Differential Equations and Modeling — Practice Quiz
CBSE · Class 12 · Applied Mathematics
Try a 4-question quiz on Differential Equations and Modeling for CBSE Class 12 Applied Mathematics: tap an answer to check it and see why.
Interactive on Super Tutor
Studying Differential Equations and Modeling? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for practice quiz and more.
Free trial, no card needed.
Quick Quiz: Differential Equations and Modeling
0/4Tap an answer to check it instantly. No sign-up needed for these 4.
Find the order and degree of the differential equation: d²y/dx² + 3(dy/dx)² - 4y = 0
Solve the differential equation: dy/dx = 2x
Find the particular solution of dy/dx = 3x² given y = 5 when x = 0
Form the differential equation by eliminating the constant 'a' from y = ae^(2x)
Sample Questions
Which of the following are solutions to dy/dx + y = 0? (Select all correct answers)
Show answer
y = e^(-x), y = 2e^(-x), y = -3e^(-x), y = ce^(-x)
Step 1: Solve dy/dx = -y by separation: dy/y = -dx. Step 2: Integrate: ln|y| = -x + C. Step 3: y = Ae^(-x) where A is any constant. All options with form Ae^(-x) are correct, while e^x gives dy/dx = e^x ≠ -y.
A population grows according to dP/dt = kP. If P(0) = 100 and P(2) = 200, find k.
Show answer
k = (ln 2)/2
Step 1: Solve dP/dt = kP: P = P₀e^(kt). Step 2: Using P(0) = 100: P = 100e^(kt). Step 3: Using P(2) = 200: 200 = 100e^(2k). Step 4: Solve: 2 = e^(2k), so 2k = ln 2, therefore k = (ln 2)/2.
The differential equation y'' + 4y = 0 has which order and degree?
Show answer
Order = 2, Degree = 1
Step 1: Identify highest derivative: y'' = d²y/dx² (second order). Step 2: Check polynomial form: equation is polynomial in derivatives. Step 3: Find power of highest derivative: (y'')¹, so degree = 1. Therefore: Order = 2, Degree = 1.
Solve: dy/dx = y/x, x > 0
Show answer
y = cx
Step 1: Separate variables: dy/y = dx/x. Step 2: Integrate both sides: ∫dy/y = ∫dx/x. Step 3: ln|y| = ln|x| + ln|c|. Step 4: ln|y| = ln|cx|, so y = cx.
+43 more questions on Differential Equations and Modeling (CBSE Class 12 Applied Mathematics)
Practise AllFrequently Asked Questions
What are the important topics in Differential Equations and Modeling for CBSE Class 12 Applied Mathematics?
How many practice questions are there for Differential Equations and Modeling?
Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Differential Equations and Modeling
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full Differential Equations and Modeling chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for CBSE Class 12 Applied Mathematics. Free to start, no card needed.