Differential Equations · NDA previous year questions

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2024 12 questions

Q892024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $y d x + (x - y^{3}) d y = 0$ be a differential equation. What are the order and degree respectively of the differential equation?
1. A.1 and 1
2. B.1 and 2
3. C.2 and 1
4. D.1 and 3
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Answer: A
Q902024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $y d x + (x - y^{3}) d y = 0$ be a differential equation. What is the solution of the differential equation?
1. A. $y^{4} + 2 x = c$
2. B. $y^{4} + 3 x = c$
3. C. $2 x y^{4} + x = c$
4. D. $4 x y - y^{4} = c$
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Answer: D
Q912024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f (x) = ∣ x^{2} - x - 2∣$ What is $\int_{0}^{2} f (x) d x$ equal to
1. A.0
2. B.1
3. C.5/3
4. D.10/3
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Answer: D
Q922024 · 1 Sept 2024
Direction : Consider the following for the items that follow : Let $f (x) = ∣ x^{2} - x - 2∣$ What is $\int_{1}^{3} f (x) d x$ equal to
1. A.2
2. B.3
3. C.4
4. D.5
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Answer: B
Q712024 · 21 Apr 2024
Let $y_{1} (x)$ and $y_{2} (x)$ be two solutions of the differential equation $\frac{d y}{d x} = x$ . If $y_{1} (0) = 0$ and $y_{2} (0) = 4$ , then what is the number of points of intersection of the curves $y_{1} (x)$ and $y_{2} (x)$ ?
1. A.No point
2. B.One point
3. C.Two points
4. D.More than two points
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Answer: A
Q722024 · 21 Apr 2024
The differential equation, representing the curve $y = e^{x} (a cos x + b sin x)$ where $a$ and $b$ are arbitrary constants, is
1. A. $\frac{d ^{2} y}{d x ^{2}} + 2 y = 0$
2. B. $\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 0$
3. C. $\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 2 y = 0$
4. D. $\frac{d ^{2} y}{d x ^{2}} + y = 0$
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Answer: C
Q732024 · 21 Apr 2024
If $f (x) = a x - b$ and $g (x) = c x + d$ are such that $f (g (x)) = g (f (x))$ , then which one of the following holds?
1. A. $f (d) = g (b)$
2. B. $f (b) + g (d) = 0$
3. C. $f (a) + g (c) = 2 a$
4. D. $f (d) + g (b) = 2 d$
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Answer: D
Q742024 · 21 Apr 2024
What is $\int_{- 1}^{1} (3 sin x - sin 3 x) cos^{2} x d x$ equal to?
1. A. $\frac{1}{4}$
2. B.0
3. C. $\frac{1}{2}$
4. D. $- \frac{1}{4}$
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Answer: B
Q752024 · 21 Apr 2024
1. A.2, 2
2. B.2, 3
3. C.5, 2
4. D.2, 5
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Answer: D
Q762024 · 21 Apr 2024
If $\frac{d y}{d x} = 2 e^{x} y^{3}$ , $y (0) = \frac{1}{2}$ then what is $4 y^{2} (2 - e^{x})$ equal to?
1. A.1
2. B.2
3. C.3
4. D.4
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Answer: A
Q772024 · 21 Apr 2024
Let $p = \int_{a}^{b} f (x) d x$ and $q = \int_{a}^{b} ∣ f (x) ∣ d x$ . If $f (x) = e^{- x}$ , then which one of the following is correct ?
1. A. $p = 2 q$
2. B. $p = - q$
3. C. $4 p = q$
4. D. $p = q$
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Answer: D
Q782024 · 21 Apr 2024
What is $\int_{0}^{π /2} \frac{a + s i n x}{2 a + s i n x + c o s x} d x$ equal to?
1. A. $\frac{π}{4}$
2. B. $\frac{π}{2}$
3. C.1
4. D.0
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Answer: A