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MATHS CHAPTER : 1 NUMBER SYSTEMS

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CHAPTER : 1 NUMBER SYSTEMS Page No: 5 Exercise 1.1 1. Is zero a rational number? Can you write it in the form  p / q , where  p  and  q are integers and  q  ≠ 0? Answer Yes. Zero is a rational number as it can be represented as 0 / 1 or 0 / 2. 2. Find six rational numbers between 3 and 4. Answer There are infinite rational numbers in between 3 and 4. 3 and 4 can be represented as 24 / 8 and 32 / 8 respectively. Therefore, six rational numbers between 3 and 4 are 25 / 8, 26 / 8, 27 / 8, 28 / 8, 29 / 8, 30 / 8. 3. Find five rational numbers between 3 / 5 and 4 / 5. Answer There are infinite rational numbers in between 3 / 5 and 4 / 5 3 / 5 = 3×6 / 5×6 = 18 / 30 4 / 5 = 4×6 / 5×6 = 24 / 30 Therefore, five rational numbers between 3 / 5 and 4 / 5 are 19 / 30, 20 / 30, 21 / 30, 22 / 30, 23 / 30. 4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. ► True, since the col
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MATHS CHAPTER : 2 POLYNOMIALS

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CHAPTER : 2 POLYNOMIALS Page No: 32 Exercise 2.1 1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) 4 x 2  - 3 x  + 7 (ii)  y 2  + √ 2 (iii) 3√ t  +  t √ 2 (iv)  y  + 2 / y (v)  x 10  +  y 3  +  t 50 Answer (i) 4 x 2  - 3 x  + 7 There is only one variable  x  with whole number power so this polynomial in one variable. (ii)   y 2  + √ 2 There is only one variable  y  with whole number power so this polynomial in one variable. (iii) 3√ 2  +  t √ 2  There is only one variable  t  but in 3√ t  power of  t  is 1 / 2 which is not a whole number so 3√ t  +  t √ 2  is not a polynomial. (iv)  y  + 2 / y There is only one variable  y  but 2 / y  = 2 y -1 so the power is not a whole number so  y  + 2 / y  is not a polynomial. (v)  x 10  +  y 3  +  t 50 There are three variable  x ,  y  and  t  and there powers are whole number so this polynomial in three variable. 2. Write the coeffi
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