Class 10 Maths Quiz

Chapter 1 : Real Numbers

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1. For some integer $m$, every even integer is of the form

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2. If two positive integers $a$ and $b$ can be expressed as $a=x^{3} y^{2}$ and $b=x y^{3} ; x, y$ being prime numbers, then $\operatorname{HCF}(a, b)$ is:

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3. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:

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4. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :

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5. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:

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6. The HCF of 36 and 78 will be:

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7. Which of the following number will be terminating?

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8. Express 0.104 in the form $\frac{p}{q}$.

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9. Express 15.75 in the form $\frac{p}{q}$.

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10. . The LCM of 8,9 and 25 will be:

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11. The LCM of 45 and 75 will be:

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12. The relation between their LCM and HCF, if numbers are positive integer.

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13. The LCM of 12,15 and 21 will be:

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14. Express 0.375 in the form $\frac{p}{q}$.

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15. The LCM of 26 and 91 will be:

Chapter Summary: Real Numbers

Chapter 1 of Class 10 Maths, Real Numbers, forms the basis of advanced mathematics. Here are the key topics covered in this chapter:

1. Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that every composite number can be expressed (factorized) as a product of prime numbers in a unique way, except for the order of primes. For example:

  • Example: 60 = 22 x 3 x 5
  • Applications: Finding LCM and HCF using prime factorization.

2. Euclid's Division Lemma

Euclid's Division Lemma states that for any two positive integers a and b, there exist unique integers q and r such that:

a = bq + r, where 0 ≤ r < b

Applications include finding the HCF of two numbers.

3. Revisiting Irrational Numbers

Proving that certain numbers, such as \( \sqrt{2} \), \( \sqrt{3} \), and \( \sqrt{5} \), are irrational involves using proof by contradiction and the properties of prime factorization.

4. Decimal Representation of Rational Numbers

Rational numbers have either a terminating or repeating decimal expansion. For example:

  • 1/2 = 0.5 (terminating)
  • 1/3 = 0.333... (non-terminating, repeating)

Why This Chapter is Important

Understanding Real Numbers is crucial as it lays the foundation for higher-level mathematical concepts and problem-solving skills. The topics in this chapter are also frequently tested in board exams.

Additional Resources

Looking for more practice? Check out these resources: