Differential Equations · NDA previous year questions

2019 10 questions

1. Q912019 · 17 Nov 2019

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

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

2. Q922019 · 17 Nov 2019

   Which one of the following is the differential equation that represents the family of curves $y=\frac{1}{2x^2-c}$ where $c$ is an arbitrary constant?

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

3. Q932019 · 17 Nov 2019

   The differential equation which represents the family of curves given by $\tan y=c(1-e^x)$ is

   1. A.$e^x\tan ydx+(1-e^x)dy=0$
   2. B.$e^x\tan ydx+(1-e^x){\sec }^{2}ydy=0$
   3. C.$e^x(1-e^x)dx+\tan ydy=0$
   4. D.$e^x\tan ydy+(1-e^x)dx=0$
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   Answer: B

4. Q942019 · 17 Nov 2019

   Consider the following statements: 1. The magnitude of $\vec{a}\times \vec{b}$ is same as the area of a triangle with sides $\vec{a}$ and $\vec{b}$ 2. If $\vec{a}\times \vec{b}=\vec{0}$ where $\vec{a}\ne \vec{0},\vec{b}\ne \vec{0}$, then $\vec{a}=\lambda \vec{b}$ Which of the above statements 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

5. Q882019 · 21 Apr 2019

   The solution of the differential equation $\frac{dy}{dx}=\cos (y-x)+1$ is

   1. A.$e^x[\sec (y-x)-\tan (y-x)]=c$
   2. B.$e^x[\sec (y-x)+\tan (y-x)]=c$
   3. C.$e^x\sec (y-x)\tan (y-x)=c$
   4. D.$e^x=c\sec (y-x)\tan (y-x)$
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   Answer: A

6. Q892019 · 21 Apr 2019

   If $y=a\cos 2x+b\sin 2x$, then

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

7. Q902019 · 21 Apr 2019

   The differential equation of the system of circles touching the y-axis at the origin is

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

8. Q912019 · 21 Apr 2019

   Consider the following in respect of the differential equation : 1. The degree of the differential equation is 1. 2. The order of the differential equation is 2. Which of the above statements 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: C

9. Q922019 · 21 Apr 2019

   What is the general solution of the differential equation $\frac{dy}{dx}+\frac{x}{y}=0$ ?

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

10. Q932019 · 21 Apr 2019

    If $\vec{a}=\hat{i}-2\hat{j}+5\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-3\hat{k}$ then what is $(\vec{b}-\vec{a})\cdot (3\vec{a}+\vec{b})$ equal to?

    1. A.106
    2. B.$-106$
    3. C.53
    4. D.$-53$
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    Answer: B