GATE MT exam:gate PYQs & Answers — Page 51

Questions 501–510 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 51 of 65

A 50 cm long rod is placed against a vertical wall such that the bottom of the rod is 30 cm away from the wall. If the bottom of the rod is pulled horizontally away from the wall at 4 cm.s⁻¹, the top of the rod starts sliding down the wall with an instantaneous velocity (in cm.s⁻¹, rounded off to two decimal places) of magnitude _____________.

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The probability of solving a problem by Student A is (1/3), and the probability of solving the same problem by Student B is (2/5). The probability (rounded off to two decimal places) that at least one of the students solves the problem is _____________.

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Numerical value of work done (rounded off to the nearest integer) by a position-dependent force

(where

and

are unit vectors) along the path,

, from (0,0) to (2,2) in the xy plane is _____________.

Diagram for Metallurgical Engineering question 38

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The estimated value of the cube root of 37 (rounded off to two decimal places) obtained from the Newton-Raphson method after two iterations (x₂) is _____________.

[Start with an initial guess value of x₀ = 1].

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The partial pressure of zinc (in torr, rounded off to two decimal places) in equilibrium with liquid lead containing 0.03 mole % zinc at 900 K is _____________.

Given: Vapour pressure of pure zinc (

) at 900 K is 0.027 atm. Henry’s law coefficient (

) for zinc at infinite dilute solution in lead on Raoultian scale is 8.55.

1 torr = 1.316 × 10⁻³ atm.

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Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:

Here, T is the temperature and r is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in W.m⁻¹, rounded off to the nearest integer) is _____________.

Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (k) = 2 W.m⁻¹.K⁻¹.

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A 50 mm (diameter) sphere of solid nickel is oxidized in a gas mixture containing 60% argon and 40% oxygen by volume. The rate of oxidation of nickel is controlled by the rate of transport of oxygen through the concentration boundary layer. The rate of oxidation (in moles of nickel per minute (mol/min), rounded off to two decimal places) is ________.

Given: Total pressure = 1 atm, Temperature = 1173 K; Concentration of oxygen at the surface of the solid = 0; Boundary layer mass transfer coefficient = 0.03

; Universal gas constant,

= 8.205

. Assume ideal gas behavior.

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Equilibrium concentration of dissolved nitrogen (in wt.%, rounded off to three decimal places) in pure liquid iron, exposed to atmospheric air at 1873 K, is ________.

Given: Sieverts’ law constant as a function of temperature (

; in Kelvin) is

where

has the dimension of

. Assume

, where

is the activity of nitrogen with respect to 1 wt.% Henrian standard state.

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Pressure drop in the granular zone of a blast furnace is 300 mm of water per meter of the bed height. The bed permeability is 0.8

. The volumetric flow rate of gas per unit area through the bed [in

, rounded off to the nearest integer] is ________.

Assume Darcy’s law is applicable and

. Density of water = 1000

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A blast furnace charged with hematite containing 90 wt.% Fe

produces liquid iron with 3.6 wt.% carbon. Coke containing 90 wt.% carbon is charged at a rate of 500 kg per Metric ton of liquid iron produced. The blast furnace top gas contains (by volume), 22% CO, 18% CO

, and balance nitrogen. The volume of the blast furnace top gas [in m

(NP), rounded off to the nearest integer] is ________.

Given: Assume ideal gas behavior, and molar volume of the gas at NP is 22.4 liter.

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GATE MT exam:gate PYQs

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

Question 44

Question 45