Law > Medical Jurisprudence > Causes of Road Accidents A traffic or road accident is defined as an accident involving at least one vehicle on a road open to public traffic in which at least one person is injured or killed. The main cause of accidents and crashes are due to human errors. Most of […]
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Law > Civil Laws > Alternate Dispute Resolution > Salient Features of Arbitration and Conciliation Act, 1996 The Arbitration and Conciliation Act, 1996 proceeds on the basis of the UN Model Law so as to make our law in accordance with the United Nations Commission on International Trade Law (UNCITRAL). This Act consolidated the law […]
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Binomial Theorem
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 […]
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Laws of Logarithms
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 […]
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Equation of Line in Space
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 […]
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Distance Formula
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 […]