Differential Equations · NDA previous year questions

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2014 13 questions

Q852014 · 28 Sept 2014
What is the degree of the differential equation $(\frac{d ^{3} y}{d x ^{3}})^{3/2} = (\frac{d ^{2} y}{d x ^{2}})^{2}$ ?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: C
Q862014 · 28 Sept 2014
What is the solution of the equation $ln (\frac{d y}{d x}) + x = 0$ ? 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: C
Q872014 · 28 Sept 2014
Eliminating the arbitrary constants B and C in the expression $y = \frac{2}{3 C} (C x - 1)^{3/2} + B$ , we get
1. A. $x [1 + (\frac{d y}{d x})^{2}] = \frac{d ^{2} y}{d x ^{2}}$
2. B. $2 x (\frac{d y}{d x}) \frac{d ^{2} y}{d x ^{2}} = 1 + (\frac{d y}{d x})^{2}$
3. C. $(\frac{d y}{d x}) \frac{d ^{2} y}{d x ^{2}} = 1$
4. D. $(\frac{d y}{d x})^{2} + 1 = \frac{d ^{2} y}{d x ^{2}}$
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Answer: B
Q882014 · 28 Sept 2014
If $∣ a ∣ = 2$ , $∣ b ∣ = 5$ and $∣ a \times b ∣ = 8$ , then what is $a \cdot b$ equal to?
1. A.6
2. B.7
3. C.8
4. D.9
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Answer: A
Q772014 · 20 Apr 2014
What is the number of arbitrary constants in the particular solution of differential equation of third order?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: A
Q782014 · 20 Apr 2014
What is the general solution of the differential equation $x d y - y d x = y^{2}$ ? where c is an arbitrary constant
1. A. $x = cy$
2. B. $y^{2} = c x$
3. C. $x + x y - cy = 0$
4. D.None of the above
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Answer: Dropped in the final answer key (full marks to everyone)
Q792014 · 20 Apr 2014
The solution of $\frac{d y}{d x} = ∣ x ∣$ is:
1. A. $y = \frac{x ∣ x ∣}{2} + c$
2. B. $y = \frac{∣ x ∣}{2} + c$
3. C. $y = \frac{x ^{2}}{2} + c$
4. D. $y = \frac{x ^{3}}{2} + c$
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Answer: A
Q802014 · 20 Apr 2014
What is the solution of $\frac{d y}{d x} + 2 y = 1$ satisfying $y (0) = 0$ ?
1. A. $y = \frac{1 - e ^{- 2 x}}{2}$
2. B. $y = \frac{1 + e ^{- 2 x}}{2}$
3. C. $y = 1 + e^{x}$
4. D. $y = \frac{1 + e ^{x}}{2}$
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Answer: A
Q812014 · 20 Apr 2014
What is the equation of a curve passing through $(0, 1)$ and whose differential equation is given by $d y = y tan x d x$ ?
1. A. $y = cos x$
2. B. $y = sin x$
3. C. $y = sec x$
4. D. $y = cosec x$
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Answer: C
Q822014 · 20 Apr 2014
Consider the following statements in respect of the differential equation $\frac{d ^{2} y}{d x ^{2}} + cos (\frac{d y}{d x}) = 0$ : 1. The degree of the differential equation is not defined. 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
Q832014 · 20 Apr 2014
For the next three (03) items that follow: The general solution of the differential equation $(x^{2} + x + 1) d y + (y^{2} + y + 1) d x = 0$ is $(x + y + 1) = A (1 + B x + C y + D x y)$ where B, C and D are constants and A is parameter. What is B equal to?
1. A. $- 1$
2. B.1
3. C.2
4. D.None of the above
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Answer: A
Q842014 · 20 Apr 2014
For the next three (03) items that follow: The general solution of the differential equation $(x^{2} + x + 1) d y + (y^{2} + y + 1) d x = 0$ is $(x + y + 1) = A (1 + B x + C y + D x y)$ where B, C and D are constants and A is parameter. What is C equal to?
1. A.1
2. B. $- 1$
3. C.2
4. D.None of the above
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Answer: B
Q852014 · 20 Apr 2014
For the next three (03) items that follow: The general solution of the differential equation $(x^{2} + x + 1) d y + (y^{2} + y + 1) d x = 0$ is $(x + y + 1) = A (1 + B x + C y + D x y)$ where B, C and D are constants and A is parameter. What is D equal to?
1. A. $- 1$
2. B.1
3. C. $- 2$
4. D.None of the above
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Answer: C