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Indian Navy INET Differential Equations — practice questions

Explore 27 free Differential Equations questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Differential Equations questions and exercises with answers

Showing questions 1–27 of 27.

For Newton's law of cooling, body at 80°C cools in room at 20°C. After time, T = 60°C. Find k if time = 5 min:Read the answer and worked solution →For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Read the answer and worked solution →Complete the definition of order and degreeRead the answer and worked solution →True or false: order and degreeRead the answer and worked solution →General solution or particular solution?Read the answer and worked solution →Match each method to the form it solvesRead the answer and worked solution →Recognising the typeRead the answer and worked solution →Complete the definition of a differential equationRead the answer and worked solution →Order the steps: solve by separating variablesRead the answer and worked solution →Tap every statement true of a general solutionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: methods of solutionRead the answer and worked solution →Order, degree, or neither?Read the answer and worked solution →Counting arbitrary constantsRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →Flip and pair: form with nameRead the answer and worked solution →Order the reasoning: from equation to particular solutionRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Tap every equation type the chapter coversRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: forms and methodsRead the answer and worked solution →Reading definitions backRead the answer and worked solution →Which belongs to which idea?Read the answer and worked solution →True or false: what a solution isRead the answer and worked solution →

Worked practice questions

For Newton's law of cooling, body at 80°C cools in room at 20°C. After time, T = 60°C. Find k if time = 5 min:

  1. k = ln 60
  2. k = 1
  3. k = (1/5) ln(3/2) ≈ 0.081 min⁻¹
  4. k = 0
Show answer and solution

Correct answer: C. k = (1/5) ln(3/2) ≈ 0.081 min⁻¹

T - T_env = (T₀ - T_env) e^(-kt). 60 - 20 = 60 e^(-5k) We have → 40 = 60 e^(-5k) → e^(-5k). So → 40 = 2/3. We have → -5k = ln(2/3) → k. So → -5k = (1/5) ln(3/2) ≈ 0.081.

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For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:

  1. $e^x$ (always the exponential)
  2. $1/x$ (the reciprocal)
  3. $\ln(x)$ (the logarithm)
  4. $x$ (since $e^{\int 1/x \, dx} = x$)
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Correct answer: D. $x$ (since $e^{\int 1/x \, dx} = x$)

IF μ = e^(∫P dx) = e^(∫(1/x) dx) = e^(ln|x|) = |x|. For x > 0, μ = x. **Multiply DE by x:** derivative of (xy) = x² integrate to get xy = x³/3 + C.

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Complete the definition of order and degree

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Missing parts
  1. Answer
    highest order
    Choices
    1. highest order
    2. lowest order
    3. first
  2. Answer
    polynomial
    Choices
    1. polynomial
    2. linear
    3. homogeneous
  3. Answer
    power
    Choices
    1. power
    2. coefficient
    3. root
Complete the statement
The order of a differential equation is the order of its {0} derivative. Its degree is defined only when the equation is a {1} equation in its derivatives, and it is then the highest {2} of the highest order derivative.
The two are defined differently, and only one of them always exists. Source: syllabus Maths Part II, Ch 9 Differential Equations.

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