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Question 1. If a:b = 5:3, find: Question 2. If x: y = 4: 7, find the value of (3𝑥 + 2𝑦): (5𝑥 + 𝑦).Solution:It is given that,𝑥: 𝑦 = 4: 7𝑥/𝑦 = 4/7Divide each term by 𝑦. Question 3. If a:b = 3:8, Question 4. If (a – b): (a + b) = 1: 11, find the ratio […]

Question 1. Which of the following sequences are in arithmetic progression?(𝑖) 2, 6, 10, 14,(𝑖𝑖) 15, 12, 9, 6,(𝑖𝑖𝑖) 5, 9, 12, 18,(𝑖𝑣) 1/2, 1/3, 1/4, 1/5Solution:(𝑖) 2, 6, 10, 14,𝑑 = 𝑎2 − 𝑎1𝑑1 = 6 − 2𝑑1 = 4𝑑2 = 10 − 6𝑑2 = 4𝑑3 = 14 − 10𝑑3 = 4Here,𝑑1 = 𝑑2 = […]

Question 1. State, whether the following statements are true or false. If false, give a reason.(i) If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.(ii) The matrices A2 × 3 and B2 × 3 are conformable for subtraction.(iii) Transpose of […]

Question 1. Find in each case the remainder when:(i) 𝑥4 − 3𝑥2 + 2𝑥 + 1 is divided by 𝑥 − 1.(ii) 𝑥3 − 3𝑥2 − 12𝑥 + 4 is divided by 𝑥 − 2.(iii) 𝑥4 + 1 is divided by 𝑥 + 1.Solution:(i) 𝑥4 − 3𝑥2 + 2𝑥 + 1 is divided by 𝑥 − […]

Question 1. The product of two consecutive integers is 56. Find the integers.Solution:Let the first number be 𝑥.And second number be 𝑥 + 1.𝑥(𝑥 + 1) = 56𝑥2 + 𝑥– 56 = 0By the splitting the middle term,𝑥2 + 8𝑥 − 7𝑥– 56 = 0𝑥(𝑥 + 8) − 7(𝑥 + 8) = 0(𝑥 + 8) (𝑥– […]

Question 1. Find which of the following equations are quadratic:(𝑖) (3𝑥– 1)2 = 5(𝑥 + 8)(𝑖𝑖) 5𝑥2 – 8𝑥 = −3(7– 2𝑥)(𝑖𝑖𝑖) (𝑥– 4)(3𝑥 + 1) = (3𝑥– 1)(𝑥 + 2)(𝑖𝑣) 𝑥2 + 5𝑥– 5 = (𝑥– 3)2(𝑣) 7𝑥3– 2𝑥2+ 10 = (2𝑥– 5)2(𝑣𝑖) (𝑥 − 1)2 + (𝑥 + 2)2 + 3(𝑥 + 1) = […]

Exercise 4A Question 1. State, true or false: (i) x<- y ⇒ – x >y (ii) -5 x ≥ 15 ⇒ x ≥ – 3 (iii) 2 x ≤- 7 ⇒ 2 x /(-4) ≥ (-7)/(-4) (iv) 7 > 5 ⇒ 1/7< 1/5 Question 2. State, whether the following statements are true or false: (i) […]