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QUESTION: 1

Q. No. 1 – 5 Carry One Mark Each

What is the adverb for the given word below?

Misogynous

Solution:

QUESTION: 2

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram?s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

Solution:

QUESTION: 3

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:

Dhoni, as well as the other team members of Indian team, _____ present on the occasion.

Solution:

QUESTION: 4

An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P, in that order. The cumulative distances travelled and the corresponding electricity consumption are shown in the table below.

The stretch where the electricity consumption per km is minimum is

Solution:

QUESTION: 5

Choose the word most similar in meaning to the given word:

Awkward

Solution:

QUESTION: 6

Q. No. 6 – 10 Carry Two Marks Each

In the following sentence certain parts are underlined and marked P, Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication.

Select the part containing an error. Choose D as your Answer: if there is no error.

Solution:

The is not required in „Q?

QUESTION: 7

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.

**Statement:**

I. All film stars are playback singers.

II. All film directors are film stars.

**Conclusions:**

I. All film directors are playback singers.

II. Some film stars are film directors.

Solution:

QUESTION: 8

Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year?s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.

Which of the statement(s) below is/are logically valid and can be inferred from the above statements?

i. The artists expected funding for the arts to increase this year.

ii. The Chief Minister was receptive to the idea of increasing funding for the arts.

iii. The Chief Minister is a prominent artist.

iv. Schools are giving less importance to arts education nowadays.

Solution:

QUESTION: 9

If a^{2} + b^{2} + c^{2} +1, then ab + bc + ac lies in the interval

Solution:

Given that

a^2 + b^2 + c^2 = 1

Therefore,

1 + 2(ab + bc + ca) ≥ 0_________ { by (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)}

ab + bc + ca ≥ -1/2

(a-b)^2 + (b-c)^2 + (c-a)^2 ≥ 0

2 [ a^2 + b^2 + c^2 - ab - bc - ca ] ≥ 0

2 [ 1 - (ab + bc + ca)] ≥ 0

Therefore, 1 ≥ (ab + bc + ca)

so, ur answer is [-1/2, 1]

*Answer can only contain numeric values

QUESTION: 10

A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer?s 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively, what distance in meters will the tiger have a run before it catches the deer?

Solution:

QUESTION: 11

**Q. No. 11 – 35 Carry One Mark Each**

If any two columns of a determinant are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

Solution:

*Answer can only contain numeric values

QUESTION: 12

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 13

Which one of the following types of stress-strain relationship best describes the behavior of brittle materials, such as ceramics and thermosetting plastics, (σ = stress and ε = strain)?

Solution:

QUESTION: 14

The function of interpolator in a CNC machine controller is to

Solution:

QUESTION: 15

Holes of diameter mm are assembled interchangeably with the pins of diameter mm.

The minimum clearance in the assembly will be

Solution:

QUESTION: 16

Simpson?s 1/3 rule is used to integrate the function between x = 0 and x = 1 using the least number of equal sub-intervals. The value of the integral is ___________

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 17

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

Solution:

QUESTION: 18

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

Solution:

*Answer can only contain numeric values

QUESTION: 19

A Carnot engine (CE-1) works between two temperature reservoirs A and B, where T_{A} = 900 K and TB = 500 K. A second Carnot engine (CE-2) works between temperature reservoirs B and C, where T_{C} = 300 K. In each cycle of CE-1 and CE-2, all the heat rejected by CE-1 to reservoir B is used by CE-2. For one cycle of operation, if the net Q absorbed by CE-1 from reservoir A is 150 MJ, the net heat rejected to reservoir C by CE-2 (in MJ) is _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 20

A stream of moist air (mass flow rate = 10.1 kg/s) with humidity ratio of mixes with a second stream of superheated water vapour flowing at 0.1 kg/s. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream is ___________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 21

Consider a steel (Young?s modulus E = 200 GPa) column hinged on both sides. Its height is 1.0m and cross-section is 10 mm × 20 mm. The lowest Euler critical buckling load (in N) is ______.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 22

