Explore Grade 10 Maths NCERT Solutions – Master Every Chapter with Ease

Grade 10 Maths NCERT Solutions for all chapters with step-by-step explanations. Get expert help to solve problems and improve your understanding of mathematics.

What is the solution to a quadratic equation of the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0? To solve a quadratic equation, you can use factoring, completing the square, or the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​.

What is the relationship between the roots and coefficients of a quadratic equation? The sum of the roots is −ba-\frac{b}{a}−ab​ and the product of the roots is ca\frac{c}{a}ac​.

How do you find the distance between two points on a coordinate plane? Use the distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​.

What does the slope of a line represent in coordinate geometry? The slope of a line represents the steepness or incline of the line, calculated as the change in yyy divided by the change in xxx.

What is the equation of a straight line in slope-intercept form? The equation of a line can be written as y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

How can you calculate the area of a triangle? The area of a triangle is 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21​×base×height.

What is the Pythagorean Theorem? In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.

What are the properties of a parallelogram? Opposite sides are equal, opposite angles are equal, and the diagonals bisect each other.

How do you find the volume of a cylinder? The volume of a cylinder is given by πr2h\pi r^2 hπr2h, where rrr is the radius of the base and hhh is the height.

What is the difference between a permutation and a combination? A permutation is an arrangement of objects where the order matters, while a combination is a selection of objects where the order does not matter.

How do you calculate the probability of an event? The probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

What is the formula for the surface area of a sphere? The surface area of a sphere is 4πr24\pi r^24πr2, where rrr is the radius.

How do you solve linear equations with two variables? To solve a system of linear equations, you can use substitution or elimination method to find the values of the variables.

What is the difference between an arithmetic sequence and a geometric sequence? In an arithmetic sequence, the difference between consecutive terms is constant, while in a geometric sequence, each term is a multiple of the previous one.

How can you calculate the median of a set of numbers? To find the median, arrange the numbers in ascending order and pick the middle value. If there are two middle values, calculate the average of those.

What is the formula for the area of a circle? The area of a circle is πr2\pi r^2πr2, where rrr is the radius of the circle.

How do you calculate the perimeter of a rectangle? The perimeter of a rectangle is calculated as 2×(length+width)2 \times (length + width)2×(length+width).

What is the difference between mean, median, and mode? The mean is the average of all numbers, the median is the middle number in an ordered list, and the mode is the number that appears most frequently.

How do you find the circumference of a circle? The circumference is 2πr2\pi r2πr, where rrr is the radius.

What is the formula for the area of a trapezium? The area of a trapezium is 12×(a+b)×h\frac{1}{2} \times (a + b) \times h21​×(a+b)×h, where aaa and bbb are the lengths of the parallel sides and hhh is the height.

How do you simplify algebraic expressions? Combine like terms, apply the distributive property, and use the rules of exponents to simplify expressions.

What is the formula for the volume of a cone? The volume of a cone is 13πr2h\frac{1}{3} \pi r^2 h31​πr2h, where rrr is the radius and hhh is the height.

How do you solve quadratic inequalities? To solve quadratic inequalities, first solve the corresponding quadratic equation, then test the intervals between the roots to determine which values satisfy the inequality.

What is the formula for the area of a rectangle? The area of a rectangle is calculated as length×width\text{length} \times \text{width}length×width.

How do you solve a linear equation in one variable? To solve a linear equation, isolate the variable on one side of the equation by performing the same operations on both sides.

What is a rational number? A rational number can be expressed as a fraction of two integers, where the denominator is not zero.

How do you calculate the compound interest? The formula for compound interest is A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}A=P(1+nr​)nt, where PPP is the principal amount, rrr is the rate of interest, nnn is the number of times interest is compounded, and ttt is the time in years.

How do you find the length of an arc of a circle? The length of an arc is given by L=θ360×2πrL = \frac{\theta}{360} \times 2\pi rL=360θ​×2πr, where θ\thetaθ is the central angle and rrr is the radius.

What is the difference between a rational and an irrational number? A rational number can be expressed as a fraction, whereas an irrational number cannot be written as a simple fraction and has non-repeating decimal expansion.

How do you solve equations with fractions? Multiply through by the least common denominator (LCD) to eliminate the fractions, then solve the resulting equation.

How do you find the probability of drawing a red card from a deck of cards? There are 26 red cards in a deck of 52 cards, so the probability is 2652=12\frac{26}{52} = \frac{1}{2}5226​=21​.

What is the difference between permutations and combinations? In permutations, the order of objects matters, whereas in combinations, the order does not matter.

How do you calculate the perimeter of a triangle? The perimeter of a triangle is the sum of the lengths of all three sides.

What is the formula for the volume of a sphere? The volume of a sphere is 43πr3\frac{4}{3} \pi r^334​πr3, where rrr is the radius.

