Here you get the CBSE Class 10 Mathematics chapter 4, Quadratic Equations: NCERT Exemplar Problems and Solutions (Part-I). This part of the chapter includes solutions for Exercise 4.1 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Quadratic Equations. 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.

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, Quadratic Equations:**

**Exercise 4.1**

**Multiple Choice Questions (MCQs)**

**Question1.** Which of the following is a quadratic equation?

**Solution: **(d)

**Explanation:**

An equation which is of the form *ax*^{2} + *bx* + *c* = 0, a ≠ 0 is called a quadratic equation.

⟹ *x*^{3} - *x*^{2} = *x*^{3} -3*x*^{2} + 3*x* - 1** **

⟹-*x*^{2} + 3*x*^{2} - 3*x* + 1 = 0** **

⟹ 2*x*^{2} - 3*x* + 1 = 0

This equation is not of the form *ax*^{2}+ *bx* + *c*, a ≠ 0. Thus, the equation is a quadratic equation.

**Question2.** Which of the following is not a quadratic equation?

This equation is not of the form *ax*^{2} + *bx* + *c*, a ≠ 0.

Thus, the equation is not quadratic.

**Question3.** Which of the following equations has 2 as a root?

(a) *x*^{2} -4*x* + 5 = 0

(b) *x*^{2} + 3*x* -12 = 0

(c) 2*x*^{2} -7*x* + 6 = 0

(d) 3*x*^{2} - 6*x* -2 = 0

**Solution: **(c)

**Explanation:**

If *k *is one of the root of any quadratic equation then* x* = *k*

i.e., *k* satisfies the equation *a**k*^{2} + *bk* + *c* = 0.

i.e., *f*(*k*) = *ak*^{2} + *bk* + *c* = 0,

(a) Putting *x* = 2 in *x*^{2} - 4*x* + 5, we get

(2)^{2} - 4(2) + 5 = 4 - 8 + 5 = 1≠0.

So, *x* = 2 is not a root of *x*^{2} - 4*x* + 5 = 0.

(b) Putting *x* = 2 in *x*^{2} + 3*x* - 12, we get

(2)^{2} + 3(2) - 12 = 4 + 6 – 12 = –2 ≠ 0

So, *x* = 2 is not a root of *x*^{2} + 3*x* – 12 ≠ 0.

(c) Putting *x* = 2 in 2*x*^{2} – 7*x* + 6, we get

2(2)^{2} – 7(2) + 6 = 2 (4) – 14+ 6 = 8 – 14 + 6 = 14 – 14 = 0

So, *x* = 2 is root of the equation 2*x*^{2} – 7*x* + 6 = 0.

(d) Putting *x* = 2 in 3*x*^{2} –6*x* –2, we get

3(2)^{2} –6(2) –2 = 12 –12 –2 = –2 ≠ 0

So, *x* = 2 is not a root of 3*x*^{2} – 6*x* –2 = 0.

⟹ *k* = 2

**Question5.** Which of the following equations has the sum of its roots as 3?

So, option (b) is correct.

**Question6.** Value(s) of *k* for which the quadratic equation 2*x*^{2} –*kx* + *k* = 0 has equal roots is/are

(a) 0

(b) 4

(c) 8

(d) 0, 8

**Solution: **(d)

**Explanation:**

For a quadratic equation of the form, *ax*^{2} + *bx* + *c* = 0, *a* ≠ 0 to have two equal real roots, its discriminant must be equal to zero, i.e., *D* = *b*^{2} –4*ac* = 0

Given equation is 2*x*^{2} – *kx* + *k* = 0

On comparing with *ax*^{2} + *bx* + *c* = 0, we get

*a* = 2, *b* = – *k* and *c* = *k*

For equal roots, the discriminant must be zero.

i.e., *D* = *b*^{2} – 4*ac* = 0

⟹ (– *k*)^{2} – 4 (2) *k* = 0

⟹ *k*^{2} – 8*k* = 0

⟹ *k* (*k* – 8) = 0

Thus, *k* = 0, 8

Hence, the required values of *k* are 0 and 8.

**Question10.** Which of the following equations has no real roots?

Hence, the equation has two distinct real roots.

**Question11.** (*x*^{2} + l)^{2} – *x*^{2} = 0 has

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real root

**Solution**: (c)

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