(I) Point a 50 Mm Above H.P. and 60 Mm Behind V.P

DME/DCLE(G) TUTOR MARKED ASSIGNMENT BET-016 ENGINEERING DRAWING

Maximum Marks : 100 Course Code : BET-016 Weightage : 30% Last Date of Submission : October 31, 2013

Note : All questions are compulsory and carry equal marks.

Q.1 Draw the projections of the following considering the Reference Line X-Y to be the same. You may keep the distance between the projectors equal to 30 mm. (i) Point ‘A’ 50 mm above H.P. and 60 mm behind V.P. (ii) Point ‘B’ 45 mm below H.P. and on V.P. (10) Q.2 Draw the projection of a line which is 65 mm long and its one end is in HP at a point 15 mm in front of the VP. The other end is in the third quadrant. The line is inclined at 60° to HP and 30° to VP. Draw the projections of line. (10) Q.3 A pentagonal sheet having all edges equal in length is placed with one edge parallel to HP. The surface of the sheet is inclined at 30° to HP and parallel to VP. If each side of sheet is 50 mm, draw its projections. (10) Q.4 Given Figure 1 shows the top-view and front of a cylinder, cut by a Sections-plane V.T. Show its Sectional-Top-View.

 40 mm Top-view

Front-view 30 65 mm

Figure 1 (10) Q.5 A regular hexagon of 35 mm side is resting on an edge in the HP and the surface of the hexagon is inclined at 45° to HP and perpendicular to VP. Draw its projections. (10) Q.6 A hexagonal pyramid of base edge 25 mm and height 70 mm is resting on one of the base edge on HP and the base makes an angle of 45° to HP, with its axis parallel to VP. Draw its projections. (10) Q.7 The orthographic views of a machine bracket are shown in Figure 2 below. Draw isometric view from these views and dimension them.

10 15  50 24 20 20 12 12

12 20 20R Figure 2 (20) Q.8 Draw the following views of the block as shown in Figure 3 by using either 1st Angle Projection or 3rd Angle Projections: (i) Top-View (ii) Front-View (iii) Side-view

20 25 25 15

30 15 20 15

100 50

Figure 3 (20) DME/DCLE(G) TUTOR MARKED ASSIGNMENT BET-021 MATHEMATICS-II

1 + x 骣 2x f( x )= log f= 2 . f ( x ) Q.1 (a) If , show that 琪 2 . 1 - x 桫1 + x

(b) Find the inverse function of the following y= x + x2 + 1.

(c) Examine the following function is even or odd f( x )= 1 + x + x2 - 1 - x + x 2 .

骣4x- x2 (d) Find the domain of definition of f (x), where f( x )= loge 琪 . 桫 3

(e) Find a function f where f (x) is of the form ax2 + bx + c ; given that f (0)= 5 , f (- 1) = 10 , f (1)= 6 . (2  5 = 10) 1- sin x p Q.2 (a) Find k, if the function is defined by f( x ) = when x and f( x ) = k when (p - 2x )2 2 p p x = is continuous at x = . 2 2 3- 6 + x (b) Find the value of : Lim . x 3 3- 6 - x

xea- ae x (c) Evaluate : Lim . x a x- a (d) Discuss the continuity of the function f (x) where it is defined as follows : f( x )= - x , x 0 =x, x > 0 (2.5  4 = 10) x2 -7 x + 6 Q.3 (a) Find the maximum and mimimum values of f (x) when f( x ) = . Also obtain x - 10 the values of x for which f (x) becomes maximum and minimum. (b) Find the maximum value of the product of the two numbers if their sum is 12. (c) Find the point on the straight line 2x+ 3 y = 6 which is closest to the origin. (4 + 3 + 3 = 10) dy Q.4 (a) Find : dx 5x y= +cos2 (2 x + 1) (i) 2 (1- x )3

1 x 1 + 骣 1 (ii) y= x x +琪1 + 桫 x

dy 骣 t (b) Find when x= a琪cos t + log tan , y = a sin t . dx 桫 2 (6 + 4 = 10) Q.5 Integrate the following

(i) sin2x cos 4 x dx

dx (ii) cos (x- a ) cos ( x - b )

x dx (iii) (x- 1) ( x2 + 4) (3 + 3 + 4 = 10)

p a dx4 sin q d q Q.6 (a) If = , find a. 蝌 2 0x+ a + x 0 cos q (b) Evaluate :

1 (i) x(tan-1 x ) 2 dx 0

1 2 (ii) dx 2 2 0 (1- 2x ) 1 - x (4 + 6 = 10)

Q.7 (a) If a, b are real and a2+ b 2 = 1 then show that the equation 1+x - i 1 - x =a - i b is satisfied by a real value of x. 1+x + i 1 - x

-1 - - 3 (b) If w = , find the value of 2

(1-w + w2 ) (1 - w 2 + w 4 ) (1 - w 4 + w 8 ) (1 - w 8 + w 16 ) .

