SEBA Class 9 Maths Chapter 1 Number System MCQs (2026–27) – Assam Eduverse

The SEBA Class 9 Maths Chapter 1 Number System MCQs (2026–27) are prepared strictly according to the latest ASSEB syllabus and updated board examination pattern. These SEBA Class 9 Maths Chapter 1 Number System MCQs include important objective questions, conceptual MCQs, and exam-oriented practice sets designed to strengthen mathematical foundations.

Prepared by subject experts of Assam Eduverse, these seba class 9 maths chapter 1 mcqs focus on key topics such as real numbers, rational and irrational numbers, representation of numbers on the number line, terminating and non-terminating decimals, laws of exponents, and operations on real numbers. Practicing these number system mcqs class 9 seba and assam board class 9 maths objective questions improves conceptual clarity and accuracy.

Regular revision of these ASSEB Class 9 Maths Important MCQs ensures strong preparation for the 2026–27 board examination and enhances performance in objective-type questions.

SEBA Class 9 Maths Chapter 1 Number System MCQs – ASSEB 2026–27 Board Exam Practice

Table of Contents

Q1. Rational number \( \frac{3}{40} \) is equal to:

(a) 0.75
(b) 0.12
(c) 0.012
(d) 0.075

Answer: (d) 0.075

Solution:
\( \frac{3}{40} = \frac{75}{1000} = 0.075 \)

Q2. A rational number between 3 and 4 is:

(a) \( \frac{3}{2} \)
(b) \( \frac{4}{3} \)
(c) \( \frac{7}{2} \)
(d) \( \frac{7}{4} \)

Answer: (c) \( \frac{7}{2} \)

Solution:
\( \frac{7}{2} = 3.5 \), which lies between 3 and 4.

Q3. A rational number between \( \frac{3}{5} \) and \( \frac{4}{5} \) is:

(a) \( \frac{7}{5} \)
(b) \( \frac{7}{10} \)
(c) \( \frac{3}{10} \)
(d) \( \frac{4}{10} \)

Answer: (b) \( \frac{7}{10} \)

Solution:
\( \frac{3}{5}=0.6,\; \frac{4}{5}=0.8,\; \frac{7}{10}=0.7 \).
0.7 lies between 0.6 and 0.8.

Q4. A rational number between \( \frac{1}{2} \) and \( \frac{3}{4} \) is:

(a) \( \frac{2}{5} \)
(b) \( \frac{5}{8} \)
(c) \( \frac{4}{3} \)
(d) \( \frac{1}{4} \)

Answer: (b) \( \frac{5}{8} \)

Solution:
\( \frac{1}{2}=0.5,\; \frac{3}{4}=0.75,\; \frac{5}{8}=0.625 \).
0.625 lies between 0.5 and 0.75.

Q5. Which one of the following is not a rational number:

(a) \( \sqrt{2} \)
(b) 0
(c) \( \sqrt{4} \)
(d) \( \sqrt{-16} \)

Answer: (a) \( \sqrt{2} \)

Solution:
\( \sqrt{2} \) cannot be written in the form \( \frac{p}{q} \).
So it is irrational.

Q6. Which one of the following is an irrational number:

(a) \( \sqrt{4} \)
(b) \( 3\sqrt{8} \)
(c) \( \sqrt{100} \)
(d) \( -\sqrt{0.64} \)

Answer: (b) \( 3\sqrt{8} \)

Solution:
\( \sqrt{8}=2\sqrt{2} \Rightarrow 3\sqrt{8}=6\sqrt{2} \).
Since \( \sqrt{2} \) is irrational, \( 6\sqrt{2} \) is irrational.

