GATE XE (Engineering Sciences) 2022 - Question 12

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Section: Engineering Mathematics | Marks: 1

Let Ξ§ ࡌ ΰ΅›π‘§ΰ΅Œπ‘₯ΰ΅…π‘–π‘¦βˆΆπ‘₯and 𝑦are real numbers, π‘–ΰ΅Œβˆšΰ΅†1 ࡟ be the set of complex numbers. Let the function π‘“αˆΊπ‘§αˆ»ΰ΅Œπ‘’αˆΊπ‘₯, π‘¦αˆ»ΰ΅…π‘– π‘£αˆΊπ‘₯, π‘¦αˆ» for π‘§ΰ΅Œπ‘₯ࡅ𝑖𝑦 Î Ξ§ be analytic in Ξ§, where π‘’αˆΊπ‘₯, π‘¦αˆ»ΰ΅Œπ‘₯ 𝑦ଷࡆ𝑦 π‘₯ΰ¬· and π‘£αˆΊπ‘₯, π‘¦αˆ»ΰ΅Œ π‘₯ΰ¬Έ 4 ΰ΅… 𝑦ସ 4 ࡆ 3 2 π‘₯ଢ𝑦ଢ. If π‘“α‡±αˆΊπ‘§αˆ» denotes the derivative of π‘“αˆΊπ‘§αˆ», then

  • A. |π‘“α‡±αˆΊΰ΅†1 ΰ΅…π‘–αˆ»|ଢࡌ1
  • B. |π‘“α‡±αˆΊΰ΅†1 ΰ΅…π‘–αˆ»|ଢࡌ7
  • C. |π‘“α‡±αˆΊΰ΅†1 ΰ΅…π‘–αˆ»|ଢࡌ8
  • D. |π‘“α‡±αˆΊΰ΅†1 ΰ΅…π‘–αˆ»|ଢࡌ10

Answer: C. |π‘“α‡±αˆΊΰ΅†1 ΰ΅…π‘–αˆ»|ଢࡌ8

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