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Civil Engineering (CE)  >  GATE Mechanical (ME) 2023 Mock Test Series  >  Test: Partial Derivatives, Gradient- 1 Download as PDF

Test: Partial Derivatives, Gradient- 1


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20 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | Test: Partial Derivatives, Gradient- 1

Test: Partial Derivatives, Gradient- 1 for Civil Engineering (CE) 2023 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The Test: Partial Derivatives, Gradient- 1 questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Partial Derivatives, Gradient- 1 MCQs are made for Civil Engineering (CE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Partial Derivatives, Gradient- 1 below.
Solutions of Test: Partial Derivatives, Gradient- 1 questions in English are available as part of our GATE Mechanical (ME) 2023 Mock Test Series for Civil Engineering (CE) & Test: Partial Derivatives, Gradient- 1 solutions in Hindi for GATE Mechanical (ME) 2023 Mock Test Series course. Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Attempt Test: Partial Derivatives, Gradient- 1 | 20 questions in 60 minutes | Mock test for Civil Engineering (CE) preparation | Free important questions MCQ to study GATE Mechanical (ME) 2023 Mock Test Series for Civil Engineering (CE) Exam | Download free PDF with solutions
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Test: Partial Derivatives, Gradient- 1 - Question 1
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Consider the function f(x) = x2 – x – 2. The maximum value of f(x) in the closed interval [–4, 4] is 

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∴ f (x )has minimum at x= 1 / 2 It Shows that a maximum value that will be at x = 4  or x = - 4 

At x = 4, f (x )= 10

∴ At x= −4, f (x ) = 18

∴ At x= −4, f (x ) has a maximum.

Test: Partial Derivatives, Gradient- 1 - Question 2
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Test: Partial Derivatives, Gradient- 1 - Question 3
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Test: Partial Derivatives, Gradient- 1 - Question 4
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The function f(x) = x3- 6x2+ 9x+25 has 
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Test: Partial Derivatives, Gradient- 1 - Question 5
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The function f(x,y) = 2x2 +2xy – y3 has 
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Test: Partial Derivatives, Gradient- 1 - Question 6
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Equation of the line normal to function f(x) = (x-8)2/3+1 at P(0,5) is  
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Test: Partial Derivatives, Gradient- 1 - Question 7
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The distance between the origin and the point nearest to it on the surface z2 = 1 + xy is 
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or pr – q2 = 4 – 1 = 3 > 0 and r = +ve

 

so f(xy) is minimum at (0,0)

 

Hence, minimum value of d2 at (0,0)

 

d2 = x2 + y2 + xy + 1 = (0)2 + (0)2 + (0)(0) + 1 = 1

 

Then the nearest point is

 

z2 = 1 + xy = 1+ (0)(0) = 1

 

or z = 1

Test: Partial Derivatives, Gradient- 1 - Question 8
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Given a function 

The optimal value of f(x, y)
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Test: Partial Derivatives, Gradient- 1 - Question 9
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For the function f(x) = x2e-x, the maximum occurs when x is equal to 
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Test: Partial Derivatives, Gradient- 1 - Question 10
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A cubic polynomial with real coefficients  
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So maximum two extrema and three zero crossing  

Test: Partial Derivatives, Gradient- 1 - Question 11
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Given y = x2 + 2x + 10, the value of 

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Test: Partial Derivatives, Gradient- 1 - Question 12
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Consider the function y = x2 – 6x + 9. The maximum value of y obtained when x varies over the interval 2 to 5 is  
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Test: Partial Derivatives, Gradient- 1 - Question 13
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Consider the function y = x2 – 6x + 9. The maximum value of y obtained when x varies over the interval 2 to 5 is  
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Correct Answer :- b

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Test: Partial Derivatives, Gradient- 1 - Question 15
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The magnitude of the gradient of the function f = xyz3 at (1,0,2) is 
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Test: Partial Derivatives, Gradient- 1 - Question 16
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The expression curl (grad f), where f is a scalar function, is  
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Test: Partial Derivatives, Gradient- 1 - Question 17
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If the velocity vector in a two – dimensional flow field is given by    the  vorticity vector, curl  

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Test: Partial Derivatives, Gradient- 1 - Question 18
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The vector field 

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Test: Partial Derivatives, Gradient- 1 - Question 19
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The angle between two unit-magnitude co-planar vectors P (0.866, 0.500, 0) and Q (0.259, 0.966, 0) will be 
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Test: Partial Derivatives, Gradient- 1 - Question 20
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Stokes theorem connects  
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