Menelaw’s Theorem Theorem: If a transversal cut the sides BC, CA, AB of a triangle in D, E, F respectively then BD/DC. CE/EA. AF/FB = -1. Proof: Let A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) be Let the transversal be ax + by + c = 0 BD/DC = The ratio in Read more about Menelaw’s Theorem[…]
Ceva’s Theorem Theorem: If the lines joining any point P, to the vertices A, B, C of a triangle meet the opposite Sides in D, E, F respectively then (BD.CE.AF)/(DC.EA.FB)=1 Proof: Let A (x₁, y₁), B (x₂, y₂), and C (x₃, y₃) be the vertices. Let us consider point P is (0, 0) We know Read more about Ceva’s Theorem[…]
Elastic Properties of Matter 1) Elasticity: The property of matter by virtue of which a body tends to regain its original shape and size after the removal of deforming force is called as Elasticity. 2) Plasticity: The property of matter by virtue of which it does not regain its original shape and size after the Read more about Elastic Properties of Matter[…]
Inverse Trigonometric Functions – Form f(f⁻¹(x)) Function of the form f(f⁻¹(x)): where f(x) is Trigonometric Function (i)Consider function f(x) = sin(sin⁻¹x). Domain of the function is [-1, 1] Also, sin (sin ⁻¹(x)) = x sin(sin⁻¹x) = x for all x ϵ [-1, 1] (ii)Consider function f(x) = cos(cos⁻¹x). Domain of the function is [-1, 1] Read more about Inverse Trigonometric Functions – Form f(f⁻¹(x))[…]
Electrical Conducting Materials for Specific Use Electrical conducting materials are the basic requirement for electrical engineering products. 1) Filament of electric bulb: It is made up of tungsten which has high resistivity, high melting point. 2) Element of heating devices (such as heater, geyser or press): It is made up of nichrome which has high Read more about Electrical Conducting Materials for Specific Use[…]
COMEDK Engineering Entrance Exam 2020 Notification Released Consortium of Medical, Engineering and Dental Colleges of Karnataka(COMEDK) is an entrance exam conducts every year in the month of May for admission into Engineering courses in Private/Professional Colleges within the State of Karnataka. COMEDK organisation conducts COMEDK UGET(Undergraduate Entrance Test)-2020 for admission into first year B.Tech/B.Arch courses Read more about COMEDK Engineering Entrance Exam 2020 Notification Released[…]
Law of Radioactive Disintegration The spontaneous breaking of a nucleus is known as Radioactive Disintegration. According to Rutherford and Soddy made experimental study of the radioactive decay of various radioactive materials and gave the following the laws: Radioactive decay is a random and spontaneous process. It is not influenced by external conditions such as temperature, Read more about Law of Radioactive Disintegration[…]
Complementary Angles Theorem: , Proof: Let . . .(1) Where , , , , , Now sin⁻¹x = θ x = sin θ x = cos (π/2 – θ) cos⁻¹x = π/2 – θ cos⁻¹x + θ = π/2. . . (2) from equation 1 and 2 sin⁻¹x = θ cos⁻¹x + θ = π/2 Read more about Complementary Angles[…]
Relation f⁻¹(x) with f⁻¹(-x) – Theorems Theorem: . Proof: , Let sin⁻¹(-x) = θ . . . (1) -x = sinθ x = -sinθ x = sin(-θ) we know that x ϵ [-1, 1] and , -θ =sin⁻¹(x) . . . (2) From equation (1) and (2) sin⁻¹(-x) = θ -θ =sin⁻¹(x) ⇒ θ = Read more about Relation f⁻¹(x) with f⁻¹(-x) – Theorems[…]
Interference of Light When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other point’s intensity is minimum. This phenomenon is called Interference of light. It is of following two types (1) Constructive Read more about Interference of Light[…]