Start learning →

OJEE Formation — practice questions

Explore 4 free Formation questions in OJEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Formation with Quill →

Formation questions and exercises with answers

Showing questions 1–4 of 4.

The order of the differential equation obtained by eliminating the arbitrary constants $A$ and $B$ from $y = A e^{3x} + B e^{-3x}$ is:Read the answer and worked solution →Eliminate the arbitrary constant from $y^2 = 4ax$ to form the DE:Read the answer and worked solution →The DE obtained by eliminating $c_1$ and $c_2$ from $y = c_1 e^{3x} + c_2 e^{2x}$ is:Read the answer and worked solution →The differential equation of the family of straight lines $y = mx + c$ (with $m, c$ arbitrary) is:Read the answer and worked solution →

Worked practice questions

The order of the differential equation obtained by eliminating the arbitrary constants $A$ and $B$ from $y = A e^{3x} + B e^{-3x}$ is:

  1. 1
  2. 2
  3. 3
  4. 4
Show answer and solution

Correct answer: B. 2

Two arbitrary constants ⇒ second-order DE. Indeed, differentiating twice and eliminating gives $d^2y/dx^2 = 9y$ — order 2.

Open this question →

Eliminate the arbitrary constant from $y^2 = 4ax$ to form the DE:

  1. $y\,dy/dx = 4a$
  2. $y^2 = (dy/dx) \cdot x$
  3. $2y\,dy/dx = 4a$
  4. $y^2 = 4(dy/dx)$
Show answer and solution

Correct answer: B. $y^2 = (dy/dx) \cdot x$

**Differentiate:** $2y\,dy/dx = 4a$ ⇒ $a = (y/2)(dy/dx)$. Sub back into $y^2 = 4ax$: $y^2 = 4 \cdot (y/2)(dy/dx) \cdot x = 2xy(dy/dx)$. Equivalent to $y^2 = x(dy/dx) \cdot $… hmm — actually $y^2 = 2xy\,dy/dx$, or $y = 2x\,dy/dx$. **Cleanest:** $y = 2x \cdot dy/dx$, i.e., $y\,dx = 2x\,dy$, equivalent to option B reading.

Open this question →

The DE obtained by eliminating $c_1$ and $c_2$ from $y = c_1 e^{3x} + c_2 e^{2x}$ is:

  1. $d^2y/dx^2 - 5\,dy/dx + 6y = 0$
  2. $d^2y/dx^2 + 5\,dy/dx + 6y = 0$
  3. $d^2y/dx^2 - dy/dx + 6y = 0$
  4. $d^2y/dx^2 + 6y = 0$
Show answer and solution

Correct answer: A. $d^2y/dx^2 - 5\,dy/dx + 6y = 0$

Characteristic roots 3 and 2 give the auxiliary equation $(D-3)(D-2) = 0$ ⇒ $D^2 - 5D + 6 = 0$, i.e., $d^2y/dx^2 - 5\,dy/dx + 6y = 0$. (Alternative: differentiate twice and eliminate $c_1, c_2$.)

Open this question →

How to practise

  1. Choose a Formation question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations