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QUESTION: 1

**Q.1 to Q.5 carry one mark each.**

Q. Complete the sentence:

Universalism is to particularism as diffuseness is to _______________.

Solution:

QUESTION: 2

Were you a bird, you ___________________ in the sky.

Solution:

QUESTION: 3

Which one of the following options is the closest in meaning to the word given below?

**Nadir**

Solution:

QUESTION: 4

Choose the grammatically INCORRECT sentence:

Solution:

QUESTION: 5

What will be the maximum sum of 44, 42, 40, ...... ?

Solution:

QUESTION: 6

**Q.6 to Q.10 carry two marks each.**

Q. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

Solution:

QUESTION: 7

A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

Solution:

QUESTION: 8

Find the sum of the expression

Solution:

QUESTION: 9

The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

Solution:

QUESTION: 10

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

Solution:

QUESTION: 11

**Q.11 to Q.35 carry one mark each.**

The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, respectively. The demand for the item is 500 units. To break even, the unit price of the items in Rs. should be

Solution:

QUESTION: 12

Therbligs refer to the

Solution:

QUESTION: 13

Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

Solution:

QUESTION: 14

Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The shear strength of aluminum is 80 MPa. The minimum punching force required in kN is

Solution:

QUESTION: 15

A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is

Solution:

QUESTION: 16

Match the CORRECT pairs.

Solution:

QUESTION: 17

In a rolling process, the state of stress of the material undergoing deformation is

Solution:

QUESTION: 18

Consider one-dimensional steady state heat conduction along x-axis (0 ≤ x ≤ L), through a plane wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.

Solution:

QUESTION: 19

A cylinder contains 5 m^{3} of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is

Solution:

QUESTION: 20

A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rockerrocker) mechanism is

Solution:

QUESTION: 21

Let X be a normal random variable with mean 1 and variance 4. The probability P{X<0} is

Solution:

QUESTION: 22

Choose the CORRECT set of functions, which are linearly dependent.

Solution:

QUESTION: 23

The eigenvalues of a symmetric matrix are all

Solution:

QUESTION: 24

The partial differential equation is a

Solution:

QUESTION: 25

Match the CORRECT pairs.

Solution:

QUESTION: 26

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E_{1} to E_{2} along the length of the rod, the normal stress developed at the section-SS is

Solution:

QUESTION: 27

For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop Δp over a length L and the wall shear stress τ_{w} are related by

Solution:

QUESTION: 28

For a ductile material, toughness is a measure of

Solution:

QUESTION: 29

A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same material, which is 8 times heavier than the original casting, will be

Solution:

QUESTION: 30

A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm^{3}/s is

Solution:

QUESTION: 31

In the 3-2-1 principle of fixture design, 3 refers to the number of

Solution:

QUESTION: 32

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

Solution:

QUESTION: 33

A company manufactures 1000 toys every day. On an average, 10% of the toys are defective and 40% of the defective toys can be reworked into defect-free ones. The average number of defect-free toys manufactured daily is

Solution:

QUESTION: 34

The type of control chart used to monitor the amount of dispersion in a sample is

Solution:

QUESTION: 35

Which one of the following is modeled based on adaptation capabilities of biological systems?

Solution:

QUESTION: 36

**Q.36 to Q.65 carry two marks each.**

Q. A company plans to purchase a machine whose uptime needs to be atleast 95%. They have shortlisted two models of the machine with the following operational characteristics:

The company should buy

Solution:

QUESTION: 37

A manufacturer produces bars designed to be of 10 mm diameter with a tolerance of ±0.1 mm. Historical data indicates that manufactured bars have an average diameter of 9.98 mm with a standard deviation of 0.15 mm. The process capability index is

Solution:

QUESTION: 38

Let (P) denote the linear programming formulation of a transportation problem with m sources and n destinations. Then, the dual linear program of (P) has

Solution:

QUESTION: 39

Following data refers to an automat and a center lathe, which are being compared to machine a batch of parts in a manufacturing shop.

Automat will be economical if the batch size exceeds

Solution:

QUESTION: 40

Cylindrical pins of mm diameter are electroplated in a shop. Thickness of the plating is micron. Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is

Solution:

QUESTION: 41

During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be

Solution:

QUESTION: 42

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potential energy of steam, the power developed in kW by the steam turbine per kg of steam flow rate, is

Solution:

QUESTION: 43

A simply supported beam of length L is subjected to a varying distributed load sin (3p x/L) Nm^{-1}, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

Solution:

QUESTION: 44

The probability that a student knows the correct answer to a multiple choice question is 2/3 . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is

Solution:

QUESTION: 45

The solution to the differential equation where k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

Solution:

QUESTION: 46

The value of the definite integral is

Solution:

QUESTION: 47

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors. where S is the sphere, x^{2} + y^{2} + z^{2} =1 and n is the outward unit normal vector to the sphere. The value of the surface integral is

