Differential Equations · NDA previous year questions

2018 12 questions

1. Q802018 · 9 Sept 2018

   The differential equation of the family of curves $y=p\cos (ax)+q\sin (ax)$, where p, q are arbitrary constants, is

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

2. Q812018 · 9 Sept 2018

   The equation of the curve passing through the point $(-1,-2)$ which satisfies $\frac{dy}{dx}=-x^2-\frac{1}{x^3}$, is

   1. A.$17x^{2}y-6x^2+3x^5-2=0$
   2. B.$6x^{2}y+17x^2+2x^5-3=0$
   3. C.$6xy-2x^2+17x^5+3=0$
   4. D.$17x^{2}y+6xy-3x^5+5=0$
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   Answer: B

3. Q822018 · 9 Sept 2018

   What is the order of the differential equation whose solution is $y=a\cos x+b\sin x+c{e}^{-x}+d$, where a, b, c and d are arbitrary constants?

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

4. Q832018 · 9 Sept 2018

   What is the solution of the differential equation $\ln \left(\frac{dy}{dx}\right)=ax+by$? where c is an arbitrary constant.

   1. A.$a{e}^{ax}+b{e}^{by}=c$
   2. B.$\frac{1}{a}{e}^{ax}+\frac{1}{b}{e}^{by}=c$
   3. C.$a{e}^{ax}+b{e}^{-by}=c$
   4. D.$\frac{1}{a}{e}^{ax}+\frac{1}{b}{e}^{-by}=c$
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   Answer: D

5. Q842018 · 9 Sept 2018
   
   1. A.Option A
   2. B.Option B
   3. C.Option C
   4. D.Option D
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   Answer: C

6. Q852018 · 9 Sept 2018

   Let $|\vec{a}|\ne 0,|\vec{b}|\ne 0$. $(\vec{a}+\vec{b}).(\vec{a}+\vec{b})=|\vec{a}{|}^2+|\vec{b}{|}^2$ holds if and only if

   1. A.$\vec{a}$ and $\vec{b}$ are perpendicular
   2. B.$\vec{a}$ and $\vec{b}$ are parallel
   3. C.$\vec{a}$ and $\vec{b}$ are inclined at an angle of $45^{\circ }$
   4. D.$\vec{a}$ and $\vec{b}$ are anti-parallel
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   Answer: A

7. Q862018 · 9 Sept 2018

   If $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$, then what is $\vec{r}\cdot (\hat{i}+\hat{j}+\hat{k})$ equal to?

   1. A.$x$
   2. B.$x+y$
   3. C.$-(x+y+z)$
   4. D.$(x+y+z)$
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   Answer: D

8. Q832018 · 22 Apr 2018

   What is the solution of the differential equation $xdy-ydx=0$?

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

9. Q842018 · 22 Apr 2018

   Which one of the following differential equations has a periodic solution? where $\mu >0$.

   1. A.$\frac{d^{2}x}{d{t}^2}+\mu x=0$
   2. B.$\frac{d^{2}x}{d{t}^2}-\mu x=0$
   3. C.$x\frac{dx}{dt}+\mu t=0$
   4. D.$\frac{dx}{dt}+\mu xt=0$
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   Answer: A

10. Q852018 · 22 Apr 2018

    The order and degree of the differential equation $y^2=4a(x-a)$, where 'a' is an arbitrary constant, are respectively

    1. A.$1,2$
    2. B.$2,1$
    3. C.$2,2$
    4. D.$1,1$
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    Answer: Dropped in the final answer key (full marks to everyone)

11. Q862018 · 22 Apr 2018

    What is the solution of $(1+2x)dy-(1-2y)dx=0$?

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

12. Q872018 · 22 Apr 2018

    What are the order and degree, respectively, of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^2=y^4+{\left(\frac{dy}{dx}\right)}^5$?

    1. A.4, 5
    2. B.2, 3
    3. C.3, 2
    4. D.5, 4
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    Answer: C