Differential Equations · NDA previous year questions

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2009 10 questions

Q412009 · 30 Aug 2009
What is the solution of the differential equation $x d y - y d x = x y^{2} d x$ ?
1. A. $y + x^{- 2} = c$
2. B. $y^{2} + 2 x^{- 1} = c$
3. C. $y + x^{- 1} = c$
4. D. $x^{2} + 2 x y^{- 1} = c$
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Answer: D
Q422009 · 30 Aug 2009
If $f (x) = a + b x + c x^{2}$ , then what is $\int_{0}^{1} f (x) d x$ equal to ?
1. A. $[f (0) + 4 f (1/2) + f (1)] /6$
2. B. $[f (0) + 4 f (1/2) + f (1)] /3$
3. C. $[f (0) + 4 f (1/2) + f (1)]$
4. D. $[f (0) + 2 f (1/2) + f (1)] /6$
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Answer: A
Q432009 · 30 Aug 2009
What is $\int \frac{a + b s i n x}{c o s ^{2} x} d x$ equal to ?
1. A. $a sec x + b tan x + c$
2. B. $a tan x + b sec x + c$
3. C. $a cot x + b cosec x + c$
4. D. $a cosec x + b cot x + c$
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Answer: B
Q442009 · 30 Aug 2009
If $e^{y} + x y = e$ , then what is the value of $\frac{d ^{2} y}{d x ^{2}}$ at $x = 0$ ?
1. A. $e^{- 1}$
2. B. $e^{- 2}$
3. C. $e$
4. D.1
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Answer: B
Q452009 · 30 Aug 2009
What is $\int \frac{l n x}{( 1 + l n x ) ^{2}} d x$ equal to ?
1. A. $\frac{1}{( 1 + l n x ) ^{3}} + c$
2. B. $\frac{1}{( 1 + l n x ) ^{2}} + c$
3. C. $\frac{x}{( 1 + l n x )} + c$
4. D. $\frac{x}{( 1 + l n x ) ^{2}} + c$
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Answer: C
Q1132009 · 30 Aug 2009
When $a$ and $b$ are eliminated from the equation $x y = a e^{x} + b e^{- x}$ , the resulting differential equation is of :
1. A.first order and first degree
2. B.first order and second degree
3. C.second order and first degree
4. D.second order and second degree
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Answer: C
Q1142009 · 30 Aug 2009
If $y = (1 + x^{1/4}) (1 + x^{1/2}) (1 - x^{1/4})$ , then what is $\frac{d y}{d x}$ equal to ?
1. A.1
2. B. $- 1$
3. C.0
4. D. $- 2 x$
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Answer: B
Q712009 · 19 Apr 2009
What are the degree and order respectively of the differential equation of the family of rectangular hyperbolas whose axes of symmetry are the coordinate axes?
1. A.1, 1
2. B.1, 2
3. C.2, 1
4. D.2, 2
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Answer: A
Q1192009 · 19 Apr 2009
What is the solution of the differential equation $\frac{d y}{d x} = e^{x - y} (e^{y - x} - e^{y})$ ?
1. A. $y = x - e^{x} + c$
2. B. $y = x + e^{x} + c$
3. C. $y = e^{x - y} - e^{y} + c$
4. D.None of the above
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Answer: A
Q1202009 · 19 Apr 2009
What is the area of the triangle formed by the lines $y - x = 0$ , $y + x = 0$ , $x = c$ ?
1. A. $c /2$
2. B. $c^{2}$
3. C. $2 c^{2}$
4. D. $c^{2} /2$
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Answer: B