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EXERCISE # 1, A., Q.1, , Very Short Answer Type Questions, , B., , Express the following in the form of p/q., , Q.15, , (i) . 3, Q.2, , (ii) .37, , Write two irrational numbers between 0.2 and, 0.21., , Q.3, , Q.16, , Short Answer Type Questions, Which of the following is, (i) rational, , (ii) irrational number, , (A) (2 + 3 ) 2, , (B) (3 + 4 ) 2, , Given that, , Write three irrational numbers between, , 75 +, , 0.202002000200002...and, , 1, 2, , 3 = 1.732, find the value of, , 48 – 192 ., , 0.203003000300003..., Q.4, , Determine a and b if, , Q.18, , If, , Write three irrational numbers between, 3 and, , Q.5, , Q.17, 5., , Find two irrational numbers between 0.5 and, , of, , 0.55., Q.6, , Find two irrational numbers lying between, 0.1 and 0.12., , Q.7, , Given a rational approximation of, , 3 correct, , 5 = 2.236 and, 1+ 2, 5+ 3, , +, , 5+ 3, 7−4 3, , 6 = 2.449, find the value, , 1− 2, 5− 3, , In the following express the result in the, , Q.20, , If p = 3 – 2 2 , determine p2 +, , 5, Q.21, , Find the simplest rationalising factor of, 5 +, , Q.10, , Express as a pure surd :, , 1, 3, , 3, , 54, , Q.12, , Simplify :, , Q.13, , Simplify :, , 6, , 5 4, , 3, , (2 4 ) 3 – 55 8 + 24 5 (2 3 ) 4, , C., Q.25, , Q.14, , If, , 3 = 1.732, find the value of, , 2, 3, , 3 + 2., , Simplify and express the results in simplest, , Q.24, , m2n 2  m2n 2  m2n 2, , ., , Q.23, , form :, Simplify : (3 5 − 2 3 ) (3 5 + 2 3 ), , p2, , x 2 − y2 + x, x 2 + y2 + y, , Evaluate :, , , , x 2 + y2 − y, x − x 2 − y2, , ., , 5+ 2 6 ., , Fill in the Blanks, Every point on the number line corresponds, to a .......................... number which may be, , ., , either ................ or ...................., CraveIITy-crave for best for JEE & NEET,NTSE& Olympiad , Kadipur,& Sultanpur (U.P.),ph: 8004894394, Number system, , ., , Simplify : 3 2 + 4 64 + 4 2500 + 6 8 ., , Simplify : 2. 40 + 3. 625 + 4. 320, , Q.11, , 1, , x, , Q.22, , 3, , 3, , 3, , x+, , 1, , If x = 7+ 4 3 , find the value of, , simplest form : 3 108a 4 b 3, Q.9, , ., , Q.19, , to two places of decimals., Q.8, , = 94 a + 3 3 b., , 15

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Q.26, , The decimal form of an irrational number is, neither ................ nor ................, , Q.27, , The decimal representation of the rational, number, , Q.28, , 8, is ............................., 27, , 0 is a/an .................... number ., ,  is irrational and, , Q.42, , Every rational number must be a whole number., , Q.43, , The number zero is both positive and negative., , Q.44, , The sum of the two prime numbers is always, even., , (Rational /Irrational), Q.29, , 7, The decimal equivalent to, is ........., 12, , Q.30, , The decimal equivalent to, , Q.31, , The common fraction equivalent to 0.09375, , 49, is .........., 396, , 22, is rational., 7, , Q.41, , Q.45, , The product of two odd numbers is always, odd., , Q.46, , A number of three digits has for its middle, digit, the sum of the other two digits. Then, the number must be a multiple of 11., , is ................, , Q.47, , If u = x2 – y2 is an even number, where x and, y are whole numbers, then u must be a, , Q.32, , The common fraction equivalent to 0.4312, , multiple of 4., , is ............., Q.48, Q.33, , Every real number is either ........... number or, , The distance between the points a and b on, the number line is equal to |b – a|., , ............... number., , D., , True/False Type Questions, , Q.34, , The sum of two rational numbers is rational., , Q.35, , The sum of two irrational numbers is, irrational., , Q.36, , The product of two rational numbers is, rational., , Q.37, , The product of two irrational numbers is, irrational., , Q.38, , The sum of a rational number and an, irrational number is irrational., , Q.39, , The product of a nonzero rational number and, an irrational number is a rational number., , Q.40, , Every real number is rational., , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number system, , 16

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ANSWER KEY, A. VERY SHORT ANSWER TYPE :, C. FILL IN THE BLANKS :, 1., , 1, (i), 3, , 37, (ii), 99, , 25. real, rational number, an irrational number, , 2. 0.2010010001..........., 0.2020020002..........., 3. 0.20201001000100001...........,, 0.202020020002..., 0.202030030003..........., 4. 1.8010010001......., 1.9010010001.......,, 2.010010001......., 5. 0.501001001....... and 0.5020020002......., 6. 0.10100100010000....... and 0.1020020002......., 7. 1.73, 9., , 3, , 2, , 8. 3ab, , 3, , 4a, , 10. 35 3 5, , 11. 33, , 12. m2n2, , 13. – 2. 5 8, , 14. 1.154, , B. SHORT ANSWER TYPE :, 15. (a) irrational, (b) rational, 1, ,b=9, 2, , 16. – 1.732, , 17. a =, , 18. – 0.213, , 19. 4, , 20. 34, , 21. (2 + 3 − 5 ) (1 – 2 3 ), , 22. 11 2, 24., , 23., , y2, x2, , 26. terminating, recurring, 27. 0.296, , 28. rational, , 29. 0.583, , 30. 0.1237, , 31., , 3, 32, , 32., , 718, 1665, , 33. rational, irrational, D. TRUE/FALSE TYPE :, 34. True, , 35. False, , 36. True, , 37. False, , 38. True, , 39. False, , 40. False, , 41. True, , 42. False, , 43. False, , 44. False, , 45. True, , 46. True, , 47. True, , 48. True, , 3+ 2, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number system, , 17

