MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Set-B

Differential Equations Class 12 Maths MCQs Questions with Answers

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have Provided Differential Equations Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 9 Quiz

Class 12 Maths Chapter 9 MCQ Online Test

You can refer to NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Differential Equations Class 12 Maths MCQ online test

Q1.	The degree of the differential equation \(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))³ + 6y⁵ = 0 is
	A. 1
	B. 2
	C. 3
	D. 5

Ans: 1

Q2.	The solution of \(\frac{dy}{dx}\) + y = e^-x, y (0) = 0 is
	A. y = e^x(x – 1)
	B. y = xe^-x
	C. y = xe^-x + 1
	D. y = (x + 1 )e^-x

Ans: y = xe^-x

Q3.	Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is
	A. cos x
	B. sec x
	C. e^{cos x}
	D. e^{sec x}

Ans: sec x

Q4.	The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
	A. y = tan^-1 x
	B. y – x = k(1 + xy)
	C. x = tan^-1 y
	D. tan (xy) = k

Ans: y – x = k(1 + xy)

Q5.	The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is
	A. \(\frac{x}{e^x}\)
	B. \(\frac{e^x}{x}\)
	C. xe^x
	D. e^x

Ans: \(\frac{e^x}{x}\)

Q6.	y = ae^mx + be^-mx satisfies which of the following differential equation?
	A. \(\frac{dy}{dx}\) + my = 0
	B. \(\frac{dy}{dx}\) – my = 0
	C. \(\frac{d^2y}{dx^2}\) – m²y = 0
	D. \(\frac{d^2y}{dx^2}\) +m²y = 0

Ans: \(\frac{d^2y}{dx^2}\) – m²y = 0

Q7.	The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is
	A. \(\frac{sin x}{sin y}\) = c
	B. sin x sin y = c
	C. sin x + sin y = z
	D. cos x cos y = c

Ans: sin x sin y = c

Q8.	The solution of x \(\frac{dy}{dx}\) + y = e^x is
	A. y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)
	B. y = xe^x + cx
	C. y = xe^x + k
	D. x = \(\frac{e^vy}{y}\) + \(\frac{k}{y}\)

Ans: y = \(\frac{e^x}{x}\) + \(\frac{k}{x}\)

Q9.	The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is
	A. (x² – y²)\(\frac{dy}{dx}\) = 2xy
	B. 2 (x² + y²)\(\frac{dy}{dx}\) = xy
	C. 2(x² – y²)\(\frac{dy}{dx}\) = xy
	D. (x² + y²) \(\frac{dy}{dx}\) = 2xy

Ans: (x² – y²)\(\frac{dy}{dx}\) = 2xy

Q10.	Family y = Ax + A³ of curves will correspond to a differential equation of order
	A. 3
	B. 2
	C. 1
	D. not finite

Ans: 2

Q11.	The general solution of \(\frac{dy}{dx}\) = 2x e^x²-y is
	A. e^x²-y = c
	B. e^-y + e^x² = c
	C. e^y = e^x² + c
	D. e^x²+y = c

Ans: e^y = e^x² + c

Q12.	The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is
	A. an ellipse
	B. parabola
	C. circle
	D. rectangular hyperbola

Ans: rectangular hyperbola

Q13.	The general solution of the differential equation \(\frac{dy}{dx}\) = e^{\(\frac{x^2}{2}\)} + xy is
	A. y = ce^{\(\frac{-x^2}{2}\)}
	B. y = ce^{\(\frac{x^2}{2}\)}
	C. y = (x + c)e^{\(\frac{x^2}{2}\)}
	D. y = (c – x)e^{\(\frac{x^2}{2}\)}

Ans: y = (x + c)e^{\(\frac{x^2}{2}\)}

Q14.	The solution of the equation (2y – 1) dx-(2x + 3)dy = 0 is
	A. \(\frac{2x-1}{2y+3}\) = k
	B. \(\frac{2y+1}{2x-3}\) = k
	C. \(\frac{2x+3}{2y-1}\) = k
	D. \(\frac{2x-1}{2y-1}\) = k

Ans: \(\frac{2x+3}{2y-1}\) = k

Q15.	The differential equation for which y = a cos x + b sin x is a solution is
	A. \(\frac{d^2y}{dx^2}\) + y = 0
	B. \(\frac{d^2y}{dx^2}\) – y = 0
	C. \(\frac{d^2y}{dx^2}\) + (a + b)y = 0
	D. \(\frac{d^2y}{dx^2}\) + (a – b)y = 0

Ans: \(\frac{d^2y}{dx^2}\) + y = 0

Q16.	The solution of \(\frac{dy}{dx}\) + y = e^-x, y (0) = 0 is
	A. y = e^-x (x – 1)
	B. y = xe^x
	C. y = xe^-x + 1
	D. y = xe^-x

Ans: y = xe^-x

Q17.	The order and degree of the differential equation (\(\frac{d^2y}{dx^3}\))² – 3\(\frac{d^2y}{dx^2}\) + 2(\(\frac{dy}{dx}\))⁴ = y⁴ are
	A. 1, 4
	B. 3, 4
	C. 2, 4
	D. 3, 2

Ans: 3, 2

Q18.	The order and degree of the differential equation [1 + (\(\frac{dy}{dx}\))²] = \(\frac{d^2y}{dx^2}\) are
	A. 1, \(\frac{3}{2}\)
	B. 2, 3
	C. 2, 1
	D. 3, 4

Ans: 2, 1

Q19.	The differential equation of the family of curves y² = 4a (x + a) is
	A. y² = 4\(\frac{dy}{dx}\) (x + \(\frac{dy}{dx}\))
	B. 2y\(\frac{dy}{dx}\) = 4a
	C. y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0
	D. 2x\(\frac{dy}{dx}\) + y(\(\frac{dy}{dx}\))² – y

Ans: y\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))² = 0

Q20.	Which of the following is the general solution of \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + y = 0
	A. y = (Ax + B)e^x
	B. y = (Ax + B)e^-x
	C. y = Ae^x + Be^-x
	D. y = A cos x + B sin x

Ans: y = (Ax + B)e^x

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT SOLUTIONS FOR CLASS 12

MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers

MCQ Questions for Class 12 Maths Chapter 9 Differential Equations with Answers Set-B

Differential Equations Class 12 Maths MCQs Questions with Answers

Class 12 Maths Chapter 9 Quiz

Class 12 Maths Chapter 9 MCQ Online Test

Differential Equations Class 12 Maths MCQ online test

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT Solution of Maths Class 12 Chapter 1

NCERT Solution of Maths Class 12 Chapter 2

NCERT Solution of Maths Class 12 Chapter 3

NCERT Solution of Maths Class 12 Chapter 4

NCERT Solution of Maths Class 12 Chapter 5

NCERT Solution of Maths Class 12 Chapter 6

NCERT Solution of Maths Class 12 Chapter 7

NCERT Solution of Maths Class 12 Chapter 8

NCERT Solution of Maths Class 12 Chapter 9

NCERT Solution of Maths Class 12 Chapter 10

NCERT Solution of Maths Class 12 Chapter 11

NCERT Solution of Maths Class 12 Chapter 12

NCERT Solution of Maths Class 12 Chapter 13

MCQ QUESTIONS WITH ANSWER

NCERT SOLUTIONS FOR CLASS 12

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