Question 180-187 of 346: Integration and Its Applications (Section A: Common) | CUET (Common University Entrance Test) UG Mathematics Common (319) | Includes PYQs | Get Solutions with Detailed Explanations

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Question 180

Section A: CommonIntegration and Its ApplicationsEvaluation of Indefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

If ∫ [ d x ( 1 − cos 4 x ) ] = − ( 1 2 ) cot x + A tan − 1 [ f ( x ) ] + c then A = ? and f ( x ) = ?

Choices

Choice (4)Response

a.

− 2 and 2 tan x

b.

2 and 2 tan x

c.

[ 1 2 2 ] and 2 tan x

d.

( 2 4 ) and [ 1 2 cot x ]

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Question 181

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

∫ [ d x { ( x + 2 ) ( ( 12 13 ) ) ( x − 5 ) ( ( 14 13 ) ) } ] = ________ + c

Choices

Choice (4)Response

a.

2 e ( [ ( − x ) 2 ] ) sec ( x 2 )

b.

e ( [ ( − x ) 2 ] ) sec ( x 2 )

c.

− e ( [ ( − x ) 2 ] ) sec ( x 2 )

d.

− 2 e ( [ ( − x ) 2 ] ) sec ( x 2 )

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Question 182

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

∫ [ d x { ( x + 2 ) ( ( 12 13 ) ) ( x − 5 ) ( ( 14 13 ) ) } ] = ________ + c

Choices

Choice (4)Response

a.

[ ( 13 ) 7 ] [ x + 2 x − 5 ] ( ( 1 13 ) )

b.

[ ( − 13 ) 7 ] [ x − 5 x + 2 ] ( ( 1 13 ) )

c.

[ ( 13 ) 7 ] [ x − 5 x + 2 ] ( ( 1 13 ) )

d.

[ ( − 13 ) 7 ] [ x + 2 x − 5 ] ( ( 1 13 ) )

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Question 183

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

∫ [ 1 + x − ( 1 x ) ] e ( [ x + ( 1 x ) ] ) d x = ________ + c

Choices

Choice (4)Response

a.

( x − 1 ) e ( [ x + ( 1 x ) ] )

b.

( x + 1 ) e ( [ x + ( 1 x ) ] )

c.

x e ( [ x + ( 1 x ) ] )

d.

− x e ( [ x + ( 1 x ) ] )

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Question 184

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

If ∫ [ 5 x + 3 { x 2 + 4 x + 10 } ] d x = k 1 ( x 2 + 4 x + 10 ) + k 2 log | ( x + 2 ) + x 2 + 4 x + 10 | + c then k 1 + k 2 = ________

Choices

Choice (4)Response

a.

1

b.

2

c.

− 1

d.

− 2

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Question 185

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

∫ [ e x d x { ( e x + 2012 ) ( e x + 2013 ) } ] = ________ + c

Choices

Choice (4)Response

a.

log [ ( e x + 2012 ) ( e x + 2013 ) ]

b.

[ ( e x + 2013 ) ( e x + 2012 ) ]

c.

[ ( e x + 2012 ) ( e x + 2013 ) ]

d.

log [ ( e x + 2013 ) ( e x + 2012 ) ]

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Question 186

Section A: CommonIntegration and Its ApplicationsIndefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

If ∫ [ 5 x d x 25 x − 1 ] = k log | 5 x + 25 x − 1 | + c then k = ________

Choices

Choice (4)Response

a.

log e 25

b.

log e ( 1 5 )

c.

log e ( 1 25 )

d.

[ 1 log e 5 ]

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Question 187

Section A: CommonIntegration and Its ApplicationsEvaluation of Indefinite Integrals

MCQ

Read the question, then carefully choose the correct answer(s).

∫ sin − 1 [ 2 x ( 1 + x 2 ) ] d x = f ( x ) − log ( 1 + x 2 ) + c then f ( x ) = ________

Choices

Choice (4)Response

a.

− x tan − 1 x

b.

x tan − 1 x

c.

2 x tan − 1 x

d.

− 2 x tan − 1 x

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