Page 1 :
IMPORTANT, MULTIPLE CHOICE QUESTIONS, (Number Systems), :-, 1.1. INTRODUCTION, 2, 6. Two rational numbers between, 3, and, are:, 1. Which of the following is a rational number?, (a) 1+ 3, (c) 2 3, (b) Tt, 2, аnd, 6., (a), (b), and, (d) 0, (CBSE 2010, 20PE}, and, 5, 2. Every rational number is:, (c), and, (d), (a) a natural number, (CBSE 200, 201}, (6) an integer, (c) a real number, 1.2. IRRATIONAL NUMBERS, (d) a whole number, (CESE 2011), 3. A rational number lying between -3 and 3 is:, 1. If Vx is irrational number, then x is:, (a) rational, (b) irrational, (a) 0, (b) -4.3, (c) 0, (d) real, (c) -3.4, (d) 1.101 1001 10001, [CBSE 2910), 1.3. REAL NUMBERS AND THEIR DECIMAL., EXPANSIONS, 4., A rational number lying between /2 and /3, 56, is:, 1000·, is:, 1. The decimal form of, (a), (b) J6, (a) 0.56 ., (b) 0.056, 2, (с) 1.6, (d) 1.9, (c) 0.0056, (d) 5.6, [CESE 2010), (CESE 2UIUI, 2., A terminating decimal is:., and, 5. The rational number between --, is:, 5, (a) natural number, (b) a whole number, |, (c) a rational number, (d) an integer, (6) -, [COSE 2011), (a) 0, 3., A number is an irrational if and only if its, decimal representation is:, (c) non-terminating, (b) non-terminating and repeating, (c) non-terminating and non-repeating, (d) terminating, 4, 3, (c) -, 10, 7, (d), 25, CBSE 2011), ICKSE 20IN IOLPE, Scanned By KagazScanner

Page 2 :
12. The value of 2.9 in the form 2 wherep and q, GOLDEN MATHEMATICS-IX, (b) JE, Which of the following is a rational number?, (a) 5, (11) 0.75, (c) 0.750 7500 75000 ..., (b) t, (CBSE 2010), (d) 0.7512, (c) 0.101 001 0001 00001, ( 0.853 S53 853, (CBSE 2010), are integers and, 2999, (a), 1000, q0, is, S. Which one of the following is an irrational, number?, 19, (b), 10, (a) 0.14, (b) 0.1416, 26, (d), 9., (CBSE 2012], (c) 0.1416, (c) 3, (d) 0.401 4001 40001 4.., (CBSE 2010), 6. Which of the following is an irrational num-, 13. The sum of 0.3 and 0.2 is :, ber?, 5, (a), 99, (b), (a) 0.15, (b) 0.1516, (d), 100, (c) 01516, 10, (d) 0.501 5001 50001 .., (CBSE 2010), [CBSE 2012), 7. Which of the following numbers is an, irrational number?, 1.4. REPRESENTATING REAL NUMBERS ON, THE NUMBER LINE, (a) V23, (b) V225, 1. The process of visualisation of representation, of numbers on the number line through a, magnifying glass is called, (a) successive magnification, (c) 0.3796, (d) 7.478, (CBSE 2010), 8. Which of the following is an irrational, number?, (b) approximation, (a) 33, (b) 3.763, (c) imagination, (c) 3.763, (d) none of these, (d) 3.101 1001 10001 ..., 2. 5.37 lies most accurately, (CBSE 2010), (a) between 5.37 and 5.38, 9. The decimal expansion of V2 is:, (b) between 5.3 and 5.4, (a) finite decimal, (c) between 5.377 and 3.378, 1.4121, (d) between 5.3777 and 5.3778, (c) non-teminating recurring, (d) non-terminating non-recurring, 1.6. OPERATIONS ON REAL NUMBERS, (CBSE 2010), 1. (Ja + 5)(Va - J5) is :, 10. п is:, (a) a + b, (a) a rational number, (b) a - b, (b) an integer, (c) 2Ja, (d) 2 J5, (c) an irational number, (CBSE 2012), (d) a whole number, 2. (a + J5) (a - J5) is equal to:, [CBSE 2010], (a) b? - a?, (c) a? - b, (b) a? - 62, (d) b² - a, 11. An irrational number between, and, is, Scanned By KagazScanner, ICBSE 2012), --..---

Page 3 :
A35, NUMBER SYSTEMS, 3. Which of the following numbers is an, 10. If /3 = 1.732 and 2 = 1.414, the value of, irrational nunber?, is:, (2) V16 - 4, (11) (3 – J5) (3 + V3), V3 - V2, (a) 0.318, (h) 3.146, (c) 5 +3, (i1)- /25, 1, (CBSE 2010, 2011}, (d) V1.732 - VI.414, (:), 3.146, 4. (-2-3) (-2+ V3) when simplified is:, {COSE 2010, (a)positive and irrational, 11. Rationalisation of the denominator of, (h)positive and rational, 1, gives:, (c)negative and irrational, V5 + V2, (r)negative and rational, [CBSE 2010, 201}, 5. (5+ /8) + (3-V2) - (V2 - 6) when simpli-, fied is:, (b) V5 + V2, (a), (V5 - JZ), (d), (ri) positive and irrational, (inegative and irrational, (c)positive and rational, (d;negative and rational, (e) V5 - V2, 3, CBSE 20111, (CBSE 2010, 201!, 1.6. LAWS OFEXPONENTS FOR REAL, NUMBERS, 5, and, 5, 6. If x =, =p/7, then the value of p, is :, 1. Ifb>0 and b2 = a, then va is equal to :, 5, (a), 25, (b), 7, (a) - b, (b) b, (c) E, (c), 25, (d), 5, [CBSE 2012, 2. If a = 2 and b = 3, then the value of ba is, [CBSE 201Z}, (u)4, (b)9, 7. (V2 +1/ /2) is equal to :, (c)2, (d) 3, 2° x7°, is:, 50, (a) 42, 5) 9/2, 3. The value of, (c) 4/V12, (d) 9, (a) 1, (b)0, [CBSE 20121, 8. V12 x 18 is equal to :, (ci), (CBSE20I, {i} 26, (h) 3/6, 4. The value of, 5°, 2° + 70, is:, (c) 4/6, [CESE2012I, (a)2, (h)0, 1, 9. Value of, V18 - V32, is equal to:, (d), [CBSE 2011, fai 2, (bj-V2 ., . 5. If xalb = 1, then the value of a is, %3D, 1, (d)- (CESE 2011E, (a)0, (b) 1, (c)-1, ()None of these., Scanned By KagazScanner

