GATE ME 2021 : Full Syllabus Rapid Mock-3 (App update required to attempt this test) for ESE & GATE ME Exams

Question 1

If

then

will be:

Question 2

A 40 mm diameter rod is to be turned on a lathe at a cutting speed of 30 m/min. The required spindle speed should be approximately:

Question 3

The condition for which the eigen values of the matrix

are positive, is

Question 4

A large number of bullets are fired in all directions with the same speed v from ground. What is the maximum area on the ground on which these bullets will spread (height of gun from ground assume negligible)-

Question 5

Match List I (Statement) with List II (Its Reason)and select the correct answer using the code given below the Lists:

Question 6

A and B can complete a piece of work in 8 days, B and C can do it in 12 days. C and A can do it in 8 days. A, B and C together can complete it in

Question 7

The percentage of metals in a mine of aluminium ore is 80%. Now the percentage of metal A is

of metals and rest is aluminium. If the mass of ore extracted from this mine is 12000 kg, the mass (in kg ) of aluminium is :

Question 8

For a constrained kinematic mechanism have 6 binary links and no higher pair. This kinematic chain have a Degree of Freedom as 1. Find the number of binary joints.

Question 9

A 100 mm × 50 mm × 50 mm steel bar free to expand is heated from 15 °C to 40 °C. What kind of stress shall be developed?

Question 10

A fair coin is tossed independently five times. The probability of the event "the number of times tails show up is less than the number of times heads show up” is

Question 11

A copper bar of 25 cm length is fixed by means of supports at its ends. Supports can yield (total) by 0.01 cm. If the temperature of the bar is raised by 100 °C, then the stress induced in the bar for if α_c = 20×10^-6/°C and E_c = 0.5×10⁵ MPa will be

Question 12

In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity

The deflection and slope of the beam at Q are respectively ___________?

Question 13

For a canteen, the actual demand for disposable cups was 500 units in January and 600 units in February. The forecast for the month of January was 400 units. The forecast for the month of March considering smoothing coefficient as 0.75 is _________

Question 14

A Gas turbine power plant is under consideration. Inlet to the pump is at 300K. Pressure ratio is Maximum temperature reached in the cycle is 1500K. Air flow rate is 4 kg/s. The power output of the turbine is _______kW. [Assume γ=1.4 and C_p = 1kJ/kg-K]

Question 15

A gas turbine power plant operates between temperature limits of 300K and 1300K employing a fuel whose specific heat is 1.012kJ/kg-K. What is the maximum work obtainable per kg of fuel in a cycle?

Question 16

A vapor power cycle is being considered. Steam enters condenser at 10 kPa. There are some losses in the condenser. Steam exits condenser at 8kPa, 30⁰C. This steam is compressed to 8.5MPa with the help of a non-ideal compressor. Efficiency of the compressor is 90%. Steam is flowing at the rate 1kg/s. Property of the steam is provided:

The amount of the power expended at compressor is,

Question 17

Select the most appropriate synonym of the given word.

PUCKER

Question 18

The maximum possible blade efficiency of a single stage impulse turbine is 80% and velocity coefficient of blade is 0.85. If inlet and outlet blade angles of turbine are 30 ° and 40 ° then the nozzle angle (in degree) will be:

Question 19

The voltage length characteristic of a direct current (dc) arc is given by
V = (20 + 40 L) Watts
Where, L is the length of the arc in cm. The power source characteristic is approximated by a straight line with an open circuit voltage = 80 V and a short circuit current = 1000 amp. The optimum arc length is _________ (in cm).

Question 20

The area of the plane region bounded by the curves and x+3y²=1 is equal to ____ sq. units.

Question 21

Match the List-1 with List-2 and select the correct answer using the codes given below (where n – factor of safety)

Question 22

In a heat exchanger, the hot liquid enters with a temperature of 200 °C and leaves at 180 °C. The cooling fluid enters at 50 °C and leaves at 130 °C. The capacity ratio of the heat exchanger is __________.

Question 23

In the sentence, identify the segment which contains the grammatical error.

When Carol made tactless remarks at work, her manager send her to a sensitivity workshop.

Question 24

Water (p = 1000 kg/m³) flows through a venturimeter with inlet diameter 80 mm and throat diameter 40 mm. The inlet and throat gauge pressures are measured to be 400 kPa and 130 kPa respectively. Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in m/s) is

Question 25

In Orthogonal turning of medium carbon steel, the specific machining energy is 8.0 J/mm³the cutting velocity, feed and depth of cut are 120 m/min, 0.6 mm/rev and 6 mm respectively. The main cutting force in N is

Question 26

Two blocks of iron and copper, both initially at 80^oC, are dropped into a large lake at 15^oC. The mass of the iron and copper blocks are 50kg and 20kg respectively. After a while the system is in thermal equilibrium due to heat transfer between the blocks and the lake water. What will
be the total entropy change for this process?

(Data : C_iron = 0.45 kJ/kg-^oC, C_copper = 0.386 kJ/kg-^oC)

Question 27

A connecting rod of a petrol engine of length l is shown in figure. Its mass m is replaced by a two masses m₁ and m₂ placed at the end centers. The distance of masses m₁ and m₂ from its centre of gravity are l₁ and l₂ respectively.

For the dynamically equivalent system, the masses m₁, m₂ and its radius of gyration (k_G) are

Question 28

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 29

The pie-chart given here shows the country’s expenditure on various sports during a particular year. Study the pie-chart and answer the question given below.

If the total amount spent on sports in the year was Rs 1,80,00,000, then the amount spent in tennis is more than the expenditure on golf by:

Question 30

The Mohr’s circle representing state of stress at a point is showing below. The resultant stress (MPa) on a plane at a 45^o from maximum principal stress (MPa) is