Practice set
Natural Numbers, Integers, Rational and Irrational Numbers — Single-Correct Practice
Ten original bilingual questions on number families, decimals and irrational arithmetic. Free, untimed lesson practice with a suggested 10 minutes, one mark per correct answer and no negative marking. This is not a full exam simulation.
Answer the questions at your own pace; your score comes at the end.
- Right answer +1. A wrong answer costs nothing.
- Questions come in Hindi and English. Switch any question with “Language”; questions in English only cannot switch.
Sample questions with solutions
A few questions from this test, with the right answer and why.
- Question 1After simplifying −√196, which option lists ALL the categories it belongs to among natural, whole, integer, rational, irrational and real numbers?
- Natural, whole, integer, rational and real
- Rational and real only
- Integer, rational and realRight answer
- Irrational and real only
Explanation√196 = 14, so −√196 = −14. It is an integer and −14 = −14/1 makes it rational. Every rational number is real. Its negative value excludes natural and whole numbers, and a rational number cannot also be irrational.
A: A negative integer is neither natural nor whole.
B: This list omits the applicable category integer.
D: A square-root symbol does not imply irrationality; this root simplifies to an integer. - Question 2For x = 0.1666…, where only the digit 6 repeats, which subtraction is correct and gives a direct proof that x = 1/6?
- 10x − x = 1
- 100x − x = 16
- 100x − 10x = 15Right answer
- 100x − 10x = 16
Explanation10x = 1.666… and 100x = 16.666…. Their repeating decimal tails are identical, so 100x − 10x = 15. Thus 90x = 15 and x = 15/90 = 1/6. The initial digit 1 is not part of the repeating block.
A: The actual difference is 1.666… − 0.1666… = 1.5, not 1.
B: The actual difference is 16.666… − 0.1666… = 16.5, not 16.
D: Subtracting the integer parts gives 16 − 1 = 15, not 16. - Question 3Let a = √7, b = −√7 and c = √28. Which statement correctly classifies a + b and ac?
- Both a + b and ac are rational.Right answer
- a + b is rational and ac is irrational.
- Both a + b and ac are irrational.
- a + b is irrational and ac is rational.
Explanationa + b = √7 − √7 = 0 = 0/1, which is rational. Also c = √28 = 2√7, so ac = √7 × 2√7 = 14, which is rational. The inputs are irrational, yet these results are rational. This does not mean such results are always rational: a + c = 3√7 is irrational, and √7 × √2 = √14 is irrational.
B: The product ac simplifies to the integer 14.
C: Both operations here produce rational values: 0 and 14.
D: The sum a + b is zero, which is rational.