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EXERCISE # 2, Which of the following statements, are True/False. (Q. 1 to 13), Q.1, Every natural number is a whole number., Q.2, , Every whole number is an integer., , Q.3, , Every whole number is a natural number., , Q.4, , Collection of whole numbers is denoted by W., , Q.5, , Collection of integers is denoted by N., , Q.6, , A real number is a rational number., , Q.7, , Every point on the number line is a real, number., , Q.8, , Reciprocal of an irrational number is an, irrational number., , Q.9, , Every real number can be expressed in the, p, form, where p and q are integers and q  0., q, , Q.10, Q.11, , Square root of every natural number is an, irrational number., , Q.17, , Visualize the position of 5.665 on the number, line, through successive magnification., , Q.18, , Visualize the representation of 1. 3 on the, number line upto 4 decimal places, that is,, upto 1.3333. Further locate 1.33333., , Q.19, , Express, , Q.20, , Express, , Q.21, , By taking  = 3.141 and, , Q.13, , The number 0.21211211121111………is an, irrational number., , Q.14, , Express the rational number, , 1, in recurring, 27, decimal form by using the recurring decimal, 59, 1, expression of, . Hence write, in, 27, 3, recurring decimal form., , Express in, (i) 2.124 ,, , 3.5 geometrically., , 5.42 geometrically and represent it, on the number line., , evaluate, , 2 + 3 2, 5, , 2 = 1.414 ,, , upto three places of, , decimals., Q.22, , Simplify the following expressions :, (i) (2 2 + 5 3 ) + ( 2 − 3 3 ), (ii) (3 + 3 ) (2 + 2 ), (iii) (3 + 5 ) (3 − 5 ), , 2, is of recurring form., 7, , Decimal expansion of, , Q.15, , Express, , Every rational number can be expressed in, the form of terminating decimal expansion., , Q.12, , 1, in decimal form and hence write, 37, 79, the decimal expansion of, ., 37, , Q.16, , Q.23, , If a = 2 + 3 + 5 and b = 3 + 3 − 5 ,, prove that a2 + b2 – 4a – 6b – 3 = 0., , Q.24, , If x = 3 + 2 2 and y = 3 − 2 2 , evaluate, x4 + y4 + 6x2y2., , Q.25, , p, form, q, , (ii) 0.237, , If x = 1 − 2 , find the value of, 1, 1, (i) x +, (ii) x −, x, x, 1, 1, (iii) x 2 + 2, (iv) x 2 − 2, x, x, 1, 1, (v) x 4 + 4, (vi) x 4 − 4, x, x, 7+ 5, , For the identity, , −, , 7− 5, , = a + 7 5b ,, 7− 5 7+ 5, determine the rational numbers a and b., CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394 Number system, 18, , Q.26

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Q.27, , Simplify the following expressions :, 1, 1, 1, 1, (i), +, +, +, 2 +1, 3+ 2, 4+ 3, 5+ 4, (ii), , Q.28, , 1, , 2 +1, Simplify :, , +, , 1, 3+2, , 9, , (i) (9) 2, , (ii) (9), , +, , −, , 3, , (iv) (36) 2, , (v) (49), , 3, 2, , −, , 2, 5 +3, , +, , 2, 5 −3, , Q.29, , Simplify :, ,  243 , (i) , ,  32 , Q.30, , −, , 4, 5, , (ii), , 3, , (343) −2, , If ax = b, by = c and cz = a, then prove that, xyz = 1. Here a, b, c are positive real numbers, and x, y, z are rational numbers., , 3, , (iii) (25) 2, 3, 2, , (vi) (.0001), , −, , 3, 4, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394, , Number system, , 19

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ANSWER KEY, 1. True, , 2. True, , 3. False, , 4. True, , 5. False, , 6. False, , 7. True, , 8. True, , 9. False, , 10. False, , 11. False, , 12. True, , 13. True, , 14. 0.037, 2.185, , 15. (i), , 2122, 47, (ii), 999, 198, , 6, , 5, 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9, , 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9, , 5.66 5.67, , 1.4, , 1.3, 1.33 1.34, , (ii), , 5.67, , 5.66, , (i), , 18., , 5.7, , 5.6, , 2, , 1, (i), , 17., , 16. 0.027, 2.135,, , (ii), , 1.34, , 1.33, 1.333 1.334, , (iii), , (iii), , 1.3333, , 5.665, , D, , D, 3.21, , 2.25, 3.5, , 19., , 20., , 1.25, M, 3.5, , C, , B, , 1, , 2.21, M, , A, 5.42, , 1, , B, , C, , E( 5.42 ), , (0), , 21. 2.105 (approx), 22. (i) 3 2 + 2 3, , (ii) 6 + 3 2 + 2 3 + 6 (iii) 4, , 24. 585, 25. (i) − 2 2 ,, 26. a = 0, b =, 27. (i), , (iv) − 4 2 ,, , (v) 34, (vi) − 24 2, , 1, 11, , 5 − 1 , (ii) 1 + 2 − 3 − 5, , 28. (i) 27, (ii), 29. (i), , (ii) 2, (iii) 6,, , 1, 1, , (iii) 125, (iv) 216, (v), , (vi) 1000, 27, 343, , 16, 1, , (ii), 81, 49, , CraveIITy-crave for best for JEE & NEET , Kadipur, Sultanpur (U.P.),ph: 8004894394, , Number system, , 20