NCERT Solutions for class 10 Maths Chapter 1: Real Numbers

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NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers are provided in this article. Real numbers in the number system are the set of rational and irrational numbers. Real numbers can be expressed in the number line and arithmetic operations can also be operated on them. The average number of questions that are asked from this chapter is usually 3.

Class 10 Maths Chapter 1 Real numbers belong to Unit 1 Number Systems which has a weightage of 10 marks in the Class 10 Maths Examination. NCERT Solutions for Class 10 Maths for Chapter 1 covers two important properties of positive integers which are Euclid's Division Lemma algorithm and the Fundamental Theorem Of Arithmetic.

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NCERT Solutions for Class 10 Maths Chapter 1

The Chapter 1 Class 10 Maths are given below –

Important Topics in Class 10 Maths Chapter 1 Real Numbers

Real Numbers is an important chapter of Class 10 Maths. The main topics of the chapter include –

Euclid’s Division Lemma states that for any two integers a and b, there exists a unique pair of integers q and r such that a = b × q + r and 0 ≤ r < b.

This lemma is equivalent to: Dividend = Divisor × Quotient + Remainder In other words, for a pair of dividend and divisor, the remainder and the quotient obtained are unique.

Prime Factorisation is the method of expressing a natural number as a product of different prime numbers.

For example: 36 = 2 × 2 × 3 × 3 is the prime factorisation of 36.

Fundamental Theorem of Arithmetic states that the prime factorisation for a given number is unique if the arrangement of the prime factors is ignored.

For example: 36 = 2 × 2 × 3 × 3 or, 36 = 2 × 3 × 2 × 3

For any 2 positive integers a and b, a × b = H.C.F × L.C.M.

For example, For 36 and 56, the HCF is 4 and the LCM is 504 36 × 56 = 2016 4 × 504 = 2016 Therefore, 36 × 56 = 4 × 504

Rational numbers are the numbers that can be written in the p/q form, where p and q are integers and q ≠ 0.

For example – 1/2, 4/5, 3/4, etc.

NCERT Solutions For Class 10 Maths Chapter 1 Exercises:

The detailed solutions for all the NCERT Solutions for Real Numbers under different exercises are as follows:

Real Numbers – Related Topics:

Real Numbers Formula	Root 2 is an irrational number	Complex Numbers
Real Numbers Important Questions	Real Numbers Formula	Real Numbers Chapter Notes

CBSE Class 10 Mathematics Study Guides:

Difference between in Maths	Math Formula	Mathematics Notes
NCERT Solutions for Class 10 Maths	Math MCQs	Geometry
Maths Study Material	Mensuration	Calculus

CBSE X Related Questions

1.
In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.
View Solution
2.
Assertion (A) : H.C.F. $(36 m^{2}, 18 m) = 18 m$, where $m$ is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
3.
A kite is flying at a height of $60 \text{ m}$ above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as $30^{\circ}$. From the bottom of the same building, the angle of elevation of kite is $45^{\circ}$. Find the length of the string and height of roof from the ground. (Use $\sqrt{3} = 1.73$)
View Solution
4.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If $OP = 13$ cm, then find the length AB and PA.
View Solution
5.
Prove that :
$\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$.
View Solution
6.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.
View Solution

View All

Similar Mathematics Concepts

Real Numbers: Euclid’s Division Lemma, Properties & Sets

Real Numbers Formula: Some Basic Properties of Real Numbers

Real Numbers Important Questions

NCERT Solutions for Class 10 Maths: Chapter-wise Solutions and Important Topics

MCQs for Real Numbers: Introduction & Explanation

Negative Numbers in Daily Life: Basic Operations & Applications

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.1

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.3

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.4

CBSE X Syllabus

Mathematics Preparation Guides

Arithmetic Progressions: Properties, Formulas and Solved Examples

Distance Formula and Derivation of Coordinate Geometry

Probability- A Theoretical Approach: An Overview and Examples

Area of Circle: Area Formula, Derivation with Solved Examples

Mode of Grouped Data

Pythagoras Theorem: Formula, Theorem, Proof and Examples

Nature of Roots of Quadratic Equation

Probability: Concepts, Problems and Solved Examples

Trigonometry: Ratios, Identities & Trigonometric Table

Heights and Distances: Applications in Trigonometry

Real Numbers: Euclid’s Division Lemma, Properties & Sets

Surface Areas and Volumes Revision Notes

Circles: Definition, Properties, Parts, Theorems

Constructions Revision Notes

Pair of Linear Equations In Two Variables Important Questions

Circles Revision Notes: Theorems of Tangent to the Circle

Statistics Important Questions

Mathematics NCERT Solutions

Euclid's Division Lemma: Proof, Finding HCF & Examples

Area of a Sector: Definition, Formulae and Solved Examples

Real Numbers: Definition, Properties and Examples

Events in Probability: Definition, Types, Examples

Relation Between HCF and LCM: Definition, Methods and Formulas

Geometric Probability: Formula, Illustration, Model

Algebra Formula: Important Formulas in Algebra & Solved Examples

Angle of Depression: Definition, Formula and Solved Examples

Cyclic Quadrilateral: Properties, Theorems and Formulas

Polynomial Notation: Types, Remainder Theorem, Linear and Quadratic Equation

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NCERT Solutions for class 10 Maths Chapter 1: Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1

Important Topics in Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions For Class 10 Maths Chapter 1 Exercises:

CBSE X Related Questions

1.
In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

2.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

4.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

5.
Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).

6.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

Similar Mathematics Concepts

Comments

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NCERT Solutions for class 10 Maths Chapter 1: Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1

Important Topics in Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions For Class 10 Maths Chapter 1 Exercises:

CBSE X Related Questions

1.In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

2.Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number. Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

4.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

5.Prove that : \(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).

6.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

2.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

4.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.

5.
Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).

6.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.