GATE XE format:mcq PYQs & Answers — Page 5

Questions 41–50 of 959. Imported answers require independent review unless marked reviewed.

One column with square cross section of side

and another column with rectangular cross section of breadth

and width

(

) are made from the same material. Both the columns have one end fixed, and the other end is free. They are subjected to axial loads along the centroidal axis.

Consider the area of cross sections of both the columns to be the same. The minimum critical Euler buckling loads of the columns with rectangular and square cross-sections are

and

, respectively.

Then

is _____.

Your answerChoose one option.

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Two prismatic rods of identical lengths are designed for the same strain energy density when subjected to the same axial load. One of the rods is made of steel (Young’s modulus = 210 GPa) and the other is made of aluminum (Young’s modulus = 70 GPa).

If the diameter of the aluminum rod is 70 mm, then which one of the following options corresponds to the diameter of the steel rod in mm?

Your answerChoose one option.

53.19

210

29.13

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A spring of stiffness

is connected to the center of a homogeneous right circular cylinder of radius

placed on a horizontal surface as shown in the figure. The cylinder is assumed to be rolling without slipping.

Considering small amplitude of oscillation, which one of the following options is the CORRECT natural frequency of the system?

Diagram for Engineering Sciences question 79

Your answerChoose one option.

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A 2D stress state of pure shear is shown in the figure.

Diagram for Engineering Sciences question 80

Which one of the following options is equivalent to the given stress state?

Figures are not to scale.

Your answerChoose one option.

Diagram for Engineering Sciences question 80 (figure 2)

Diagram for Engineering Sciences question 80 (figure 3)

Diagram for Engineering Sciences question 80 (figure 4)

Diagram for Engineering Sciences question 80 (figure 5)

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The point Q of a thin rigid equilateral triangular plate PQR is constrained to move in a horizontal channel. Point P of the same plate is constrained to move in the vertical channel as shown in the figure. The length of the side PQ is 4 m.

At the instant when the angle

rad and the velocity of point Q in the positive x direction is 20 m/s, which one of the following options is the magnitude of the angular velocity vector of the line SR on the plate in rad/s?

Diagram for Engineering Sciences question 81

Your answerChoose one option.

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Consider any substance whose mass specific heat capacity at constant pressure and mass specific heat capacity at constant volume are

and

, respectively. If the gas constant is

, which ONE of the following relations is CORRECT for the substance at all conditions?

Your answerChoose one option.

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Consider a mixture of ideal gases: nitrogen (N₂) and carbon-dioxide (CO₂), at 25 °C and 101 kPa. The molar mass of N₂ is 28 kg/kmol and the molar mass of CO₂ is 44 kg/kmol. If the molar mass of the mixture is 34 kg/kmol, which ONE of the following mixture compositions is possible?

Your answerChoose one option.

62.5% N₂ and 37.5% CO₂ by mass

62.5% N₂ and 37.5% CO₂ by volume

37.5% N₂ and 62.5% CO₂ by mass

37.5% N₂ and 62.5% CO₂ by volume

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In a mixing chamber hot water enters at a temperature of 80 °C with a flow rate of 0.5 kg/s. From another entry, cold water enters the chamber at 20 °C. The desired temperature after mixing at the exit of the chamber is 40 °C. There is no water leakage and the mixing happens at adiabatic conditions. Assume the specific heat capacity of water is 4.2 kJ/kg-K. For a steady state operation, the mass flow rate (in kg/s) of the cold-water stream is

Your answerChoose one option.

2.0

1.5

1.0

0.5

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Which ONE of the following statements is CORRECT?

Your answerChoose one option.

For an ideal gas, specific enthalpy (

) is a function of both temperature and pressure.

Internal energy (

), entropy (

), and enthalpy (

) are path functions.

Heat transferred (

) and work done (

) are state (point) functions.

Temperature (

), pressure (

), and specific volume (

) are intensive properties.

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A mixture of carbon-dioxide (CO₂), nitrogen (N₂) and oxygen (O₂) are introduced in a rigid and impermeable tank containing only liquid water (H₂O). Assume that the components are non-reacting and un-dissociated. The system is kept isolated till an equilibrium is achieved, where only two phases are present. The degrees-of-freedom of the equilibrium mixture, as obtained from the phase rule, is

Your answerChoose one option.

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GATE XE format:mcq PYQs

Question 77

Question 78

Question 79

Question 80

Question 81

Question 88

Question 89

Question 90

Question 91

Question 92