Exercise 2.1 Q1. The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case Solution 1 Exercise 2.2 Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.(i) `x^2` – 2x … Read more
Q1. Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Solution 1 Q2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 … Read more
Q1. Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225 Step 1Since 225 > 135, we can apply Euclid’s division lemma to a = 225 and b = 135 to find q and r such that:225 = 135q … Read more
Q1. Prove that `sqrt{5}` is irrational. Solution 1 Q2. Prove that 3 + `2sqrt{5}` is irrational. Solution 2. Q3. Prove that the following are irrationals: (i) `frac{1}{sqrt{5}}` (ii) 7 `sqrt{5}`(iii) 6 + `sqrt{2}` Solution 3. ‹Exercise 1.2 Exercise 1.4›
Q1. 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(i) `frac{13}{3125}` (ii) `frac{17}{8}` (iii) `frac{64}{455}` (iv) `frac{15}{1600}` (v) `frac{29}{343}` (vi)`frac{23}{2^3 5^2}` (vii) `frac{129}{2^2 5^7 7^5}`(viii) `frac{6}{15}` (ix) `frac{35}{50}` (x) `frac{77}{210}` Solution 1 Q2. Write down the decimal expansions of those … Read more
Q1. Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7) Solution 1 Q2. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear. Solution 2. Q3. Find the … Read more
Q1. Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3. Solution 1 Q2. Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3). Solution 2. Q3. To conduct Sports Day activities, in your rectangular … Read more
Q1. Find the area of the triangle whose vertices are: (i) (2, 3), (–1, 0), (2, – 4) (ii) (–5, –1), (3, –5), (5, 2). Solution 1 Q2. In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, –2), (5, 1), (3, k) (ii) (8, 1), (k, … Read more
Q1. Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b) Solution 1 Q2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A … Read more