CLASS 09 · CHAPTER 01

Number Systems
Practice Questions

20 curated NCERT questions to test your problem-solving skills. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

Which of the following numbers is an irrational number?

Q2MCQ1 Mark

The value of (64)^(1/2) is:

Q3MCQ1 Mark

The decimal expansion of an irrational number is always:

Q4MCQ1 Mark

The rationalising factor of 1 / (√7 - 2) is:

Q5Assertion-Reason1 Mark

Assertion (A): √2 is an irrational number. Reason (R): The square root of any positive prime number is an irrational number.

Q6Assertion-Reason1 Mark

Assertion (A): 0.333... can be expressed in the form 1/3. Reason (R): Every non-terminating repeating decimal is a rational number.

Q7Short Answer2 Marks

Simplify: (√5 + √2)(√5 - √2).

Q8Short Answer2 Marks

Find three rational numbers between 3/5 and 4/5.

Q9Short Answer2 Marks

Simplify: (3 + √3)(2 + √2).

Q10Short Answer2 Marks

Evaluate: (81)^(3/4).

Q11Short Answer2 Marks

Rationalise the denominator of 1 / (√5 + √2).

Q12Long Answer3 Marks

Express 0.4777... in the form p/q.

Q13Long Answer3 Marks

If (5 + 2√3)/(7 + 4√3) = a + b√3, find a and b.

Q14Long Answer3 Marks

Simplify: [ (25)^(3/2) × (243)^(3/5) ] / [ (16)^(5/4) × (8)^(4/3) ].

Q15Long Answer3 Marks

Represent √9.3 on the number line geometrically.

Q16Case Study4 Marks

Case Study Scenario: Students represent 3.765 on a number line using successive magnification method. Question: Find between which two integers 3.765 lies and first magnification interval.

Q17Case Study4 Marks

Case Study Scenario: Triangular garden base = (√7 + √3) m and height = (√7 - √3) m. Question: Find area of garden.

Q18PYQ5 Marks

Simplify: (2/3 √40 - 3/4 √160 + 3 √625).

Q19PYQ5 Marks

If x = 3 + 2√2, find x + 1/x and x² + 1/x².

Q20PYQ5 Marks

Number Systems Practice Questions