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← GATE CH 2020 (with Solutions).pdf

Q16

FAILMCQpage 6holdmath reviewREVIEW_MATHP2UNREVIEWED
type=MCQ · page=6 · marks=1 · content_conf=0.7999999999999999 · math_conf=1

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Source / evidence

file: GATE CH 2020 (with Solutions).pdf
pages: 6–6

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Extracted16 / 67

Consider the following unit step function. f (t ) 1 t 3 The Laplace transform of this function is

Options

  1. A.
    (e−3s)/s
  2. B.
    (e−3s)/s2(e - 3s) / s^2
  3. C.
    (e−3s)/3s
  4. D.
    (e−6s)/s

Answer

A

Solution

Given : From figure the function
0;0<t<30;0< t<3
f (t )
1;3<t<∞1;3< t< ∞
Now taking Laplace transform,
L[f(t)] = ∞e^{-}^s^ᵗ⋅f(t)dt
[VISUAL / REVIEW — NO INVENTED LATEX]
L[f(t)] = ³f(t)e^{-}^s^ᵗdt+∞f(t)e^{-}^s^ᵗdt
[VISUAL / REVIEW — NO INVENTED LATEX]
L[f(t)] = ³0e^{-}^s^ᵗdt+∞1.e^{-}^s^ᵗdt
[VISUAL / REVIEW — NO INVENTED LATEX]
[]∞[]∞
L[f(t)]=0+/frac(e−st)(−s)L[f(t)] = 0+/frac{(e-st)}{(−s)}
L[f(t)]=/frac(e−∞)(−s)−/frac(e−s/times33)(−s)L[f(t)] = /frac{(e-∞)}{(−s)}-/frac{(e-s /times 33)}{(−s)}
L[f(t)]=0+/frac(e−3s)sL[f(t)] = 0+/frac{(e-3s)}{s}
L[f(t)]=/frac(e−3s)sL[f(t)] = /frac{(e-3s)}{s}
Hence, the correct option is (A).

Why review

Category: REVIEW_MATH · Priority: P2 · Disposition: extraction_defect

Extractor validation_status=low_confidence.

Suggested action: compare_pdf_and_extracted

Human review

state=UNREVIEWED · resolution=— · trust=UNRESOLVED · WAVE-12 priority=P2
Review actions

Writes a viewer overlay only. Never converts verification REVIEW into automatic PASS.

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Math review evidence

solution · REVIEW_REQUIRED · visual_fallback
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Current normalized
[VISUAL / REVIEW — NO INVENTED LATEX]
method=unicode_normalize
Resolver / candidate
[VISUAL / REVIEW — NO INVENTED LATEX]
status=not_attempted
reason=
Reason for review: mangled_solution_math_demoted
solution · REVIEW_REQUIRED · visual_fallback
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page=6 bbox=—
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03
Current normalized
[VISUAL / REVIEW — NO INVENTED LATEX]
method=unicode_normalize
Resolver / candidate
[VISUAL / REVIEW — NO INVENTED LATEX]
status=not_attempted
reason=
Reason for review: mangled_solution_math_demoted
solution · REVIEW_REQUIRED · visual_fallback
Source clip
no clip
page=6 bbox=—
asset=—
Raw text
03
Current normalized
[VISUAL / REVIEW — NO INVENTED LATEX]
method=unicode_normalize
Resolver / candidate
[VISUAL / REVIEW — NO INVENTED LATEX]
status=not_attempted
reason=
Reason for review: mangled_solution_math_demoted

Provenance status

Source PDF: GATE CH 2020 (with Solutions).pdf
SegmentPageBBoxAssetEquationLink
option_B6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
solution6——none—REVIEW
Equations:none

Dimensions

  • structurePASS
  • question_textPASS
  • optionsFAIL
  • answerPASS
  • solutionPASS
  • mathREVIEW
  • cross_entityPASS

Issues

  • option_B_operator_set_changed_raw_vs_derived
  • content_flags_math_review_required
  • solution_math_review_required
  • solution_math_no_latex_no_visual