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# GATE ME 2021: Toppers Mini Mock Quiz 1 (App update required to attempt this test)

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Question 1

In this question, a sentence has been split into 4 parts labeled as ‘a’ to ‘d’. Only one of these parts has an error. Error could be in the form of a missing word, an extra word or in grammar. Identify the part that has an error.

Question 2

Which answer figure will complete the pattern in the question figure?

Question Figure : Question 3

Choose the most appropriate alternative from the options given below to complete the following sentence:
Despite several _____ the mission succeeded in its attempt to resolve the conflict.

Question 4

Rajaram’s monthly income is distributed in 5 expense heads namely house rent, groceries, transport expenses, electricity and water expenses and finally under the head miscellaneous expenditure. After meeting these expenses, the remaining amount (which is non zero) goes towards savings which is a fixed percentage of his income every month. It is known that these amounts can be expressed as percentage of his income as 6 distinctive integers. The percentage expenses under 5 heads are 5 integers such that difference between 2 consecutive expenses is a constant. The minimum percentage of his income that he saves per month is _______.

Question 5

Given that N is a 4 digit positive integer and we plan to plant exactly N trees in a memorial park. How many distinct values of N are possible such that each row of trees planted has as many trees as the number of columns?

Question 6

Given below is information related to installed capacity and generation of electricity in India for a specific year: The closest integral value of capacity utilization for the entire country in the year under consideration is ________ %.
[Capacity utilization is the ratio of Electricity generated per hour and Installed capacity. Assume that all plants work 365 days a year for 24 hours per day].

Question 7 is

Question 8

Using Gauss- Seidel method , starting form [0,0,0]
x1+ x2 – x3 = 1,
x1+ 4x2 + x3 =15,
3x1+ 2x2+ 3x3= 20.
Find (2x3+ x2 – x1) after two iterations approximately.

Question 9

There were p pigeons and s sparrows in a cage. One fine morning m birds escaped to freedom. If the caretaker was able to figure out by only looking (not counting) into the cage that at least one pigeon had escaped, based on the knowledge that m = 7, then which of the following cannot be the value of the number of sparrows and pigeons?

Question 10

A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?

Question 11

A gas from a rigid bottle of compressed inert gas is used to inflate a balloon, originally folded completely flat to a 0.8 m3. The work interaction (in KJ) is (assume the pressure in balloon is atmospheric at all times)

Question 12

A solar collector receiving solar radiation at the rate of 0.5 KW/m2 at temperature 80 and transforms it to a fluid within heat engine. The engine rejects energy as heat at temperature of 25 . The minimum collector area (in m2 ) if the plant produces 2 KW of useful shaft power is

Question 13

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m3 flowing through a pipe. The acceleration due to gravity is 9.81 m/s2. If the manometric fluid is water (density 1000 kg/m3) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is _____ Question 14

For a gas metal arc welding using copper wire as electrode, the welding speed is 10mm/sec with a current and voltage of 150 A and 40 V. The rate of the pool formation is observed to be 400 mm /sec. If the specific melt energy is 10 J/mm The efficiency of the welding is in %.

Question 15

The work required (magnitude in KJ/kg) to compress the steam isentropically from 1 bar to 8 bar. Assume the initial state of vapour is saturated vapour. Use the following table: Question 16 For the cantilever beam as shown, the deflection at free end is given by _______.

Question 17

In the parallel-plate configuration shown, steady-flow of an incompressible Newtonian fluid is established by moving the top plate with a constant speed, U0 = 1m/s. If the force required on the top plate to support this motion is 0.75 N per unit area (in m2 ) of the plate then the viscosity of the fluid between the plates is __________ N-s/m2 Question 18

The degree of freedom of the given mechanism is __________ Question 19

If the elongation factor during rolling of an ingot is 1.56, the minimum number of passes to produce a section 180 × 180 mm from an ingot of 460 × 460 mm are

Question 20

A single degree of freedom system has a mass of 3Kg , stiffness 10 N/m and viscous damping ratio 0.the dynamic magnification factor at an excitation frequency of 1.9 rad/sec_____

Question 21

In a drawing operation the initial diameter of the blank is given as 100mm and final diameter of the blank is 50mm. Find the load required for the operation. Given = 1000 Mpa

Question 22

A 150 mm diameter shaft supporting a load of 10 kN has a speed of 1500 rpm. The shaft runs in a bearing whose length is 1.5 times the diameter. The coefficient of friction is 0.02.Heat generated due to friction in kW (upto 3 decimal places) will be

Question 23

In a rolling process, sheet of 25 mm thickness is rolled to obtain 20% reduction. Roll is of diameter 500 mm and rotates at 250 rpm. The roll strip contact length will be _____ mm.

Question 24

A fluid having kinematic viscosity 0.9 stoke is flowing through a pipe of 10 cm diameter. The flow through the pipe becomes critical at velocity(m/s) of?

Question 25

Air is enclosed inside a rigid vessel at the initial temperature 1000K and pressure 4 bar is employed as a heat source. What is the maximum work in kJ/kg that can be developed by operating a heat engine, assuming the atmospheric pressure is 1 bar and temperature is 300K.

Question 26

A long rod of 30 mm diameter, its base is placed in a furnace with a large portion of it projecting into the room air at 25°C. After steady state achieved, the temperature at two points, 120 mm apart, are found to be 125°C and 90°C respectively. The thermal conductivity of rod material is (take heat transfer coefficient between the rod surface and the surrounding air is 30 \W/m2K)

Question 27

During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is 0.5 m. The feed given to the zero degree rake angle tool is 0.25 mm/rev. The shear strain produced during the operation is____ .

Question 28

The inertia force acting on the piston for the following slider crank mechanism will be : Question 29

Equation of damping vibration is given find the natural frequency (Hz) of damped vibration.

Question 30

The horizontal and vertical hydrostatic forces Fx and Fy on the semi-circular gate, having a width ω into the plane of figure, are Question 31

A petrol engine is supplied with fuel which has a calorific value of 45000kJkg. The pressure in the cylinder at 30% and 70% of the compression stroke are 1.5bar and 2.8bar. Assuming that compression follows the law p = constant, find the compression ratio.

Question 32

A solid aluminum shaft, 5 cm diameter and 1 m long, is to be replaced by a tubular steel shaft of the same length and the same outside diameter (i.e. 5 cm), such that each of the two shaft could have the same angle of twist per unit torsional moment over the total length. Modulus of rigidity of steel is three times that of aluminium. The inner diameter of the tubular shaft is

Question 33

Find out the average life L50 of roller bearings in million revolutions when subjected to a radial force of 2500 N and axial load of 2500 N and basic dynamic capacity 22000 N.Take X=1, Y=1.( Enter the answer accurate up to two digits)

Question 34

A spherical shaped orange (k= 0.3W/m) 80mm in diameter undergoes ripening process and generates 5000W/m3 of energy. If external temperature of orange is 10℃ and it is surrounded by air having heat transfer coefficient 20W/m2-k then the maximum temperature (℃) in at the centre of orange will be

Question 35 Determine total float and independent float for activity 3-4
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