RS Aggarwal Class 10 Solutions

Written by K. MenonPublished on 12 June 2026

rs aggarwal class 10 solutions help students check Maths exercises step by step, understand the method, and correct calculation mistakes before exams. This page gives chapter-wise entry points, exercise-wise guidance, worked sample solutions, formula reminders, common mistakes, and notes on whether the book is being used for CBSE or ICSE practice.

Author: K. Menon, M.Sc., ICSE/ISC Maths and Science teacher for Classes 6 to 12.

RS Aggarwal Class 10 Solutions: Chapter-wise Maths Answers

How to use this solution page

Open the chapter that matches your textbook.
Solve the question once before checking the answer.
Compare every step, not only the final answer.
Write the formula or theorem beside your correction.

Chapter-wise solution index

Section	Chapter or topic	Exercise-wise use	Available entry
Chapter 1	Real Numbers	Euclid algorithm, HCF, LCM, decimal expansion	rs aggarwal class 10 solutions chapter 1
Chapter 2	Polynomials	Zeroes, coefficients, division algorithm	Use the Polynomials exercise page when available
Chapter 3	Pair of Linear Equations in Two Variables	Substitution, elimination, cross-multiplication, word problems	Use the Linear Equations exercise page when available
Chapter 4	Quadratic Equations	Factorisation, formula method, nature of roots	Use the Quadratic Equations exercise page when available
Chapter 5	Arithmetic Progressions	$n$ th term and sum of first $n$ terms	Use the AP exercise page when available
Chapter 6	Triangles	Similarity and Pythagoras theorem	Use the Triangles exercise page when available
Chapter 7	Coordinate Geometry	Distance, section formula, area of triangle	Use the Coordinate Geometry exercise page when available
Chapter 8	Introduction to Trigonometry	Ratios, standard angles, complementary angles	Use the Trigonometry exercise page when available
Chapter 9	Trigonometric Identities	Identity proofs and simplification	Use the Identities exercise page when available
Chapter 10	Heights and Distances	Angle of elevation and depression	Use the Heights and Distances exercise page when available
Chapter 11	Circles	Tangent properties and proofs	Use the Circles exercise page when available
Chapter 12	Areas Related to Circles	Sectors, segments, combined figures	Use the Areas exercise page when available
Chapter 13	Surface Areas and Volumes	Cylinder, cone, sphere, frustum, conversion of solids	Use the Mensuration exercise page when available
Chapter 14	Statistics	Mean, median, mode, cumulative frequency	Use the Statistics exercise page when available
Chapter 15	Probability	Simple probability with equally likely outcomes	Use the Probability exercise page when available
Edition-specific section	Statistics in some later chapter numbering	Mean, median, mode, table questions	rs aggarwal class 10 ex 18a solutions

Exercise-wise answer links

Exercise labels vary by edition. Match the chapter title, exercise label, and question number in your book before comparing a class 10 rs aggarwal solution. Basic exercises usually test direct formulas; mixed exercises test method choice; word problems test equation formation; proof questions test statement and reason.

What each worked solution will include

The question or required part is restated before the working.
Steps are shown in the order a student should write them.
The formula or theorem is named before use.
The final answer is written clearly with units where needed.
An alternative method is added when it helps check the answer.

Before You Start: CBSE, ICSE, and Textbook Match

RS Aggarwal Class 10 for CBSE/NCERT-based practice

RS Aggarwal Class 10 solutions CBSE searches usually refer to NCERT-based Class 10 Maths practice. The common chapter set includes Real Numbers, Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Trigonometry, Circles, Mensuration, Statistics, and Probability. Students should still follow the latest school syllabus and sample paper.

How ICSE students should verify their prescribed Maths book

ICSE students should first check the school booklist, teacher instructions, and current CISCE Mathematics syllabus. If your school has prescribed another ICSE-focused text, use that for homework and use icse class 10 maths solutions ml aggarwal where it matches your book.

Difference between RS Aggarwal and Understanding Mathematics Class 10

Point	RS Aggarwal Class 10	Understanding Mathematics Class 10 or ICSE-focused book
Typical use	CBSE and NCERT-based practice in many schools	ICSE practice when prescribed by the school
Syllabus match	Use when the topic matches the CBSE/NCERT pattern	Use when it matches CISCE and school planning
Exercise order	May differ by edition	May include ICSE-specific sequencing
Best use before exams	Extra practice after textbook work	Main practice if prescribed by school

When ICSE students can still use RS Aggarwal for extra practice

ICSE students can use RS Aggarwal Class 10 ICSE searches only after matching the subtopic with their syllabus. Algebra, trigonometry, mensuration, statistics, and probability often overlap, but the prescribed ICSE book remains the main source.

