Real Numbers

Bihar Board Class 10 · Mathematics · 62 past questions

1. Q1 2026

   According to Euclid's division lemma for any two given positive integers $a$ and $b$, there exist unique…

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2. Q2 2026

   According to Euclid's division algorithm the HCF of 867 and 255 is

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3. Q3 2026

   Product of prime factors of 7429 is

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4. Q4 2026

   If $c$ and $d$ are the LCM and HCF of two numbers $a$ and $b$ respectively then

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5. Q5 2026

   Which of the following numbers is a rational number ?

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6. Q6 2026

   The number whose generalised form is $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ is said to be

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7. Q7 2026

   The number whose decimal expansion is neither terminating nor repeating is said to be

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8. Q8 2026

   $(3-2\sqrt{5})^2 =$

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9. Q9 2025

   Which of the following fractions has terminating decimal expansion ?

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10. Q10 2025

    In the form of $\dfrac{p}{2^n \times 5^m}$, $0{\cdot}505$ can be written as

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11. Q11 2025

    If in division algorithm $a = bq + r$, $b = 4$, $q = 5$ and $r = 1$, then what is the value of $a$?

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12. Q12 2024

    $\sqrt{\frac{64}{81}}+\sqrt{\frac{16}{9}}$ is

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13. Q13 2024

    The product of two irrational numbers $3+\sqrt{6}$ and $3-\sqrt{5}$ will be a/an

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14. Q14 2024

    The simplest form of $(0.\overline{3} + 0.\overline{4})$ is

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15. Q15 2024

    If $156 = 2^x \times 3^y \times 13^z$, then $x + y + z =$

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16. Q16 2024

    $\sqrt{10} \times \sqrt{15}$ is

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17. Q17 2024

    In the form of $\frac{p}{2^n \times 5^m}$, $0.105$ can be written as

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18. Q18 2024

    If H.C.F. of two numbers = 25 and L.C.M = 50 then the product of numbers will be

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19. Q19 2024

    If in division algorithm $a = bq + r$, $b = 61$, $q = 27$ and $r = 32$, then what is the value of $a$ ?

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20. Q20 2024

    If $q$ is a positive integer, which of the following is an odd positive integer?

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21. Q21 2024

    The H.C.F. of two consecutive odd numbers is

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22. Q22 2023

    $\frac{\sqrt{81}}{2}$ is

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23. Q23 2023

    What is the exponent of 2 in prime factorization of 192 ?

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24. Q24 2023

    If in division algorithm a = bq + r, a = 72, q = 8 and r = 0, then what is the value of b?

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25. Q25 2023

    Which of the following has terminating decimal expansion?

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26. Q26 2023

    If q is a positive integer, which of the following is not an odd positive integer ?

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27. Q27 2023

    The HCF of two consecutive even numbers is

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28. Q28 2023

    The sum of a rational and an irrational number is which type of number?

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29. Q29 2023

    The product of two numbers is 8670 and their HCF is 17. What is their LCM?

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30. Q30 2023

    Which of the following is a rational number?

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31. Q31 2023

    If 130 = 15 × 8 + 10 and 15 = 5 x 3 + 0, then HCF (130, 15) will be

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32. Q32 2022

    The exponent of 2 in the prime factorisation of 64 is

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33. Q33 2022

    H.C.F. $(p, q) \times$ L.C.M. $(p, q)$ is equal to

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34. Q34 2022

    Which of the following is the smallest natural number ?

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35. Q35 2022

    Which of the following is a rational number ?

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36. Q36 2022

    Which of the following is an irrational number ?

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37. Q37 2022

    If $p$ and $q$ are two prime numbers then their HCF will be

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38. Q38 2022

    $0.\overline{13} =$

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39. Q39 2022

    The H.C.F. of 18 and 72 is

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40. Q40 2022

    The rationalising factor of $\sqrt{12}$ is

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41. Q41 2022

    If $p$ is a positive integer then the form of positive even integer is

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42. Q42 2022

    Which of the following has terminating decimal expansion ?

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43. Q43 2022

    Which of the following has non-terminating decimal expansion ?

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44. Q44 2020

    If HCF of 65 and 117 is in the form of $65m - 117$ then the value of $m$ is

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45. Q45 2020

    The ratio of the LCM and HCF of 2, 10 and 20 is

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46. Q46 2020

    If $a$ and $b$ are prime numbers then LCM of $a$ and $b$ is

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47. Q47 2020

    Which of the following is a prime number ?

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48. Q48 2020

    Which of the following is a rational number ?

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49. Q49 2020

    The HCF of the smallest composite number and smallest prime number is

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50. Q50 2019

    The ratio between the LCM and HCF of 5, 15 and 20 is -

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51. Q51 2019

    LCM of two numbers a and 18 is 36 and HCF is 2, then the value if 'a' is -

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52. Q52 2019

    If p and q are two prime numbers, then their HCF is -

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53. Q53 2019

    Which of the following is not irrational?

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54. Q54 2019

    The product of the smallest prime number and the smallest composite number is -

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55. Q55 2018

    Every point on a number line represents -

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56. Q56 2018

    Which of the following numbers has terminating decimal expansion?

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57. Q57 2018

    The least number, which is perfect square and is divisible by each 16, 20, and 24 is -

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58. Q58 2018

    The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one of the number is 280 then…

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59. Q59 2018

    23.$\dot{4}\dot{3}$ can be expressed in the form of $\frac{p}{q}$ (p, q are integers, $q \neq 0$) -

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60. Q60 2018

    The square root of 64 divided by the cube root of 64 is -

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61. Q61 2018

    $\sqrt{10} \times \sqrt{15}$ is equal to -

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62. Q62 2017

    $\sqrt{5}$ is a number-

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