SkEdu Q1. For what value of k will the consecutive terms 2k + 1, 3k + 3, 5k – 1 form an AP? Solution 1 Q2. Find the 9th term from the end of the AP. 5, 9, 13,…, 185. Solution 1 Q3. In the following situation form an arithmatic Progression. The cost of digging a … Read more
Exercise 7.2› Choose the correct answer from the given four options: Q1. The distance of the point P (2, 3) from the x-axis is(A) 2 (B) 3 (C) 1 (D) 5 Solution 1 Q2. The distance between the pointsA (0, 6) and B (0, –2) is (A) 6 (B) 8 (C) 4 (D) 2 Solution … Read more
‹Exercise 7.3 Q1. If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle. Solution 1 Q2. A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. … Read more
Co-ordinate Geometry is a branch of mathematics that focuses on the study of the position and movement of points, lines, and shapes in two-dimensional (2D) and three-dimensional (3D) space. It is a fundamental tool for understanding the fundamentals of physics, engineering, and many other scientific and engineering disciplines. In CBSE Class 10, co-ordinate geometry is … Read more
Q1. Find the coordinate of the point which divide the line joining the points A (-1,7) and B(4, -3) in the ratio 2 : 3. Solution: Let point P (X,Y) be the point divide the line joining points AB in 2 : 3 Here, `x_1 = – 1` `y_1 = 7` `x_2 = 4` … Read more
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