NCERT Exemplar Solution for CBSE Class 10 Mathematics Chapter: Polynomials (Part-I)

Jun 19, 2017 14:39 IST

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT ExemplarHere you get the CBSE Class 10 Mathematics chapter 2, Polynomials: NCERT Exemplar Problems and Solutions (Part-I). This part of the chapter includes solutions for Exercise 2.1 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Polynomials. This exercise comprises of only the Multiple Choice Questions (MCQs) framed from various important topics in the chapter. Each question is provided with a detailed solution.

CBSE Class 10 Mathematics Syllabus 2017-2018

NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Polynomials:

Exercise 2.1

Multiple Choice Questions (MCQs)

Q. 1 If one of the zeroes of the quadratic polynomial (k – 1)x2 + kx +1 is −3 then the value of k is

(a) 4/2

(b)  −4/3

(c) 2/3

(d) −2/3

Sol. (a)

Explanation:

We know that If α is the one of the zeroes of the quadratic polynomial f (x) = ax2 + bx + c then, f (α) must be equal to 0.

Given, −3 is one of the zeroes of the quadratic polynomial say (k – 1)x2 + kx +1.

Let’s take p(x) = (k – 1)x2 + kx +1   

Then,               p (−3) = 0

⟹                   (k – 1)(−3)2 + k(−3)+1 = 0

⟹                   9(k – 1) − 3k + 1 = 0

⟹                   9k – 9 − 3k + 1 = 0

⟹                   6k – 8 = 0

⟹                   k = 4/3

Q. 2 A quadratic polynomial, whose zeroes are -3 and 4, is

(a) x2x + 12

(b) x2 + x + 12

(c) x2/2 – x/2 − 6

(d) 2x2 + 2x − 24

Sol. (c)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar 

Q.3 If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and − 3, then

(a) a = − 7, b = − 1

(b) a = 5, b = − 1

(c) a = 2, b = − 6

(d) a = 0, b = − 6

Sol. (d)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

NCERT Solutions for CBSE Class 10 Maths

Q.4 The number of polynomials having zeroes as −2 and 5 is

(a) 1

(b) 2

(c) 3

(d) More then 3

Sol. (d)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 5 If one of the zeroes of the cubic polynomial  is zero, the product of then other two zeroes is

(a) –c/a

(b) c/a

(c) 0

(d) –b/a

Sol. (b)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 6 If one of the zeroes of thee cubic polynomial  is – 1 , then the product of the other two zeroes is

(a)

(b)

(c)

(d)

Sol. (a)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 7 The zeroes of the quadratic polynomial x2 + 99 x + 127 are

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equal

Sol. (b)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 8 The zeroes of the quadratic polynomial x2 + kx + k where, k ≠ 0.

(a) cannot both be positive

(b) cannot both be negative

(c) are always unequal

(d) are always equal

Sol. (a)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 9 If the zeroes of the quadratic polynomial ax2 + bx + c where, c ≠ 0, are equal, then

(a) c and a have opposite signs

(b) c and b have opposite signs

(c) c and a have same signs

(d) c and b have the same signs

Sol. (c)

Explanation:

For equal root, b2 – 4ac = 0

⟹       b2 = 4ac

As b2 is always positive so 4ac must be positive, i.e. product of a and c must be positive i.e., a and c must have same sign either positive or negative.

Q. 10 If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it

(a) has no linear term and the constant term is negative

(b) has no linear term and the constant term is positive

(c) can have a linear term but the constant term is negative

(d) can have a linear term but the constant term is positive

Sol. (a)

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Q. 11 Which of the following is not the graph of a quadratic polynomial?

Class 10 Mathematics NCERT Exempla, NCERT Exemplar Solution, Polynomials Class 10 NCERT Exemplar

Sol. (d)

Explanation: For a quadratic polynomial the curve must cross the X-axis on at most two points but in option (d) the curve crosses the X-axis on the three points, so it does not represent the quadratic polynomial.

CBSE Class 10 NCERT Textbooks & NCERT Solutions

NCERT Exemplar Problems and Solutions Class 10 Science: All Chapters

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