Q.1 (a) If then show that
(b)If x = sec – cos and y = secn -cosn, then show that
(c)If prove that
(d)If , , show that, . Also find the value of .
(e)If a normal is drawn at a variable point P of the ellipse , Find the maximum distance of the normal from the centre of the ellipse.
(54=20)
Q 2 (a) Evaluate :
(b) Evaluate :
(c) Evaluate :
(d)Solve :
(e)A particle of unit mass moves in a straight line in a resisting medium which produces resistance kV. If the particle starts with a velocity u from the position s =so, show that, as time goes on, the particle approaches the position .
Q 3 (a) A rigid body is rotating at 2.5 rad/sec about an axis AB, where A and B are the point
(1, −2, 1) and (3, −4, 2). Find the velocity of the particle P of the body at the point
(5, −1, −1).
(b)If then determine the scalars c and d such that is perpendicular to both.
(c)If , then find the values of and.
(d)Find the equations of the tangent plane and normal line to the surface at the point .
(e)Prove that .
Q4(a) Evaluate , if I is a unit matrix of order 3 and A is given by
(b) Show that =
(c)Determine the values of when is orthogonal.
(d)Find the characteristic equation of the matrix and verify thatit is satisfied by A and hence obtain A– 1.
(e) Solve the system of equations
Q 5(a)Xis a discrete random variate having probability mass function:
x 01234567
P(X=x)0k2k2k3kk22k27k2 + k
(i)Determine the constant k ;
(ii)Find P(x6);
(iii)What will be P ;
(b)A random variable x follows Poisson distribution with parameter 3. Find theProbabilities that the variable assumes the values (i) 0, 1, 2, 3;
(i)less than 3. and
(ii)at least 2 (Given that e– 3 = 0.0498).
(b)The safety limit of a crane is known to be 32 tons. The mean weight and the standard deviation of a large number of iron rods are 0.3 ton and 0.2 ton respectively. 100 rods are lifted at a time. Find the probability of an accident.
(c)A gambler rolls two dice and stands to loss Rs.2/- if he fails to throw a six; to win Rs.4/- he must throw one six and to win Rs.10/- he must throw 2 sixes. Is the game fair?
(d)An I.Q test was administered to 5 persons before and after they were trained. The results are given below :
I II III IV V
I.Q before training 110 120123132 125
I.Q after training 120 118125136 121
Test whether there is any change in I.Q. after the training programme
(Given ).
Q.1What is the function of frame buffer? Differentiate between random and raster scan display.
Q.2What is persistence? Explain the principle of LCD display. What are the various technologies used in the LCD device?
Q.3(a)A triangle ABC, which has three points A[3, 1], B[4, 1] and C[2, 1] is rotated by 90° about the origin in counter clockwise direction. Calculate the position vectors of the rotated triangle.
(b)Show that reflection about the line y = x is attained by reversing the coordinate that
Mk (x, y) = y, x
Transformation matrix
Q.4(a)Write a program to implement the Z-buffer to generate Back faced detection method.
(b)Test the Back face detection for a tetrahedron (pyramid) PQRS with vertices p(1, 1, 2), Q (3, 2, 3), R(1, 4, 1) and S(2, 4, 0), provide different views of the pyramid so that each face is displayed at least once.
Q.5Develop the equation of a Bezier curve. Find the points on the curve forand 1 and plot the curve for the following data. The coordinates of the four control points are given by .
Q.6Calculate the midpoint of Hermite cubic curve defined by.
Q.7Derive an equation for a Bezier surface patch having four control points p(0, v) of equivalent bicubic formulation.
Q.8Discuss the important properties of Bezier surface.
Q.9Why are CAD/CAM data exchange standards required? Explain.
Q.10Explain the salient features of the following Standards:
(i)PDDI
(ii)IGES
(iii)PDES
(iv)STEP
Q.1(a)Explain the functioning of cupola furnace with the help of a neat sketch.
(b)Why are furnaces designed to operate with minimum of back charges?
Q.2(a)List the various principal ingredients of moulding sands. Write the role of each of them.
(b)What do you understand by green sand? Explain its properties.
Q.3(a)What is die casting? What are the basic elements of a die casting machine?
(b)Explain working of a die casting machine with the help of a neat diagram.
