Tiêu đề Integrated Series 9th Class Maths - Solutions.pdf ✅

Class 9 Mathematics Table of Content 1. Number System 1 – 19 2. Polynomials 20 – 57 3. Coordinate Geometry 58 – 83 4. Linear Equations in One and Two Variables 84 – 106 5. Lines and Angles & Euclid's Geometry 107 – 121 6. Triangles 122 – 139 7. Quadrilaterals 140 – 152 8. Areas of Parallelograms and Triangles 153 – 174 9. Circles 175 – 194 10. Surface Areas and Volumes 195 – 230 11. Statistics 231 – 243 12. Probability 244 – 262 13. Surds & Logarithms 263 – 298 14. Trigonometry 299 – 313

Class 9 – Maths | I-9 Number System 1 1. Number System Solutions LEVEL-I 1. Correct option: (C) Given numbers 2 3 and 5 3 . Equivalent numbers of 2 3 and 5 3 are: 2 3 × 2 2 = 4 6 and 5 3 × 2 2 = 10 6 The numbers between 4 6 and 10 6 are 5 6 , 6 6 , 7 6 , 8 6 , 9 6 So, from the given options 5 6 and 7 6 are the two numbers that are between 2 3 and 5 3 . Hence, the correct option is (C). 2. Correct option: (D) Option (A): 17 119 = 17÷17 119÷17 = 1 7 Option (B): 14 57 = 14 57 Option (C): 21 38 = 21 38 Option (D): 21 57 = 21÷3 57÷3 = 7 19 So, from the given option the rational number 21 57 is equivalent to 7 19 . Hence, the correct option is (D). 3. Correct option: (D) The product of two irrational number is sometimes rational and sometimes irrational. Example: √3 × √3 = 3 Here √3 is irrational and 3 is rational. The product of two irrational number is rational. √2 × √3 = √5 Here √2, √3, and √5 are irrational. The product of two irrational number is irrational. Hence, the correct option is (D). 4. Correct option: (A) The product of non-zero rational number with an irrational number is always an irrational number. Example: 2 × √3 = 2√3
Class 9 – Maths | I-9 Number System 2 Here 3 is rational and √3 and 2√3 is irrational. The product of two numbers is irrational. Hence, the correct option is (A). 5. Correct option: (B) Let x = 0. 54̅̅̅̅ = 0.545454 ... Since two digits are repeating, we multiply x by 100. 100x = 54.5454 ... 100x = 54 + 0.545454 ... 100x = 54 + x 99x = 54 x = 54 99 x = 54÷9 99÷9 = 6 11 So, the simplest form of 0. 54̅̅̅̅ is 6 11 . Hence, the correct option is (B). 6. Correct option: (C) Step 1: Let x = 2. 45̅̅̅̅ = 2.454545 ... Since two digits are repeating, we multiply x by 100. 100x = 245.4545 ... 100x = 243 + 2.4545 ... 100x = 243 + x 99x = 243 x = 243 99 Step 2: Let y = 0. 36̅̅̅̅ = 0.363636 ... Since two digits are repeating, we multiply y by 100. 100y = 36.3636 ... 100y = 36 + 0.363636 ... 100y = 36 + y 99y = 36 y = 36 99 Step 3: 2. 45̅̅̅̅ + 0. 36̅̅̅̅ = x + y 2. 45̅̅̅̅ + 0. 36̅̅̅̅ = 243 99 + 36 99 2. 45̅̅̅̅ + 0. 36̅̅̅̅ = 279 99 = 31 11 Hence, the correct option is (C).