Class 12 Mathematics Chapter 9 Differential Equations MCQ Questions with Answer

Class 12 Differential Equations MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Differential Equations Class 12, which will help them all through their board test.

Class 12 Differential Equations MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 9 Differential Equations. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Differential Equations Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Differential Equations MCQ with answers given below.

Question 1. Solution of the differential equation dx/x +dy/y =0 is
(a) 1/x+1/y=c
(b) log x. log y = c
(c) xy = c
(d) x + y = c

Question 2. Differential equation which has solution of the form y = Acosax + Bsinax , where A and B are arbitrary constants is
(a) d²y/dx² -α2y = 0
(b) d²y/dx² + α2y = 0
(c) d²y/dx² + αy = 0
(d) d²y/dx² – αy = 0

Question 3. The degree of the differential equation x2(d2y/dx2) = (x dy/dx -y)3 is
(a) 1
(b) 2
(c) 3
(d) 6

Question 4. The solution of the differential equation 2x.dy/dx – y = 3 represents a family of
(a) straight lines
(b) circles
(c) parabolas
(d) ellipses

Question 5. The degree of the differential equation d2y/dx2 +3(dy/dx)2 =x2log(d2y/dx2)is
(a) 1
(b) 2
(c) 3
(d) Not defined

Question 6. The order and degree of differential equation [1+(dy/dx)2]2 = d2y/dx2 respectively, are
(a) 1, 2
(b) 2, 2
(c) 2, 1
(d) 4, 2

Question 7. Which of the following is not a homogeneous function of x and y?
(a) x2 + 2xy
(b) 2x – y
(c) cos2(y/x)+y/x 
(d) sin x – cos y

Question 8. The solution of the differential equation xdy/dx + 2y = x² is
(a) y=x²+C/4x²
(b) y=x²/4+C
(c) y=x²+C/x²
(d) y=x²+C/4x²

Question 9. A solution of the differential equation (dy/dx)2 -xdy/dx +y=0 is
(a) y = 2
(b) y = 2x
(c) y = 2x – 4
(d) y = 2×2 – 4

Question 10. The number of solution of dy/dx =y+1/y-1 when y(1) = 2 is
(a) none
(b) one
(c) two
(d) infinite

Question 11. The order of the differential equation of all circles of given radius a is
(a) 1
(b) 2
(c) 3
(d) 4

Question 12. The degree of the differential equation (d²y/dx²)² + (dy/dx)² = xsin(dy/dx) is
(a) 1
(b) 2
(c) 3
(d) Not defined

Question 13. The order and degree of a differential equation d2y/dx2+(dy/dx)1/4 +x1/5=0,respectively are
(a) 2 and not defined
(b) 2 and 2
(c) 2 and 3
(d) 3 and 3

Question 14. Solution of dy/dx -y = 1, y(0) = 1 is given by
(a) xy = –ex
(b) xy = –e–x
(c) xy = –1
(d) y = 2ex – 1

Question 15. If y = e–x (A cos x + Bsinx) , then it is a solution of
(a) d²y/dx² +2dy/dx =0
(b) d²y/dx² – 2d²y/dx² + 2y = 0
(c) d²y/dx² +2dy/dx + 2y = 0
(d) d²y/dx²+2y=0

Question 16. Integrating factor of xdy/dx-y = x⁴ – 3x is
(a) x
(b) log x
(c) 1/x
(d) –x

Question 17. The integrating factor of the differential equation dy/dx (xlogx) +y = 2logx is
(a) ex
(b) log x
(c) log(log x)
(d) x

Question 18. The degree of the differential equation [1+(dy/dx)²]^3/2 = d²y/dx² is
(a) 4
(b)3/2
(c) Not defined
(d) 2

Question 19. Which of the following is a second order differential equation?
(a) (y’)2 + x = y²
(b) y” + y = sinx
(c) y”’ + (y”)2 + y = 0
(d) y’ = y2

Question 20. The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
(a) x e^y + x² = C
(b) x e^x + y² = C
(c) y e^x + x² = C
(d) y e^y + x² = C

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Differential Equations Class 12 MCQ are ready by the subject specialists themselves.

Question 21. The order and degree of the differential equation d4y/dx4 =y + (dy/dx)⁴ are respectively
(a) 4, 1
(b) 4, 2
(c) 2, 2
(d) 2, 4

Question 22. The differential equation of the family of lines passing through the origin is
(a) dy/dx =x
(b) dy/dx =y
(c) xdy/dx-y =0
(d) x+dy/dx =0

Question 23. The degree of the differential equation (1+dy/dx)³ = (d²y/dx)² is
(a) 1
(b) 2
(c) 3
(d) 4

Question 24. Solution of the differential equation x dy/dx+y =x ex
(a) xy = ex (1 – x) + C
(b) xy = ex (x + 1) + C
(c) xy = ey (y – 1) + C
(d) xy = ex (x – 1) + C

Question 25. Integrating factor of the differential equation (1- x2)dy/dx – xy = 1 is
(a) –x 
(b) x/1 +x²
(c) √(1 -x2)
(d)1/2 log(1-x²)

Question 26. The integrating factor of the differential equation x dy/dx – y = 2×2 is
(a) e–x
(b) e–y
(c) 1/x
(d) x

Fill in the blanks

Question 1. The integrating factor of the differential equation x(dy/dx)+ 2y = x² is _____________ . 

Question 2. The number of arbitrary constants in the general solution of a differential equation of order three is _______.

Question 3. The solution of differential equation cot y dx = x dy is _____________ .

Question 4. The degree of the differential equation 1+(dy/dx)² = is _____________

Question 5. The order of the differential equation 3(d²y/dx²)-5(dy/dx)³ +2y =0 is   

Question 6. The number of arbitrary constant (s) in a particular solution of the differential equation tan x dx + tan y dy = 0 is _____________ . 

Question 7. The solution of the differential equation X(dy/dx)+2y=x² is_____________ .

Question 8. The general solution of the differential equation dy/dx =x²/y² is___________ .

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