Differential Equations · NDA previous year questions

2023 10 questions

1. Q512023 · 3 Sept 2023

   Consider the following for the next items that follow: A parabola passes through (1, 2) and satisfies the differential equation $\frac{dy}{dx}=\frac{2y}{x},x>0,y>0$. What is the directrix of the parabola ?

   1. A.$y=-\frac{1}{8}$
   2. B.$y=\frac{1}{8}$
   3. C.$x=-\frac{1}{8}$
   4. D.$x=\frac{1}{8}$
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   Answer: A

2. Q692023 · 3 Sept 2023

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

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

3. Q702023 · 3 Sept 2023

   What is the differential equation of all parabolas of the type $y^2=4a(x-b)$?

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

4. Q742023 · 16 Apr 2023

   Consider the following for the next two (02) items that follow : Suppose E is the differential equation representing family of curves $y^2=2cx+2c\sqrt{c}$ where c is a positive parameter. What is the order of the differential equation ?

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

5. Q752023 · 16 Apr 2023
   
   1. A.2
   2. B.3
   3. C.4
   4. D.Degree does not exist
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   Answer: B

6. Q762023 · 16 Apr 2023

   Consider the following for the next three (03) items that follow : Let $f(x)=\left|\begin{array}{ccc}\cos x& x& 1\\ 2\sin x& x^2& 2x\\ \tan x& x& 1\end{array}\right|$ What is f(0) equal to ?

   1. A.-1
   2. B.0
   3. C.1
   4. D.2
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   Answer: B

7. Q772023 · 16 Apr 2023
   
   1. A.-1
   2. B.0
   3. C.1
   4. D.2
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   Answer: B

8. Q782023 · 16 Apr 2023
   
   1. A.-1
   2. B.0
   3. C.1
   4. D.2
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   Answer: A

9. Q952023 · 16 Apr 2023

   A solution of the differential equation ${\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2-x\frac{\mathrm{dy}}{\mathrm{dx}}=0$ is

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

10. Q962023 · 16 Apr 2023

    If $f(x)=x^2+2$ and $g(x)=2x-3$, then what is $(f\circ g)(1)$ equal to ?

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