Question # 1

The general solution of differential equation of order n contains n arbitrary constants, which can be determined by ------------ initial value conditions.

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1

0

2

n

The technique or method to find such a function whose derivative is given involves the inverse process of differentiation called:

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Differentiation

Integration

Differential

None of these

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e^2x sin x + c

e^2xcosx + c

-e^2xsin x + c

-e^2xcosx + c

Area between x-axis and the curve:

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32

16

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a cosec (ax + b)

cot (ax + b)

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e^-x sin x + c

-e^-x sin x + c

e^-xcosx + c

-e^-xsin x + c

If y = sin x then dy =

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cosy dx

cos x

cosx dx

cos xdy

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tan x + c

-tan x + c

sec x + c

-sec x + c

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Integration

Integrand

Constant of integration

None of these

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e^ax

f(x)

e^axf(x)

e^{ax + f(x)}

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2

1

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cosec x + c

-cosec x + c

cot x + c

- cot x + c

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ln |sin x|

- ln |sin x|

ln |cos x|

-ln |cos x|

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equal to each other

not equal to each other

nearly equal to each other

None of these

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cot x

- cot x

cosec x cot x

-cosec x cot x

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f(x)

ln |f(x)|

f'(x)

ln |f'(x)|

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Integration

Integration w.r.t.x.

Differentiation

Differentiation w.r.t.x

If the lower limit is a constant and the upper limit is a variable, then the integral is a function of:

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x

y

lower limit

upper limit

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Integration

Integrand

Constant of integration

None of these

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36

42

48

12

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domain

range

lower limit

upper limit

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