Formation of Differential Equations MCQs

Formation of Differential Equations MCQs – Class 12 Maths

Formation of Differential Equations MCQs

Class: CBSE Class 12
Subject: Mathematics
Section: Differential Equations
Topic: Formation of Differential Equations MCQs
Exam Focus: CBSE Board Examinations

Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination preparation. Detailed explanations help in clear conceptual understanding of forming differential equations.

Q1. Order of DE formed by eliminating one constant is:

a) 1
b) 2
c) 0
d) Depends

Answer: a)

Number of constants equals order.

Q2. y = Cx ⇒ formed DE:

a) y = x dy/dx
b) dy/dx = x
c) y = 0
d) None

Answer: a)

Q3. y = C ⇒ differential equation:

a) dy/dx = 0
b) y = 0
c) x = 0
d) dy

Answer: a)

Q4. y = Ceˣ ⇒ DE:

a) dy/dx = y
b) dy/dx = x
c) y = x
d) None

Answer: a)

Q5. y = C sin x ⇒ DE:

a) dy/dx = C cos x
b) y'' + y = 0
c) dy/dx = y
d) None

Answer: b)

Q6. Family with two constants gives order:

a) 2
b) 1
c) 3
d) 0

Answer: a)

Q7. y = C₁x + C₂ ⇒ order:

a) 2
b) 1
c) 0
d) 3

Answer: a)

Q8. Eliminating constants means:

a) Differentiation
b) Integration
c) Limits
d) Graph

Answer: a)

Q9. y² = Cx ⇒ DE:

a) 2y dy/dx = C
b) 2y dy/dx = y²/x
c) dy/dx = x
d) None

Answer: b)

Q10. Formation uses:

a) Differentiation
b) Integration
c) Limits
d) Matrices

Answer: a)

Q11. y = Cx² ⇒ DE:

a) dy/dx = 2y/x
b) dy/dx = x
c) y = x
d) None

Answer: a)

Q12. y = C/x ⇒ DE:

a) x dy/dx + y = 0
b) dy/dx = x
c) y = x
d) None

Answer: a)

Q13. y = Ce^{2x} ⇒ DE:

a) dy/dx = 2y
b) dy/dx = y
c) y = x
d) None

Answer: a)

Q14. y = C cos x ⇒ DE:

a) y'' + y = 0
b) dy/dx = y
c) dy/dx = x
d) None

Answer: a)

Q15. Number of arbitrary constants equals:

a) Order
b) Degree
c) Variable
d) Limit

Answer: a)

Q16. Formation removes:

a) Constants
b) Variables
c) Derivatives
d) Limits

Answer: a)

Q17. y = mx + C ⇒ constants:

a) Two
b) One
c) Three
d) None

Answer: a)

Q18. Higher constants ⇒ higher:

a) Order
b) Degree
c) Limit
d) Graph

Answer: a)

Q19. DE represents:

a) Family of curves
b) Line
c) Point
d) Angle

Answer: a)

Q20. Formation process requires:

a) Differentiation repeatedly
b) Integration
c) Limits
d) Graph

Answer: a)

Differentiate equal to number of constants.

Formation of Differential Equations MCQs

Formation of Differential Equations MCQs

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