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# System prepended metadata

title: 'HW Set 1 (Chapter 1), HS 1st Year'

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### HW Set-1
1. Which of the following are sets? Justify your answer.
    - The collection of all whole numbers less than 10.
    - The collection of good hockey players in India.
    - The collection of all questions in chapter 1.
    - The collection of all difficult chapters in your mathematics book.
    - A collection of Hindi novels written by Munshi Prem Chand.
    - A team of 11 best cricket players of India.
    - The collection of all the months of the year whose names begin with the letter $M$.
    - The collection of all interesting books.
    - The collection of all short boys of your class.
    - The collection of all those students of your class whose ages exceed 15 years.
    - The collection of all rich persons of Assam.
    - The collection of all persons of Assam whose assessed annual incomes exceed (say) ₹10 lakh in the financial year 2024-25.
    - The collection of all interesting dramas written by Shakespeare.
2. Let $A$ be the set of all even whole numbers less than 10.
    - Write $A$ in roster form.
    - Fill in the blanks with the appropriate symbol $\in$ or $\notin$:
        - $0 \ldots A$
        - $10 \ldots A$
        - $3 \ldots A$
        - $6 \ldots A$
3. Write the following sets in roster form:
    - $A=\{x: x$ is a natural number, $30 \leq x<36\}$.
    - $B=\{x: x$ is an integer and $-4<x<6\}$.
    - $C=\{x: x$ is a two-digit number such that the sum of its digits is 9$\}$.
    - $D=\left\{x: x\right.$ is an integer, $\left.x^{2} \leq 9\right\}$.
    - $E=\{x: x$ is a prime number, which is a divisor of 42$\}$.
    - $F=\{x: x$ is a letter in the word 'MATHEMATICS'$\}$.
    - $G=\{x: x$ is a prime number and $80<x<100\}$.
    - $H=\{x: x$ is a perfect square and $x<50\}$.
    - $I=\left\{x: x \in R\right.$ and $\left.x^{2}+x-12=0\right\}$.
    - $J=\left\{x: x \in N, x\right.$ is a multiple of 5 and $\left.x^{2}<400\right\}$.
4. List all the elements of each of the sets given below:
    - $A=\{x: x=2 n, n \in \mathbb{N}$ and $n \leq 5\}$.
    - $B=\{x: x=2 n+1, n \in \mathbb{N}$ and $n<5\}$.
    - $C=\left\{x: x=\frac{1}{n}, n \in \mathbb{N}\right.$ and $\left.n<6\right\}$.
    - $D=\left\{x: x=n^{2}, n \in \mathbb{N}\right.$ and $\left.2 \leq n \leq 5\right\}$.
    - $E=\left\{x: x \in \mathbb{Z}\right.$ and $\left.x^{2}=x\right\}$.
    - $F=\left\{x: x \in \mathbb{Z}\right.$ and $\left.-\frac{1}{2}<x<\frac{13}{2}\right\}$.
    - $G=\left\{x: x=\frac{1}{(2 n-1)}, n \in \mathbb{N}\right.$ and $\left.1 \leq n \leq 5\right\}$.
    - $H=\{x: x \in \mathbb{Z},|x| \leq 2\}$.
5. Write each of the sets given below in set-builder form:
    - $A=\left\{1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, \frac{1}{36}, \frac{1}{49}\right\}$
    - $B=\left\{\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50}\right\}$
    - $C=\{53,59,61,67,71,73,79\}$
    - $D=\{-1,1\}$
    - $E=\{14,21,28,35,42, \ldots, 98\}$