1 (c) Find the value of : (1+ i )5 . (4 + 3 + 3 = 10) cosx- sin x 0 -1 Q.8 (a) If f( x )= sin x cos x 0 , show that [f( x )] = f ( - x ) . 0 0 1

轾2 0 轾0 1 -1 - 1 - 1 (b) If A = 犏 and B = 犏 , verify that (AB ) = B A . 臌3 1 臌2 4 轾3- 4 (c) Express 犏 as the sum of a symmetric and a skew symmetric matrix. 臌1- 1 (4 + 3 + 3 = 10) 1 cos (a - b ) cos ( g - a ) Q.9 (a) Without expanding, prove that cos (a - b ) 1 cos ( b - g ) = 0 . cos (g - a ) cos ( b - g ) 1

(b) Solve the following system of equations by Cramer’s rule 2 3 10 4 6 5 6 9 20 + + =4; - + = 1 and + - = 2 . x y z x y z x y z

x+ a x x x x x+ b x x (c) Evaluate : . x x x+ c x x x x x+ d

(4 + 3 + 3 = 10) Q.10 (a) Compute standard deviation from the following data of the income of 10 employees of a firm by : (i) taking deviation from actual mean, and (ii) taking deviaiton from assumed mean 640 Income (Rs.) : 600 620 640 620 680 670 680 640 700 650. (b) Calculate arithmetic mean and standard deviation :

Value Frequency More than 800 14 More than 700 44 More than 600 96 More than 500 175 More than 400 381 More than 300 527 More than 200 615 More than 100 600

(c) The mean and standard deviation of a set of 100 observations were worked as 40 and 5 respectively by a computer, who by mistake took the value of 50 in place of 40 for one observation. Recalculate the correct mean and standard deviation. (4 + 3 + 3 = 10) DME/DCLE(G) TUTOR MARKED ASSIGNMENT BET-022 STRENGTH OF MATERIALS

Q.1 (a) Define the following terms : (i) Factor of Safety (ii) Shear Stress and Shear Strain (iii) Modulus of Elasticity (iv) Resilience (v) Strain Energy (b) A tensile test is carried out on a bar of mild steel of diameter 2.25 cm. The bar yields under load of 8 x 104 N; it attains a maximum load of 15 x 10 4 N breaks finally at a load of 7 x 10 4 N. Estimate (i) tensile stress at yield point (ii) ultimate Stress (iii) average stress at breaking point if the diameter of the neck is 1.2 cm. (5+5) Q.2 (a) A Steel tube 3.2 cm internal diameter, 0.25 cm thick and 4 m long is covered and lined throughout with copper tubes of 0.508 cm thick. The three tubes are firmly united at their ends. This compound tube is subjected to tension and stress produced in the steel tube is 60 MPa. Determine (a) the elongation of the tube, (b) stress in the copper tube, 11 11 (c) load carries by the combined tubes. Take Es = 2.1  10 Pa and Ec =1.1  10 Pa. (b) The efficiencies of longitudinal and circumferential joints in a cylindrical drum are 75% and 40% respectively. The drum is 2250 mm long with wall thickness 12 mm. Find the safe air pressure if the allowable stress in the shell material is 120 MPa. (5+5) Q.3 (a) Discuss the various types of beam with suitable examples. (b) A beam 8.0 m long made of wood with a square cross-section (400 mm) is floating in sea water. Two equal just sufficient weights are placed on the beam at 2.0 m away from each end to immerse in the sea. Find the magnitude of the weights. Also draw S.F.D and B.M.D for the beam. Take unit weight of timber and sea water 6400 N/m and 10200 N/m respectively. (5+5) Q.4 (a) A simply supported beam having circular cross-section of diameter 0.01778 m is loaded by the two concentrated load of 88.96 kN each applied 0.3048 from the ends of the beam. Determine the maximum flexural stress in the beam. (b) Write some important points showing some characteristics of shear force and bending moment diagrams. (5+5) Q.5 (a) A beam of hollow square cross-section (5 cm x and 5 cm) with 0.6 cm uniform thickness is subjected to shearing force 50 kN in the direction of one of the diagonal of the cross section. Determine maximum shearing stress developed and draw shearing stress distribution across the section. (b) Discuss the assumptions made in case of pure symmetrical bending. (5+5) Q.6 (a) Derive differential equation of deflection curve in a beam. (b) Draw the shear stress distribution diagram for a channel section (12 cm x 6 cm x 1.5 cm) of a beam subjected to shear force 50 kN at a Section. Also find the ratio between the maximum and minimum shear stresses.