How Every Solution Is Presented

Question restated exactly before the solution

Each solved section begins with the question number and the needed question statement. For long textbook questions, keep the book open and match the diagram, values, and subpart.

Step-by-step working in ordered steps

Every calculation is written in the order expected in a notebook. Proof questions include a reason beside the main statement.

Formula used and why it applies

The formula is named before substitution. For example, the quadratic formula applies to $ax^2+bx+c=0$ , where $a\ne0$ , and a trigonometric identity must respect denominator restrictions.

Final answer highlighted clearly

The last line gives the final answer in bold. Units are added for area, volume, length, and probability where needed.

Alternative method where useful

Alternative methods are included when they reduce calculation or help verification, such as elimination instead of substitution in simultaneous equations.

Chapter 1 to Chapter 5 Solutions

Real Numbers solutions

Real Numbers questions test Euclid division algorithm, HCF, LCM, rational and irrational numbers, and decimal expansion.

Question: Find the HCF of $96$ and $404$ by Euclid division algorithm.

Step 1: Divide the larger number by the smaller number.

404=96\times4+20

Step 2: Continue division using the remainder.

96=20\times4+16

20=16\times1+4

16=4\times4+0

Formula and reasoning: In Euclid division algorithm, the last non-zero remainder is the HCF.

Final answer: $\operatorname{HCF}(96,404)=4$ .

Polynomials solutions

For $ax^2+bx+c$ , the sum of zeroes is $-\frac{b}{a}$ and the product of zeroes is $\frac{c}{a}$ . Always check signs while comparing coefficients.

Pair of Linear Equations in Two Variables solutions

Define variables first in word problems. Then choose substitution, elimination, or cross-multiplication according to the coefficients.

Quadratic Equations solutions

Quadratic equations require the form $ax^2+bx+c=0$ , where $a\ne0$ .

Question: Solve $x^2-5x+6=0$ .

Step 1: Split the middle term.

x^2-5x+6=x^2-2x-3x+6

Step 2: Factorise by grouping.

x(x-2)-3(x-2)=0

(x-2)(x-3)=0

Step 3: Use the zero product rule.

x-2=0\quad\text{or}\quad x-3=0

Formula and reasoning: If $pq=0$ , then $p=0$ or $q=0$ .

Final answer: $x=2$ or $x=3$ .

Arithmetic Progressions solutions

Use $a_n=a+(n-1)d$ and $S_n=\frac{n}{2}[2a+(n-1)d]$ . Identify $a$ , $d$ , and $n$ before substituting.

Chapter 6 to Chapter 10 Solutions

Triangles solutions

Triangles questions use similarity, Basic Proportionality Theorem, its converse, and Pythagoras theorem. Write corresponding sides in the same order.

Coordinate Geometry solutions

The distance between $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Substitute coordinates only after writing the formula.

Introduction to Trigonometry solutions

Use ratios in a right triangle and standard values of $0^\circ$ , $30^\circ$ , $45^\circ$ , $60^\circ$ , and $90^\circ$ . Do not mix values from different angles.

Trigonometric Identities solutions

In identity questions, simplify one side, usually the more complicated side.

Question: Prove that $\dfrac{1-\sin^2\theta}{\cos^2\theta}=1$ , where $\cos\theta\ne0$ .

Step 1: Start with the left hand side.

\frac{1-\sin^2\theta}{\cos^2\theta}

Step 2: Use $\sin^2\theta+\cos^2\theta=1$ , so $1-\sin^2\theta=\cos^2\theta$ .

Step 3: Substitute and simplify.

\frac{1-\sin^2\theta}{\cos^2\theta}=\frac{\cos^2\theta}{\cos^2\theta}=1

Formula and reasoning: Division is valid because $\cos\theta\ne0$ .

Hence proved.

Heights and Distances solutions

Draw a right triangle from the line of sight. Use $\tan\theta=\frac{\text{opposite side}}{\text{adjacent side}}$ when height and horizontal distance are involved.

Chapter 11 to Chapter 15 Solutions

Circles solutions

The tangent at a point of a circle is perpendicular to the radius through the point of contact. Tangents from an external point are equal.

Areas Related to Circles solutions

For sectors, use $\frac{\theta}{360^\circ}$ of the full circle area or circumference as required. For combined figures, split the figure into known parts.

Surface Areas and Volumes solutions

Mensuration answers need units. Area is in square units and volume is in cubic units.

Question: Find the curved surface area of a cylinder with radius $7\ \text{cm}$ and height $10\ \text{cm}$ . Take $\pi=\frac{22}{7}$ .

Step 1: Use the curved surface area formula.

