{"id":24643,"date":"2021-06-19T15:21:44","date_gmt":"2021-06-19T09:51:44","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=24643"},"modified":"2022-03-02T10:38:14","modified_gmt":"2022-03-02T05:08:14","slug":"ncert-solutions-for-class-9-maths-chapter-2-ex-2-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-1\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1"},"content":{"rendered":"

These NCERT Solutions for Class 9 Maths<\/a> Chapter 2 Polynomials Ex 2.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.1<\/h2>\n

Question 1.
\nWhich of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
\n(i) 4x2<\/sup> – 3x + 7
\n(ii) y2<\/sup> + \u221a2
\n(iii) 3\u221at + t\u221a2
\n(iv) y + \\(\\frac{2}{y}\\)
\n(v) x10<\/sup> + y3<\/sup> + t50<\/sup>
\nSolution:
\n(i) Yes, 4x2<\/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

\"NCERT<\/p>\n

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

\"NCERT<\/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>\n

Question 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

\"NCERT<\/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

\"NCERT<\/p>\n

(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<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 Questions and Answers are prepared by our highly skilled subject experts. 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