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.
\(17 \times 11 \times 13 + 11\) is
- a prime number.
- multiple of 17.
- a composite number.
- an odd number.
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2.
Determine the ratio in which the line \(2x + y = 6\) divides the line segment joining the points (1, 3) and (2, 5).
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3.
Find the H.C.F. and L.C.M. of 408 and 312.
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4.
Find the missing frequencies p and q in the following frequency distribution, when sum of frequencies is 40 and mean is 19 :
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5.
There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylindrical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm. Considering mushroom a solid object, answer the following questions:

36(i) What is the total height of a mushroom ?
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6.
In a circular museum hall of radius 14 m, some statues are displayed. Statues are kept inside the inner concentric circle of radius 7 m. One such statue lying in sector OAB, is fenced along line segments OA, AP, PB and BO where P is a point on outer circle. Based on above information, answer the following questions:

37(i) Find \(m\angle AOP\).
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