Air enters a diesel engine with a density of 1.0 kg/m3. The compression ratio is 21. At steady state, the air intake is 30 × 10–3 kg/s and the net work output is 15 kW. The mean effective pressure (kPa) is _______.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 23

Match the following products with preferred manufacturing processes:

Solution:

*Answer can only contain numeric values

QUESTION: 24

Under certain cutting conditions, doubling the cutting speed reduces the tool life to of the original. Taylor?s tool life index(n) for this tool-workpiece combination will be _______

Solution:

QUESTION: 25

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque τ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, θ versus time

Solution:

QUESTION: 26

Solution:

*Answer can only contain numeric values

QUESTION: 27

Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is 1.0 m, cross-sectional area is 200 mm_{2}; Young?s modulus E = 200 GPa. The force in the truss AB (in N) is ______

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 28

Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?

Solution:

We have Probability distribution function of Normal Distribution

QUESTION: 29

Given two complex numbers the argument of in degrees is

Solution:

QUESTION: 30

The Blasius equation related to boundary layer theory is a

Solution:

*Answer can only contain numeric values

QUESTION: 31

A swimmer can swim 10 km in 2 hours when swimming along the flow of a river. While swimming against the flow, she takes 5 hours for the same distance. Her speed in still water (in km/h) is ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

Let Swimmer = x

River = y

QUESTION: 32

For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is

Solution:

QUESTION: 33

Which one of the following is the most conservative fatigue failure criterion?

Solution:

QUESTION: 34

In a linear arc welding process, the heat input per unit length is inversely proportional to

Solution:

QUESTION: 35

What is the deformation or dynamic factor if sum of errors on meshing teeth of steel pinion and gear is 32 x 10^{-3} mm?

Solution:

QUESTION: 36

**Q. No. 36 – 65 Carry One Mark Each**

Q. A 10 mm diameter electrical conductor is covered by an insulation of 2 mm thickness. The conductivity of the insulation is 0.08 W/m-K and the convection coefficient at the insulation surface is 10 W/m^{2}-K. Addition of further insulation of the same material will

Solution:

QUESTION: 37

A machine element is subjected to the following bi-axial state of stress; σ_{x} = 80 MPa; σ_{y} = 20 MPa; τ_{xy} = 40MPa. If the shear strength of the material is 100 MPa, the factor of safety as per Tresca?s maximum shear stress theory is

Solution:

QUESTION: 38

The probability of obtaining at least two “SIX” in throwing a fair dice 4 time is

Solution:

*Answer can only contain numeric values

QUESTION: 39

A horizontal plate has been joined to a vertical post using four rivets arranged as shown in

figure. The magnitude of the load on the worst loaded rivet (in N) is ________

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 40

Temperature of nitrogen in a vessel of volume 2 m^{3} is 288 K. A U-tube manometer connected to the vessel shows a reading of 70 cm of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K, atmospheric pressure is 1.01325 bar, acceleration due to gravity is 9.81 m/s^{2} and density of mercury is 13600 kg/m^{3}. The mass of nitrogen (in kg) in the vessel is _______.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 41

The solidification time of a casting is proportional to , where V is the volume of the casting and A is the total casting surface area losing heat. Two cubes of same material and size are cast using sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is

Solution:

QUESTION: 42

Match the following pairs:

Solution:

*Answer can only contain numeric values

QUESTION: 43

Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, 20 percent of the mass is extracted for process heating and the remaining steam expands isentropically to 9 kPa.

Inlet to turbine: P = 14 MPa, T = 560°C, h = 3486 kJ/kg, s = 6.6 kJ/(kg.K)

Intermediate stage: h = 27776 kJ/kg

Exit of turbine: P = 9 kPa, h_{f} = 174 kJ/kg, h_{g} = 2574 kJ/kg,

s_{f} = 0.6 kJ/(kg.K), s_{g} = 8.1 kJ/(kg.K)

If the flow rate of steam entering the turbine is 100 kg/s, then the work output (in MW) is _______.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 44

Water (ρ = 1000 kg/m^{3}) 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 ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 45

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 _______.

