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By Karan Singh Bisht
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Updated on 14 Aug 2026, 14:39 IST
RD Sharma Class 10 Maths Solutions for 2026–27 provide clear, step-by-step answers to the questions and exercises in the RD Sharma Mathematics textbook. Infinity Learn offers these solutions chapter-wise to help students understand mathematical concepts, check their methods and practise different types of problems for the Class 10 Maths examination.
The solutions cover important topics from algebra, geometry, coordinate geometry, trigonometry, mensuration, statistics and probability. Each solution explains the method used to solve the question so that students can understand the reasoning behind the answer instead of memorising only the final result.
Students can use the RD Sharma Solutions for Class 10 Maths after studying the relevant concept from their school textbook. Regular practice can help improve calculation accuracy, problem-solving speed, mathematical reasoning and confidence while attempting unfamiliar questions.
| Particular | Details |
| Resource | RD Sharma Class 10 Maths Solutions |
| Academic session | 2026–27 |
| Class | Class 10 |
| Subject | Mathematics |
| Solution format | Chapter-wise and exercise-wise |
| Access format | Online solutions and PDF links |
| Main topics | Algebra, geometry, trigonometry, mensuration, statistics and probability |
| Useful for | Concept practice, homework, revision and exam preparation |
| Provided by | Infinity Learn |
Infinity Learn provides chapter-wise RD Sharma Class 10 Maths Solutions so students can access the required chapter without searching through the complete book. Select a chapter below to view its solutions and download the corresponding PDF.
| Chapter Name | Solutions |
| RD Sharma Solutions for Chapter 1: Real Numbers | Download PDF |
| RD Sharma Solutions forChapter 2: Polynomials | Download PDF |
| RD Sharma Solutions for Chapter 3: Pair of Linear Equations in Two Variables | Download PDF |
| RD Sharma Solutions for Chapter 4: Quadratic Equations | Download PDF |
| RD Sharma Solutions for Chapter 5: Arithmetic Progressions | Download PDF |
| RD Sharma Solutions for Chapter 6: Co-Ordinate Geometry | Download PDF |
| RD Sharma Solutions for Chapter 7: Triangles | Download PDF |
| RD Sharma Solutions for Chapter 8: Circles | Download PDF |
| RD Sharma Solutions for Chapter 9: Trigonometric Ratios | Download PDF |
| RD Sharma Solutions for Chapter 10: Trigonometric Identities | Download PDF |
| RD Sharma Solutions for Chapter 11: Heights and Distances | Download PDF |
| RD Sharma Solutions for Chapter 12: Areas Related to Circles | Download PDF |
| RD Sharma Solutions for Chapter 13: Surface Areas and Volumes | Download PDF |
| RD Sharma Solutions for Chapter 14: Statistics | Download PDF |
| RD Sharma Solutions for Chapter 15: Probability | Download PDF |
RD Sharma Class 10 Maths Solutions are worked-out answers to the examples and exercise questions in the Class 10 RD Sharma Mathematics textbook. They show the mathematical steps, formulae, calculations and reasoning required to reach the correct answer.
The solutions are most useful when students first attempt a problem independently and then compare their method with the explained answer. This approach helps identify calculation mistakes, misunderstood concepts and missing steps.
Chapter 1 introduces the properties of real numbers and important number-system concepts. Students learn about Euclid’s division lemma, prime factorisation, the Fundamental Theorem of Arithmetic, highest common factor and least common multiple.
The solutions explain the calculations systematically and help students understand how number properties can be applied to proof-based and problem-solving questions.
Important topics: Euclid’s division lemma, HCF, LCM, prime factorisation, irrational numbers and decimal expansion.
The Polynomials chapter explains zeroes of polynomials and the relationship between zeroes and coefficients. Students also practise forming polynomials and solving questions involving linear, quadratic and cubic expressions.
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The chapter-wise solutions demonstrate the correct algebraic method and help students avoid sign and calculation errors.
Important topics: Degree of a polynomial, zeroes, coefficients, polynomial identities and division algorithm.
This chapter focuses on solving two linear equations involving two variables. Students learn graphical and algebraic methods, including substitution, elimination and cross-multiplication.
The solutions also explain how linear equations are used to represent practical situations through word problems.
Important topics: Graphical method, substitution method, elimination method, cross-multiplication and consistency of equations.
Quadratic Equations introduces equations of the form (ax^2+bx+c=0). Students learn to solve them through factorisation, completing the square and the quadratic formula.
The chapter also explains the discriminant and how it determines the nature of the roots.