(5+5) Tt G q Q.7 (a) Derive the following expression, considering the theory of torsion. = = . Jg L (b) A solid circular shaft transmits 75 KW power at 200 r.p.m. Find the suitable diameter of the shaft if the twist in the shaft not to exceed 10o in 2 meters length and shear stress is limited to 50 MPa. Take G = 100 MPa. (5+5)

Q.8 (a) A flat steel bar, 25 mm wide by 6mm thick and 1 m long is bent by couples applied at the ends so, that the mid point deflection is 20 mm. Compute the stress in the bar and magnitude of the couples. E = 200 GPA. (b) Determine Euler’s Crippling load for I-section just 40 cm x 20 cm x 1 cm and 5 m long which is used as a column with both ends fixed. E = 2.0 X 105 MPa. (5+5) Q.9 (a) Discuss the Buckling Load and Slenderness Ratio. (b) An Allowable axial load for a column of a length l with both ends fixed is 30 kN. Three different columns made of same material, same length and section having the following end conditions : (i) Both the ends are hinged, (ii) one end is fixed other end is free and (iii) one end is fixed, other end is hinged. What are the allowable loads for the three columns with conditions given above? (5+5) Q.10 (a) Discuss the Euler Theory of column. (b) Using Euler’s theory, calculate lining value of slenderness ratio for which it is not valid 5 2 2 for long columns (E = 2  10 N/mm and c = 325 N/mm ). (5+5)

DCLE (G)

TUTOR MARKED ASSIGNMENT BET-023 ELEMENTS OF SURVEY

Q.1 (a) Differentiate between the whole circle bearing and quadrantial bearing system of measurement of magnetic bearings. (b) Convert the WCB to QB and vice-versa : S 28o-14 E, S 47o-26 W, N 58o-24 W, 132o-12, 236o-37, 334o-52 Q.2 The following consecutive readings were taken with a dumpy level and a 4 m level staff on a continuously rising ground at common interval of 30 m. 3.016 at A, 1.579, 0.956, 3.844, 2.534, 1.689, 1.035, 0.962, 3.938, 3.644, 2.846, 1.953, 0.936, 0.585 at B. The elevation of A was 512.155. Make up a level book and find the RL’s of the various stations and apply the usual checks. Determine the gradient of the line AB. Q.3 Explain briefly the various methods of locating contours. Q.4 State the three point problems. Name the various methods of solution. Which of the above methods would you adopt and why? Explain in detail the method you will adopt. Q.5 Explain clearly the step-wise procedure of measurement of a horizontal angle by the method of repetition with a theodolite. Q.6 Can you use a theodolite as a levelling instrument. If yes give the step-wise procedure. Q.7 Write short notes on : (i) Reciprocal levelling and profile levelling. (ii) Radiation method of plane table survey. Q.8 Define surveying. What are the principles of surveying? Explain them briefly. Q.9 A plot was surveyed with a 30 m chain which was found to be accurate at the commencement of the work and 20 cm too long at closure. The map of the plot was drawn to a scale of RP 1/10,000. The area of the plot surveyed was found to be 80 cm 2 on the map. Calculate the actual area of the plot. Q.10 Define ranging and discuss its utility in a chain survey. Explain the use of a line ranger. DCLE (G) TUTOR MARKED ASSIGNMENT BET-026 WORKSHOP TECHNOLOGY

Q.1 (a) List various types of chisels used in carpentry work. Describe the use of any one with sketch. (b) What is “Setting of saw teeth”? Why is it done? Q.2 How are the patterns classified? Explain the use of “Sweep-pattern” with sketch. Q.3 What is “File”? Name the different parts of a flat-file with a neat sketch. Differentiate between “Dieing” and “Tapping” processes. Q.4 Why are stakes used in sheet metal work? Describe various types of stakes with net sketches. Q.5 (a) What is the purpose of a “Core” in moulding process? Indicate only the name of 3-types of “Core”. (b) Distinguish between “facing sand” and “parting sand”. Q.6 Describe different types of Gas Welding Technique, with the help of neat sketches. Differentiate between High Pressure and Low Pressure gas welding. Q.7 (a) Name the different types of operations performed on lathe machine. Explain any one. (b) Explain the terms “Accessories” and “Attachments” of lathe machine. Make a list of different accessories and attachments used with lathe machine. Q.8 What operations are performed in “Smithying” and “Forging work”. Explain with neat sketches. Q.9 (a) Describe in brief the characteristics of a god oil-paint. (b) What are the main constituents of an oil-paint? Explain with examples. Q.10 Define the term “Heat Treatment”. For what reasons steel may be heated. Explain any one method of heat treatment in details.