Differential Equations · NDA previous year questions

2017 7 questions

1. Q832017 · 10 Sept 2017

   The order and degree of the differential equation are respectively

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

2. Q1162017 · 10 Sept 2017

   The differential equation of minimum order by eliminating the arbitrary constants $A$ and $C$ in the equation $y=A[\sin (x+C)+\cos (x+C)]$ is

   1. A.$y^{\prime \prime }+(\sin x+\cos x)y^{\prime }=1$
   2. B.$y^{\prime \prime }=(\sin x+\cos x)y^{\prime }$
   3. C.$y^{\prime \prime }=(y^{\prime }{)}^2+\sin x\cos x$
   4. D.$y^{\prime \prime }+y=0$
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   Answer: D

3. Q1182017 · 10 Sept 2017

   The solution of the differential equation $\frac{dy}{dx}=\frac{y{\varphi }^{\prime }(x)-y^2}{\varphi (x)}$ is

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

4. Q882017 · 23 Apr 2017

   What are the degree and order respectively of the differential equation $y=x{\left(\frac{dy}{dx}\right)}^2+{\left(\frac{dx}{dy}\right)}^2$ ?

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

5. Q892017 · 23 Apr 2017

   What is the differential equation corresponding to $y^2-2ay+x^2=a^2$ by eliminating $a$? where $p=\frac{dy}{dx}$.

   1. A.$(x^2-2y^2)p^2-4pxy-x^2=0$
   2. B.$(x^2-2y^2)p^2+4pxy-x^2=0$
   3. C.$(x^2+2y^2)p^2-4pxy-x^2=0$
   4. D.$(x^2+2y^2)p^2-4pxy+x^2=0$
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   Answer: A

6. Q902017 · 23 Apr 2017

   What is the general solution of the differential equation $ydx-(x+2y^2)dy=0$?

   1. A.$x=y^2+cy$
   2. B.$x=2c{y}^2$
   3. C.$x=2y^2+cy$
   4. D.None of the above
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   Answer: C

7. Q912017 · 23 Apr 2017

   What is the solution of the differential equation $\ln \left(\frac{dy}{dx}\right)-a=0$?

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