Match the vector calculus expressions in List-I with their values in List-II: List-I (A) The unit normal to the surface x 3 - xyz + z 3 = 1 at (1, 1, 1) (B) If φ = y x 2 + y 2 , then (∇φ)| (1,0) = (C) If F⃗ = x 2 î + 2z 2 ĵ - 3y 2 k̂, then (∇ × F⃗)| (0,-1,-1) = (D) If φ = y x 2 + y 2 , then (∇φ)| (0,1) × î = List-II (I) k̂ (II) ĵ (III) 10 î (IV) 1 3 (2 î - ĵ + 2 k̂)

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Mathematics · Vector Calculus

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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(A) - (IV), (B) - (II), (C) - (III), (D) - (I)

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Answer 1

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Answer 2

(A) - (IV), (B) - (II), (C) - (I), (D) - (III)

Answer 3

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

Answer 4

(A) - (IV), (B) - (II), (C) - (III), (D) - (I)

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