Vertex Form: The Vertex Form of a parabola is given as ${y - k = a{\left( {x - h} \right)^2}}$, where (h, k) is the vertex of the parabola. This form is used to find the equation of a parabola when the vertex and the value of a are given.
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Standard Form: The Standard Form of a parabola is given as ${{\left( {x - h} \right)^2} = 4a\left( {y - k} \right)}$, where (h, k) is the vertex of the parabola. This form is used to find the equation of a parabola when the vertex and the value of a are given.
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Focus-Directrix Form: The Focus-Directrix Form of a parabola is given as ${{\left( {x - h} \right)^2} = 4a\left( {y - k} \right)}$, where the focus of the parabola is ${\left( {h,k + \dfrac{1}{{4a}}} \right)}$, and the directrix of the parabola is ${y = k - \dfrac{1}{{4a}}}$. This form is used to find the equation of a parabola when the focus and the directrix are given.
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Latus Rectum Form: The Latus Rectum Form of a parabola is given as ${y = mx + \dfrac{a}{m}}$, where m is the slope of the tangent to the parabola at any point on it. This form is used to find the equation of the latus rectum of the parabola.
Important Topics Covered in JEE Main
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Most Important Chapters of Maths JEE Main 2025 |
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Complex Numbers and Quadratic Equations |
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram, algebra of complex number, modulus, and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient, nature of roots, the formation of quadratic equations with given roots. |
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Circle, Conic Sections |
A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency. |
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Integral Calculus |
Integral is an anti-derivative, Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities. Evaluation of simple integrals of the type $\int{\dfrac{dx}{x^2+a^2}}, \int{\dfrac{dx}{\sqrt{x^2 \pm a^2}}}, \int{\dfrac{dx}{a^2-x^2}}, \int{\dfrac{dx}{\sqrt{a^2-x^2}}}, \int{\dfrac{dx}{ax^2+bx+c}}, \int{\dfrac{dx}{\sqrt{ax^2+bx+c}}}, \int{\dfrac{(px+q)dx}{ax^2+bx+c}}, \int{\dfrac{(px+q)dx}{\sqrt{ax^2+bx+c}}}, \int{\sqrt{a^2 \pm x^2}dx}, \int{\sqrt{x^2-a^2}dx}$ Integraliss the limit of a sum. The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. |
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Three Dimensional Geometry |
Coordinates of a point in space, the distance between two points, section formula, directions ratios, direction cosines, and the angle between two intersecting lines. Skew lines, the shortest distance between them, and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, and coplanar lines. |
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Vector Algebra |
Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product. |
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Probability |
Probability of an event, addition, and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution. |
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Trigonometry |
Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions, and their properties, heights, and distance. |
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Permutations and Combinations |
The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications. |
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Sequence and Series |
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression. |
Students Can Practice Other Study Materials With The JEE Main Maths Important Questions.
You should understand that covering only important questions and previous year's questions will not work for you. You should refer to reference books from various renowned authors. Having concept clarity is must and a strong foundation is very much needed to crack the exam and solve the complex questions.
Why Use Other Study Materials?
Comprehensive Coverage: Important questions focus on high-weightage topics, but JEE Main can ask questions from any part of the syllabus. By studying textbooks like NCERT and reference books such as R.D. Sharma or Arihant, students get a complete view of all the chapters and concepts needed for the exam.
Better Problem-Solving Skills: Solving a wide variety of problems helps build problem-solving skills. Practice papers, mock tests, and previous years’ papers present different types of questions, including tricky and challenging ones. This improves speed, accuracy, and the ability to think quickly during the actual exam.
Understanding Concepts Deeply: Maths requires a strong understanding of concepts and formulas. Other study materials, like detailed explanations and solved examples in textbooks, help students understand concepts in depth, which is necessary to solve difficult questions that may not be included in the “important” category.
Improved Time Management: Practicing mock tests and timed sample papers trains students to manage their time effectively. It teaches them how to approach questions efficiently, helping them complete the exam within the time limit.
How useful are Important Questions for the JEE Main Exam?
Focused Learning: Important questions highlight the most critical topics that have a high chance of appearing in the exam. By focusing on these, students can prioritize their preparation and make sure they are well-prepared for the areas that matter the most.
Saves Time: The JEE Main syllabus is vast, and covering every single topic in depth can be challenging, especially when time is limited. Important questions allow students to target high-weightage areas and save time by not diving too deep into less significant topics.
Boosts Confidence: Practicing important questions regularly helps students become familiar with the types of questions they are likely to face in the exam. This builds confidence, as they know they have prepared well for common question patterns.