Rajasthan Board Class 10 Mathematics — Flashcards for Quick Revision

A: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. For example: 12 = 2² × 3 (unique f

A: For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Here, a is the dividend, b is the divisor, q is the quotient, and r is the remainder.

A: A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. Note: 1 is not considered a prime number.

A: A polynomial is an algebraic expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents. The degree of a polynomial i

A: The expressions 1/x-1, √x + 2, and 1/x² + 2x + 3 are NOT polynomials because they contain negative exponents (1/x = x⁻¹) or fractional exponents (√x = x^(1/2)). Only 2x² - 3x + 1 is a polynomial as it

A: A linear polynomial is a polynomial of degree 1. General form: ax + b, where a ≠ 0. Examples: 2x - 3, √3x + 5, y + √2. Note that expressions like 2x + 5 - x² are not linear polynomials because the hig

A: A linear equation in two variables is an equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Examples: 2x + 3y - 6 = 0, x - y +

A: A pair of linear equations in two variables consists of two linear equations involving the same two variables. Example: 2x + 3y = 6 and x - y = 1. The solution is the common values of x and y that sat

A: A pair of linear equations that has at least one solution is called a consistent pair. This includes cases with exactly one solution (unique) or infinitely many solutions. Example: x + y = 3 and 2x -