Differential Equations · NDA previous year questions

2013 12 questions

1. Q832013 · 11 Aug 2013

   What is the order of the differential equation ${\left(\frac{dy}{dx}\right)}^2+\frac{dy}{dx}-{\sin }^{2}y=0$ ?

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

2. Q842013 · 11 Aug 2013

   $y=2\cos x+3\sin x$ satisfies which of the following differential equations? 1. $\frac{d^{2}y}{d{x}^2}+y=0$ 2. ${\left(\frac{dy}{dx}\right)}^2+\frac{dy}{dx}=0$ Select the correct answer using the code given below.

   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: A

3. Q852013 · 11 Aug 2013

   The differential equation of all circles whose centres are at the origin is

   1. A.$\frac{dy}{dx}=\frac{y}{x}$
   2. B.$\frac{dy}{dx}=\frac{x}{y}$
   3. C.$\frac{dy}{dx}=-\frac{x}{y}$
   4. D.None of the above
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   Answer: C

4. Q862013 · 11 Aug 2013

   What is $\int {\sin }^{2}xdx+\int {\cos }^{2}xdx$ equal to? where $c$ is an arbitrary constant.

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

5. Q872013 · 11 Aug 2013

   What is $\int e^{e^x}{e}^{x}dx$ equal to? where $c$ is an arbitrary constant.

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

6. Q892013 · 14 Apr 2013

   The differential equation of the curve $y=\sin x$ is

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

7. Q902013 · 14 Apr 2013

   The degree and order respectively of the differential equation $\frac{dy}{dx}=\frac{1}{x+y+1}$ are

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

8. Q912013 · 14 Apr 2013

   What is the degree of the differential equation ${\left(\frac{d^{4}y}{d{x}^4}\right)}^{3/5}-5\frac{d^{3}y}{d{x}^3}+6\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+5=0$ ?

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

9. Q922013 · 14 Apr 2013

   The general solution of the differential equation $x\frac{dy}{dx}+y=0$ is where $c$ is an arbitrary constant.

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

10. Q932013 · 14 Apr 2013

    What is the area of the triangle bounded by the sides $x=0,y=0$ and $x+y=2$ ?

    1. A.1 square unit
    2. B.2 square unit
    3. C.4 square unit
    4. D.8 square unit
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    Answer: B

11. Q942013 · 14 Apr 2013

    The general solution of the differential equation $\ln \left(\frac{dy}{dx}\right)+x=0$ is where c is an arbitrary constant.

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

12. Q952013 · 14 Apr 2013

    If $\vec{\beta }$ is perpendicular to both $\vec{\alpha }$ and $\vec{\gamma }$ where $\vec{\alpha }=\hat{k}$ and $\vec{\gamma }=2\hat{i}+3\hat{j}+4\hat{k}$, then what is $\vec{\beta }$ equal to ?

    1. A.$3\hat{i}+2\hat{j}$
    2. B.$-3\hat{i}+2\hat{j}$
    3. C.$2\hat{i}-3\hat{j}$
    4. D.$-2\hat{i}+3\hat{j}$
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    Answer: B