ANNUAL EXAM PYQS · CHAPTER 01

Number Systems
CBSE Most Repeated PYQs

Solve official Class 9 Annual Examination Questions for Number Systems. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1Annual Exam 2024MCQ

1 Mark

Which of the following numbers is an irrational number?

Q2Annual Exam 2023MCQ

1 Mark

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

Q3CBSE Pattern PYQMCQ

1 Mark

The decimal expansion of an irrational number is always:

Q4Annual Exam 2022MCQ

1 Mark

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

Q5CBSE Model PYQAssertion-Reason

1 Mark

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

Q6Annual Exam 2021Assertion-Reason

1 Mark

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

Q7Annual Exam 2024Short Answer

2 Marks

Simplify: (√5 + √2)(√5 - √2).

Q8Annual Exam 2023Short Answer

2 Marks

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

Q9CBSE Pattern PYQShort Answer

2 Marks

Simplify: (3 + √3)(2 + √2).

Q10Annual Exam 2022Short Answer

2 Marks

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

Q11CBSE Model PYQShort Answer

2 Marks

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

Q12Annual Exam 2021Long Answer

3 Marks

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

Q13Annual Exam 2024Long Answer

3 Marks

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

Q14Annual Exam 2023Long Answer

3 Marks

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

Q15CBSE Pattern PYQLong Answer

3 Marks

Represent √9.3 on the number line geometrically.

Q16Annual Exam 2022Case Study

4 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.

Q17CBSE Model PYQCase Study

4 Marks

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

Q18Annual Exam PYQPYQ

5 Marks

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

Q19Annual Exam PYQPYQ

5 Marks

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

Q20Annual Exam PYQPYQ

5 Marks

Number Systems CBSE Most Repeated PYQs

Which of the following numbers is an irrational number?

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

The decimal expansion of an irrational number is always:

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

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

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

Simplify: (√5 + √2)(√5 - √2).

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

Simplify: (3 + √3)(2 + √2).

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

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

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

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

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

Represent √9.3 on the number line geometrically.

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.

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

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

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

Find x if 2^(x-7) × 5^(x-4) = 1250.

Number Systems
CBSE Most Repeated PYQs