Differential Equations · NDA previous year questions

2020 7 questions

1. Q742020 · 6 Sept 2020

   The order and degree of the differential equation $k\frac{dy}{dx}=\int {\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^{\frac{2}{3}}dx$ are respectively

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

2. Q752020 · 6 Sept 2020

   What is ${\lim }_{x\to 0}\frac{\sin x\log (1-x)}{x^2}$ equal to?

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

3. Q762020 · 6 Sept 2020

   If $f(x)=3x^2-5x+p$ and $f(0)$ and $f(1)$ are opposite in sign, then which of the following is correct?

   1. A.$-2<p<0$
   2. B.$-2<p<2$
   3. C.$0<p<2$
   4. D.$3<p<5$
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   Answer: C

4. Q822020 · 6 Sept 2020

   The solution of the differential equation $dy=(1+y^2)dx$ is

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

5. Q832020 · 6 Sept 2020

   What is $\int (e^{\log x}+\sin x)\cos xdx$ equal to?

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

6. Q952020 · 6 Sept 2020

   The function $u(x,y)=c$ which satisfies the differential equation $x(dx-dy)+y(dy-dx)=0$, is

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

7. Q992020 · 6 Sept 2020

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

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