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# GATE ME 2021 : Full Syllabus Rapid Mock-1 (App update required to attempt this test)

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Question 1

A box contains tags marked 1, 2 ....... 100. Two tags are chosen at random without replacement. The probability that the numbers on the tags will be consecutive integers is _______.

Question 2

Munendra is flying an areoplane named Lufthansa Airlines. He flew it 300km in the east direction and took left turn and flew 700km. Again he took left turn and flew 400km. Now Munendra is flying his areoplane in which direction?

Question 3

For matrix the eigen value corresponding to the eigen vector [] is

Question 4

A system will be thermodynamic equilibrium only if it is in __________.

A) Thermal equilibrium

B) Mechanical equilibrium

C) Chemical equilibrium

A) Thermal equilibrium

B) Mechanical equilibrium

C) Chemical equilibrium

Question 5

The poisson’s ratio of for a perfectly incompressible linear elastic material is

Question 6

Cinsider the 2-D steady flow field

V=(2xy-5y^{2})i+(4x^{2}+3xy)j

The number of stagnation points in the flow field is

Question 7

The fit on a hole shaft basic system is specified as H7-q5 then this fit belongs to

Question 8

If the conjugate of a complex number is then that complex number is

Question 9

**In the sentence, identify the segment which contains the grammatical error. If the sentence has no error, then select 'No error'.**

Although he studied regularly, his marks didn't improving.

Question 10

Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If

*D*_{1}and*D*_{2}are the diameters of the inner and outer tubes respectively, then the view factor*F*_{22}is given byQuestion 11

A man can row at 5 km/h in still water. If the river is flowing at 1 km/h, it takes him 75 min to row to a place and back. How far is the place?

Question 12

Two pipes of length 2500 m each and diameters 80 cm and 60 cm respectively, are connected in parallel. The coefficient of friction for each pipe is 0.006 . The total flow is equal to 250 liters/s, the rate of flow (in liters/s) in larger pipe is _______.

Question 13

Two castings of the same metal have the same surface area. One castings is in the form of a sphere and the other is a cube. What is the ratio of the solidification time for the sphere to that of the cube?

Question 14

The free body diagram of member AB is :-

Question 15

Mohan and Ramesh working together do a piece of work in 20 days. Mohan alone can do it in 28 days. Ramesh alone will do the work in

Question 16

In an industrial application, FEA analysis was integrated with failure theories to design materials. So the equation derived or used for safe design is;

Question 17

A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:

If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of the activity S without delaying the completion of the project is ___________

Question 18

The following table showing the percentage of the total population of a state in different age groups.

Out of every 50,000 people, find the approximate number of persons below the age of 35?

Question 19

In an ideal VCR cycle of used R- 134A as refrigerant used as a heat pump. The enthalpy at inlet to compressor and exit of compressor are 110kJ/kg and 235kJ/kg respectively. The enthalpy at exit of condenser is 95kJ/kg. If work input to compressor in 5kW then calculate rate of heat extraction from evaporator(kW) and COP of heat pump.

Question 20

In compressor of a Refrigerator, air enters in the axial flow compressor & leaves the compressor axially. Calculate the degree of reaction, if the component of air responsible for whirl is leaving the compressor at one-third the average blade velocity of rotor if the flow velocity at inlet and outlet remain same.

Question 21

2 kg of air initially at 7 bar pressure and 400 K expands polytropically (PV

^{1.2}= Constant) until the pressure is reduced to one-fifth value.The change in entropy (in kJ/K ) is _____. (Take R= 0.287 kJ/kgK and γ=1.4)Question 22

A 20° full depth involute system have a pinion of diameter 300 mm and number of teeth on pinion is 60. If the length of line of action is 20 mm, then the contact ratio is _______.

Question 23

The radius of gyration of a double symmetric cross-section pinned-pinned column is 350mm. The distance between two point of contraflexure along its length is 10m. The slenderness ratio of the given column is _____.(correct to two decimal place)

Question 24

Solution of y dx − x dy = x

^{2}y dx isQuestion 25

P is an orthogonal matrix and A is a periodic matrix with period 4 and Q=PAP

^{T}. If P^{T}Q^{2003}P is equal to A^{a}, then the value of ‘a’ is _________.Question 26

A flywheel of moment of inertia 9.8 kg m

^{2}fluctuates by 30 rpm, if the fluctuation in the speed is not to exceed ±3%, Then the mean angular speed of the flywheel is. Take ∆E = 3 kJQuestion 27

A machine tool company decides to make four sub-assemblies through three contractors differing in efficiency. Given below are the estimates of the time in hours matrix. The minimum time in minutes is?

Question 28

Steam flows at the rate of 5 at a particular section in a reaction turbine where the diameter of blade is 2m and the velocity of flow is 6m/s. What is the blade height of section _________mm.

Question 29

For a vibration system, equation of motion is given as

The value of frequency of damped vibration is __________ (in rad/s).

The value of frequency of damped vibration is __________ (in rad/s).

Question 30

A block moves horizontally on a smooth surface with a speed of 40 m/s break into two equal parts move continuing in same direction. If one of the parts moves with 50 m/s velocity then fractional change in kinetic energy is

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