GATE ME topic:manufacturing PYQs & Answers — Page 81

Questions 801–810 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 81 of 104

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all three balls are red is

Your answerChoose one option.

1/72

1/55

1/36

1/27

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The Fourier cosine series for an even function

is given by

The value of the coefficient

for the function

Your answerChoose one option.

−0.5

0.0

0.5

1.0

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The rank of the matrix

Your answerChoose one option.

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The divergence of the vector field

Your answerChoose one option.

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According to the Mean Value Theorem, for a continuous function f (x) in the interval [a, b], there exists a value ξ in this interval such that

Your answerChoose one option.

f (ξ)(b − a)

f (b)(ξ − a)

f (a)(b − ξ)

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Consider a function

which depends on position

and time

. The partial differential equation

is known as the

Your answerChoose one option.

Wave equation

Heat equation

Laplace’s equation

Elasticity equation

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F (z) is a function of the complex variable z = x + iy given by

For what value of k will F (z) satisfy the Cauchy-Riemann equations?

Your answerChoose one option.

−1

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is the solution of the differential equation

, the value of

Your answerChoose one option.

−2

−1

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A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

Diagram for Mechanical Engineering question 5

The tensions in the strings are

Your answerChoose one option.

T₁ = 100 N and T₂ = 0 N

T₁ = 0 N and T₂ = 100 N

T₁ = 75 N and T₂ = 25 N

T₁ = 25 N and T₂ = 75 N

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The minimum axial compressive load,

, required to initiate buckling for a pinned-pinned slender column with bending stiffness

and length

Your answerChoose one option.

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GATE ME topic:manufacturing PYQs

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