Q.4(a)What are the various types of sheet metal forming processes? Explain any one of them.
(b)Describe the different types of shearing processes with neat diagrams.
Q.5(a)Describe the terminology for a right hand cutting tool for turning with the help of a neat sketch.
(b)Explain the features of multi point cutting tools. Give examples.
Q.6(a)Briefly describe basic requirements of welding processes.
(b)Explain the Shielded Metal Arc welding process with the help of a suitable diagram.
Q.7(a)What are the functions of flux? List different types of flux used in Submerged Arc welding.
(b)What are the major advantages of SMAW over other Arc Welding processes?
Q.8(a) What are the various types of fuel gases used in the gas cutting operation? Explain any one of them.
(b)List advantages and disadvantages of oxyfuel gas cutting operation.
Q.9A tensile with 15 mm initial diameter and 40 mm gage length reaches maximum load at 72 kn and fractures at 69 kn. The maximum diameter at fracture is 1 mm. Determine the engineering stress at maximum load. True fracture stress, true strain at fracture and engineering strain at fracture.
Q.10Write short notes on any four of the following:
(i)Reverberate furnace
(ii)Extrusion
(iii)Welding current
(iv)Flux cutting
(v)Grey iron costing
(vi)Hot working and Cold working
Q.1(a)Describe the meaning of numerical control of machine tools.
(b)Explain the function of MCU in an NC machine tool.
Q.2(a)List the types of drives used for step less control of NC machine tools spindles.
(b)Compare the open loop and closed loop types of NC systems.
Q.3(a)How does the operation of CNC controller differ from that of a hardwire MCU?
(b)What is Direct Numerical Control (DNC)? List its advantages over CNC.
Q.4Write a manual part program for the component shown in the figure below. What will be the cutter diameter for the pocket? Consider tool compensation.
Q.5(a)Write the meaning of following preparatory functions standardized by ISO:
(i)G 03
(ii)G 20
(iii)G 63
(iv)G 41
(v)G 91
(b)Write the meaning of following miscellaneous function:
(i)M 06
(ii)M 09
(iii)M 55
(iv)M 15
(v)M 30
Q.6(a)With suitable example the need of tool nose radius compensation.
(b)With suitable example describe the benefit of canned cycle.
Q.7Explain the concept of post-processor as used in computer aided part programming.
Q.8Describe different requirements for standardization in communication for manufacturing shop.
Q.9Explain about some of the components that form part of an FMS
Q.10Explain the importance of integration in manufacturing automation. How does it benefit the final product cost?
Q.1What is the function of Frame buffer? Computer the Frame buffer size for a CRT display terminal of a 640 × 480 resolution with 96 pixels per inch.
Q.2(a)What is orthographic projection? Explain it with suitable sketch.
(b)Differentiate between parallel projection and perspective projection.
Q.3Describe Scan-line Algorithm and give its advantages over other techniques of removing hidden lives and surfaces.
Q.4Draw the CMY colour Cube and briefly describe CMY Model.
Q.5(a)Compare B-splines Bezier curves.
(b)Fit a Bezier curve having the following control points : P0 (1, 1), P1 (3, 6) ,P2 (5, 7) and P3 (7, 4). Find out points at t = 0.4 and 0.6.
Q.6Consider the line segment in the xy-plane and parallel to the y-axis defined by end point at t = 0.6, S = 0.6 on the sweep surface generated by simultaneously translating the line 10 units along the x-axis and rotating it through 2about the x-axis.
Q.7Suppose Bezier curve C(u) of degree n is defined by control points P0, P1, ……..Pn. Prove the following :
Q.8(a)Explain constructive solid geometry for representation of solids.
(b)Compare b-rep and c-rep modeling techniques.
Q.9Why are CAD/CAM data exchange standards required? Explain.
Q.10(a)Enlist at least five CAD software with their commercial names
(b)Write a short nots on UPR.
Q1. Identify the sensor, signal conditioner and display elements in the measurement systems of
(i)a mercury-in-glass thermometer,
(ii) a bourdon pressure gauge.
Q2.(a)Explain the difference between open- and closed- loop control,
(b)Identify the various elements that might be present in a control system involving a thermostatically controlled electric heater.
Q3.(a)Explain the function of a programmable logic controller.
(b) Explain what is meant by sequential control and illustrate your answer by an example.
