Differential Equations Test

Result

Differential Equations Test - 6

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Question 1
1 / -0.25

The degree of the equation

A
2

B
0

C
1

D
3

Solution

2
Question 2
1 / -0.25

General solution of

A
y = 2sin(x + c)

B
y = 2cosx + c

C
y = 2sin(2x) + c

D
y = 2sinx² + c

Solution
Question 3
1 / -0.25

In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs1000 is deposited with this bank, how much will it worth after 10 years (e^0.5 = 1.648).

A
Rs 1848

B
Rs 1648

C
Rs 1948

D
Rs 1748

Solution

When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :
Question 4
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At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (–4, –3). Find the equation of the curve given that it passes through (–2, 1).

A
(x + 3)² = y + 4

B
(x + 5)² = 2y + 3

C
(x + 4)² = y + 3

D
(x + 5)² = 2y + 3

Solution

Slope of the line segment joining the point of contact P (x , y) to the point (- 4 , - 3) =
Question 5
1 / -0.25

Solution of

A
logy = 2{x −log|x|} + C

B
logy = {x+log|x|} + C

C
logy = {x −log|x|} + C

D
None of these

Solution
Question 6
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Find the order and degree of

A
2, degree undefined

B
4, degree undefined

C
1, degree undefined

D
3, degree undefined

Solution

Order = 3 , degree not defined ,because the function y ’present in exponential form.
Question 7
1 / -0.25

A
y = 1 + Ae^x

B
y = 1 + Ae^−x

C
y = 1 + Ae^−3x

D
y = B + Ae^−x

Solution
Question 8
1 / -0.25

A

B

C

D
None of these

Solution
Question 9
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Solution of x dy −ydx =

A

B

C

D

Solution
Question 10
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A

B

C

D
None of these

Solution