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Q15

FAILMCQpage 5holdmath reviewREVIEW_MATHP2UNREVIEWED

type=MCQ · page=5–6 · marks=1 · content_conf=0.7999999999999999 · math_conf=0.55

Original PDF5

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Source / evidence

file: GATE CH 2020 (with Solutions).pdf

pages: 5–6

assets/questions/Q015/residual_03b3980cee39.png

Extracted15 / 67

Consider the following continuously differentiable function v(x,y,

[VISUAL / REVIEW — NO INVENTED LATEX] Source math clip

Where i , jandk represent the respective unit vectors along the x ,yandz directions in the Cartesian coordinate system. The curl of this function is

Options

A.
y(11 x+16 z)
B.
$- 3 x^2 i - 8 y^2 j + 5 z(x + y) k$
C.
6 xyi−16 yz j+5 xy k
D.
$(5 xz - 8 y ²) i - 5 yz j - 3 x^2 k$

Answer

Solution

.

∇ /times V = /frac{/frac{/frac{∂}{∂x∂}}{∂y∂}}{∂z}

3x^2y_8y^2z_5xyz

∇ /times V = iˆ[5xz-8y^2]-ˆj[5yz]+kˆ[−3x^2]

∇ /times V = [5xz-8y^2]iˆ-[5yz]ˆj+[−3x^2]kˆ

Hence, the correct option is (D)

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.

ActionFieldReason

No overlay recorded yet.

Math review evidence

stem · REVIEW_REQUIRED · —

Source clip

page=5 bbox=[36,578.02,456,592.1]

asset=assets/questions/Q015/residual_03b3980cee39.png

Raw text

z)=3 x² yi+8 y² z j+5 xyz k

Current normalized

z) = 3 x^2 yi + 8 y^2 z j + 5 xyz k

method=unicode_normalize

Resolver / candidate

[VISUAL / REVIEW — NO INVENTED LATEX]

status=REVIEW

reason=fraction_bar_ambiguous

Reason for review: unmatched_paren, structure:unparsed_tail, structure:unmatched_paren, fraction_bar_ambiguous

Provenance status

Source PDF: GATE CH 2020 (with Solutions).pdf

Segment	Page	BBox	Asset	Equation	Link
stem	5	`[36,578.02,456,592.1]`	`assets/questions/Q015/residual_03b3980cee39.png`	`—`	`PASS`
option_B	5	`—`	`—`none	`—`	`REVIEW`
option_D	5	`—`	`—`none	`—`	`REVIEW`
solution	5	`—`	`—`none	`—`	`REVIEW`
solution	5	`—`	`—`none	`—`	`REVIEW`
solution	5	`—`	`—`none	`—`	`REVIEW`
solution	5	`—`	`—`none	`—`	`REVIEW`
solution	5	`—`	`—`none	`—`	`REVIEW`

Equations:none

Dimensions

structurePASS
question_textPASS
optionsFAIL
answerPASS
solutionPASS
mathREVIEW
cross_entityPASS

Issues

option_B_operator_set_changed_raw_vs_derived
option_D_operator_set_changed_raw_vs_derived
stem_math_review_required