Example 01: Expand (a + b)2 Solution: Expanding Binomially (a + b)2 = 2C0a2 + 2C1a2-1b1 + 2C2b2 (a + b)2 = (1)a2 + (2)a1b1 + (1)b2 (a + b)2 = a2 + 2ab+ b2 Note: (a – b)2 = a2 – 2ab+ b2 Example 02: Expand (a + b)3 Solution: Expanding Binomially (a + […]
Science > Mathematics > Algebra > Logarithms > Use of Laws of Logarithms Set – III In the last article, we have studied to solve problems on the use of laws of logarithms to prove given logarithmic expression. In this article, we shall study to solve more problems on these laws to prove given relation […]
Science > Mathematics > Algebra > Logarithms > Laws of Logarithm In this article, we shall study the laws of logarithm and their proofs. Laws of logarithm are very important in mathematics and every student should have confidence in using them. Laws of Product: loga(mn) = logam + logan, where a, m, n are positive […]
In this article, we shall study to write vector and cartesian equation of a line in Space. Theorem – 1 (Vector Equation of Line in Space): The vector equation of a straight line passing through a fixed point with position vector a and parallel to a given vector b is r = a + λ b. Where […]
In this article, we shall study Jacobi’s Method to find the solution of simultaneous equations. Example 01: Solve the following equations by Jacobi’s Method, performing three iterations only. 20x + y – 2z = 17, 3x + 20 y – z + 18 = 0, 2x – 3y + 20 z = 25. Solution: Given […]
In this article, we shall study to find the distance between two points using the distance formula when the coordinates of the two points are given. Example 01: Find the distance between the following pairs of points : (2, 3), (4, 1) Let A(2, 3) ≡ (x1, y1) and B(4, 1) ≡ (x2, y2) be […]
In this article, we shall study to find the value of trigonometric expressions involving standard angles. Trigonometric functions values of some standard angles are given below: Evaluate the following: Example 01: sin20c + sin2(π/6)c + sin2(π/3)c + sin2(π/2)c = (0)2 + (1/2)2 + (√3/2)2 + (1)2 = 0 + 1/4 + 3/4 + 1 […]
Science > Mathematics > Pair of Straight Lines > To Find the Condition When Relation Between Slopes is Given In this article, we shall discuss problems to find the condition when the relation between slopes of lines represented by a joint equation is given. Example – 18: If the slope of one of the lines […]
Science > Mathematics > Pair of Straight Lines > To Find Value of Constant When Relation Between Slopes is Given In this article, we shall study to solve problems to find the value of constant or to prove the given relation when the relation between slopes of the line represented by the joint equation is […]
In this article, we shall study the use of the bisection method to solve an equation. Intermediate Value Theorem : If a function f is continuous on closed interval [a, b] and f (a). f (b) < 0, i.e. ƒ (a) and ƒ (b) are opposite signs, then there exists at least one c ∈ […]