Differential Equations · NDA previous year questions

2012 11 questions

1. Q842012 · 19 Aug 2012

   What is the degree of the differential equation $\frac{d^{3}y}{d{x}^3}+2{\left(\frac{d^{2}y}{d{x}^2}\right)}^2-\frac{dy}{dx}+y=0$?

   1. A.6
   2. B.3
   3. C.2
   4. D.1
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   Answer: D

2. Q852012 · 19 Aug 2012

   Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible?

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

3. Q862012 · 19 Aug 2012

   The differential equation representing the family of curves $y=a\sin (\lambda x+\alpha )$ is:

   1. A.$\frac{d^{2}y}{d{x}^2}+{\lambda }^{2}y=0$
   2. B.$\frac{d^{2}y}{d{x}^2}-{\lambda }^{2}y=0$
   3. C.$\frac{d^{2}y}{d{x}^2}+\lambda y=0$
   4. D.None of the above
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   Answer: A

4. Q872012 · 19 Aug 2012

   The differential equation $y\frac{dy}{dx}+x=a$ where ‘a’ is any constant represents:

   1. A.A set of straight lines
   2. B.A set of ellipses
   3. C.A set of circles
   4. D.None of the above
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   Answer: C

5. Q882012 · 19 Aug 2012

   For the differential equation ${\left(\frac{dy}{dx}\right)}^2-x\left(\frac{dy}{dx}\right)+y=0$, which one of the following is not its solution?

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

6. Q892012 · 19 Aug 2012

   What is the general solution of the differential equation $x^{2}dy+y^{2}dx=0$? where c is the constant of integration

   1. A.$x+y=c$
   2. B.$xy=c$
   3. C.$c(x+y)=xy$
   4. D.None of the above
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   Answer: C

7. Q902012 · 19 Aug 2012

   What is the general solution of the differential equation $e^x\tan ydx+(1-e^x){\sec }^{2}ydy=0$? where c is the constant of integration

   1. A.$\sin y=c(1-e^x)$
   2. B.$\cos y=c(1-e^x)$
   3. C.$\cot y=c(1-e^x)$
   4. D.None of the above
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   Answer: D

8. Q692012 · 15 Apr 2012

   Which one of the following differential equations is not linear?

   1. A.$\frac{d^{2}y}{d{x}^2}+4y=0$
   2. B.$x\frac{dy}{dx}+y=x^3$
   3. C.$(x-y{)}^2\frac{dy}{dx}=9$
   4. D.${\cos }^{2}x\frac{dy}{dx}+y=\tan x$
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   Answer: C

9. Q872012 · 15 Apr 2012

   What is the solution of the differential equation $\frac{dy}{dx}+\frac{y}{x}=0$ ? where c is a constant

   1. A.$xy=c$
   2. B.$x=cy$
   3. C.$y=cx$
   4. D.None of the above
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   Answer: A

10. Q882012 · 15 Apr 2012

    What is the degree of the differential equation $y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^{-1}$ ?

    1. A.1
    2. B.2
    3. C.-1
    4. D.Degree does not exist.
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    Answer: B

11. Q892012 · 15 Apr 2012

    What is ${\int }_0^1\frac{{\tan }^{-1}x}{1+x^2}dx$ equal to ?

    1. A.$\frac{\pi }{4}$
    2. B.$\frac{\pi }{8}$
    3. C.$\frac{{\pi }^2}{8}$
    4. D.$\frac{{\pi }^2}{32}$
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    Answer: D