Partial Derivatives MCQ Quiz in తెలుగు - Objective Question with Answer for Partial Derivatives - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Last updated on Mar 16, 2025

పొందండి Partial Derivatives సమాధానాలు మరియు వివరణాత్మక పరిష్కారాలతో బహుళ ఎంపిక ప్రశ్నలు (MCQ క్విజ్). వీటిని ఉచితంగా డౌన్‌లోడ్ చేసుకోండి Partial Derivatives MCQ క్విజ్ Pdf మరియు బ్యాంకింగ్, SSC, రైల్వే, UPSC, స్టేట్ PSC వంటి మీ రాబోయే పరీక్షల కోసం సిద్ధం చేయండి.

Latest Partial Derivatives MCQ Objective Questions

Partial Derivatives Question 1:

यदि u = exyz, तब \(\rm \frac{\partial^3 u}{\partial x \partial y \partial z}\) पर (1, 1, 1) _____ है।

  1. 5e
  2. 3e
  3. 2e
  4. 4e

Answer (Detailed Solution Below)

Option 1 : 5e

Partial Derivatives Question 1 Detailed Solution

\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)

\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)

\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)

= xy(xz)exyz + xexyz

\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)

\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)

= (1 + 3xyz + x2y2z2) exyz

x, y, z = 1, 1, 1 रखने पर हमें प्राप्त होता है

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (1 + 3 + 1) e\)

= 5e

Top Partial Derivatives MCQ Objective Questions

Partial Derivatives Question 2:

यदि u = exyz, तब \(\rm \frac{\partial^3 u}{\partial x \partial y \partial z}\) पर (1, 1, 1) _____ है।

  1. 5e
  2. 3e
  3. 2e
  4. 4e

Answer (Detailed Solution Below)

Option 1 : 5e

Partial Derivatives Question 2 Detailed Solution

\(\rm \frac{\partial u}{\partial z} = xye^{xyz}\)

\(\rm \frac{\partial }{\partial y} \left( \rm \frac{\partial u}{\partial z} \right)= \rm \frac{\partial }{\partial y}(xye^{xyz})\)

\(\rm \frac{\partial^2 u}{\partial y \partial z} = xy \rm \frac{\partial }{\partial y}(e^{xyz}) + e^{xyz} \rm \frac{\partial }{\partial y}(xy)\)

= xy(xz)exyz + xexyz

\(\rm \frac{\partial }{\partial x} \left(\frac{\partial^2 u}{\partial y \partial z} \right) = \rm \frac{\partial }{\partial x}(x^2 yz + x) e^{xyz}\)

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (x^2 yz + x) yze^{xyz} + e^{xyz} (2xyz + 1)\)

\(\rm = e^{xyz} (x^2 y^2 z^2 + xyz + 2xyz + 1)\)

= (1 + 3xyz + x2y2z2) exyz

x, y, z = 1, 1, 1 रखने पर हमें प्राप्त होता है

\(\rm \frac{\partial^3 u}{\partial x \partial y \partial z} = (1 + 3 + 1) e\)

= 5e

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