1. Find HCF by factorization method (i) \( 21x^2y, 35xy^2 \) \[21x^2y = 3 \cdot 7 \cdot x^2 \cdot y, \quad 35xy^2 = 5 \cdot 7 \cdot x \cdot y^2\] \[\text{HCF} = 7xy\] (ii) \( 4x^2 – 9y^2, 2x^2 – 3xy \) \[4x^2 – 9y^2 = (2x + 3y)(2x – 3y), \quad 2x^2 – 3xy…
Question 1: Factorize by identifying common factors (i) \( 6x + 12 \) \[= 6(x + 2)\] (ii) \( 15y^2 + 20y \) \[= 5y(3y + 4)\] (iii) \( -12x^2 – 3x \) \[= -3x(4x + 1)\] (iv) \( 4a^2b + 8ab^2 \) \[= 4ab(a + 2b)\] (v) \( xy – 3x^2 + 2x \)…
1. Questions, Options, Correct Answers, and Reasons (i) The set builder form of the set \( \left\{1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \dots \right\}\) is: (a) \(\{x \, | \, x = \frac{1}{n}, \, n \in W\}\) (b) \(\{x \, | \, x = \frac{1}{2n + 1}, \, n \in W\}\) (c) \(\{x \, | \, x…
Binary relations and functions are fundamental concepts in mathematics that describe relationships between elements of sets. They are widely used in various fields, from computer science to economics. Functions, in particular, serve as mathematical models for real-world phenomena. This article covers binary relations, the definition and types of functions, their domain and range, function notation,…
Express the following numbers in scientific notation: (i) \( 2000000 \) \[2000000 = 2.0 \times 10^6\] (ii) \( 48900 \) \[48900 = 4.89 \times 10^4\] (iii) \( 0.0042 \) \[0.0042 = 4.2 \times 10^{-3}\] (iv) \( 0.0000009 \) \[0.0000009 = 9.0 \times 10^{-7}\] (v) \( 73 \times 10^3 \) \[73 \times 10^3 = 7.3 \times…
