NCERT Exemplar Problems – Class 10 Mathematics
Chapter 2: Polynomials
Multiple Choice Questions (Exercise 2.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. If one of the zeroes of the quadratic polynomial \((k-1)x^{2} + kx + 1\) is \(-3\), then the value of \(k\) is
(A) \(\dfrac{4}{3}\)
(B) \(-\dfrac{4}{3}\)
(C) \(\dfrac{2}{3}\)
(D) \(-\dfrac{2}{3}\)
Correct Answer: (A)
2. A quadratic polynomial, whose zeroes are \(-3\) and \(4\), is
(A) \(x^{2} - x + 12\)
(B) \(x^{2} + x + 12\)
(C) \(\dfrac{x^{2}}{2} - \dfrac{x}{2} - 6\)
(D) \(2x^{2} + 2x - 24\)
Correct Answer: (C)
3. If the zeroes of the quadratic polynomial \(x^{2} + (a+1)x + b\) are \(2\) and \(-3\), then
(A) \(a = -7\), \(b = -1\)
(B) \(a = 5\), \(b = -1\)
(C) \(a = 2\), \(b = -6\)
(D) \(a = 0\), \(b = -6\)
Correct Answer: (D)
4. The number of polynomials having zeroes as \(-2\) and \(5\) is
(A) 1
(B) 2
(C) 3
(D) more than 3
Correct Answer: (D)
5. Given that one of the zeroes of the cubic polynomial \(ax^{3} + bx^{2} + cx + d\) is zero, the product of the other two zeroes is
(A) \(-\dfrac{c}{a}\)
(B) \(\dfrac{c}{a}\)
(C) \(0\)
(D) \(-\dfrac{b}{a}\)
Correct Answer: (B)
6. If one of the zeroes of the cubic polynomial \(x^{3} + ax^{2} + bx + c\) is \(-1\), then the product of the other two zeroes is
(A) \(b - a + 1\)
(B) \(b - a - 1\)
(C) \(a - b + 1\)
(D) \(a - b - 1\)
Correct Answer: (A)
7. The zeroes of the quadratic polynomial \(x^{2} + 99x + 127\) are
(A) both positive
(B) both negative
(C) one positive and one negative
(D) both equal
Correct Answer: (B)
8. The zeroes of the quadratic polynomial \(x^{2} + kx + k\), \(k \neq 0\),
(A) cannot both be positive
(B) cannot both be negative
(C) are always unequal
(D) are always equal
Correct Answer: (A)
9. If the zeroes of the quadratic polynomial \(ax^{2} + bx + c\), \(c \neq 0\) are equal, then
(A) \(c\) and \(a\) have opposite signs
(B) \(c\) and \(b\) have opposite signs
(C) \(c\) and \(a\) have the same sign
(D) \(c\) and \(b\) have the same sign
Correct Answer: (C)
10. If one of the zeroes of a quadratic polynomial of the form \(x^{2} + ax + b\) 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.
Correct Answer: (A)
11. Which of the following is not the graph of a quadratic polynomial?
(A) [Parabola opening upwards]
(B) [Parabola opening downwards]
(C) [Graph with a local maximum and minimum – cubic-like shape]
(D) [Graph that is not a parabola / has more than two turning points or discontinuous]
Note: Refer to the original NCERT Exemplar book for the exact four graphs. The correct option is the one that does not represent a quadratic polynomial.
Correct Answer: (D)
Answers taken from the official NCERT Exemplar answer key at the end of the book.