\text{Curved surface area}=2\pi rh

Step 2: Substitute $r=7\ \text{cm}$ , $h=10\ \text{cm}$ , and $\pi=\frac{22}{7}$ .

2\times\frac{22}{7}\times7\times10=440

Formula and reasoning: The question asks for curved surface area, so $2\pi rh$ is used, not total surface area.

Final answer: $440\ \text{cm}^2$ .

Statistics solutions

RS Aggarwal statistics class 10 questions require correct table columns: class interval, frequency, midpoint, $fx$ , deviation, or cumulative frequency.

Probability solutions

Use $P(E)=\frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}$ . A probability must lie between $0$ and $1$ .

Statistics Class 10: Worked Solutions and Table Format

Mean questions using direct, assumed mean, and step-deviation methods

Sample question: Find the mean for the following grouped data.

Class interval	Frequency $f$	Midpoint $x$	$fx$	$d=x-25$	$fd$
$0-10$	$3$	$5$	$15$	$-20$	$-60$
$10-20$	$5$	$15$	$75$	$-10$	$-50$
$20-30$	$9$	$25$	$225$	$0$	$0$
$30-40$	$3$	$35$	$105$	$10$	$30$
Total	$\sum f=20$		$\sum fx=420$		$\sum fd=-80$

Step 1: Use the direct method.

\bar{x}=\frac{\sum fx}{\sum f}=\frac{420}{20}=21

Step 2: Check by assumed mean $A=25$ .

\bar{x}=A+\frac{\sum fd}{\sum f}=25+\frac{-80}{20}=21

Formula and reasoning: Both methods give the same mean when table totals are correct.

Final answer: Mean $=21$ .

Median questions with cumulative frequency tables

Class interval	Frequency $f$	Cumulative frequency
$0-10$	$3$	$3$
$10-20$	$5$	$8$
$20-30$	$9$	$17$
$30-40$	$3$	$20$

Step 1: $N=20$ , so $\frac{N}{2}=10$ . The first cumulative frequency greater than $10$ is $17$ , so the median class is $20-30$ .

Step 2: Use $L=20$ , $cf=8$ , $f=9$ , and $h=10$ .

\text{Median}=L+\frac{\frac{N}{2}-cf}{f}\times h=20+\frac{10-8}{9}\times10=\frac{200}{9}

Formula and reasoning: $cf$ is the cumulative frequency before the median class.

Final answer: Median $=\frac{200}{9}$ , or approximately $22.22$ .

Mode questions using grouped data

Symbol	Meaning	Value
$L$	Lower limit of modal class	$20$
$f_1$	Frequency of modal class	$9$
$f_0$	Frequency before modal class	$5$
$f_2$	Frequency after modal class	$3$
$h$	Class size	$10$

Step 1: The modal class is $20-30$ , since its frequency $9$ is highest.

Step 2: Substitute in the formula.

\text{Mode}=L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h=20+\frac{9-5}{2(9)-5-3}\times10=24

Formula and reasoning: The modal class is chosen by highest frequency, not by class width.

Final answer: Mode $=24$ .

Common table mistakes in statistics

For $10-20$ , the midpoint is $\frac{10+20}{2}=15$ , not $10$ or $20$ .
In median, $cf$ means cumulative frequency before the median class.
The modal class is chosen by highest frequency, not by the widest class interval.
Recheck $\sum f$ , $\sum fx$ , and $\sum fd$ before substitution.

Important Formulas Used in RS Aggarwal Class 10 Maths

Algebra formulas

Topic	Formula
Quadratic formula	$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Discriminant	$D=b^2-4ac$
AP $n$ th term	$a_n=a+(n-1)d$
AP sum	$S_n=\frac{n}{2}[2a+(n-1)d]$

Geometry and circle formulas

Topic	Formula or result
Distance formula	$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Area of triangle	$\frac{1}{2}\|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\|$
Tangent-radius	Radius is perpendicular to tangent at point of contact
Equal tangents	Tangents from an external point are equal

Trigonometry identities

Identity	Use
$\sin^2\theta+\cos^2\theta=1$	Simplification
$1+\tan^2\theta=\sec^2\theta$	Convert $\tan\theta$ and $\sec\theta$
$1+\cot^2\theta=\cosec^2\theta$	Convert $\cot\theta$ and $\cosec\theta$
$\tan\theta=\frac{\sin\theta}{\cos\theta}$	Ratio conversion when $\cos\theta\ne0$

Mensuration formulas

Figure or solid	Formula
Circle area	$\pi r^2$
Cylinder curved surface area	$2\pi rh$
Cylinder volume	$\pi r^2h$
Cone volume	$\frac{1}{3}\pi r^2h$
Sphere surface area	$4\pi r^2$

Statistics and probability formulas

Topic	Formula
Mean	$\bar{x}=\frac{\sum fx}{\sum f}$
Median	$\text{Median}=L+\frac{\frac{N}{2}-cf}{f}\times h$
Mode	$\text{Mode}=L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$
Probability	$P(E)=\frac{\text{favourable outcomes}}{\text{total equally likely outcomes}}$

Common Mistakes While Solving RS Aggarwal Class 10 Questions

Skipping conditions in quadratic equations

Forgetting $a\ne0$ in $ax^2+bx+c=0$ .
Using $b^2+4ac$ instead of $b^2-4ac$ .
Not verifying roots in the original equation.

