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Vectors are mathematical objects that have both magnitude and direction. They are used in physics and engineering to represent quantities such as force, velocity, and displacement. Mathematics Notes for Class 12 Chapter 7 The vector, whose initial point is the origin Oand whose terminal point is P i.e., OP is called: Position vector The dot product of unit … Read more
A conic section is a curve formed by the intersection of a plane and a double-napped cone. The four main types are circles, ellipses, parabolas, and hyperbolas, each with distinct properties and equations. Mathematics Notes For Class 12 Chapter 6 A function which is to be maximized or minimized is called an: Objective function The … Read more
“Learn about linear inequalities and linear programming, techniques used to solve optimization problems by finding the best outcome within given constraints.” Mathematic 12 Class Chapter 5 Notes The inequality x < a is the closed half plane to the _________ of the boundary line x = a: Left A function which is to be maximized or minimized … Read more
“Explore the basics of Analytic Geometry, which combines algebra and geometry to study shapes, lines, and curves using coordinate systems and equations.” Important questions of Chapter 4 Mathematics Class 12 Equation of horizontal line through (a, b) is: x = b The point of concurrency of medians of triangle is called: Centroid y = c … Read more
“Discover integration in calculus, the process of finding the area under curves, summing infinitesimal changes, and solving problems related to accumulation and total quantities.” Mathematics Class 12 Chapter 3 Notes ? Cos(ax+b)dx=: (ax+b)n+1/a(n+1) +c The differentiate of x is given by: sin-1 (x/a) + c ? Sin(ax+b)dx=: y= -Cos x + c If y= x2-1 then dy =: … Read more
“Learn about differentiation in calculus, a fundamental concept that explores how functions change, calculating the rate of change or slope at any given point.” Mathematics Chapter 2 Class 12 Derivative of ?x (cos x) w.r.t x is: Cos x /2?x -?xSin x If y = eax, then y4=: a4eax dy/dx = dy/dx . dx/du is called: … Read more
“Explore the concepts of functions and limits in mathematics. Understand how functions map inputs to outputs and how limits describe the behavior of functions as they approach specific points.” Solutions of Mathematics Class 12 Chapter 1 If f(x) = x sec x, then f(0): 0 f(x) = sin x + cos x is ———— function: … Read more