MCQ

MCQ 11 Mark

Systems that exhibit exponential growth have a constant doubling time, which is given by:

✓
$\frac{\log 2}{k}$
B
$\frac{k}{\log 2}$
C
k. $\log 2$
D
None of these

Answer

Correct option: A.

$\frac{\log 2}{k}$

A
Explanation: If a quantity decays exponentially, the half-life is the amount of time it takes the quantity to be reduced by half. It is given by $\frac{\log 2}{k}$

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MCQ 21 Mark

Systems that exhibit exponential decay have a constant half-life, which is given by:

✓
$\frac{\log 2}{k}$
B
$\frac{k}{\log 2}$
C
$k \cdot \log 2$
D
None of these

Answer

Correct option: A.

$\frac{\log 2}{k}$

A
Explanation: If a quantity decays exponentially, the half-life is the amount of time it takes the quantity to be reduced by half. It is given by $\frac{\log 2}{k}$

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MCQ 31 Mark

Systems that exhibit exponential decay follow a model of the form:

A
$y=y_0 e^{k t}$
✓
$y=y_0 e^{-k t}$
C
$y=y_0 e^{k / t}$
D
None of these

Answer

Correct option: B.

$y=y_0 e^{-k t}$

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MCQ 41 Mark

Systems that exhibit exponential growth increase according to the mathematical model $y=y_0 e^{k t}$ where $y_0$ represents the initial state of the system and k > 0 is a constant, is called the.........constant

✓
Growth
B
Decay
C
Simple
D
Normal

Answer

Correct option: A.

Growth

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MCQ 51 Mark

The order and degree (if defined) of differential equation $y^{\prime \prime}+y^2+e^{y^{\prime}}=0$ are:

A
3,1
✓
3, not defined
C
not defined, 3
D
1,3

Answer

Correct option: B.

3, not defined

(B) 3, not defined
Explanation: The highest order derivative present is $y^{\prime \prime \prime}$ so its order is 3. Here the term $e^y$ is not a polynomial in $y^{\prime}$, so the degree of the given differential equation is not defined.

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MCQ 61 Mark

The order and degree (if defined) of differential equation $\left(y^{\prime \prime \prime}\right)^2+\left(y^{\prime \prime}\right)^3+\left(y^{\prime}\right)^4+y^5$ = 0 are:

A
3,1
B
1,3
✓
3,2
D
2,3

Answer

Correct option: C.

3,2

(C) 3,2
Explanation: The highest order derivative present is $y^{\prime \prime \prime}$ prime prime and its raised to power 2. So, its order is 3 and degree is 2.

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MCQ 71 Mark

The order and degree (if defined) of differential equation $\left(\frac{d y}{d x}\right)^4+3 y\left(\frac{d^2 y}{d x^2}\right)=0$ are:

A
4,1
B
1,4
C
4,4
✓
2,1

Answer

Correct option: D.

2,1

(D) 2,1
Explanation: The highest order derivative present is $\frac{d^2 y}{d x^2}$ and its raised to power 1. So, its degree is 1 and order is 2.

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MCQ 81 Mark

The order and degree (if defined) of differential equation $\frac{d^2 y}{d y^2}+\frac{d y}{d y}-6 y=0$ are

A
1,1
✓
2,1
C
1,2
D
2,2

Answer

Correct option: B.

2,1

(B) 2,1
Explanation: The highest order derivative present is $\frac{d^2 y}{d x^2}$ and its raised to power 1. So, its degree is 1 and order is 2.

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MCQ 91 Mark

The order and degree (if defined) of differential equation $x \frac{d y}{d x}+2 y=x^2 x \neq 0$ are:

✓
1,1
B
1,0
C
0,1
D
not defined

Answer

Correct option: A.

1,1

(A) 1,1
Explanation: The highest order derivative present is $\frac{d y}{d x}$ and its raised to power 1. So, its degree is 1 and order is also 1.

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MCQ 101 Mark

The order and degree (if defined) of differential equation $y d x+\left[x \log \left(\frac{y}{x}\right)-2 x\right] d y=0$ are:

✓
1,1
B
1,0
C
0,1
D
not defined

Answer

Correct option: A.

1,1

(A) 1,1
Explanation: Given differential equation, $y d x+x \log \left(\frac{y}{x}\right)-2 x d y=0$
$\Rightarrow\left[2 x-x \log \left(\frac{y}{x}\right)\right] d y=y d x$
$\Rightarrow \quad \frac{d y}{d x}=\frac{y}{2 x-x \log \left(\frac{y}{x}\right)}$
The highest order derivative present is $\frac{d y}{d x}$ and it is raised to power 1 . So, its order is 1 and degree is also 1.

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MCQ 111 Mark

The order and degree (if defined) of differential equation $\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2$ are:

A
3,2
✓
2,2
C
3,3
D
not defined

Answer

Correct option: B.

2,2

(B) 2,2
Explanation: The highest order derivative present is $\frac{d^2 y}{d x^2}$ and it is raised to power 2. So, its order is 2 and degree is also 2.

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MCQ 121 Mark

The order and degree (if defined) of differential equation $\left(\frac{d S}{d x}\right)^4+2 S \frac{d^2 S}{d t^2}=0$ are:

A
1,2
✓
2,1
C
1,1
D
4,2

Answer

Correct option: B.

2,1

(B) 2,1
Explanation: The highest order derivative present is $\frac{d^2 S}{d t^2}$ and it is raised to power 1 . So, its order is 2 and degree is 1.

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MCQ 131 Mark

The order and degree (if defined) of differential equation $\frac{d y}{d x}=k y$ where k is a scalar are:

✓
1,1
B
0,1
C
1,0
D
not defined

Answer

Correct option: A.

1,1

(A) 1,1
Explanation: The highest order derivative present is $\frac{d y}{d x}$ and it is raised to power 1. So, its order is 1 and degree is also 1

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MCQ 141 Mark

The order of the differential equation $2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0$ is:

✓
2
B
1
C
$0$
D
not defined

Answer

Correct option: A.

(A) 2
Explanation, $2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0$
The highest order derivative present in the given differential equation is $\frac{d^2 y}{d x^2}$. Therefore, its order is two.

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Applied Maths MCQ

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