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Worksheet, Chapter – 1 (Number Systems), , [A] Multiple choice Questions, 1. Between two rational numbers, (a) there is no rational number, (b) there is exactly one rational number, (c) there are infinitely many rational numbers, (d) there are only rational numbers and no irrational number, 2. The value of 1.999…in the form of p/q where p and q are integers is, (a) 19/10, , (b) 1999/1000, , (c) 2, , (d) 1/9, , 3. The product of any two irrational numbers is, (a) always an irrational number, (b) always a rational number, (c) always an integer, (d) sometimes rational, sometimes irrational, 4. Which of the following is irrational?, (a) √4 /9, , (b) √12/√3, , (c) √7, , (d) √81, , (b) 3√3, , (c) 4√6, , (d) 6, , 5. 2√3 + √3 is equal to, (a) 2√6, 6. The value of, (a) 2, , √𝟑𝟐+ √𝟒𝟖, is equal to, √𝟖+ √𝟏𝟐, , (b) √2, , (c) 4, , (d) 8
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3. (𝟓)𝟔𝐱 = (𝟏𝟐𝟓)𝟐 , then x = ……………………., 4. 0.14 is a………………… decimal., 5. (2+√3) (2-√3) is a/an ……………..number., 6. Number of rational numbers between 13 and 17 is………………….., 7. 34 × 33 = ………………………, 8. The decimal form of an irrational number is ……………., 9. √rs = …………., 10. an = b can also be written as …………., 11. The square root of 64 divided by the cube root of 64 is …………, 12. The decimal representation of a rational number is either ………….. or ……………….., 13. 710. 810 = …………….., 14. The p/q form of 0.15 is ………………, 15. The equivalent rational number of 7/9, whose denominator is 45 is ………….., , [C] Short Answer Type Questions., 1. Is, , √𝟗𝟖, √𝟐, , a rational number or not?, 𝟐, , 2. Simplify the number (√𝟐 + √𝟓) ., 3. Calculate the decimal number which represents the fraction 7/8., 4. Express 0.𝟒𝟕 bar in the form of p/q where p & q are integers and q ≠ 0., 5. Find two rational numbers between 4 and 5., 6. If a=2 and b=3, the find the value of ab + ba, 7. Simplify, , 𝟔 − 𝟒√𝟑, 𝟔 + 𝟒√𝟑, , by rationalizing the denominator.
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8. Find the decimal representation of 8/3., 9. Find any two irrational numbers between 0.5 and 0.55, 10. Simplify: 8√3 - 2√3 + 4√3., 𝟏, 11. Express 3 in the form of decimal., 𝟖, , 12. Evaluate: 255 × 260 – 297 × 218., 13. Are irrational numbers cannot be represented by points on the number line?, 14. Define rational number with an example., 15. Simplify: √72 + √800 - √18., , [D] Long Answer Type Questions., 1. Represent √5 on the number line., 2. Find the decimal expansion of, , 1, 7, , ., , 3. Find five rational numbers between 0.6 and 0.8, 4. Express 0.2𝟑𝟓 in the form of p/q., 5. Visualise 4.575 on the number line, using successive magnification., 6. Represent geometrically the number √5.26 on the number line., 7. Simplify the following:, (a) (125), , -1/3, , (b) (, , 𝟔𝟒 −3/2, , ), 𝟐𝟓, , (c) (625)-1/4, , 𝟓, , (d) √(𝟑𝟐)−𝟑, , 8. Find four rational numbers between 1/6 and 1/5., 9. Visualise the representation of 6.3𝟕 on the number line upto 4 decimal places., 10. If, , 𝟑 + √𝟕, 𝟑 − √𝟕, , = 𝐚 + 𝐛√𝟕 , find the values of a & b.
