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Number Systems — Class 9 CBSE Mathematics MCQs with Solutions
Free Class 9 CBSE Mathematics Number Systems MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — easy
Which of the following is an irrational number?
A. √4
B. 0.1416
C. 0.1010010001... ✓ Correct
D. 22/7
Solution: A non-terminating, non-recurring decimal represents an irrational number.
Q2 — easy
Decimal expansion of 1/7 is non-terminating recurring. Rational numbers have decimal expansions that are either terminating or:
A. Non-terminating non-recurring
B. Non-terminating recurring ✓ Correct
C. Terminating recurring
D. Infinite non-repeating
Solution: Rational numbers exhibit terminating or non-terminating repeating decimal expansions.
Q3 — easy
Rationalising the denominator of 1/(√7 − √6) gives:
A. √7 − √6
B. √7 + √6 ✓ Correct
C. 13
D. 1
Solution: Multiply numerator and denominator by (√7 + √6): 1(√7 + √6)/[(√7)² − (√6)²] = √7 + √6.
Q4 — easy
Simplify: (64)^(1/3) =
A. 2
B. 4 ✓ Correct
C. 8
D. 16
Solution: 64 = 4³, so (4³)^(1/3) = 4.
Q5 — easy
Simplify: (2^(2/3)) × (2^(1/3)) =
A. 2 ✓ Correct
B. 4
C. 2^(2/9)
D. 1
Solution: 2^(2/3 + 1/3) = 2^1 = 2.
Q6 — easy
Value of (16)^(3/4) is:
A. 4
B. 8 ✓ Correct
C. 12
D. 16
Solution: 16 = 2⁴, so (2⁴)^(3/4) = 2³ = 8.
Q7 — easy
Sum of a rational number and an irrational number is always an:
A. Rational number
B. Irrational number ✓ Correct
C. Integer
D. Natural number
Solution: The sum or difference of a rational and an irrational number is always irrational.
Q8 — easy
Between any two distinct rational numbers, how many rational numbers exist?
A. Only 1
B. Only 10
C. Infinitely many ✓ Correct
D. None
Solution: Infinitely many rational numbers lie between any two given rational numbers.
Q9 — easy
Express 0.333... in p/q form:
A. 1/3 ✓ Correct
B. 3/10
C. 33/100
D. 1/9
Solution: 0.3̄ = 3/9 = 1/3.
Q10 — easy
Simplify: (√5 + √2)(√5 − √2) =
A. 3 ✓ Correct
B. 7
C. √3
D. 10
Solution: Using (a+b)(a−b) = a² − b²: (√5)² − (√2)² = 5 − 2 = 3.
Q11 — easy
Value of (81)^(0.16) × (81)^(0.09) =
A. 3 ✓ Correct
B. 9
C. 81
D. 1
Solution: 81^(0.16 + 0.09) = 81^(0.25) = (3⁴)^(1/4) = 3.
Q12 — easy
Every rational number is a:
A. Natural number
B. Whole number
C. Real number ✓ Correct
D. Integer
Solution: The set of real numbers includes all rational and irrational numbers.
Q13 — easy
Simplify: (√3 + √7)² =
A. 10
B. 10 + 2√21 ✓ Correct
C. 10 + √21
D. 21
Solution: (a+b)² = a² + b² + 2ab = 3 + 7 + 2√21 = 10 + 2√21.
Q14 — easy
If x = 2 + √3, then x + (1/x) =
A. 2
B. 4 ✓ Correct
C. 2√3
D. 0
Solution: 1/x = 2 − √3. Thus x + 1/x = (2 + √3) + (2 − √3) = 4.
Q15 — easy
Value of (1/3³)⁷ in exponential notation is:
A. 3²¹
B. 3⁻²¹ ✓ Correct
C. 3¹⁴
D. 3⁻¹⁴
Solution: (3⁻³)⁷ = 3⁻²¹.