How do you calculate the area of a parallelogram? The area of a parallelogram is base×height\text{base} \times \text{height}base×height.

What is the probability of drawing a king from a deck of cards? There are 4 kings in a deck of 52 cards, so the probability is 452=113\frac{4}{52} = \frac{1}{13}524​=131​.

How do you simplify a rational expression? Factor both the numerator and denominator and cancel out any common factors.

What is the formula for the area of a rhombus? The area of a rhombus is 12×d1×d2\frac{1}{2} \times d_1 \times d_221​×d1​×d2​, where d1d_1d1​ and d2d_2d2​ are the lengths of the diagonals.

What is a binomial expression? A binomial expression is an algebraic expression that has two terms, such as (a+b)(a + b)(a+b).

How do you calculate the simple interest on a loan? Simple interest is calculated using the formula I=P×r×tI = P \times r \times tI=P×r×t, where PPP is the principal, rrr is the rate of interest, and ttt is the time in years.

What is the sum of the angles in a triangle? The sum of the interior angles of any triangle is always 180 degrees.

How do you calculate the probability of getting a sum of 7 when rolling two dice? There are 6 favorable outcomes for a sum of 7, so the probability is 636=16\frac{6}{36} = \frac{1}{6}366​=61​.

How do you convert a fraction to a decimal? Divide the numerator by the denominator to get the decimal equivalent.

What is the formula for the area of a sector of a circle? The area of a sector is θ360×πr2\frac{\theta}{360} \times \pi r^2360θ​×πr2, where θ\thetaθ is the central angle and rrr is the radius.

What is the method of completing the square in algebra? Completing the square involves transforming a quadratic expression into a perfect square trinomial by adding or subtracting a constant.

How do you calculate the height of a triangle given its area and base? The height can be found using the formula height=2×areabase\text{height} = \frac{2 \times \text{area}}{\text{base}}height=base2×area​.

What is a factor of a polynomial? A factor is a number or expression that divides another number or expression without leaving a remainder.

How do you find the midpoint of a line segment in coordinate geometry? The midpoint is found by averaging the x-coordinates and y-coordinates of the two endpoints: (x1+x22,y1+y22)\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)(2x1​+x2​​,2y1​+y2​​).

How do you solve an equation with two variables? You can solve the equation using substitution or elimination, where you solve one equation for one variable and substitute that into the other.

How do you calculate the percentage increase or decrease? The percentage change is given by New Value−Old ValueOld Value×100\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100Old ValueNew Value−Old Value​×100.

Top Indian Books for Grade 10 Maths NCERT Solutions

Mathematics for Class 10 by R.S. Aggarwal (S. Chand Publication)
This book offers a comprehensive understanding of all the topics from the NCERT curriculum. It includes solved examples, practice problems, and detailed explanations. The content is structured to enhance the problem-solving abilities of students, focusing on concepts like algebra, geometry, and trigonometry.

Concise Mathematics for Class 10 by R.S. Aggarwal (S. Chand Publication)
This book presents concepts in a simplified manner and is ideal for students who want to strengthen their fundamentals. The book includes multiple types of questions, including examples, MCQs, and subjective problems for practice.

Class 10 Mathematics by R.D. Sharma (Dhanpat Rai & Co.)
R.D. Sharma's books are well-known for their detailed explanations and step-by-step approach. This book covers all the key chapters like Linear Equations, Probability, and Coordinate Geometry with a large number of practice questions.

Mathematics Class 10 by K.C. Sinha (Rathi Publication)
This book provides an extensive collection of practice problems that help in mastering different mathematical concepts. The author also includes brief theory sections along with numerous solved examples for better understanding.

All in One Mathematics by Arihant (Arihant Publications)
The "All in One" series is a favorite among students preparing for board exams. This book includes NCERT solutions, exam-oriented questions, chapter-wise practice sets, and sample papers. It covers all aspects from theory to application, ideal for revision.

Mathematics for Class 10 by K. Kumar (K.K. Publications)
A reliable book for clearing concepts in algebra, geometry, and statistics. With a blend of solved examples and unsolved questions, this book helps in building a deep understanding of Grade 10 Maths topics.

Objective Mathematics Class 10 by R.D. Sharma (Dhanpat Rai & Co.)
Focused primarily on objective questions, this book helps students to prepare effectively for competitive exams and board exams. It includes multiple-choice questions, short-answer questions, and long-answer problems.

Mathematics Class 10 by M.L. Aggarwal (Vikas Publication)
This book is known for its clear explanations and extensive set of questions for practice. Each chapter ends with review exercises that help reinforce the topics covered, with answers given at the back of the book.

Success Master Mathematics Class 10 by G. Tewani (Success Publications)
Offering chapter-wise theory and practice questions, this book is designed for those who need both basic and advanced level questions. It includes explanations followed by a variety of question types, including real-life application problems.

