Differential Equations · NDA previous year questions

2021 9 questions

1. Q862021 · 14 Nov 2021

   What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?

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

2. Q872021 · 14 Nov 2021

   What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

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

3. Q882021 · 14 Nov 2021

   What is the differential equation of $y=A-\frac{B}{x}$?

   1. A.$x{y}_2+y_1=0$
   2. B.$x{y}_2+2y_1=0$
   3. C.$x{y}_2-2y_1=0$
   4. D.$2x{y}_2+y_1=0$
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   Answer: B

4. Q892021 · 14 Nov 2021

   What is ${\int }_0^{\pi }\ln \left(\tan \frac{x}{2}\right)\mathrm{d}x$ equal to?

   1. A.0
   2. B.$\frac{1}{2}$
   3. C.1
   4. D.2
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   Answer: A

5. Q812021 · 18 Apr 2021

   If the general solution of a differential equation is $y^2+2cy-cx+c^2=0$, where $c$ is an arbitrary constant, then what is the order of the differential equation?

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

6. Q822021 · 18 Apr 2021

   What is the degree of the following differential equation?

   
   1. A.1
   2. B.2
   3. C.3
   4. D.Degree is not defined
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   Answer: A

7. Q832021 · 18 Apr 2021

   Which one of the following differential equations has the general solution $y=a{e}^x+b{e}^{-x}$?

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

8. Q842021 · 18 Apr 2021

   What is the solution of the following differential equation? $\ln \left(\frac{dy}{dx}\right)+y=x$

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

9. Q852021 · 18 Apr 2021

   What is $\int e^{(2\ln x+\ln x^2)}\mathrm{d}x$ equal to?

   1. A.$\frac{x^4}{4}+c$
   2. B.$\frac{x^3}{3}+c$
   3. C.$\frac{2x^5}{5}+c$
   4. D.$\frac{x^5}{5}+c$
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   Answer: D