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# GATE ME 2021: Toppers Mini Mock Quiz 4 (App update required to attempt this test)

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Question 1

Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured yellow, Red, Green such that each colour appears only two times on the dice. If the dice is thrown thrice the probability of obtaining red colour on top face of the dice at least twice is _______

Question 2

Three years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today.

The present age of the baby is

The present age of the baby is

Question 3

If the subject is having the action done to it, then the verb is said to be in the _________.

Question 4

The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a thriving business in India. However, the commercial use of this technology is not legal in India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton, and planted in 15% of the cotton growing area in the 2017 Kharif season.

Which one of the following statements can be inferred from the given passage?

Question 5

A monkey is trying to reach the top of a tree. He climbs 3 feet in a minute but slides down by 1.5 feet after each climb. If he reaches the top of the tree in 58 minutes, then the maximum possible height of the tree is ________ feets.

Question 6

If represents the complex potential for an electric field.

If then what would be equivalent to function ϕ.

Question 7

When the Newton-Raphson method is applied to solve the equation F(x)= x

^{3}+2x-1, the solution at the end of the first iteration with the initial guess value as x_{0}= 1.2 isQuestion 8

A building contractor under took to build a cooperative society flats in 100 days. He employed 110 men. After 45 days, he found that only one fourth of the flats could be built. In order to complete the work in time, how many more men should be employed?

Question 9

The value of where and C is the curve y

^{2}= 4x in the XY-plane from (0, 0) to (4, 4), is ____.Question 10

A/An ________ is a word placed in front of a noun to specify quantity or to clarify what the noun refers to.

Question 11

A cantilever beam is supported by spring at the free end as shown in figure. It is loaded by an external force of 30kN at the free end. The stiffness of the spring is 150N/mm. The length of beam is 1.5m and Modulus of elasticity is 200GPa. The beam is circular with cross section of 40mm. The deflection of beam is

Question 12

A block is projected along a rough horizontal road with a speed of 10 m/s. If the coefficient of kinetic friction is 0.10, how far it travel before coming to rest?

Question 13

A shopkeeper for soaps forecasts the demand at the rate of 1000 per months for the next three months. The actual demand turned out to be 800,1320 and 1400. The BIAS of the forecast will be __________.

Question 14

Moist air at a pressure of 100 kPa is compressed to 500 kPa, and then cooled to 35 ºc in an after cooler. The air at the entry to the after cooler is unsaturated and becomes just saturated at the exit of the after cooler. The saturated pressure of water at 35 ºc is 5.268 kPa. The partial pressure of water vapour (in kPA. in moist air entering the compressor is closest to

Question 15

A spherical balloon 1.5 m diameter is completely immersed in water and chained to the bottom. If the chain has a tension of 10 kN, the weight of the ballon in air is ________.

Question 16

A shaft of size mm mate with hole of size mm then maximum possible clearance(in mm) in the assembly will be_____.

Question 17

For locating a plane structure a diamond pin locator is widely used. How many degrees of freedom is locked by each diamond pin and how many degree of freedom is locked in total for this application.

Question 18

A small project consists of the following activities and the respective duration of activities in days are also mentioned.

The total float and independent float for the activity 2-5 respectively are

The total float and independent float for the activity 2-5 respectively are

Question 19

A coin is thrown by a man at an angle of 30 ° above the ground level of height 2.7m with the horizontal velocity of 20m/s is cought by another man at a height of 0.7m above the ground. Determine the displacement of the coin travelled. (g=10m/s

^{2}) (in metres)Question 20

An inclined manometer using mercury has a least count of 3mm. If the minimum pressure difference that can be measured is 100 Pa, the sensitivity of the manometer is?

