MCQ Questions | Class 10 Maths Chapter 4 | Quadratic Equations with Answers

MCQ | Quadratic Equations Class 10 | Sat B

Check the below NCERT MCQ Questions for Class 10 Maths Chapter 4 Quadratic Equations with Answers Pdf free download. MCQ Questions for Class 10 Maths with Answers were prepared based on the latest exam pattern. We have Provided Quadratic Equations Class 10 Maths MCQs Questions with Answers to help students understand the concept very well.

Objective Question | NCERT Maths Class 10

NCERT Solutions Class 10 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	10th
Subject:	Maths
Chapter:	4
Chapters Name:	Quadratic Equations
Medium:	English

Ncert Solutions for Class 10 Maths | Objective Type Questions

You can refer to NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Quadratic Equations | Class 10 Maths | NCERT Solutions

Q1.	Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are
	A. 9,1
	B. -9,1
	C. 9, -1
	D. -9, -1

Ans: 9,1
Explaination:Reason: Correct sum = 8 + 2 = 10 from Mohan
Correct product = -9 x -1 = 9 from Sohan
∴ x² – (10)x + 9 = 0
⇒ x² – 10x + 9 = 0
⇒ x² – 9x – x + 9
⇒ x(x – 9) – 1(x – 9) = 0
⇒ (x-9) (x-l) = 0 .
⇒ Correct roots are 9 and 1.

Q2.	Which of the following are the roots of the quadratic equation, x² - 9x + 20 = 0 by factorisation?
	A. 3,4
	B. 4, 5
	C. 5, 6
	D. 6, 7

Ans: 4, 5

Q3.	The cubic equation has degree
	A. 1
	B. 2
	C. 3
	D. 4

Ans: 3

Q4.	Find the two consecutive odd positive integers, sum of whose square is 290
	A. 15, 17
	B. 9, 11
	C. 13, 15
	D. 11, 13

Ans: 11, 13

Q5.	The sum of the roots of the quadratic equation 3×² – 9x + 5 = 0 is
	A. 3
	B. 6
	C. -3
	D. 2

Ans: -3

Q6.	Value(s) of k for which the quadratic equation 2x² -kx + k = 0 has equal roots is
	A. 0
	B. 4
	C. 8
	D. 0 and 8

Ans: 0 and 8

Q7.	If a, p are the roots of the equation (x – a) (x – b) + c = 0, then the roots of the equation (x – a) (x – P) = c are
	A. a, b
	B. a, c
	C. b, c
	D. none of these

Ans: a, b

Q8.	The value of b² - 4ac for equation 3x² - 7x - 2 = 0 is
	A. 49
	B. 0
	C. 25
	D. 73

Ans: 73

Q9.	If the roots of px² + qx + 2 = 0 are reciprocal of each other, then
	A. P = 0
	B. p = -2
	C. p = ±2
	D. p = 2

Ans: p = 2

Q10.	The two consecutive odd positive integers, sum of whose squares is 290 are
	A. 13, 15
	B. 11, 13
	C. 7, 9
	D. 5, 7

Ans: 11, 13

Q11.	The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then
	A. 2a = b + c
	B. 2c = a + b
	C. b = a + c
	D. 2b = a + c

Ans: 2b = a + c

Q12.	If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then
	A. P = 0
	B. p = -2
	C. p = ±2
	D. p = 2

Ans: p = 2
Explaination:Reason: here α = \(\frac{1}{β}\)
∴ αβ = 1
⇒ \(\frac{2}{p}\) = 1
∴ p = 2

Q13.	The roots of the equation 7x² + x – 1 = 0 are
	A. real and distinct
	B. real and equal
	C. not real
	D. none of these

Ans: real and distinct
Explaination:Reason: Here a = 2, b = 1, c = -1
∴ D = b² – 4ac = (1)² – 4 × 2 × (-1) = 1 + 8 = 9 > 0
∴ Roots of the given equation are real and distinct.

