In this article you will get CBSE Class 10 Mathematics chapter 2, Polynomials: NCERT Exemplar Problems and Solutions (Part-I). Every question has been provided with a detailed solution. All the questions given in this article are very important to prepare for CBSE Class 10 Board Exam 2017-2018.
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) x2 – x + 12
(b) x2 + x + 12
(c) x2/2 – x/2 − 6
(d) 2x2 + 2x − 24
Sol. (c)
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)
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)
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)
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)
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)
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)
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)
Q. 11 Which of the following is not the graph of a quadratic polynomial?
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.