Chapter 5 Arithmetic Progressions Ex 5.1
Chapter 5 Arithmetic Progressions Ex 5.1 Question 1. Solution: (i) Given: a1 = ₹ 15 a2 = ₹ 15 + ₹ 8 = ₹ 23 a3 = ₹ 23 + ₹ 8 = ₹ 31 List of fares is ₹ 15, ₹ 23, ₹ 31 and a2 – a1 = ₹ 23 – ₹ 15 = ₹ 8 a3 – a2 = […]
Chapter 4 Quadratic Equations Ex 4.4
Chapter 4 Quadratic Equations Ex 4.4 Question 1.Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x² -3x + 5 = 0 (ii) 3×2 – 4√3x + 4 = 0 (iii) 2×2-6x + 3 = 0 Solution:(i) 2×2 – 3x + 5 = 0 This is of […]
Chapter 4 Quadratic Equations Ex 4.3
Chapter 4 Quadratic Equations Ex 4.3 Question 1.Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2×2 – 7x + 3 = 0 (ii) 2×2 + x – 4 = 0 (iii) 4×2 + 4√3x + 3 = 0 (iv) 2×2 + x + 4 = 0 Solution: Question […]
Chapter 4 Quadratic Equations Ex 4.2
Chapter 4 Quadratic Equations Ex 4.2 Question 1. Find the roots of the following quadratic equations by factorisation: (i) x2 -3x – 10 = 0 (ii) 2×2 + x – 6 = 0 (iii) √2×2 + 7x + 5√2 = 0 (iv) 2×2 – x + 18 = 0 8 (v) 100 x2 – 20 X + 1 = 0 Solution: Question […]
Chapter 4 Quadratic Equations Ex 4.1
Chapter 4 Quadratic Equations Ex 4.1 Question 1. Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x – 2x = (- 2) (3-x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x – 3) (2x + 1) = x (x + 5) (v) (2x – […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7 Question 1. The age of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 Question 1. Solve the following pairs of equations by reducing them to a pair of linear equations: Solution:By cross multiplication methodBy cross multiplication methodBy cross multiplication methodBy cross multiplication methodsolving for u and v by cross multiplication method:By cross multiplication method:By cross multiplication method: […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 Question 1. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (i) x – 3y – 3 = 0 3x – 9y – […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 Question 1. Solve the following pair of linear equations by the elimination method and the substitution (i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2 (iii) 3x – 5y […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 Question 1. Solve the following pair of linear equations by the substitution method, (i) x + y = 14, x – y = 4 (ii) s – t = 3, s/3 + t/2 = 6 (iii) 3x – y = 3, 9x – 3y = 9 (iv) 0.2x […]