GATE ME kind:question PYQs & Answers — Page 5

Questions 41–50 of 1040. Imported answers require independent review unless marked reviewed.

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

Diagram for Mechanical Engineering question 41

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A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young’s modulus of the material of the beam is 200 GPa and moment of inertia of the beam is

. The natural frequency of the beam in rad/s is

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A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat transfer coefficient for both the fins. If the diameter of the circular fin is equal to the side length of the square fin, then the ratio of heat transfer rates before and after the replacement is

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For an ideal regenerative Rankine cycle, as shown in the figure below, which one of the following options is the correct representation of temperature-entropy (T-s) diagram?

Diagram for Mechanical Engineering question 44

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Consider the Euler variables of polyhedral objects namely, P1, P2, P3, and P4 as given in the table below.

Polyhedral objects	Faces (F)	Edges (E)	Vertices (V)	Bodies (B)
P1	6	12	8	1
P2	5	8	5	1
P3	5	12	8	1
P4	10	24	16	1

Which one of the following options is NOT a topological valid closed polyhedral object as per Euler’s law?

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An objective function

of primal variables (

and

) is described below:

Minimize

subject to

is the objective function of the dual of

, and

represent the corresponding dual variables.

Which one of the following options represents the correct form of

Your answerChoose one option.

Maximize

subject to

Maximize

subject to

Maximize

subject to

Maximize

subject to

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Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given in the table below.

Job	Due date	Work remaining (in days)
M	26	5
N	24	10
O	28	10
P	31	5

Which job(s) has/have critical ratio less than unity?

Your answerChoose one option.

Job N and Job O

Job M and Job N

Job P

Job O and Job P

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A block of 50 kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is 0.3. Neglecting pulley friction, the minimum value of M required to start the upward motion of the block is ______ kg (rounded off to 1 decimal place).

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A simply supported beam is subjected to an external point load

as shown in the figure below. The beam has a rectangular cross-section of 20 mm × 45 mm. A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is 3 MPa. Neglecting the mass of the beam, the magnitude of the applied load is ______ kN (rounded off to 1 decimal place).

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A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a given instant is 6 m/s. At that instant, the magnitude of absolute velocity of the midpoint G is ______ m/s (rounded off to 2 decimal places).

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GATE ME kind:question PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50