NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Exercise 5.1 Page 99 1. In which of the following situations, does the list of numbers involved make an arithmetic progression and why? (i) The taxi fare after each km when the fare is ₹ 15 for the first km and ₹ 8 for each additional km. (i) Let tn be the taxi fare for first n km. Then t1 … [Read more...] about Exercise 5.1

# Maths

## Exercise 4.4

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.4 Page 91 1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (i) 2x2 – 3x + 5 = 0 2x2 – 3x + 5 = 0 Comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3 and c = 5 We know, Discriminant = b2 – 4ac = ( – 3)2 – 4 (2) … [Read more...] about Exercise 4.4

## Exercise 4.3

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.3 Page 87 1. Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2x2 – 7x + 3 = 0 Given 2x2 - 7x + 3 =0 $ \begin{equation} \begin{aligned} &\Rightarrow 2\left(x^{2}-\frac{7}{2} x+\frac{3}{2}\right)=0\\\\ &\Rightarrow … [Read more...] about Exercise 4.3

## Exercise 4.2

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.2 Page 76 1. Find the roots of the following quadratic equations by factorisation: (i) x2 – 3x – 10 = 0 Given, x2 – 3x – 10 =0 Taking LHS, =>x2 – 5x + 2x – 10 =>x(x – 5) + 2(x – 5) =>(x – 5)(x + 2) The roots of this equation, x2 – 3x – 10 = 0 are the values of x for … [Read more...] about Exercise 4.2

## Exercise 4.1

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.1 Page 73 1. Check whether the following are quadratic equations: (i) (x + 1)2 = 2(x – 3) Given, (x + 1)2 = 2(x – 3) By using the formula for (a+b)2 = a2+2ab+b2 ⇒ x2 + 2x + 1 = 2x – 6 ⇒ x2 + 7 = 0 Since the above equation is in the form of ax2 + bx + c = 0. ∴ the given … [Read more...] about Exercise 4.1

## Exercise 3.7

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.7 (Optional) Page 68 1. The ages 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 the ages of Ani and Biju. The age difference between … [Read more...] about Exercise 3.7

## Exercise 3.6

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.6 Page 67 1. Solve the following pairs of equations by reducing them to a pair of linear equations: (i) 1/2x + 1/3y = 2 1/3x + 1/2y = 13/6 Let us assume 1/x = m and 1/y = n , then the equation will change as follows. m/2 + n/3 = 2 ⇒ 3m+2n-12 = 0 .....(i) m/3 + … [Read more...] about Exercise 3.6

## Exercise 3.5

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.5 Page 62 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 and 3x – 9y – 2 = 0 (ii) 2x + y = 5 and 3x + 2y … [Read more...] about Exercise 3.5

## Exercise 3.4

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.4 Page 56 1. Solve the following pair of linear equations by the elimination method and the substitution method: (i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2 (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7 (iv) x/2+ 2y/3 = -1 and x-y/3 = 3 (i) x + y = 5 … [Read more...] about Exercise 3.4

## Exercise 3.3

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.3 Page 53 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 + 0.3y = 1.3 0.4x + 0.5y = 2.3 (v) √2 x+√3 y = 0 √3 x-√8 y = … [Read more...] about Exercise 3.3