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-A 

MCQ Questions for Class12 Maths Chapter 9 Differential Equations

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. Integration factor of differential equation \(\frac{dy}{dx}\) + py = Q, where P and IQ are functions of x is
A. ∫epdx
B. \(_{e}\)∫pdx
C. \(_{e}\)-∫pdx
D. None of these
Ans: None of these
Q2. The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is
A. 0.4 π cm/s
B. 0.8 π cm/s
C. 0.8 cm/s
D. None of these
Ans: 0.8 π cm/s
Q3. The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is
A. x – y = k(1 + xy)
B. log (1 + y) = x + \(\frac{x^2}{2}\) + k
C. log (1 + x) + y + \(\frac{y^2}{2}\) = k
D. None of these
Ans: log (1 + y) = x + \(\frac{x^2}{2}\) + k
Q4. The degree of the differential equation
(\(\frac{d^2y}{dx}\))² + (\(\frac{dy}{dx}\))² = x sin \(\frac{dy}{dx}\) is
A. 1
B. 2
C. 3
D. not defined
Ans: not defined
Q5. The degree of differential equation
[1 + (\(\frac{dy}{dx}\))²]\(\frac{3}{2}\) = \(\frac{d^2y}{dx^2}\) is
A. 4
B. \(\frac{3}{2}\)
C. 2
D. not defined
Ans: 2
Q6. The order and degree of the differential equation
\(\frac{d^2y}{dx^2}\) + (\(\frac{dy}{dx}\))\(\frac{1}{4}\) + x\(\frac{1}{3}\) = 0 respectvely, are
A. 2 and not defined
B. 2 and 2
C. 2 and 3
D. 3 and 3
Ans: 2 and not defined
Q7. If y = e-x (A cos x + B sin x), then y is a solution of
A. \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) = 0
B. \(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + 2y = 0
C. \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
D. \(\frac{d^2y}{dx^2}\) + 2y = 0
Ans: \(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0
Q8. The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is
A. \(\frac{d^2y}{dx^2}\) – α²y = 0
B. \(\frac{d^2y}{dx^2}\) + α²y = 0
C. \(\frac{d^2y}{dx^2}\) + αy = 0
D. \(\frac{d^2y}{dx^2}\) – αy = 0
Ans: \(\frac{d^2y}{dx^2}\) + α²y = 0
Q9. Solution of differential equation xdy – ydx = Q represents
A. a rectangular hyperbola
B. parabola whose vertex is at origin
C. straight line passing through origin
D. a circle whose centre is at origin
Ans: straight line passing through origin
Q10. Integrating factor of the differential equation cos x \(\frac{dy}{dx}\) + y sin x = 1 is
A. cos x
B. tan x
C. sec x
D. sin x
Ans: sec x
Q11. Solution of the differential equation tan y sec² x dx + tan x sec² y dy + 0 is .
A. tan x + tan y = k
B. tan x – tan y = k
C. \(\frac{tan x}{tan y}\) = k
D. tan x.tan y = k
Ans: tan x.tan y = k
Q12. Family r = Ax + A³ of curves is represented by the differential equation of degree
A. 1
B. 2
C. 3
D. 4
Ans: 2
Q13. Integrating factor of \(\frac{xdy}{dx}\) – y = x4 – 3x is
A. x
B. log x
C. \(\frac{1}{2}\)
D. -x
Ans: \(\frac{1}{2}\)
Q14. Solution of \(\frac{dy}{dx}\) – y = 1 y(0) = 1 is given by
A. xy = -ex
B. xy = -e-x
C. xy = -1
D. y = 2ex – 1
Ans: y = 2ex – 1
Q15. The number of solutions of \(\frac{dy}{dx}\) = \(\frac{y+1}{x-1}\) when y(1) = 2 is
A. none
B. one
C. two
D. infinite
Ans: one
Q16. Which of the following is a second order differential equation?
A. (y’)² + x = y²
B. y’y” + y = sin x
C. y” + (y”)² + y = 0
D. y’ = y²
Ans: y’y” + y = sin x
Q17. Integrating factor of the differential equation
(1 – x²) \(\frac{dy}{dx}\) – xy = 1 is
A. -x
B. \(\frac{x}{1+x^2}\)
C. \(\sqrt{1-x^2}\)
D. \(\frac{1}{2}\) log(1 – x²)
Ans: \(\sqrt{1-x^2}\)
Q18. tan-1 x + tan-1 y = c is the general solution of the differential equation
A. \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)
B. \(\frac{dy}{dx}\) = \(\frac{1+x^2}{1+y^2}\)
C. (1 + x²)dy + (1 + y²)dx = 0
D. (1 +x²2)dx+(1 + y²)dy = 0
Ans: (1 + x²)dy + (1 + y²)dx = 0
Q19. The differential equation y \(\frac{dy}{dx}\) + x = c represents
A. Family of hyperbolas
B. Family of parabolas
C. Family of ellipses
D. Family of circles
Ans: Family of circles
Q20. The general solution of ex cos y dx – ex sin y dy = 0 is
A. ex cos y = k
B. ex sin y = k
C. ex = k cos y
D. ex = k sin y
Ans: ex cos y = k

