NCERT Exemplar Problems – Class 10 Mathematics
Chapter 4: Quadratic Equations
Multiple Choice Questions (Exercise 4.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. Which of the following is a quadratic equation?
(A) \( x^{2} + 2x + 1 = (4 - x)^{2} + 3 \)
(B) \( -2x^{2} = (5 - x)\left(2x - \dfrac{2}{5}\right) \)
(C) \( (k + 1)x^{2} + \dfrac{3}{2}x = 7 \), where \( k = -1 \)
(D) \( x^{3} - x^{2} = (x - 1)^{3} \)
Correct Answer: (D)
2. Which of the following is not a quadratic equation?
(A) \( 2(x - 1)^{2} = 4x^{2} - 2x + 1 \)
(B) \( 2x - x^{2} = x^{2} + 5 \)
(C) \( (\sqrt{2}x + 3)^{2} + x^{2} = 3x^{2} - 5x \)
(D) \( (x^{2} + 2x)^{2} = x^{4} + 3 + 4x^{3} \)
Correct Answer: (C)
3. Which of the following equations has 2 as a root?
(A) \( x^{2} - 4x + 5 = 0 \)
(B) \( x^{2} + 3x - 12 = 0 \)
(C) \( 2x^{2} - 7x + 6 = 0 \)
(D) \( 3x^{2} - 6x - 2 = 0 \)
Correct Answer: (C)
4. If \( \dfrac{1}{2} \) is a root of the equation \( x^{2} + kx - \dfrac{5}{4} = 0 \), then the value of \( k \) is
(A) \( 2 \)
(B) \( -2 \)
(C) \( \dfrac{1}{4} \)
(D) \( \dfrac{1}{2} \)
Correct Answer: (A)
5. Which of the following equations has the sum of its roots as 3?
(A) \( 2x^{2} - 3x + 6 = 0 \)
(B) \( -x^{2} + 3x - 3 = 0 \)
(C) \( \sqrt{2}x^{2} - \dfrac{3}{2}x + 1 = 0 \)
(D) \( 3x^{2} - 3x + 3 = 0 \)
Correct Answer: (B)
6. Values of \( k \) for which the quadratic equation \( 2x^{2} - kx + k = 0 \) has equal roots is
(A) 0 only
(B) 4
(C) 8 only
(D) 0, 8
Correct Answer: (D)
7. Which constant must be added and subtracted to solve the quadratic equation \( 9x^{2} + \dfrac{3}{4}x - 2 = 0 \) by the method of completing the square?
(A) \( \dfrac{1}{8} \)
(B) \( \dfrac{1}{64} \)
(C) \( \dfrac{1}{4} \)
(D) \( \dfrac{9}{64} \)
Correct Answer: (B)
8. The quadratic equation \( 2x^{2} - \sqrt{5}x + 1 = 0 \) has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots
Correct Answer: (C)
9. Which of the following equations has two distinct real roots?
(A) \( 2x^{2} - 3\sqrt{2}x + \dfrac{9}{4} = 0 \)
(B) \( x^{2} + x - 5 = 0 \)
(C) \( x^{2} + 3x + 2\sqrt{2} = 0 \)
(D) \( 5x^{2} - 3x + 1 = 0 \)
Correct Answer: (B)
10. Which of the following equations has no real roots?
(A) \( x^{2} - 4x + 3\sqrt{2} = 0 \)
(B) \( x^{2} + 4x - 3\sqrt{2} = 0 \)
(C) \( x^{2} - 4x - 3\sqrt{2} = 0 \)
(D) \( 3x^{2} + 4\sqrt{3}x + 4 = 0 \)
Correct Answer: (A)
11. \( (x^{2} + 1)^{2} - x^{2} = 0 \) has
(A) four real roots
(B) two real roots
(C) no real roots
(D) one real root
Correct Answer: (C)
Answers taken from the official NCERT Exemplar answer key.