Q14.	The equation 12x² + 4kx + 3 = 0 has real and equal roots, if
	A. k = ±3
	B. k = ±9
	C. k = 4
	D. k = ±2

Ans: k = ±3
Explaination:Reason: Here a = 12, b = 4k, c = 3
Since the given equation has real and equal roots
∴ b² – 4ac = 0
⇒ (4k)² – 4 × 12 × 3 = 0
⇒ 16k² – 144 = 0
⇒ k² = 9
⇒ k = ±3

Q15.	If -5 is a root of the quadratic equation 2x² + px – 15 = 0, then
	A. p = 3
	B. p = 5
	C. p = 7
	D. p = 1

Ans: p = 7
Explaination:Reason: Since – 5 is a root of the equation 2x² + px -15 = 0
∴ 2(-5)² + p (-5) – 15 = 0
⇒ 50 – 5p -15 = 0
⇒ 5p = 35
⇒ p = 7

Q16.	If the roots of the equations ax² + 2bx + c = 0 and bx² – 2√ac x + b = 0 are simultaneously real, then
	A. b = ac
	B. b2 = ac
	C. a2 = be
	D. c2 = ab

Ans: b2 = ac
Explaination:Reason: Given equations have real roots, then
D₁ ≥ 0 and D₂ ≥ 0
(2b)² – 4ac > 0 and (-2√ac)² – 4b.b ≥ 0
4b² – 4ac ≥ 0 and 4ac – 4b2 > 0
b² ≥ ac and ac ≥ b²
⇒ b² = ac

Q17.	The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then
	A. 2a = b + c
	B. 2c = a + b
	C. b = a + c
	D. 2b = a + c

Ans: 2b = a + c
Explaination:Reason: Since roots are equal
∴ D = 0 => b² – 4ac = 0
⇒ (c – a)² -4(b – c) (a – b) = 0
⇒ c² – b² – 2ac -4(ab -b² + bc) = 0 =>c + a-2b = 0 => c + a = 2b
⇒ c² + a² – 2ca – 4ab + 4b² + 4ac – 4bc = 0
⇒ c² + a² + 4b² + 2ca – 4ab – 4bc = 0
⇒ (c + a – 2b)² = 0
⇒ c + a – 2b = 0
⇒ c + a = 2b

Q18.	A chess board contains 64 equal squares and the area of each square is 6.25 cm². A border round the board is 2 cm wide. The length of the side of the chess board is
	A. 8 cm
	B. 12 cm
	C. 24 cm
	D. 36 cm

Ans: 24 cm

Q19.	One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Their present ages are
	A. 7 years, 49 years
	B. 5 years, 25 years
	C. 1 years, 50 years
	D. 6 years, 49 years

Ans: 7 years, 49 years

Q20.	The sum of the squares of two consecutive natural numbers is 313. The numbers are
	A. 12, 13
	B. 13,14
	C. 11,12
	D. 14,15

Ans: 12, 13

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

MCQ Questions | Class 10 Maths Chapter 4

MCQ Questions | Class 10 Maths Chapter 4 | Quadratic Equations with Answers

MCQ | Quadratic Equations Class 10 | Sat B

Objective Question | NCERT Maths Class 10

Ncert Solutions for Class 10 Maths | Objective Type Questions

Quadratic Equations | Class 10 Maths | NCERT Solutions

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

Ncert Solutions for Class 10 Maths Chapter 1

Ncert Solutions for Class 10 Maths Chapter 2

Ncert Solutions for Class 10 Maths Chapter 3

Ncert Solutions for Class 10 Maths Chapter 4

Ncert Solutions for Class 10 Maths Chapter 5

Ncert Solutions for Class 10 Maths Chapter 6

Ncert Solutions for Class 10 Maths Chapter 7

Ncert Solutions for Class 10 Maths Chapter 8

Ncert Solutions for Class 10 Maths Chapter 9

Ncert Solutions for Class 10 Maths Chapter 10

Ncert Solutions for Class 10 Maths Chapter 11

Ncert Solutions for Class 10 Maths Chapter 12

Ncert Solutions for Class 10 Maths Chapter 13

Ncert Solutions for Class 10 Maths Chapter 14

Ncert Solutions for Class 10 Maths Chapter 15

NCERT SOLUTIONS

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