Exemplar Problems in Mathematics for Class 10 by NCERT (NCERT)
This book provides an extensive collection of higher-level problems from various chapters of the NCERT curriculum. It challenges students and encourages critical thinking, making it ideal for enhancing problem-solving skills.

Mathematics for Class 10 by C.B. Gupta (Pustak Mahal)
The book includes a variety of problems ranging from easy to complex, offering a solid foundation in mathematics. The clear explanations and concise theory make it a great resource for both classwork and revision.

Understanding Mathematics for Class 10 by M.C. Sharma (Vikas Publication)
This book is a great reference for building conceptual clarity in mathematics. It provides detailed solutions and a variety of practice questions, perfect for reinforcing the understanding of complex topics.

Target Mathematics Class 10 by S.K. Gupta (R.K. Publishers)
With a focus on conceptual learning and thorough practice, this book is designed to help students achieve excellent marks in board exams. It contains important questions, practice sets, and tips for exam preparation.

NCERT Exemplar Problems in Mathematics Class 10 (NCERT)
A perfect resource for students who want to dive deeper into mathematical problems. The book includes challenging problems designed to improve logical reasoning and critical thinking, complementing the main textbook.

Mathematics Class 10 (ICSE) by S.K. Aggarwal (Aristocrat Publishers)
Though focused on ICSE syllabus, this book includes many useful exercises and examples for students of the CBSE curriculum as well. It covers essential topics like quadratic equations and surface area and volume.

Class 10 Mathematics by D.K. Aggarwal (Ramesh Publishing House)
This book is known for its clear, systematic presentation of mathematical concepts and a vast array of solved examples and practice questions. The exercises are arranged according to their level of difficulty.

Objective Mathematics for Class 10 by K.K. Gupta (R.L. Publishing)
Aimed at preparing students for various competitive exams, this book includes objective questions with answers and detailed explanations for quick learning and effective practice.

Mathematics for Class 10 by S.L. Loney (S. Chand Publication)
Known for its well-structured content, this book offers clear explanations and numerous exercises on every concept. It’s a great choice for students looking to excel in both board exams and competitive tests.

Complete Mathematics for Class 10 by K.K. Verma (Orient BlackSwan)
A book tailored for students who aim for excellence, it provides detailed theory and a wide variety of questions with solutions. It includes tips for solving problems quickly and efficiently.

Mathematics for Class 10 by S.C. Gupta (Laxmi Publications)
This book covers all the essential topics of Grade 10 mathematics with a good number of problems for practice. Students can expect to find comprehensive solutions and an extensive range of questions for each chapter.

Grade 10 Maths NCERT Solutions – A Comprehensive Guide to Mastering the Subject

Mathematics is one of the most important subjects for Grade 10 students, and mastering it can open doors to better academic performance and future career opportunities. The Grade 10 Maths NCERT Solutions are designed to help students understand core mathematical concepts, providing them with step-by-step solutions to problems. Whether you are preparing for your board exams or just trying to improve your grasp of mathematical principles, these solutions are an invaluable resource.

The NCERT Maths solutions are aligned with the curriculum prescribed by the CBSE and are designed to be comprehensive and accessible. One of the key advantages of using the NCERT solutions is that they are created by experts in the field, ensuring that students get detailed and accurate explanations to help with every topic.

Grade 10 Maths primarily focuses on topics like Algebra, Geometry, Trigonometry, Probability, and Coordinate Geometry. The NCERT Solutions offer clear explanations of these subjects, making it easier for students to understand complex problems and solve them efficiently. Each chapter is broken down into smaller sections, and practice exercises at the end of each section help reinforce the material covered.

For students struggling with problem-solving techniques, these solutions provide step-by-step guides that teach the process of tackling difficult questions. By following the solutions, students can understand the logic behind each problem and improve their ability to approach similar problems in the future. Additionally, the solutions include important formulas, shortcuts, and tricks to solve problems quickly and accurately.

A notable feature of the NCERT solutions is their focus on conceptual clarity. Rather than just memorizing formulas and solutions, students are encouraged to understand the “why” and “how” behind each concept. This approach promotes long-term retention of the material and helps students apply their knowledge to real-world problems.

Students preparing for their exams can benefit from revision notes and sample papers included in many NCERT solutions. These resources offer practice questions from previous years' exams, giving students a taste of what to expect during their final assessments. Furthermore, solving sample papers enhances speed and accuracy, which are crucial for time-bound exams.

Incorporating NCERT Solutions into your study routine allows you to develop a deeper understanding of Grade 10 Maths. Whether it’s mastering the basics or tackling more advanced topics, these solutions provide the right mix of theory, application, and practice to ensure academic success.

To make the most of these resources, students should dedicate consistent time to practicing problems, reviewing solutions, and seeking help when necessary. With the right tools and determination, mastering Grade 10 Maths becomes a more achievable and rewarding task.