GATE ME topic:mechanics PYQs & Answers — Page 97

Questions 961–970 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 97 of 104

Consider the matrix

. Which one of the following statements about P is INCORRECT?

Your answerChoose one option.

Determinant of P is equal to 1.

P is orthogonal.

Inverse of P is equal to its transpose.

All eigenvalues of P are real numbers.

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The surface integral

over the surface

of the sphere

, where

and

is the unit outward surface normal, yields____________

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For the vector

, the value of

is ______.

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Consider the differential equation

with initial conditions

and

. The value of

is ________.

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A parametric curve defined by

in the range

is rotated about the X- axis by 360 degrees. Area of the surface generated is

Your answerChoose one option.

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Consider the matrix

whose eigenvectors corresponding to eigenvalues

and

are

and

, respectively. The value of

is ________.

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P (0, 3), Q (0.5, 4), and R (1, 5) are the three points on the curve defined by

. Numerical integration is carried out using both Trapezoidal rule and Simpson’s rule within limits

and

for the curve. The difference between the two results will be

Your answerChoose one option.

0.25

0.5

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is a complex analytic function of

, where

, then

Your answerChoose one option.

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The velocity profile inside the boundary layer for flow over a flat plate is given as

, where

is the free stream velocity and

is the local boundary layer thickness. If

is the local displacement thickness, the value of

Your answerChoose one option.

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Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s²) of point P of the block with respect to fixed point O is ________.

Diagram for Mechanical Engineering question 30

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GATE ME topic:mechanics PYQs

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Question 30

Question 30