Solution:

QUESTION: 48

The function f (t ) satisfies the differential equation and the auxiliary conditions, The Laplace transform of f (t) is given by

Solution:

QUESTION: 49

A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg-m^{2} is

Solution:

QUESTION: 50

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

Solution:

QUESTION: 51

Two cutting tools are being compared for a machining operation. The tool life equations are:

where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher tool life if the cutting speed in m/min exceeds

Solution:

QUESTION: 52

In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be

Solution:

QUESTION: 53

In water jet machining, the water jet is issued through a 0.3 mm diameter orifice at a pressure of 400 MPa. The density of water is 1000 kg/m3. The coefficient of discharge is 1.0. Neglecting all losses during water jet formation through the orifice, the power of the water jet in kW is

Solution:

QUESTION: 54

A linear programming problem is shown below.

Maximize

3x + 7y

Subject to

3x + 7y ≤ 10

4x + 6y ≤ 8

x, y ≥ 0

It has

Solution:

QUESTION: 55

Consider a two machine flow shop where jobs are first processed in Machine X and then in Machine Y, in the same sequence. The processing times of four jobs (1, 2, 3 and 4) on the machines are:

The sequence of jobs on the machines that minimizes make span is

Solution:

QUESTION: 56

Match the CORRECT pairs.

Solution:

QUESTION: 57

A firm produces 120 units of product in every 8 hour shift. Four operations as given below are needed to manufacture each unit of product.

The above operations are to be assigned to workstations, such that one or more operations are performed in each workstation. Only one unit of product will be processed in each workstation at a time. The minimum number of workstations that will achieve the production target, without violating the precedence constraints, is

Solution:

QUESTION: 58

**Common Data Questions**

**Common Data for Questions 58 and 59:**

A disc of 200 mm outer and 80 mm inner diameter is faced at a feed of 0.1 mm/rev with a depth of cut of 1 mm. The facing operation is undertaken at a constant cutting speed of 90 m/min in a CNC lathe. The main

(tangential) cutting force is 200 N.

Q. Neglecting the contribution of the feed force towards cutting power, the specific cutting energy in J/mm^{3 }is

Solution:

QUESTION: 59

**Common Data Questions**

**Common Data for Questions 58 and 59:**

A disc of 200 mm outer and 80 mm inner diameter is faced at a feed of 0.1 mm/rev with a depth of cut of 1 mm. The facing operation is undertaken at a constant cutting speed of 90 m/min in a CNC lathe. The main

(tangential) cutting force is 200 N.

Q. Assuming approach and over-travel of the cutting tool to be zero, the machining time in min is

Solution:

QUESTION: 60

**Common Data for Questions 60 and 61:**

The demand for soap at a retailer is 40 kg per day. The retailer buys soap from a company in bulk at the

cost of Rs. 50 per kg. The retailer incurs a cost of Rs. 200 to place an order to the company, and a holding

cost of Rs. 0.1 per kg per day to store the soap. The lead time between the placing and receiving of orders

is 3 days. The retailer’s current ordering policy is to order 200 kg every 5 days.

Q. To avoid stock out situations, the retailer needs to place orders when the inventory level (in kg) drops to

Solution:

QUESTION: 61

**Common Data for Questions 60 and 61:**

The demand for soap at a retailer is 40 kg per day. The retailer buys soap from a company in bulk at the

cost of Rs. 50 per kg. The retailer incurs a cost of Rs. 200 to place an order to the company, and a holding

cost of Rs. 0.1 per kg per day to store the soap. The lead time between the placing and receiving of orders

is 3 days. The retailer’s current ordering policy is to order 200 kg every 5 days.

Q. If the retailer uses an optimum order policy to minimize the total cost, the saving in Rs. in the total

cost as compared to the current policy will be

Solution:

QUESTION: 62

**Linked Answer Questions**

**Statement for Linked Answer Questions 62 and 63:**

A project consists of seven activities, whose durations are independent normal random variables, as shown

in the table below. Activities are identified by their beginning node i and ending node j.

Q. The critical path of the project, based on the mean activity duration, is

Solution:

QUESTION: 63

**Linked Answer Questions**

**Statement for Linked Answer Questions 62 and 63:**

A project consists of seven activities, whose durations are independent normal random variables, as shown

in the table below. Activities are identified by their beginning node i and ending node j.

Let φ denote the cumulative distribution function of the standard normal random variable. The probability that all activities on the critical path, based on the mean activity duration, are completed in 22 days is

Solution:

QUESTION: 64

**Statement for Linked Answer Questions 54 and 55:**

In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and

cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the

friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q. The orthogonal rake angle of the cutting tool in degree is

Solution:

QUESTION: 65

**Statement for Linked Answer Questions 64 and 65:**

In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and

cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the

friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q. The normal force acting at the chip-tool interface in N is

Solution:

### Production, Industrial Engineering

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