Important topics: Standard form, factorisation, quadratic formula, discriminant, nature of roots and word problems.
This chapter explains sequences in which the difference between consecutive terms remains constant. Students learn to identify an arithmetic progression, find its common difference and calculate a particular term or the sum of several terms.
Step-by-step solutions make it easier to translate word problems into arithmetic progression formulae.
Important topics: First term, common difference, nth term, sum of n terms and application-based problems.
Coordinate Geometry connects algebra with geometrical figures on a coordinate plane. Students learn to calculate the distance between two points, divide a line segment in a given ratio and find the area of a triangle using its coordinates.
The solutions explain formula substitution and simplification in a structured way.
Important topics: Cartesian plane, coordinates, distance formula, section formula and area of a triangle.
The Triangles chapter covers similarity and proportional relationships between geometrical figures. Students apply similarity criteria and important theorems to calculate unknown sides and prove geometrical relationships.
The solutions help students organise proofs using statements, reasons and relevant theorems.
Important topics: Similar triangles, Basic Proportionality Theorem, similarity criteria and areas of similar triangles.
This chapter studies tangents drawn to a circle and their relationship with the radius. Students learn important tangent properties and use them in geometrical proofs and numerical questions.
The solutions provide a logical sequence for identifying the relevant theorem and applying it correctly.
Important topics: Tangent, point of contact, radius, equal tangents and tangent-related theorems.
Trigonometric Ratios introduces the relationship between the sides and angles of a right-angled triangle. Students learn sine, cosine, tangent, cosecant, secant and cotangent.
The chapter also covers trigonometric values of standard angles and complementary-angle relationships.
Important topics: Six trigonometric ratios, standard angles, complementary angles and right-angled triangles.
This chapter develops the use of standard trigonometric identities. Students simplify expressions and prove relationships involving different trigonometric ratios.
The solutions show every transformation clearly, helping students understand which identity should be applied at each step.
Important topics: Pythagorean identities, reciprocal identities, quotient identities and identity-based proofs.
Heights and Distances applies trigonometry to practical situations involving the height of an object or the distance between two points.
Students learn to draw a suitable diagram, identify the angle of elevation or depression and select the correct trigonometric ratio.
Important topics: Angle of elevation, angle of depression, line of sight, height and horizontal distance.
This chapter covers the circumference and area of a circle, along with the areas of sectors and segments. Students also solve questions involving combined circular figures.
The solutions explain how to divide a complex figure into simpler shapes before applying the required formulae.
Important topics: Circumference, area of a circle, sector, segment, arc length and combined figures.
Surface Areas and Volumes deals with three-dimensional shapes such as cubes, cuboids, cylinders, cones, spheres and hemispheres.
Students calculate curved surface area, total surface area and volume, including questions in which solids are combined or converted from one form to another.
Important topics: Cube, cuboid, cylinder, cone, sphere, hemisphere, frustum and combined solids.
The Statistics chapter introduces methods for analysing grouped data. Students learn to calculate mean, median and mode and interpret frequency distributions.
The solutions show the construction of tables and the correct use of statistical formulae.
Important topics: Grouped data, frequency distribution, mean, median, mode and cumulative frequency.
Probability explains how to measure the likelihood of an event. Students identify possible outcomes, favourable outcomes and the total sample space before applying the probability formula.
The solutions help students understand how to interpret the conditions of an experiment before calculating the result.
Important topics: Random experiment, outcome, event, sample space, favourable outcomes and theoretical probability.
The following formulas cover important Class 10 Maths topics, including real numbers, polynomials, quadratic equations, arithmetic progressions, coordinate geometry, trigonometry, circles, mensuration, statistics and probability.
Euclid’s Division Lemma:
a = bq + r, where 0 ≤ r < b
Relationship between HCF and LCM:
HCF × LCM = Product of the two positive integers
For a quadratic polynomial ax² + bx + c, where α and β are its zeroes:
Sum of zeroes:
α + β = −b/a
Product of zeroes:
αβ = c/a
Polynomial formed using the zeroes:
p(x) = k(x − α)(x − β), where k ≠ 0
For a monic quadratic polynomial:
p(x) = x² − (α + β)x + αβ
The general form of two linear equations is:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Conditions for solutions:
One unique solution:
a₁/a₂ ≠ b₁/b₂
No solution:
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Infinitely many solutions:
a₁/a₂ = b₁/b₂ = c₁/c₂
Cross-multiplication formulas:
x = (b₁c₂ − b₂c₁) / (a₁b₂ − a₂b₁)
y = (c₁a₂ − c₂a₁) / (a₁b₂ − a₂b₁)
These formulas apply when a₁b₂ − a₂b₁ ≠ 0.
