Chapter 2 Polynomials Exercise 2.1
Chapter 2 Polynomials Exercise 2.1 Question 1. The graphs of y = p(x) are given in figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Solution: The number of zeroes of p(x) in each graph given; are
Chapter 1 Real Numbers Ex 1.4
Chapter 1 Real Numbers Ex 1.4 Question 1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: Solutions: Question 2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. Solutions: In […]
Chapter 1 Real Numbers Ex 1.3
Chapter 1 Real Numbers Ex 1.3 Question 1. Prove that √5 is irrational. Solutions: Question 2. Prove that 3 + 2√5 is irrational. Solutions: Let us assume that 3 + 2√5 is rational. ∴ There exists co-prime integers a and b(b ≠ 0) such that But this contradicts the fact that √5 is irrational. This […]
Chapter 1 Real Numbers Ex 1.2
Chapter 1 Real Numbers Ex 1.2 Question 1. Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429. Solutions: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429.So, 7429 = 17 x 19 x 23 Question 2. Find the LCM and HCF of the […]
Chapter 1 Real Numbers Ex 1.1
Chapter 1 Real Numbers Ex 1.1 Question 1. Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255. Solutions: (i) Given numbers are 135 and 225. On applying Euclid’s division algorithm, we have 225 = 135 x 1 + 90 Since the remainder 90 ≠ […]
Chapter 16 Playing with Numbers
Chapter 16 Playing with Numbers Very Short Answer Type Question 1. Write the following numbers in generalised form. (a) ab (b) 85 (c) 132 (d) 1000 Solution: (a) ab = 10 × a + 1 × b = 10a + b (b) 85 = 10 × 8 + 1 × 5 = 10 × 8 […]
Chapter 16 Playing with Numbers Exercise 16.2
Chapter 16 Playing with Numbers Exercise 16.2 Question 1. If 21y5 is a multiple of 9, where y is a digit, what is the value of y? Solution: A number is divisible by 9 if the sum of its digits is also divisible by 9. Sum of the digits of 21y5 = 2 + 1 […]
Chapter 16 Playing with Numbers Exercise 16.1
Chapter 16 Playing with Numbers Exercise 16.1 Find the values of the letters in each of the following and give reasons for the steps involved. Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: 3 × B = B ⇒ B = D 3 × A = CA ⇒ […]
Chapter 15 Introduction to Graphs
Chapter 15 Introduction to Graphs Question 1. Write the coordinates of each point shown is the graph. Solution: Question 2. From the given figure, choose the letters indicate the location of the points. (i) (3, 1) (ii) (0, 5) (iii) (3, 0) (iv) (1, 2) (v) (2, 3) (vi) (8, 12) (vii) (6, 10) (viii) […]
Chapter 15 Introduction to Graphs Exercise 15.3
Chapter 15 Introduction to Graphs Exercise 15.3 Question 1. Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples (b) Distance travelled by car. (i) How much distance did the car cover during the period 7:30 am to 8 am? (ii) What was the time when […]