Page 4 :
Scanned By KagazScanner (CBSE 2012), GOLDEN MATHEMATICSIX, 6. When 1515 is divided by 3/3,the quotient, 54, equals:, 250, is:, 14., (a) 5/3, (b) 3/5, 9, (a) 25, (b) 3, (c) 5/5, (d) 3/3 (CHSE 2010), 27, (c), 125, (d), 5, (CDSE 20101, 7. The value of (243)5 is equal to:, 15. (0.001)13 is equal to, (a) 5, (b) 3, (a)0.1, (b) 0.001, (c) 6, (d) 1, (CDSE 2011), (c) 0.01, (d) 0.0001, 8. The value of 216 - 125 is:, (a) 1, (b} 0, 135, (CBSE 2010), 16. The simplified form of, is:, (c) 2, ()-1, 133, 9. Simplified value of (25)3 x(5)3 is:, 2, (a) 25, (b) 3, (a) 1315, (b) 1315, (c) 1, (d) 5 (CBSE 2010, 2011), 2, (c) 133, (d) 13 15, 10. The value of J(3-) is:, (CBSE 2011), (a), (b) 9, 17. The value of VV22 is equal to:, 1, (d), (0) 2., (c)-3, (b) 26, (CBSE 20111, (c), (d) 26, [CBSE 2010], 11. The value of (64)-2 is:, 1, 1, 18. If x12 = 4924, then x is equal to:, 1, (b), 8, (a) 49, (b) 2, (c) 12, (d) 7, [CBSE 2011), (c) 8, (d), 64, 64, then the value of x is, 2*, (CBSE 2010), 19. If 8* =, (a) 3, 12. Simplified value of (16) 4 x V16 is:, (b) 1, 1, (a) 16, 3, (b) 4, (d); (CBSE 201!, (c) 1, (d) 0, (CHSE 2010), 2, 13, The simplified value of (81)-14x V81 is :, 20. Value of (81-", is :, (a) 9, (h) 3, (c) 1, (u) 0, [CBSE 2012), (a) 3, (b) 3, (c) 9, (d)

Page 5 :
A37, NUMBER SYSTEMS, ANSWERS, 1.1. Introduction, 2. (c), 1.4. Representating Real Numbers on the, Number Line, 3. (a), 4. (c), 1. (d), 5. (c), 1. (а), 2. (d), 6. (с), 1.5. Operations on Real Numbers, 2. (с), 1.2. Irrational Numbers, 3. (c), 4. (b), 1. (b), 1. (d), 8. (c), 7. (b), 11. (d) ., 5. (с), 6. (b), 1.3. Real, Numbers, and, their Decimal, 9. (d), 10. (b), Expansions, 1.6. Laws of Exponents for Real Numbers, 2. (b), 1. (b), 2. (с), 3. (c), 4. (d), 5. (d), 7. (a), 8. (d), 1. (Б), 3. (а), 4. (а), 6. (d), 10. (с), 11. (c), 5. (a), 6. (c), 7. (b), 8. (а), 9. (d), 12. (с), 13. (b), · 9. (d), 10. (d), 11. (a), 12. (с), 13. (с), 14. (b), 15. (а), 16. (d), 17. (с), 18. (d), 19. (d), 20. (а)., HINTS/SOLUTIONS, 1.3. Real Numbers and their Decimal, Expansions, 1.1. Introduction, 1. Evident, 2. Evident, 1. Obviously, 56, = 0.056, 3. Evident, 1000, 2. A number whose decimal expansion is termi-, nating is a rational number., 4. /2 = 1.414 ..., ..., = 1.732.., 3. By definition., 1.414.. < 1.6... <1.732.., 4. 0.853 853853, ...... = 0.853, being a non-ter-, 2, 5., 5, minating recurring decimal expansion, is a, rational number., 10, 5. 0.401 4001 40001 4..., being a non-termi-, nating non-recurring decimal expansion, is an, irrational number., 4, 10, 2, 3, 4, >, 10, 10, 10, 6. 0.501 5001 50001, ,being a non-terminat-, ing, non-repeating decimal expansion, is an, irrational number., 2, 4 5, 10, 6., -3-, %3D, 3 6' 3, 6., 7. The decimal expansion of /23 is non-termi-, nating non-recurring number., 8. A number whose decimal expansion is non-, terminating non-recurring is an irrational, number., 4, 5, <-<-<, 6 6, 7.10, 6, 1.2. Irrational Numbers, 1. Evident, Scanheid aByrtáagazbaBaner