Differential Equations · NDA previous year questions

2022 5 questions

1. Q982022 · 4 Sept 2022

   Consider the following statements: 1. The degree of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}+\cos \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=0$ is 1. 2. The order of the differential equation ${\left(\frac{{\mathrm{d}}^2\mathrm{y}}{\mathrm{d}{\mathrm{x}}^2}\right)}^3+\cos \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=0$ is 2. Which of the statements above is/are correct?

   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: B

2. Q992022 · 4 Sept 2022

   What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?

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

3. Q1002022 · 4 Sept 2022

   What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?

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

4. Q572022 · 10 Apr 2022

   What is the degree of the differential equation $1+{\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)}^4={\left(\frac{{\mathrm{d}}^{2}y}{\mathrm{d}{x}^2}\right)}^{\frac{4}{3}}$?

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

5. Q582022 · 10 Apr 2022

   A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant) ?

   1. A.$\frac{\ln 2}{100}$
   2. B.$\frac{\ln 5}{100}$
   3. C.$\frac{\ln 10}{100}$
   4. D.$\frac{2\ln 2}{100}$
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   Answer: A