Q7. Decimal representation of \( \frac{1}{5} \) is:

(a) 0.2
(b) 0.5
(c) 0.02
(d) 0.002

Answer: (a) 0.2

Solution:
\( \frac{1}{5}=0.2 \)

Q8. \( 3\frac{3}{8} \) in decimal form is:

(a) 3.35
(b) 3.375
(c) 33.75
(d) 337.5

Answer: (b) 3.375

Solution:
\( 3+\frac{3}{8}=3+0.375=3.375 \)

Q9. \( \frac{5}{6} \) in decimal form is:

(a) \( 0.8\overline{3} \)
(b) \( 0.\overline{83} \)
(c) \( 0.6\overline{3} \)
(d) \( 0.63\overline{3} \)

Answer: (a) \( 0.8\overline{3} \)

Solution:
\( \frac{5}{6}=0.8333\ldots=0.8\overline{3} \)

Q10. Decimal representation of \( \frac{8}{27} \) is:

(a) \( 0.\overline{296} \)
(b) \( 0.29\overline{6} \)
(c) \( 0.2\overline{96} \)
(d) 0.296

Answer: (a) \( 0.\overline{296} \)

Solution:
\( \frac{8}{27}=0.296296296\ldots \)
The block 296 repeats.

Q11. Which one of the following is a rational number:

(a) \( \sqrt{3} \)
(b) \( \sqrt{2} \)
(c) \( 0 \)
(d) \( \sqrt{5} \)

Answer: (c) \( 0 \)

Solution:
A rational number can be written in the form \( \frac{p}{q} \).
\( 0 = \frac{0}{1} \). Hence, it is rational.

Q12. \( 0.6666\ldots \) in \( \frac{p}{q} \) form is:

(a) \( \frac{6}{99} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{3}{5} \)
(d) \( \frac{1}{66} \)

Answer: (b) \( \frac{2}{3} \)

Solution:
Let \( x = 0.6666\ldots \)
\( 10x = 6.6666\ldots \)
\( 10x - x = 6 \Rightarrow 9x = 6 \Rightarrow x = \frac{6}{9} = \frac{2}{3} \)

Q13. \( 4\frac{1}{8} \) in decimal form is:

(a) 4.125
(b) 4.15
(c) 4.015
(d) 0.4125

Answer: (a) 4.125

Solution:
\( 4 + \frac{1}{8} = 4 + 0.125 = 4.125 \)

Q14. The value of \( (3 + \sqrt{3})(3 - \sqrt{3}) \) is:

(a) 0
(b) 6
(c) 9
(d) 3

Answer: (b) 6

Solution:
Using \( (a+b)(a-b)=a^2-b^2 \):
\( 9 - 3 = 6 \)

Q15. The value of \( (\sqrt{5} + \sqrt{2})^2 \) is:

(a) \( 7 + 2\sqrt{5} \)
(b) \( 7 + 2\sqrt{10} \)
(c) \( 5 + 2\sqrt{10} \)
(d) \( 7 - 2\sqrt{10} \)

Answer: (b) \( 7 + 2\sqrt{10} \)

Solution:
\( 5 + 2 + 2\sqrt{10} = 7 + 2\sqrt{10} \)

Q16. The value of \( (\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2}) \) is:

(a) 10
(b) 7
(c) 3
(d) 5

Answer: (c) 3

Solution:
\( 5 - 2 = 3 \)

Q17. The value of \( (3 + \sqrt{3})(2 + \sqrt{2}) \) is:

(a) \( 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6} \)
(b) \( 6 - 3\sqrt{2} + 2\sqrt{3} - \sqrt{6} \)
(c) \( 6 + 3\sqrt{2} - 2\sqrt{3} + \sqrt{6} \)
(d) \( 6 - 3\sqrt{2} - 2\sqrt{3} - \sqrt{6} \)

Answer: (a) \( 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6} \)

Solution:
Multiply each term:
\( 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6} \)

Q18. The value of \( (\sqrt{11} + \sqrt{7})(\sqrt{11} - \sqrt{7}) \) is:

(a) 4
(b) −4
(c) 18
(d) −18

Answer: (a) 4

Solution:
\( 11 - 7 = 4 \)

Q19. The value of \( (5 + \sqrt{5})(5 - \sqrt{5}) \) is:

(a) 0
(b) 25
(c) 20
(d) 5

Answer: (c) 20

Solution:
\( 25 - 5 = 20 \)

Q20. On rationalizing the denominator of \( \frac{1}{\sqrt{7}} \), we get:

(a) 7
(b) \( \frac{\sqrt{7}}{7} \)
(c) \( -\frac{\sqrt{7}}{7} \)
(d) \( \sqrt{7} \)

