GATE ME year:2022 PYQs & Answers — Page 10

Questions 91–100 of 130. Imported answers require independent review unless marked reviewed.

The system of linear equations in real

given by

involves a real parameter

and has infinitely many non-trivial solutions for special value(s) of

. Which one or more among the following options is/are non-trivial solution(s) of

for such special value(s) of

Your answerSelect all correct options. You can choose more than one.

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A is a

real matrix of rank 2. For the set of homogeneous equations

, where

is a zero vector and

is a vector of unknown variables, which of the following is/are true?

Your answerSelect all correct options. You can choose more than one.

The given set of equations will have a unique solution.

The given set of equations will be satisfied by a zero vector of appropriate size.

The given set of equations will have infinitely many solutions.

The given set of equations will have many but a finite number of solutions.

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Let a random variable

follow Poisson distribution such that

The value of

is __________ (round off to 2 decimal places).

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The lengths of members BC and CE in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude

are applied as shown, each at the mid-length of the respective member on which it acts. Which one or more of the following members do not carry any load (force)?

Diagram for Mechanical Engineering question 47

Your answerSelect all correct options. You can choose more than one.

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Consider two vectors:

Magnitude of the component of

orthogonal to

in the plane containing the vectors

and

is _________ (round off to 2 decimal places).

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If the sum and product of eigenvalues of a

real matrix

are 4 and

respectively, then

is _____ (in integer).

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A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________ kN (in integer).

Diagram for Mechanical Engineering question 49

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Given

is a circle of radius 2 with the centre at the origin. If the contour

is traversed anticlockwise, then the value of the integral

is _______ (round off to one decimal place).

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Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A vertical force

acts on the pin R as shown. When the included angle

, the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At

, impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P (

) is _________ (round off to two decimal places).

Diagram for Mechanical Engineering question 50

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A shaft of length

is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is

and the external diameter of the rim is

, as shown in the figure. The modulus of rigidity of the core and rim materials are

and

, respectively. It is given that

and

. When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be

and

, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio

is _____ (round off to 2 decimal places).

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GATE ME year:2022 PYQs

Question 46

Question 46

Question 47

Question 47

Question 48

Question 48

Question 49

Question 49

Question 50

Question 50