Differential Equations · NDA previous year questions

2016 6 questions

1. Q862016 · 18 Sept 2016

   What are the degree and order respectively of the differential equation satisfying $e^{y\sqrt{1-x^2}+x\sqrt{1-y^2}}=c{e}^x$, (where $c>0$, $|x|<1$, $|y|<1$)?

   1. A.1, 1
   2. B.1, 2
   3. C.2, 1
   4. D.2, 2
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   Answer: A

2. Q892016 · 18 Sept 2016

   What is the order of the differential equation $\frac{dx}{dy}+\int ydx=x^3$?

   1. A.1
   2. B.2
   3. C.3
   4. D.Cannot be determined
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   Answer: B

3. Q902016 · 18 Sept 2016

   Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?

   1. A.${\left(y-x\frac{dy}{dx}\right)}^2=1-{\left(\frac{dy}{dx}\right)}^2$
   2. B.${\left(y+x\frac{dy}{dx}\right)}^2=1+{\left(\frac{dy}{dx}\right)}^2$
   3. C.${\left(y-x\frac{dy}{dx}\right)}^2=1+{\left(\frac{dy}{dx}\right)}^2$
   4. D.${\left(y+x\frac{dy}{dx}\right)}^2=1-{\left(\frac{dy}{dx}\right)}^2$
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   Answer: C

4. Q912016 · 18 Sept 2016

   Consider the following for the next two (02) items that follow : Let $\vec{a}=\hat{i}+\hat{j}$, $\vec{b}=3\hat{i}+4\hat{k}$ and $\vec{b}=\vec{c}+\vec{d}$, where $\vec{c}$ is parallel to $\vec{a}$ and $\vec{d}$ is perpendicular to $\vec{a}$. What is $\vec{c}$ equal to?

   1. A.$\frac{3(\hat{i}+\hat{j})}{2}$
   2. B.$\frac{2(\hat{i}+\hat{j})}{3}$
   3. C.$\frac{\hat{i}+\hat{j}}{2}$
   4. D.$\frac{\hat{i}+\hat{j}}{3}$
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   Answer: A

5. Q922016 · 18 Sept 2016

   Consider the following for the next two (02) items that follow : Let $\vec{a}=\hat{i}+\hat{j}$, $\vec{b}=3\hat{i}+4\hat{k}$ and $\vec{b}=\vec{c}+\vec{d}$, where $\vec{c}$ is parallel to $\vec{a}$ and $\vec{d}$ is perpendicular to $\vec{a}$. If $\vec{d}=x\hat{i}+y\hat{j}+z\hat{k}$, then which of the following equations is/are correct? 1. $y-x=4$ 2. $2z-3=0$ Select the correct answer using the code given below :

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: D

6. Q802016 · 17 Apr 2016

   What are the order and degree respectively of the differential equation whose solution is $y=cx+c^2-3c^{3/2}+2$, where $c$ is a parameter?

   1. A.1, 2
   2. B.2, 2
   3. C.1, 3
   4. D.1, 4
   Show answer

   Answer: D