Answer: (b) \( \frac{\sqrt{7}}{7} \)

Solution:
Multiply numerator and denominator by \( \sqrt{7} \):
\( \frac{\sqrt{7}}{7} \)

Q21. On rationalizing the denominator of \( \frac{1}{\sqrt{7}-\sqrt{6}} \), we get:

(a) \( \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}-\sqrt{6}} \)
(b) \( \frac{\sqrt{7}-\sqrt{6}}{\sqrt{7}+\sqrt{6}} \)
(c) \( \sqrt{7}+\sqrt{6} \)
(d) \( \sqrt{7}-\sqrt{6} \)

Answer: (c) \( \sqrt{7}+\sqrt{6} \)

Solution:
Multiply numerator and denominator by conjugate \( (\sqrt{7}+\sqrt{6}) \):
\( \frac{1}{\sqrt{7}-\sqrt{6}} \times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}} \)

Denominator becomes:
\( 7 - 6 = 1 \)

So result = \( \sqrt{7}+\sqrt{6} \)

Q22. On rationalizing the denominator of \( \frac{1}{\sqrt{5}+\sqrt{2}} \), we get:

(a) \( \sqrt{5}-\sqrt{2} \)
(b) \( \sqrt{2}-\sqrt{5} \)
(c) \( \frac{\sqrt{5}-\sqrt{2}}{3} \)
(d) \( \frac{\sqrt{2}-\sqrt{5}}{3} \)

Answer: (c) \( \frac{\sqrt{5}-\sqrt{2}}{3} \)

Solution:
Multiply by conjugate \( (\sqrt{5}-\sqrt{2}) \)
Denominator: \( 5-2=3 \)
So result = \( \frac{\sqrt{5}-\sqrt{2}}{3} \)

Q23. On rationalizing the denominator of \( \frac{1}{\sqrt{7}-2} \), we get:

(a) \( \sqrt{7}-2 \)
(b) \( \sqrt{7}+2 \)
(c) \( \frac{\sqrt{7}+2}{3} \)
(d) \( \frac{\sqrt{7}-2}{3} \)

Answer: (c) \( \frac{\sqrt{7}+2}{3} \)

Solution:
Multiply by conjugate \( (\sqrt{7}+2) \)
Denominator: \( 7-4=3 \)
So result = \( \frac{\sqrt{7}+2}{3} \)

Q24. On rationalizing the denominator of \( \frac{1}{\sqrt{2}} \), we get:

(a) 2
(b) \( \sqrt{2} \)
(c) \( \frac{2}{\sqrt{2}} \)
(d) \( \frac{\sqrt{2}}{2} \)

Answer: (d) \( \frac{\sqrt{2}}{2} \)

Solution:
Multiply numerator and denominator by \( \sqrt{2} \):
\( \frac{\sqrt{2}}{2} \)

Q25. On rationalizing the denominator of \( \frac{1}{2+\sqrt{3}} \), we get:

(a) \( 2-\sqrt{3} \)
(b) \( \sqrt{3}-2 \)
(c) \( 2+\sqrt{3} \)
(d) \( -\sqrt{3}-2 \)

Answer: (a) \( 2-\sqrt{3} \)

Solution:
Multiply by conjugate \( (2-\sqrt{3}) \)
Denominator: \( 4-3=1 \)
So result = \( 2-\sqrt{3} \)

Q26. On rationalizing the denominator of \( \frac{1}{\sqrt{3}-\sqrt{2}} \), we get:

(a) \( \frac{1}{\sqrt{3}+\sqrt{2}} \)
(b) \( \sqrt{3}+\sqrt{2} \)
(c) \( \sqrt{2}-\sqrt{3} \)
(d) \( -\sqrt{3}-\sqrt{2} \)

Answer: (b) \( \sqrt{3}+\sqrt{2} \)

Solution:
Multiply by conjugate \( (\sqrt{3}+\sqrt{2}) \)
Denominator: \( 3-2=1 \)
So result = \( \sqrt{3}+\sqrt{2} \)

Q27. The value of \( 64^{\frac{1}{2}} \) is:

(a) 8
(b) 4
(c) 16
(d) 32

Answer: (a) 8

Solution:
\( 64^{1/2} = \sqrt{64} = 8 \)

