Differential Equations · NDA previous year questions

2015 8 questions

1. Q902015 · 27 Sept 2015

   The degree of the differential equation $$\frac{dy}{dx}-x={\left(y-x\frac{dy}{dx}\right)}^{-4}\text{ is}$$

   1. A.2
   2. B.3
   3. C.4
   4. D.5
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   Answer: D

2. Q912015 · 27 Sept 2015

   The solution of $\frac{dy}{dx}=\sqrt{1-x^2-y^2+x^2{y}^2}$ is where $c$ is an arbitrary constant

   1. A.${\sin }^{-1}y={\sin }^{-1}x+c$
   2. B.$2{\sin }^{-1}y=\sqrt{1-x^2}+{\sin }^{-1}x+c$
   3. C.$2{\sin }^{-1}y=x\sqrt{1-x^2}+{\sin }^{-1}x+c$
   4. D.$2{\sin }^{-1}y=x\sqrt{1-x^2}+{\cos }^{-1}x+c$
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   Answer: C

3. Q922015 · 27 Sept 2015

   The differential equation of the family of circles passing through the origin and having centres on the $x$-axis is

   1. A.$2xy\frac{dy}{dx}=x^2-y^2$
   2. B.$2xy\frac{dy}{dx}=y^2-x^2$
   3. C.$2xy\frac{dy}{dx}=x^2+y^2$
   4. D.$2xy\frac{dy}{dx}+x^2+y^2=0$
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   Answer: B

4. Q932015 · 27 Sept 2015

   The order and degree of the differential equation of parabolas having vertex at the origin and focus at $(a,0)$ where $a>0$, are respectively

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

5. Q942015 · 27 Sept 2015

   The area of the square, one of whose diagonals is $3\hat{i}+4\hat{j}$ is

   1. A.12 square unit
   2. B.12.5 square unit
   3. C.25 square unit
   4. D.156.25 square unit
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   Answer: B

6. Q912015 · 19 Apr 2015

   What is the solution of the differential equation $\frac{ydx-xdy}{y^2}=0$? where $c$ is an arbitrary constant.

   1. A.$xy=c$
   2. B.$y=cx$
   3. C.$x+y=c$
   4. D.$x-y=c$
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   Answer: B

7. Q922015 · 19 Apr 2015

   What is the solution of the differential equation $\sin \left(\frac{dy}{dx}\right)-a=0$? where $c$ is an arbitrary constant.

   1. A.$y=x{\sin }^{-1}a+c$
   2. B.$x=y{\sin }^{-1}a+c$
   3. C.$y=x+x{\sin }^{-1}a+c$
   4. D.$y={\sin }^{-1}a+c$
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   Answer: A

8. Q932015 · 19 Apr 2015

   What is the solution of the differential equation $\frac{dx}{dy}+\frac{x}{y}-y^2=0$? where $c$ is an arbitrary constant.

   1. A.$xy=x^4+c$
   2. B.$xy=y^4+c$
   3. C.$4xy=y^4+c$
   4. D.$3xy=y^3+c$
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   Answer: C