Standard form of a quadratic equation:
ax² + bx + c = 0, where a ≠ 0
Quadratic formula:
x = [−b ± √(b² − 4ac)] / 2a
Discriminant:
D = b² − 4ac
Nature of roots:
If D > 0, the equation has two distinct real roots.
If D = 0, the equation has two equal real roots.
If D < 0, the equation has no real roots.
Common difference:
d = a₂ − a₁
nth term of an arithmetic progression:
aₙ = a + (n − 1)d
Last term:
l = a + (n − 1)d
Sum of the first n terms:
Sₙ = n/2 [2a + (n − 1)d]
When the last term is known:
Sₙ = n/2 (a + l)
Here, a is the first term, d is the common difference, n is the number of terms and l is the last term.
Distance between two points A(x₁, y₁) and B(x₂, y₂):
AB = √[(x₂ − x₁)² + (y₂ − y₁)²]
Distance of a point P(x, y) from the origin:
OP = √(x² + y²)
Section formula:
If point P divides the line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n, then:
P = [(mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)]
Midpoint formula:
M = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Area of a triangle using coordinates:
Area = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
If the area is zero, the three points are collinear.
If triangle ABC is similar to triangle DEF:
AB/DE = BC/EF = AC/DF
Ratio of the areas of two similar triangles:
Area of triangle ABC / Area of triangle DEF = (AB/DE)²
Basic Proportionality Theorem:
In triangle ABC, if DE is parallel to BC, then:
AD/DB = AE/EC
Tangent-radius theorem:
The tangent at any point of a circle is perpendicular to the radius passing through the point of contact.
OT ⟂ PT
Tangents drawn from an external point:
PA = PB
For an angle θ in a right-angled triangle:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cosec θ = Hypotenuse / Perpendicular
sec θ = Hypotenuse / Base
cot θ = Base / Perpendicular
Reciprocal relationships:
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Other relationships:
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
sin² θ + cos² θ = 1
1 + tan² θ = sec² θ
1 + cot² θ = cosec² θ
Equivalent forms:
sec² θ − tan² θ = 1
cosec² θ − cot² θ = 1
sin (90° − θ) = cos θ
cos (90° − θ) = sin θ
tan (90° − θ) = cot θ
cot (90° − θ) = tan θ
sec (90° − θ) = cosec θ
cosec (90° − θ) = sec θ
For a right-angled triangle:
tan θ = Height / Horizontal distance
Height = Horizontal distance × tan θ
Horizontal distance = Height / tan θ
Circumference of a circle:
C = 2πr
Area of a circle:
A = πr²
Length of an arc:
Arc length = (θ/360°) × 2πr
Area of a sector:
Area of sector = (θ/360°) × πr²
Perimeter of a sector:
Perimeter = 2r + (θ/360°) × 2πr
Area of a minor segment:
Area of minor segment = Area of minor sector − Area of triangle
Area of a major segment:
Area of major segment = πr² − Area of minor segment
Here, r is the radius and θ is the angle at the centre of the circle.
Lateral surface area:
LSA = 2h(l + b)
Total surface area:
TSA = 2(lb + bh + hl)
Volume:
V = lbh
Diagonal:
d = √(l² + b² + h²)
Lateral surface area:
LSA = 4a²
Total surface area:
TSA = 6a²
Volume:
V = a³
Diagonal:
d = a√3
Curved surface area:
CSA = 2πrh
Total surface area:
TSA = 2πr(r + h)
Volume:
V = πr²h
Slant height:
l = √(r² + h²)
Curved surface area:
CSA = πrl
Total surface area:
TSA = πr(l + r)
Volume:
V = 1/3 πr²h
Surface area:
SA = 4πr²
Volume:
V = 4/3 πr³
Curved surface area:
CSA = 2πr²
Total surface area:
TSA = 3πr²
Volume:
V = 2/3 πr³
Class mark:
xᵢ = (Upper class limit + Lower class limit) / 2
Total frequency:
N = Σfᵢ
Mean by direct method:
Mean = Σfᵢxᵢ / Σfᵢ
Mean by assumed-mean method:
Mean = a + (Σfᵢdᵢ / Σfᵢ)
where:
dᵢ = xᵢ − a
Mean by step-deviation method:
Mean = a + h(Σfᵢuᵢ / Σfᵢ)
where:
uᵢ = (xᵢ − a) / h
Median of grouped data:
Median = l + [(N/2 − cf) / f] × h
Here:
l = Lower boundary of the median class
N = Total frequency
cf = Cumulative frequency before the median class
f = Frequency of the median class
h = Class width
Mode of grouped data:
Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Here:
l = Lower boundary of the modal class
f₁ = Frequency of the modal class
f₀ = Frequency of the class before the modal class
f₂ = Frequency of the class after the modal class
h = Class width
Empirical relationship:
Mode ≈ 3 Median − 2 Mean
The symbol ≈ is used because this relationship is approximate.