Using the wrong trigonometric identity

Writing $1-\sin^2\theta=\sin^2\theta$ instead of $1-\sin^2\theta=\cos^2\theta$ .
Cancelling terms across addition.
Dividing by $\cos\theta$ or $\sin\theta$ without checking the value is not zero.

Forgetting units in mensuration

Area must be in square units, such as $\text{cm}^2$ .
Volume must be in cubic units, such as $\text{cm}^3$ .
Curved surface area and total surface area are not the same.

Confusing class interval and frequency in statistics

The class interval $20-30$ is not the frequency.
Class width and midpoint are different.
Median class is selected from cumulative frequency.

Writing only the answer without reasoning

In proofs, write the theorem or identity.
In word problems, define the variable.
In probability, write the total number of equally likely outcomes.

Chapter area	Common mistake	Correction
Quadratic equations	Wrong discriminant sign	Use $D=b^2-4ac$
Trigonometry	Ignoring denominator restrictions	Check conditions such as $\cos\theta\ne0$
Mensuration	Wrong surface-area formula	Underline curved, total, or volume in the question
Statistics	Wrong cumulative frequency	Add frequencies row by row
Probability	Wrong sample space	List all equally likely outcomes

Exam Preparation Notes: Is RS Aggarwal Enough?

How to combine textbook exercises with board syllabus

Use the official syllabus as the checklist and your prescribed textbook as the main source. Use RS Aggarwal for extra questions only where the topic matches.

When to solve extra RS Aggarwal questions

Solve extra questions after you can complete the prescribed exercise without help. Extra practice is useful in quadratic equations, trigonometry, coordinate geometry, mensuration, statistics, and probability.

Why previous year papers and sample papers are still needed

Previous papers and sample papers test time management, mixed-topic selection, and answer format. A chapter exercise usually tests one topic at a time.

How to revise weak chapters before exams

Write the exact weak subtopic.
Revise one formula and one solved example.
Solve three questions without looking at the answer.
Correct the wrong step and try one similar question.

Exam-weightage note: Do not rely on old fixed weightage. Board pattern and emphasis can vary by session. Use the latest official syllabus, school textbook, sample papers, and previous papers where applicable.

PDF and Offline Use Guidance

How to use solutions responsibly for self-checking

Solve first, compare second, correct third. Do not start with the answer.

Why students should avoid copying answers without solving

Copying does not show whether you can choose the method in a new question. Maths marks depend on method, substitution, calculation, and final answer.

What to check before downloading any PDF

Check that the PDF is authorised and not a copied scan.
Check edition, chapter title, and exercise label.
Avoid files that force unrelated downloads.
For younger students, use a relevant class resource such as rs aggarwal class 7 pdf.

Safe study workflow: solve, compare, correct, revise

Solve: Attempt the question without help.
Compare: Read the worked solution step by step.
Correct: Rewrite the wrong step with the right formula.
Revise: Try a similar question later.

Frequently Asked Questions

Is RS Aggarwal Class 10 Maths enough for board exam preparation?

It is useful for extra practice, but it should be used with the official syllabus, prescribed textbook, sample papers, and previous papers where applicable. Do not use one practice book as the only source for board preparation.

Are RS Aggarwal Class 10 solutions for CBSE or ICSE?

RS Aggarwal Class 10 solutions are most commonly used for CBSE and NCERT-based practice. ICSE students should verify their prescribed textbook and CISCE syllabus before using them.

How should I use RS Aggarwal Class 10 solutions without copying answers?

Attempt the question first, then compare the steps. Write down the exact mistake, such as a wrong formula, sign error, or table total error, and then solve one similar question again.

Can ICSE students use RS Aggarwal Class 10 Maths?

ICSE students can use it for extra practice when the chapter matches the CISCE syllabus and school textbook. For school homework and exam preparation, the prescribed book should come first.

Where can I find step-by-step RS Aggarwal Class 10 solutions?

Use the chapter-wise links on the page and match the chapter title and exercise label with your textbook edition. Exercise numbers can vary by edition, so the chapter topic is the safer match.