Question 21

Match the following Theories:

Question 22

A cubical block of aluminum of side 220 mm is placed at a depth of 4 km in sea water. The change in the volume of block (in mm

^{3}), when placed in sea water is (take mass density of sea water is 1020 kg/m^{3}, E_{Al}= 70GPa, Poisson ratio = 0.25)Question 23

As shown in the figure a U-tube manometer is used to measure the pressure of oil (sp. gravity= 0.8) flowing in a pipeline. The right limb of manometer contains mercury and is open to atmosphere. The difference in level of mercury is 15cm. What will be the difference in the level (in cm) of mercury if pressure of the oil in the pipeline is reduced to 10 kPa

Question 24

A ship moves horizontally in sea and its axis is 12 m below the surface of water. A U- tube manometer containing a fluid of specific gravity 2.5 connected along its axis and also a pitot-tube is attached just front of ship. The difference in the level of fluid in U–tube manometer is found to be 150 mm. The speed of the ship (in m/s) is (take specific gravity of sea water is 1.1)

Question 25

In a single pass rolling operation a strip of width 200 mm and thickness 25 mm undergoes 25% reduction in thickness The bite angle in degrees is 5.345. Calculate the diameter (mm) of rollers?

Question 26

A hollow cylinder of a material that has a thermal conductivity of 3.46 W/m-K

where r is in cm & log is Natural logarithmic function. then the heat transfer rate per unit length is _________ kW.

^{0}C has an inner radius of 7.5 cm and an outer radius of 15 cm. The temperature of the inner surface is 150^{0}C and the temperature profile is given bywhere r is in cm & log is Natural logarithmic function. then the heat transfer rate per unit length is _________ kW.

Question 27

A vessel of volume of 0.05 m

^{3}contains a mixture of saturated steam and saturated water at a temperature of 250. The mass of liquid is 10 kg. The specific enthalpy (kJ/kg) of mixture is-Use the following table:

Question 28

A steel connecting rod is subjected to a reversed axial load of 180 kN. The required diameter of rod (in mm) using Soderberg's equation take the factor of safety N = 2, is

[Take,σ

_{ut }= 1070 MPa, σ_{yt}=910 MPa and Assume, No column action and Endurance limit for reversed axial load is half the Ultimate tensile strength]Question 29

A body of mass m kg is attached by two truss member each having a cross sectional area of 50 mm

If the value of maximum stress in the truss is 3.4 MPa then the value of mass m (in kg) is closest to

^{2}making an angle of 30 and 60 with horizontal as shown in fig.If the value of maximum stress in the truss is 3.4 MPa then the value of mass m (in kg) is closest to

Question 30

A spur gear having 30 teeth and a module of 1.4 mm. It rotates at 360 rpm. The addendum of the gear is given as 1.12. Determine its circular pitch

Question 31

The compression ratio of an Otto cycle is 8. The initial value of ratio of specific heat is 1.4. Find the percentage change in efficiency of air standard otto cycle if value of C

_{v}increases by 1%Question 32

Following data relate to a gear in mesh.

Module=4mm

Number of Teeth=75

Base circle radius=141mm

The pressure angle ’ ϕ’ will be (in degrees)__________(in nearest integer).

Module=4mm

Number of Teeth=75

Base circle radius=141mm

The pressure angle ’ ϕ’ will be (in degrees)__________(in nearest integer).

Question 33

The temperature – entropy (T-S) diagram for steam power plant cycle is shown in fig. The capacity of steam power plant (in kg/KWh) is

The property values at different state are shown below in table:

Question 34

A four stroke SI engine has six cylinder of 8 cm bore and 10 cm stroke. The engine is coupled to a brake having a torque arm radius of 35 cm. At 3500 rev/min, with all cylinders firing, the net brake load is 300 N. When each cylinder in turn is rendered inoperative, the average net brake load produced at the same speed by the remaining five cylinders is 240 N. Indicated mean effective pressure of the engine is _____ bar.

Question 35

Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30 °C and the relative humidity is 55%. Given that the saturation pressure of water at 30 °C is 4246 Pa, the mass of water vapor per kg of dry air is _____________ grams

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