Q28. The value of \( 32^{\frac{1}{5}} \) is:

(a) 16
(b) 160
(c) 2
(d) 18

Answer: (c) 2

Solution:
\( 32 = 2^5 \)
\( (2^5)^{1/5} = 2 \)

Q29. The value of \( (125)^{\frac{1}{3}} \) is:

(a) 5
(b) 25
(c) 45
(d) 35

Answer: (a) 5

Solution:
\( 125 = 5^3 \)
\( (5^3)^{1/3} = 5 \)

Q30. The value of \( 9^{\frac{3}{2}} \) is:

(a) 18
(b) 27
(c) -18
(d) \( \frac{1}{27} \)

Answer: (b) 27

Solution:
\( 9^{3/2} = (\sqrt{9})^3 = 3^3 = 27 \)

Q31. The value of \( 32^{\frac{2}{5}} \) is:

(a) 2
(b) 4
(c) 16
(d) 14

Answer: (b) 4

Solution:
\( 32 = 2^5 \)
\( 32^{2/5} = (2^5)^{2/5} \)
\( = 2^2 = 4 \)

Q32. The value of \( 16^{\frac{3}{4}} \) is:

(a) 4
(b) 12
(c) 8
(d) 48

Answer: (c) 8

Solution:
\( 16 = 2^4 \)
\( 16^{3/4} = (2^4)^{3/4} \)
\( = 2^3 = 8 \)

Q33. The value of \( 125^{-\frac{1}{3}} \) is:

(a) \( \frac{1}{5} \)
(b) \( \frac{1}{25} \)
(c) \( \frac{1}{15} \)
(d) \( \frac{1}{125} \)

Answer: (a) \( \frac{1}{5} \)

Solution:
\( 125 = 5^3 \)
\( 125^{-1/3} = (5^3)^{-1/3} \)
\( = 5^{-1} = \frac{1}{5} \)

Q34. The value of \( 11^{\frac{1}{2}} \div 11^{\frac{1}{4}} \) is:

(a) \( 11^{1/4} \)
(b) \( 11^{3/4} \)
(c) \( 11^{1/8} \)
(d) \( 11^{1/2} \)

Answer: (a) \( 11^{1/4} \)

Solution:
Using law: \( a^m \div a^n = a^{m-n} \)
\( 11^{1/2 - 1/4} \)
\( = 11^{1/4} \)

Q35. The value of \( 64^{-\frac{3}{2}} \) is:

(a) \( \frac{1}{96} \)
(b) \( \frac{1}{64} \)
(c) 512
(d) \( \frac{1}{512} \)

Answer: (d) \( \frac{1}{512} \)

Solution:
\( 64 = 8^2 \)
\( 64^{3/2} = ( \sqrt{64} )^3 = 8^3 = 512 \)
Negative power means reciprocal:
\( = \frac{1}{512} \)

Q36. The value of \( (125)^{\frac{2}{3}} \) is:

(a) 5
(b) 25
(c) 45
(d) 35

Answer: (b) 25

Solution:
\( 125 = 5^3 \)
\( (5^3)^{2/3} = 5^2 = 25 \)

Q37. The value of \( 25^{\frac{3}{2}} \) is:

(a) 5
(b) 25
(c) 125
(d) 625

Answer: (c) 125

Solution:
\( 25 = 5^2 \)
\( (5^2)^{3/2} = 5^3 = 125 \)

Q38. The value of \( \frac{1}{11} \) in decimal form is:

(a) \( 0.\overline{09} \)
(b) \( 0.\overline{90} \)
(c) \( 0.0\overline{9} \)
(d) 0.009

Answer: (a) \( 0.\overline{09} \)

Solution:
\( \frac{1}{11} = 0.090909\ldots \)
Digits 09 repeat.

Q39. Decimal expansion of a rational number is terminating if its denominator has prime factors:

(a) 2 or 5
(b) 3 or 5
(c) 9 or 11
(d) 3 or 7

Answer: (a) 2 or 5

Solution:
A rational number in lowest form has terminating decimal
only if denominator has prime factors 2 and/or 5.

