2<\/sup> – 3x + 7 is polynomial of one variable. As x has degree 2 in it and the only x is one variable.<\/p>\n(ii) Yes, y is only one variable.<\/p>\n
(iii) No as 3\u221at + t\u221a2 can be written as \\(3 t^{\\frac{1}{2}}+t \\sqrt{2}\\), Here the exponent of t in \\(3 t^{\\frac{1}{2}}\\) is \\(\\frac {1}{2}\\) which is not a whole number.<\/p>\n
(iv) No, as y + \\(\\frac{2}{y}\\) can be written as y + 2y-1<\/sup> where exponent of y in \\(\\frac{2}{y}\\) is -1, which is not a whole number.<\/p>\n(v) Yes, it is a polynomial in three variables x, y, and 1.<\/p>\n
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Question 2. \nWrite the co-efficients of x2<\/sup> in each of the following: \n(i) 2 + x2<\/sup> + x \n(ii) 2 – x2<\/sup> + x3<\/sup> \n(iii) \\(\\frac{\\pi}{2} x^{2}+x\\) \n(iv) \\(\\sqrt{2 x}-1\\) \nSolution: \n(i) We have given that the equation 2 + x2<\/sup> + x \nwe can also write 1x2<\/sup> + 1x + 2 \nTherefore, the coefficient of x2<\/sup> in this equation is 1.<\/p>\n(ii) we have given that the equation: \n2 – x2<\/sup> + x3<\/sup> \nwe can also write \nx3<\/sup> – 1x2<\/sup> + 2 \nTherefore, the coefficient of x2<\/sup> in this equation is -1.<\/p>\n(iii) We have given that the equation \n\\(\\frac{\\pi}{2} x^{2}+x\\) \nor, \\(\\frac{\\frac{22}{7} x^{2}+1 x}{2}\\) (since \u03c0 = \\(\\frac {22}{7}\\)) \nor, \\(\\frac{22}{7 \\times 2} x^{2}+1 x\\) \nor, \\(\\frac{11}{7} x^{2}+1 x\\) \nTherefore, the coefficient of x2<\/sup> in this equation is \\(\\frac{11}{7}\\).<\/p>\n(iv) We have given that the equation \u221a2x – 1. \nWe can also write 0x2<\/sup> + \u221a2x – 1 \nTherefore, the coefficient of x2<\/sup> in this equation is 0.<\/p>\n <\/p>\n
Question 3. \nGive one example each of a binomial of degree 35, and of a monomial of degree 100. \nSolution: \nWe know that polynomials having only two terms is called binomial. \nTherefore, the example of a binomial of degree 35 is ax35<\/sup> + b where a and b are any real number. \nAgain, the example of a monomial of degree 100 is ax100<\/sup> where a is any real number.<\/p>\nQuestion 4. \nWrite the degree of each of the following polynomials: \n(i) 5x3<\/sup> + 4x2<\/sup> + 7x \n(ii) 4 – y2<\/sup> \n(iii) 5t – \u221a7 \n(iv) 3 \nSolution: \n(i) We know that the highest power of the variable in a polynomial is called the degree of the polynomial. \nIn polynomial 5x3<\/sup> + 4x2<\/sup> + 7x. \nThe highest power of variable x is 3. \nTherefore, the degree of polynomial 5x3<\/sup> + 4x2<\/sup> + 7x is 3.<\/p>\n(ii) In polynomial 4 – y2<\/sup>, the highest power of the variable y is 2. \nTherefore, the degree of the polynomial 4 – y2<\/sup> is 2.<\/p>\n(iii) In polynomial 5t – 5, the highest power of the variable t is 1. \nTherefore, the degree of polynomial 5t – 5 is 1.<\/p>\n
(iv) The only term here is 3 which can be written as 3x0<\/sup>: So the highest power of the variable x is 0. \nTherefore, the degree of the polynomial 3 is 0.<\/p>\n <\/p>\n
Question 5. \nClassify the following as linear, quadratic and cubic polynomials \n(i) x2<\/sup> + x \n(ii) x – x3<\/sup> \n(iii) y + y2<\/sup> + 4 \n(iv) 1 + x \n(v) 3t \n(vi) r2<\/sup> \n(vii) 7x3<\/sup> \nSolution: \n(i) In polynomial x2<\/sup> + x the highest power of the variable x is 2. So the degree of the polynomial is 2. \nWe know that the polynomial of degree 2 is called a quadratic polynomial. \nTherefore, polynomial x2<\/sup> + x is a quadratic polynomial.<\/p>\n(ii) In polynomial x – x3<\/sup>, the highest power of the variable x is 3. So the degree of the polynomial is 3. \nWe know that the polynomial of degree 3 is called a cubic polynomial. \nTherefore, polynomial x – x3<\/sup> is a cubic polynomial.<\/p>\n(iii) In polynomial y + y2<\/sup> + 4, the highest power of the variable y is 2. So the degree of the polynomial is 2. \nWe know that the polynomial of degree 2 is called a quadratic polynomial. \nTherefore, polynomial y + y2<\/sup> + 4 is a quadratic polynomial.<\/p>\n(iv) In polynomial 1 + x, the highest power of the variable x is 1. So the degree of the polynomial is 1. \nWe know that the polynomial of degree 1 is called a linear polynomial. \nTherefore, polynomial 1 + x is a linear polynomial.<\/p>\n
(v) In polynomial 3t, the highest power of the variable t is 1. So, the degree of the polynomial is 1. \nWe know that the polynomial of degree 1 is called a linear polynomial. \nTherefore, polynomial 3t is a linear polynomial.<\/p>\n
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(vi) In polynomial r2<\/sup>, the highest power of the variable r is 2. So, the degree of the polynomial is 2. \nWe know that the polynomial of degree 2 is called a quadratic polynomial. \nTherefore, polynomial r is a quadratic polynomial.<\/p>\n(vii) In polynomial 7x3<\/sup>, the highest power of the variable x is 3. So the degree of the polynomial is 3. \nWe know that the polynomial of degree 3 is called a cubic polynomial. \nTherefore polynomial 7x3<\/sup> is a cubic polynomial.<\/p>\n","protected":false},"excerpt":{"rendered":"These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.1 Question 1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. …<\/p>\n
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n