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# GATE ME 2021 : Full Syllabus Rapid Mock-2 (App update required to attempt this test)

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Question 1

In a flywheel, Cf represents coefficient of speed fluctuation, then which among the following expression will show ratio of ωmax / ωmin:

Question 2

Which of the following statements are correct?

a) Taylor series of a function can be expanded only when f(z) is analytic about z = a

b) Laurent series of a function can be expanded even if f(z) is not analytic about z = a

c) Taylor series of a function can be expanded irrespective of f(z) is analytic or non-analytic about z = a

d) Laurent series of a function can be expanded only when f(z) is analytic about z = a

Question 3

In order to avoid tendency of separation at the throat in a Venturimeter the ratio of the diameter at throat to the diameter of pipe should be:

Question 4

Five students namely Priyanka, Mary, Asha, Sunil and Ryan are standing in a straight line. Priyanka stands ahead of Ryan. Sunil is standing between Ryan and Asha. Ryan is standing between Sunil and Mary. Who is standing first in the line?

Question 5

A pure substance at 8 MPa and 400 °C is having a specific internal energy of 2864 kJ/kg and a specific volume of 0.03432 m3/kg. Its specific enthalpy (in kJ/kg) is ______.

Question 6

Albert mixes two varieties of cocoa costing \$20/kg, \$25/kg and sells the mixture at a profit of 20% at \$28/kg. What is the approximate percentage of \$20 cocoa in the mixture?

Question 7

Three particles starts their motion from the origin at the same time, the first moves with a velocity u1 along the x-axis, the second moves along the y-axis with a velocity u2 and the third along the straight line y = x. Then, the velocity of the third particle so that all the three always lie on the same line is -

Question 8

Select the set of letters that when sequentially placed in the blanks of the given letter series will complete the series.

ST _ _ S _ OPS _ _P

Question 9

If then is

Question 10

An ideal gas goes through the cycle (1-2-3-4-1) given in the figure. What is the value of (V2 – V3)?

Question 11

There are 3 fair coins and 1 false coin with tails on both sides. A coin is chosen at random and tossed 4 times. If ‘tails’ occurs in all 4 times, then the probability that the false coin has been chosen for tossing is ___.

Question 12

A solar collector having an area of 80 m2 receives solar radiation and transforms it to the internal energy of fluid at an overall efficiency (η) of 50%. Now this high energy fluid is supplied to a heat engine having an efficiency of 40%. If the heat rejected to sink is 30kW. Then power developed by the engine (in kW) and irradiation to solar collector (in kw/m2) respectively are __________.

Question 13

An orthogonal turning operation is carried out under the following conditions: rake angle = 5 ° and Chip thickness ratio is given 0.6. The shear angle (in degrees) in this turning process is_______

Question 14

The integral is evaluated along the circle traversed in counter clockwise direction. The integral is equal to

Question 15

The length of the fixed link of a crank and slotted lever mechanism is 250 mm and that of the crank is 100 mm. If the length of the slotted lever is 450 mm then the length of the stroke of the shaper is ______ (mm)

Question 16

Laminar boundary layer flow past the square plate arrangements is shown in figure. Comparing to the friction drag of a single plate (1), how much larger is the drag of four plates together as in configurations (2) Question 17

The annual demand of the company is the 10000 units per year. The ordering cost per order is Rs 100 per year and the carrying cost is Rs10 per unit per year and the shortage is allowed. The shortage cost is Rs 5 per unit per year. Maximum inventory is_______.

Question 18

A fluid having density ρ is flowing with inlet velocity V through a uniformly varying pipe bend at right angle as shown in the figure. The inlet cross-section area of the pipe is twice the outlet cross-section area. If the pressure P at both the ends is same, then the angle made by the resultant force exerted on the pipe bend with the horizontal is Question 19

At a cross section of a beam,the maximum compressive stress at top is 800 kg/cm2 and the maximum tensile stress at bottom is 200 kg/cm2.The depth of cross section is 10 cm.The depth of neutral axis from the top of the section is x.Then x is equal to _______.

Question 20

A body is placed on a frictionless horizontal plane. The body is connected with an elastic spring which is initially unstretched. The plane is then gradually lifted from 0 º to 90 º then the curve between extension of spring Δl and angle of inclination θ is– Question 21

In the sentence, identify the segment which contains the grammatical error. If the sentence has no error, then select 'No error'.
Boston was found in 1630 by Puritan colonists from England.

Question 22

A rectangular hole of size 150mm X 60mm is to be made on a 8 mm thick sheet having ultimate tensile strength and shear strength of 500MPa & 300MPa respectively. The punching force required (in KN) is__________.

Question 23

A uniform meter stick of mass M is hinged at one end and supported in a horizontal position by a string attached to the other end as shown in figure. If the string is cut, then the initial angular acceleration of the stick is- Question 24

A vapor power cycle is being considered. Steam enters boiler at 8.4MPa, but unlike ideal boiler, steam leaves it at 8MPa and 5000C. Because of losses in the pipeline, steam enters the Turbine at 7.5MPa, 4500C. Turbine expands it to 10kPa.

Properties of the steam, at different locations of the cycle is given, in the table. Efficiency of the cycle is ______%. [Neglect the pump work]

Question 25

A cantilever beam of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. what is the bending moment at fixed end?

Question 26

The principal stresses at a point inside a solid object are σ1 = 100 MPa, σ2 = 100 MPa and σ3 = 0MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca theory is nT and the factor of safety calculated using Von-Mises theory is nV. Which one of the following relations is TRUE?

Question 27

Stream of mass flow rate 0.4Kg/s, relative humidity of 30% and DBT 28 is mixed adiabatically with stream of mass flow rate 0.3kg/s, relative humidity of 40% and DBT 33 , mixed air is sensibly cooled to 23 .

Take total pressure of 100KPa is assumed to be constant throughout the process, saturation pressure at 28 as 3.783 KPa, Saturation pressure at 33 as 5.03 KPa, Saturation pressure at 23 as 2.81 Kpa.

Find final relative humidity ____________%

Question 28

Using the Clausius–Clapeyron equation find the enthalpy of vaporization(in kJ/kg). The following data is given:  At 200°C, vg=0.1275 m3/kg  and V= 0.001157 m3/kg and change of pressure with respect to temperature .

Question 29

The given eigen values of the following matrix are represented by and  The value of is ___.

Question 30

Select the word which means the same as the group of words given.

A person who attracts attention with a flashy style

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