Solution:

*Answer can only contain numeric values

QUESTION: 46

Consider a spatial curve in three-dimensional space given in parametric form by

The length of the curve is ______

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 47

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is

Solution:

QUESTION: 48

A triangular facet in a CAD model has vertices: P_{1}(0, 0, 0); P_{2}(1, 1, 0) and P_{3}(1, 1, 1). The area of the facet is

Solution:

*Answer can only contain numeric values

QUESTION: 49

In a slab rolling operation, the maximum thickness reduction (Δh_{max}) is given by Δh_{max} = μ2R, where R is the radius of the roll and μ is the coefficient of friction between the roll and the sheet. If μ = 0.1, the maximum angle subtended by the deformation zone at the centre of the roll (bite angle in degree) is ______.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 50

Find the solution of which passes through the origin and the point (142,3/4)

Solution:

QUESTION: 51

For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively

Solution:

*Answer can only contain numeric values

QUESTION: 52

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is ______

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 53

A DC welding power source has a linear voltage-current (V-I) characteristic with open circuit voltage of 80 V and a short circuit current of 300 A. For maximum arc power, the current (in Amperes) should be set as _____.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 54

A well insulated rigid container of volume 1 m^{3 }contains 1.0 kg of an ideal gas [C_{p} = 1000 J/(kg.K) and C_{v} = 800 J/(kg.K)] at a pressure of 10^{5} Pa. A stirrer is rotated at constant rpm in the container for 1000 rotations and the applied torque is 100 N-m. The final temperature of the gas (in K) is _________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 55

A pinion with radius r_{1}, and inertia I_{1} is driving a gear with radius r_{2} and inertia I_{2}. Torque τ_{1 }is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F_{1} and F_{2}) of interaction. Which of the following relations hold true?

Solution:

*Answer can only contain numeric values

QUESTION: 56

A cantilever beam with flexural rigidity of 200 Nm^{2} is loaded as shown in the figure. The deflection (in mm) at the tip of the beam is _____.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 57

In the assembly shown below, the part dimensions are:

Assuming the normal distribution of part dimensions, the dimension L_{4} in mm for assembly condition would be:

Solution:

QUESTION: 58

A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity (CG) of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface.

Given in addition that the eccentric mass = 2 grams, eccentricty = 2.19 mm, mass of the mobile = 90 grams, g = 9.81 m/s^{2}. Uniform speed of the motor in RPM for which the mobile will get just lifted off the ground at the end Q is approximately

Solution:

*Answer can only contain numeric values

QUESTION: 59

A precision instrument package (m = 1 kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assuming that the isolation is designed with its natural frequency significantly lesser than 60 Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

QUESTION: 60

Following data refers to the activities of a project, where, node 1 refers to the start and node 5 refers to the end of the project

The critical path (CP) in the network is

Solution:

QUESTION: 61

For flow through a pipe of radius R, the velocity and temperature distribution are as follows:

,where C_{1} and C_{2} are constants

The bulk mean temperature is given by with U_{m} being the mean velocity of flow. The value of T_{m} is

Solution:

*Answer can only contain numeric values

QUESTION: 62

Consider an ant crawling along the curve (x – 2)^{2 }+ y2 = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 63

Air (ρ = 1.2 kg/m3 and kinematic viscosity, v = 2 × 10^{–5} m^{2}/s) with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is , the total drag force (in N) per unit width of the plate is ________.

(**Important** - Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 64

The velocity field of an incompressible flow is given by

*V = (a _{1}x + a_{2}y + a_{3}z)i + (b_{1}x + b_{2}y + b_{3}z)j + (c_{1}x + c_{2}y + c_{3}z)k*, where a

(**Important **- Enter only the numerical value in the answer)

Solution:

*Answer can only contain numeric values

QUESTION: 65

An orthogonal cutting operation is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15 and width of cut is 6 mm. It is observed that the chip thickness is 0.015 mm, the cutting force is 60 N and the thrust force is 25 N. The ratio of friction energy to total energy is __________

(correct to two decimal places)

Solution:

F=F_{C}sinα+F_{T}cosα

F=60sin15+25cos15

F=39.67N….(ii)

Ratio of frictional enery to Total energy will be,

### MCQ: Mechanical Engineering, GATE

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