Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2 Question 1. Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number […]
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1
Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 Question 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting)? Represent this situation algebraically and graphically. […]
Chapter 2 Polynomials Ex 2.4
Chapter 2 Polynomials Ex 2.4 Question 1. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and the coefficients in each case: Solution:(i) Comparing the given polynomial with ax3 + bx2 + cx + d, we get: a = 2, b – 1, c = -5 […]
Chapter 2 Polynomials Ex 2.3
Chapter 2 Polynomials Ex 2.3 Question 1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder, in each of the following: (i) p(x) = x3 – 3×2 + 5x -3, g(x) = x2-2 (ii) p(x) =x4 – 3×2 + 4x + 5, g(x) = x2 + 1 -x (iii) p(x) = x4 – 5x + 6, […]
Chapter 2 Polynomials Ex 2.2
Chapter 2 Polynomials Ex 2.2 Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6×2 – 3 – 7x (iv) 4u2 + 8u (v) t2 -15 (vi) 3×2 – x – 4 Solution: Question 2. Find a […]
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 ≠ […]