Probability of an event:
P(E) = Number of favourable outcomes / Total number of equally likely outcomes
In mathematical form:
P(E) = n(E) / n(S)
Probability range:
0 ≤ P(E) ≤ 1
Probability of a certain event:
P(S) = 1
Probability of an impossible event:
P(∅) = 0
Probability of a complementary event:
P(not E) = 1 − P(E)
Therefore:
P(E) + P(not E) = 1
The solutions break each problem into logical steps. This helps students understand the process and locate the exact step where an error occurred.
RD Sharma includes multiple problems based on individual concepts. Practising different variations helps students become more comfortable with unfamiliar questions.
The solutions connect mathematical formulae with their applications. This is particularly useful in algebra, coordinate geometry, trigonometry and mensuration.
Regular written practice can help students calculate more accurately and select an appropriate solution method more quickly.
Chapter-wise solutions allow students to review a question without waiting for classroom assistance. However, they should be used after making an independent attempt.
Topics such as quadratic equations, coordinate geometry, trigonometry, statistics and probability continue in higher classes. A clear understanding at the Class 10 level can make later mathematical study easier.
Read the concept and solved examples from the textbook or classroom notes before beginning an exercise.
Write the complete solution without immediately checking the answer. Even an incorrect attempt can reveal which step needs improvement.
Compare the formula, method, calculation and final result with the RD Sharma solution. Do not look only at the final answer.
Record recurring mistakes such as incorrect signs, skipped steps, formula confusion and calculation errors. Review this notebook weekly.
Solve challenging questions again after a few days without referring to the solution. This checks whether the method has been understood.
Once a concept is clear, solve a set of questions within a fixed time. This helps improve speed for school and board examinations.
Prepare a chapter-wise formula sheet and revise it frequently. Apply each formula to at least one example instead of memorising it in isolation.
RD Sharma Solutions can be used as an additional practice resource after completing the prescribed textbook questions. They expose students to different problem formats and provide detailed methods for questions that require several steps.
For effective preparation, students should:
RD Sharma should support the main school curriculum, not replace the prescribed textbook, classroom instruction or official sample papers.
| Common Mistake | Better Approach |
| Reading the answer before attempting the problem | Try the question independently first |
| Memorising a solution | Understand why each step is used |
| Skipping calculation steps | Show the formula, substitution and simplification |
| Solving only easy questions | Include a balanced mix of basic and challenging problems |
| Ignoring incorrect answers | Identify and record the reason for each error |
| Practising without revision | Reattempt difficult problems after a few days |
| Using the wrong chapter edition | Match the solution number with the textbook edition |
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RD Sharma Class 10 Maths Solutions are detailed, step-by-step answers to the questions and exercises in the RD Sharma Mathematics textbook for Class 10.
RD Sharma Solutions follows a 15-chapter sequence, beginning with Real Numbers and ending with Probability. Students should match the chapter numbering with the edition of the RD Sharma textbook they are using.
Infinity Learn provides chapter-wise RD Sharma Solutions for Class 10. Select Download PDF next to the required chapter.
They are useful for additional concept practice and exposure to different problem types. Students should first complete the prescribed textbook and then use RD Sharma for further practice.
It is not necessary for every student to solve every question. Students can prioritise chapters and exercises based on their syllabus, teacher guidance, available time and areas requiring more practice.
The solutions are organised chapter-wise, and the individual chapter pages can be structured exercise-wise so students can quickly locate the required question.
RD Sharma is a supplementary practice resource. Complete preparation should also include the prescribed textbook, classroom notes, official sample papers and previous-year questions.
First solve the problem independently. Then compare the formula, method, calculations and final answer with the solution and correct any errors.
It can strengthen foundational skills such as algebraic manipulation, geometry, trigonometry and problem-solving. Dedicated competitive-exam preparation requires separate material at the appropriate level.
Quadratic Equations, Arithmetic Progressions, Coordinate Geometry, Trigonometry, Areas Related to Circles, Surface Areas and Volumes, Statistics and Probability involve frequent formula application.