Differential Equations · NDA previous year questions

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2010 10 questions

Q622010 · 22 Aug 2010
What does the differential equation $y \frac{d y}{d x} + x = k$ ( $k$ is any constant) represent?
1. A.A family of circles having centre on the $y$ -axis
2. B.A family of circles having centre on the $x$ -axis
3. C.A family of circles touching the $x$ -axis
4. D.A family of ellipses
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Answer: B
Q712010 · 22 Aug 2010
What is the differential equation to family of parabolas having their vertices at the origin and foci on the $x$ -axis?
1. A. $y = 2 x y^{'}$
2. B. $x = 2 y y^{'}$
3. C. $x y = y^{'}$
4. D. $x = y y^{'}$
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Answer: A
Q782010 · 22 Aug 2010
What is the degree of the differential equation $(1 + \frac{d y}{d x})^{4} = (\frac{d ^{2} y}{d x ^{2}})^{2}$ ?
1. A. $1$
2. B. $2$
3. C. $4$
4. D. $8$
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Answer: B
Q832010 · 22 Aug 2010
Which one of the following is the differential equation to family of circles having centre at the origin?
1. A. $(x^{2} - y^{2}) \frac{d y}{d x} = 2 x y$
2. B. $(x^{2} + y^{2}) \frac{d y}{d x} = 2 x y$
3. C. $\frac{d y}{d x} = (x^{2} + y^{2})$
4. D. $x d x + y d y = 0$
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Answer: D
Q842010 · 22 Aug 2010
What is the area under the curve $f (x) = x e^{x}$ above the $x$ -axis and between the lines $x = 0$ and $x = 1$ ?
1. A. $1/2$ square unit
2. B. $1$ square unit
3. C. $3/2$ square units
4. D. $2$ square units
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Answer: B
Q852010 · 22 Aug 2010
What does the solution of the differential equation $x \frac{d y}{d x} = y$ represent?
1. A.Family of straight lines through the origin
2. B.Family of circles with their centres at the origin
3. C.Family of parabolas with their vertices at the origin
4. D.Family of straight lines having slope $1$ and not passing through the origin
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Answer: A
Q852010 · 18 Apr 2010
What is the solution of the differential equation $a (x \frac{d y}{d x} + 2 y) = x y \frac{d y}{d x}$ ? where k is a constant.
1. A. $x^{2} = k y e^{\frac{y}{a}}$
2. B. $y x^{2} = k y e^{\frac{y}{a}}$
3. C. $y^{2} x^{2} = k y e^{\frac{y ^{2}}{a}}$
4. D.None of the above
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Answer: D
Q922010 · 18 Apr 2010
What is the solution of the differential equation $3 e^{x} tan y d x + (1 + e^{x}) sec^{2} y d y = 0$ ? where c is a constant of integration.
1. A. $(1 + e^{x}) tan y = c$
2. B. $(1 + e^{x})^{3} tan y = c$
3. C. $(1 + e^{x})^{2} tan y = c$
4. D. $(1 + e^{x}) sec^{2} y = c$
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Answer: B
Q942010 · 18 Apr 2010
What is the differential equation for $y^{2} = 4 a (x - a)$ ?
1. A. $y y^{'} - 2 x y y^{'} + y^{2} = 0$
2. B. $y y^{'} (y y^{'} + 2 x) + y^{2} = 0$
3. C. $y y^{'} (y y^{'} - 2 x) + y^{2} = 0$
4. D. $y y^{'} - 2 x y y^{'} + y = 0$
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Answer: C
Q962010 · 18 Apr 2010
What is the degree of the differential equation $\frac{d ^{2} y}{d x ^{2}} - 1 + (\frac{d y}{d x})^{3} = 0$ ?
1. A.1
2. B.2
3. C.3
4. D.6
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Answer: B