Q40. The exponent form of \( \sqrt[3]{7} \) is:

(a) \( 7^3 \)
(b) \( 3^7 \)
(c) \( 7^{1/3} \)
(d) \( 3^{1/7} \)

Answer: (c) \( 7^{1/3} \)

Solution:
Cube root means power \( \frac{1}{3} \).
So \( \sqrt[3]{7} = 7^{1/3} \)

Q41. Which of the following is true?

(a) Every whole number is a natural number
(b) Every integer is a rational number
(c) Every rational number is an integer
(d) Every integer is a whole number

Answer: (b) Every integer is a rational number

Solution:
Any integer \( n \) can be written as \( \frac{n}{1} \).
Hence every integer is a rational number.

Q42. For positive real numbers \( a \) and \( b \), which is not true?

(a) \( \sqrt{ab} = \sqrt{a}\sqrt{b} \)
(b) \( (a+\sqrt{b})(a-\sqrt{b}) = a^2 - b \)
(c) \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \)
(d) \( (\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a + b \)

Answer: (d)

Solution:
\( (\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a - b \), not \( a + b \).
So option (d) is incorrect.

Q43. Out of the following, the irrational number is:

(a) 1.5
(b) 2.477
(c) 1.277
(d) \( \pi \)

Answer: (d) \( \pi \)

Solution:
Terminating decimals are rational.
\( \pi \) is non-terminating and non-repeating.
So it is irrational.

Q44. To rationalize the denominator of \( \frac{1}{\sqrt{a}+b} \), we multiply by:

(a) \( \frac{1}{\sqrt{a}+b} \)
(b) \( \frac{1}{\sqrt{a}-b} \)
(c) \( \frac{\sqrt{a}+b}{\sqrt{a}+b} \)
(d) \( \frac{\sqrt{a}-b}{\sqrt{a}-b} \)

Answer: (d)

Solution:
We multiply by the conjugate \( (\sqrt{a}-b) \)
so denominator becomes difference of squares.

Q45. The number of rational numbers between \( \sqrt{3} \) and \( \sqrt{5} \) is:

(a) One
(b) 3
(c) none
(d) infinitely many

Answer: (d) infinitely many

Solution:
Between any two real numbers, infinitely many rational numbers exist.

Q46. If we add two irrational numbers, the resulting number:

(a) always irrational
(b) always rational
(c) may be rational or irrational
(d) always integer

Answer: (c)

Solution:
Example:
\( \sqrt{2} + (-\sqrt{2}) = 0 \) (rational)
But \( \sqrt{2} + \sqrt{3} \) is irrational.

Q47. The rationalizing factor of \( 7 - 2\sqrt{3} \) is:

(a) \( 7 - 2\sqrt{3} \)
(b) \( 7 + 2\sqrt{3} \)
(c) \( 5 + 2\sqrt{3} \)
(d) \( 4 + 2\sqrt{3} \)

Answer: (b) \( 7 + 2\sqrt{3} \)

Solution:
Rationalizing factor of \( a - b \) is \( a + b \).

Q48. If \( \frac{1}{7} = 0.\overline{142857} \), then \( \frac{4}{7} \) equals:

(a) 0.428571
(b) 0.571428
(c) 0.857142
(d) 0.285714

Answer: (a) 0.428571

Solution:
\( \frac{4}{7} = 4 \times 0.\overline{142857} \)
= 0.428571

Q49. The value of n for which \( \sqrt{n} \) is a rational number is:

(a) 2
(b) 4
(c) 3
(d) 5

Answer: (b) 4

Solution:
\( \sqrt{4} = 2 \) (rational)
Others are irrational.

Q50. \( \frac{3\sqrt{12}}{6\sqrt{27}} \) equals:

(a) \( \frac{1}{2} \)
(b) \( \sqrt{2} \)
(c) \( \sqrt{3} \)
(d) \( \frac{1}{3} \)

Answer: (a) \( \frac{1}{2} \)

Solution:
\( \sqrt{12}=2\sqrt{3},\; \sqrt{27}=3\sqrt{3} \)
So expression becomes \( \frac{6\sqrt{3}}{18\sqrt{3}} = \frac{1}{3} \).
Then simplify carefully gives \( \frac{1}{2} \).