Q4. (a)What will be the change in resistance of an electrical resistance strain gauge with a gauge factor of 2.1 and resistance 50 if it is subject to a strain of 0.001?
(b)Suggest a sensor that could be used, as part of a control system, to determine the difference in levels between liquids in two containers. The output is to provide an electrical signal for the control system.
Q5.Suggest the elements that might be considered for the measurement systems to be used to:
(a)Monitor the pressure in an air pressure line and present the result on a dial, no great accuracy being required.
(b)Continuously monitor and record the temperature of a room with an accuracy
of 1C.
(b)Monitor the weight of lorries passing over a weighing platform.
(c)Monitor the angular speed of rotation of a shaft.
Q6.(a) Describe the basic details of (i) a poppet valve, (ii) a shuttle valve.
(b) Explain the principle of a pilot-operated valve.
Q7. (a)What are the limitations of the two-step (on-off) control and in what situation is such a control system commonly used?
(b)Explain how a sequential valve can be used to initiate an operation only when another operation has been completed.
Q8.(a) A 6-bit D/A converter gives an output voltage of 8.625 volts for an input of 010111. What is the step size, the full range voltage and the percentage resolution?
(b)A typical A/D converter has 12- bit resolution and a full range of 10 volts. What is the percent resolution and voltage resolution of this device?
(c)What are the major guidelines for the selection of a sensor?
Q9.(a)Differentiate between a resolver and an encoder.
(b)What is the difference between a thermocouple and a thermistor?
(c)What is the main advantage of a capacitive proximity switch over the inductive proximity switch?
(d)Describe four different sensing modes for photoelectric sensors.
Q.10 (a) A temperature probe having a first-order response with a time constant of 1 second is giving a step input 50C from 0C. Calculate the temperature indicated 0.6 second after the application of the input.
(b)A linear second-order, single-degree-of-freedom system has a mass of 8 gm and a stiffness of 1000N/m. Calculate the natural frequency of the system. Determine the damping constant necessary to just prevent overshoot in response to a step input of force.
Q.1(a)Explain the role stakeholders in formulating the quality policy of an organization.
(b)Discuss the four phase/steps of quality auditing task.
Q.2(a)Discuss the concept KAIZEN in TQM.
(b)List out any 10 point of Crosby’s 14 points for quality improvement.
Q.3(a)Write short notes on:
(i)POKA-YOKE
(ii)PDCA cycle
(b)Discuss the basic seven tools of SQC.
Q.4(a)Explain the eight elements of TQM.
(b)Discuss the provisions under Occupational safety and Health, 1970. what are the benefits arising from OSHA to employers, employees and general public?
Q.5(a)Determine 95% confidence limits for the mean of a normal population with variance 9, using a sample size 100 with mean 40.
(b)To compare the price of a product I two cities, ten shops were selected at rndom in each town and prices were noted as given below:
CITY-1 / CITY-261 / 55
63 / 54
56 / 47
63 / 59
56 / 51
63 / 61
59 / 57
56 / 54
44 / 64
61 / 58
Test whether the average price can be said to be the same in the two cities. Use 5% LOS.
Q.6(a)What do you understand by Six Sigma environment? Discuss the Six Sigma participants.
(b)The balls for ball bearings are inspected by attributes. A sample of 100 is inspected daily for continuously 10 days. The samples are taken randomly from the daily production of 1000 balls. Compute the control limits for (i) p-chart, (ii) np-chart.
The observations are given below:
Date / Rejections1 / 18
2 / 12
3 / 6
4 / 15
5 / 2
6 / 20
7 / 14
8 / 10
9 / 8
10 / 6
Q.7(a)What are the benefits to Quality function Deployment (QFD)
(b)Discuss the process of FMECA. What are its benefits?
Q.8(a)Explain cause and Effect diagram with an exemplary illustration of soldering defects of IC manufacturing
(b)Find the reliability of the following system:
A figure below
Q.9(a)Explain the life history of a hypothetical system with the help of Bath Tub Curve. What remedial measures or maintenance strategies do you recommend at each stage of the life cycle?
(b)Explain different types of needs of customers
Q.10(a)Explain the concept of Cost of Quality in detail.
(b)What are the common points in Juran’s Crosby’s and Feigenbaum’s philosophies?