Differential Equations · NDA previous year questions

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2011 17 questions

Q242011 · 21 Aug 2011
What is the degree of the differential equation $(\frac{d ^{3} y}{d x ^{3}})^{\frac{2}{3}} + 4 - 3 (\frac{d ^{2} y}{d x ^{2}}) + 5 (\frac{d y}{d x}) = 0$ ?
1. A.3
2. B.2
3. C.2/3
4. D.Not defined
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Answer: B
Q412011 · 21 Aug 2011
What is the equation of the curve passing through the point $(0, \frac{π}{3})$ satisfying the differential equation $sin x cos y d x + cos x sin y d y = 0$ ?
1. A. $cos x cos y = \frac{3}{2}$
2. B. $sin x sin y = \frac{3}{2}$
3. C. $sin x sin y = \frac{1}{2}$
4. D. $cos x cos y = \frac{1}{2}$
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Answer: D
Q262011 · 17 Apr 2011
What is the degree of the following differential equation?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: B
Q272011 · 17 Apr 2011
What is the sum of $3 + \frac{1}{3} + \frac{1}{3 3} + \dots$ ?
1. A. $\frac{3}{2}$
2. B. $\frac{3 3}{2}$
3. C. $\frac{2 3}{3}$
4. D. $3$
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Answer: B
Q282011 · 17 Apr 2011
What does the differential equation $y \frac{d y}{d x} + x = a$ (where $a$ is a constant) represent?
1. A.A set of circles having centre on the $y$ -axis
2. B.A set of circles having centre on the $x$ -axis
3. C.A set of ellipses
4. D.A pair of straight lines
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Answer: B
Q292011 · 17 Apr 2011
If $A = [α 1 01]$ and $B = [1201]$ such that $A^{2} = B$ , then what is the value of $α$ ?
1. A. $- 1$
2. B.1
3. C.2
4. D.4
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Answer: B
Q302011 · 17 Apr 2011
What is the value of $n$ , if $P (15, n - 1) : P (16, n - 2) = 3 : 4$ ?
1. A.10
2. B.12
3. C.14
4. D.15
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Answer: C
Q502011 · 17 Apr 2011
If the solution of the differential equation $\frac{d y}{d x} = \frac{a x + 3}{2 y + f}$ represents a circle, then what is the value of $a$ ?
1. A.2
2. B.1
3. C. $- 2$
4. D. $- 1$
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Answer: C
Q702011 · 17 Apr 2011
1. A. $\frac{d ^{3} y}{d x ^{3}} = 0$
2. B. $\frac{d ^{2} x}{d y ^{2}} = c$
3. C. $\frac{d ^{3} x}{d y ^{3}} = 1$
4. D. $\frac{d ^{3} y}{d x ^{3}} = c$
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Answer: A
Q712011 · 17 Apr 2011
For the next five (5) items that follow : The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11. How many students learn precisely two languages?
1. A.55
2. B.40
3. C.30
4. D.13
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Answer: C
Q722011 · 17 Apr 2011
How many students learn at least two languages?
1. A.15
2. B.30
3. C.45
4. D.55
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Answer: C
Q732011 · 17 Apr 2011
What is the total strength of the class?
1. A.124
2. B.100
3. C.96
4. D.66
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Answer: A
Q742011 · 17 Apr 2011
How many students learn English and French?
1. A.30
2. B.43
3. C.45
4. D.73
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Answer: A
Q752011 · 17 Apr 2011
How many students learn at least one language?
1. A.45
2. B.51
3. C.96
4. D.None of the above
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Answer: C
Q762011 · 17 Apr 2011
If $I_{n} = \int_{0}^{\frac{π}{4}} tan^{n} x d x$ then what is $I_{n} + I_{n - 2}$ equal to?
1. A. $1/ n$
2. B. $1/ (n - 1)$
3. C. $n / (n - 1)$
4. D. $1/ (n - 2)$
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Answer: B
Q1182011 · 17 Apr 2011
What is the solution of the differential equation $\frac{d y}{d x} + \frac{1 - y ^{2}}{1 - x ^{2}} = 0$ ? where $c$ is a constant.
1. A. $sin^{- 1} y + sin^{- 1} x = c$
2. B. $sin^{- 1} y - sin^{- 1} x = c$
3. C. $2 sin^{- 1} y + sin^{- 1} x = c$
4. D. $2 sin^{- 1} y - sin^{- 1} x = c$
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Answer: A
Q1192011 · 17 Apr 2011
If $z = 1 + cos \frac{π}{5} + i sin \frac{π}{5}$ then what is $∣ z ∣$ equal to ?
1. A. $2 cos \frac{π}{5}$
2. B. $2 sin \frac{π}{5}$
3. C. $2 cos \frac{π}{10}$
4. D. $2 sin \frac{π}{10}$
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Answer: C