MCQ Questions for Class 12 Maths


NCERT Solution of Maths Class 12


Class 12 Maths

NCERT Solution of Maths Class 12 Chapter 1

    MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions Set-A
    MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions Set-B
    MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions Set-C

NCERT Solution of Maths Class 12 Chapter 2

    MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Set-A
    MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Set-B
    MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Set-C
    MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Set-D

NCERT Solution of Maths Class 12 Chapter 3

    MCQ Questions for Class 12 Maths Chapter 3 Matrices Set-A
    MCQ Questions for Class 12 Maths Chapter 3 Matrices Set-B
    MCQ Questions for Class 12 Maths Chapter 3 Matrices Set-C
    MCQ Questions for Class 12 Maths Chapter 3 Matrices Set-D

NCERT Solution of Maths Class 12 Chapter 4

    MCQ Questions for Class 12 Maths Chapter 4 Determinants Set-A
    MCQ Questions for Class 12 Maths Chapter 4 Determinants Set-B
    MCQ Questions for Class 12 Maths Chapter 4 Determinants Set-C

NCERT Solution of Maths Class 12 Chapter 5

    MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability Set-A
    MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability Set-B
    MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability Set-C
    MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability Set-D

NCERT Solution of Maths Class 12 Chapter 6

    MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives Set-A
    MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives Set-B
    MCQ Questions for Class 12 Maths Chapter 6 Application of Derivatives Set-C

NCERT Solution of Maths Class 12 Chapter 7

    MCQ Questions for Class 12 Maths Chapter 7 Integrals Set-A
    MCQ Questions for Class 12 Maths Chapter 7 Integrals Set-B
    MCQ Questions for Class 12 Maths Chapter 7 Integrals Set-C

NCERT Solution of Maths Class 12 Chapter 8

    MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals Set-A
    MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals Set-B

NCERT Solution of Maths Class 12 Chapter 9

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

NCERT Solution of Maths Class 12 Chapter 10

    MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra Set-A
    MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra Set-B
    MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra Set-C
    MCQ Questions for Class 12 Maths Chapter 10 Vector Algebra Set-D

NCERT Solution of Maths Class 12 Chapter 11

    MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry Set-A
    MCQ Questions for Class 12 Maths Chapter 11 Three Dimensional Geometry Set-B

NCERT Solution of Maths Class 12 Chapter 12

    MCQ Questions for Class 12 Maths Chapter 12 Linear Programming Set-A

NCERT Solution of Maths Class 12 Chapter 13

    MCQ Questions for Class 12 Maths Chapter 13 Probability Set-A
    MCQ Questions for Class 12 Maths Chapter 13 Probability Set-B

NCERT SOLUTIONS FOR CLASS 12

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