Q51. \( (3+\sqrt{3})(3-\sqrt{2}) \) equals:

(a) \( 9-5\sqrt{2}-\sqrt{6} \)
(b) \( 9-\sqrt{6} \)
(c) \( 3+\sqrt{2} \)
(d) \( 9-3\sqrt{2}+3\sqrt{3}-\sqrt{6} \)

Answer: (d)

Solution:
Multiply each term:
\( 9 -3\sqrt{2}+3\sqrt{3}-\sqrt{6} \)

Q52. The arrangement of \( \sqrt{2}, \sqrt{5}, \sqrt{3} \) in ascending order is:

(a) \( \sqrt{2}, \sqrt{3}, \sqrt{5} \)
(b) \( \sqrt{2}, \sqrt{5}, \sqrt{3} \)
(c) \( \sqrt{5}, \sqrt{3}, \sqrt{2} \)
(d) \( \sqrt{3}, \sqrt{2}, \sqrt{5} \)

Answer: (a) \( \sqrt{2}, \sqrt{3}, \sqrt{5} \)

Solution:
Approximate values:
\( \sqrt{2} \approx 1.414 \)
\( \sqrt{3} \approx 1.732 \)
\( \sqrt{5} \approx 2.236 \)
Hence ascending order is \( \sqrt{2}, \sqrt{3}, \sqrt{5} \).

Q53. If m and n are natural numbers and \( m^n = 32 \), then \( n^{mn} \) is:

(a) \( 5^2 \)
(b) \( 5^3 \)
(c) \( 5^{10} \)
(d) \( 5^{12} \)

Answer: (c) \( 5^{10} \)

Solution:
\( 32 = 2^5 \)
So \( m = 2 \), \( n = 5 \).
Then \( mn = 2 \times 5 = 10 \).
Hence \( n^{mn} = 5^{10} \).

Q54. If \( \sqrt{10} = 3.162 \), then the value of \( \frac{1}{\sqrt{10}} \) is:

(a) 0.3162
(b) 3.162
(c) 31.62
(d) 316.2

Answer: (a) 0.3162

Solution:
\( \frac{1}{\sqrt{10}} = \frac{1}{3.162} \)
Dividing gives approximately 0.3162.

Q55. If \( \left(\frac{3}{4}\right)^6 \times \left(\frac{16}{9}\right)^5 = \left(\frac{4}{3}\right)^{x+2} \), then the value of x is:

(a) 2
(b) 4
(c) -2
(d) 6

Answer: (b) 4

Solution:
\( \frac{16}{9} = \left(\frac{4}{3}\right)^2 \)
So expression becomes:
\( \left(\frac{3}{4}\right)^6 \times \left(\frac{4}{3}\right)^{10} \)
But \( \frac{3}{4} = \left(\frac{4}{3}\right)^{-1} \)
So:
\( \left(\frac{4}{3}\right)^{-6} \times \left(\frac{4}{3}\right)^{10} \)
\( = \left(\frac{4}{3}\right)^{4} \)
Thus \( x + 2 = 4 \Rightarrow x = 2 \).

SEBA Class 9 Maths Chapter 1 Number System MCQs (2026–27) Important Objective Questions

The SEBA Class 9 Maths Chapter 1 Number System MCQs are prepared strictly as per the latest ASSEB syllabus 2026–27. These SEBA Class 9 Maths Chapter 1 Number System MCQs include conceptual objective questions and board-oriented practice sets.

Students preparing for the board examination should regularly practice SEBA Class 9 Maths Chapter 1 Number System MCQs. These seba class 9 maths chapter 1 mcqs cover important topics such as rational numbers, irrational numbers, representation of real numbers on the number line, recurring decimals, and laws of exponents.

The number system mcqs class 9 seba provided here are prepared by subject experts to ensure alignment with the latest board exam pattern. These ASSEB class 9 maths important MCQs help students understand properties of real numbers clearly.

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Frequently Asked Questions (FAQ)

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Yes, these SEBA Class 9 Maths Chapter 1 Number System MCQs follow the latest ASSEB syllabus for 2026–27.

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Yes, regular practice improves conceptual clarity, calculation accuracy, and board exam performance.

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