CBSE Class 12 Applied Mathematics — Flashcards

A: Modular Arithmetic is a system of arithmetic for integers that deals with remainders only. X mod Y = R means when X is divided by Y, the remainder is R. For example: 29 mod 3 = 2 (since 29 = 3 × 9 + 2

A: 1. Addition: (A + B) mod C = (A mod C + B mod C) mod C 2. Subtraction: (A - B) mod C = (A mod C - B mod C) mod C 3. Multiplication: (A × B) mod C = (A mod C × B mod C) mod C These properties allow us

A: a ≡ b (mod m) means 'a is congruent to b modulo m'. Two conditions must be satisfied: 1. (a - b) is divisible by m 2. a mod m = b mod m For example: 41 ≡ 21 (mod 5) because 41 - 21 = 20 is divisible b

A: A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Each member of this arrangement is called an element of the matrix. Example: A = [2 3]

A: The order of a matrix is expressed as m × n, where 'm' is the number of rows and 'n' is the number of columns. It is read as 'm by n'. Example: Matrix A = [1 2 3] [4 5 6] has

A: A square matrix is a matrix in which the number of rows equals the number of columns (m = n). Example: B = [2 -1 3] [0 4 -2] [1 5 7] This is a 3×3 square matrix.

A: An implicit function is one where the dependent variable cannot be explicitly expressed in terms of the independent variable. Example: x² + y² = 25. Here, y cannot be easily written as y = f(x) in a s

A: Differentiating both sides with respect to x: 3x² + 3y²(dy/dx) = 3a[y + x(dy/dx)] 3x² + 3y²(dy/dx) = 3ay + 3ax(dy/dx) Rearranging: 3y²(dy/dx) - 3ax(dy/dx) = 3ay - 3x² dy/dx(3y² - 3ax) = 3ay - 3x² Ther

A: Parametric functions represent x and y in terms of a parameter t: x = g(t), y = f(t). To find dy/dx, we use the chain rule: dy/dx = (dy/dt)/(dx/dt) This formula applies when dx/dt ≠ 0. Example: If x =