Upcoming SlideShare
×

4th Semester Civil Engineering (2013-December) Question Papers

4,297 views

Published on

Published in: Education
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
4,297
On SlideShare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
109
0
Likes
0
Embeds 0
No embeds

No notes for slide

4th Semester Civil Engineering (2013-December) Question Papers

1. 1. e "v r i,"1'{ I L' 1OMAT41 USN Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4 Engineering Mathematics - lV Max. Marks:100 Time: 3 hrs. Note: Answer FIVEfull questions, selecting at least TWO questions from each port. a) o o ... L I a. d () b. -.o oo l1 troo .= ol c. ts Emplo,y Taylor's series method to obtain the value of y at 2 a. x: 0.1 and 0.2 for the differential * =rr+ 3e* . y(0) : 0 considering upto fourth d.gr.. t*rrn. dx (06 Marks) y":i +y2using modified Determinethe value of ywhenx:0.1, giventhaty(0):1and Euler's lormula. Take h : 0.05. . Apply Adams-Bashforth method to solve the equatron y(1. i50 oi do o> PART_A equation OJ ox ... I): Solve t 1.233, =t* y(.2): dv )---!-;;'1t+y). : v(O) = Q,z(0):1atx:0.3 grven dx 1.979. Evaluate y(1.4). t.548,:y11.3) r*. 9- -xy. (07 Marks) oO bQi ,€ b. c. 1, by taking h : 0.3. Applying (06 Marks) Applying Picard's method to compute y(1.1) from the second approximation to the solution (07 Marks) of the differential equation y" * fy': x'. Given that y(1) : 1, y'(1) : 1. Using the Mitni's method obtain an approximate solution at the point x *= t-ZV!. " dx dx' 5ir : (07 Marks) Runge-Kutta method of fourth order. a= y(1) y(0.41 : give rhat y(0) :0. y'(0) 0. y(0.2) : 0.0795. y'(0.4) :0.3937.y(0.6) :0.1762.y'(0.6) : : 0.8 of the problem 0.02. y'(0.2): 0.1996. (07 Marks) 0.5689. p- 6. o" oj !o 5.: }'(ts boe i al) o= 3 a. b. (06 Marks) Derive Cauchy-Riemann equations in Cartesian form. Give tr.-- v (x - yXx2 + 4xy + f(z): y2; find the analytic function c. tf f(z): u * iv is an analyic tunction then prove thrt (* | f(r) u + iv. l) . [* (07 Marks) |f (r) I) =1f '1ztl) (07 Marks) o-B tr> Xo ()- (r< - o o C.l 4 a. b. Z o c. Find the image of the straight lines parallel to coordinate axes in z-plane under the (06 Marks) transformationw: z2 Find the bilinear transformation which maps the points z : l, i, -1 on to the points w:0, (07 Marks) 1, oo. where c is the circle Evaluate r,f---gj-. (z + ll(z + 2) I zl : I of2 3. (07 Marks)
2. 2. 1OMAT4l PART _ B 5 a. Find the solution of the Laplace equation in cylindrical system leading to Besseis differential (06 Marks) equation. If c. 6 a. b. c. 7 a. .lm cx and B are two distinct roots of J,(x) : I 0, then prove that fx J, (ux) o + n. Eipq*ur (x) : *o - 2*' + l* - 4x + 5 in terms of legendre polynomial. J,, (BX)di = O, r;... ,, ' """ (07 Marks) (07 Marks) A coiilfufttee consists of 9 students, 2 from first year, 3 from second year and 4 from third year. 3 st'"udepts are to be removed at random. What is the probability that (i) 3 students belongs to different class (ii) 2 belongs to the same class and third belongs to different (06 Marks) class. (iii) All the 3 belongs to the same class. State and prove Ba\$Cs :::'::"' '1""''r theorem. :'::: "t (07 Marks) The chance that adodtirw^ill diagnose a disease correctly is 600/o. The chance that a patient will die after correct diagncise is 40Yo and the chanCe bf death after wrong diagnose is 70o/o. (07 Marks) If a patient dies, what is the bhhrpE that diseasdWas conectly diagnosed. The probability distribut ion of finite random variable x is siven by the following table: x 0 o(x) 0 : ') 1 Ir J 4 5 6 7 2k 2k 3k k 2k 7k'+k Find k, p(x < 6), p(x > 6), p(3 < x < 6) (06 Marks) b. Obtain the mean and variance of Poisson distribution. (07 Marks) c. The life of an electric bulb is normally distributed wiXh average life of 2000 hours and standard deviation of 60 hours. Out of 2500 bulbs, find the number of bulbs that are likely (07 Marks) to last between 1900 And 2100 hours. Given that p(0 < z < 1.57) : 0.4525. 8 a. b. , l' '.,'- Explain the foilbwing i) Null hy sis ',,; terms: (ii) Type I and Tlpe II error . ,- , ,,':"-" (iiil Confidgnce limits. (06 Marks) The weight of workers in a large factory are normally distributediWith mean 68 kgs, and starydard deviation 3 kgs. If 80 samples consisting of 35 workers each are chosen, how many of,80 samples will have the mean between 67 and 68.25 kgs. Given p(0 < z < 2) : 0.4772 and p(0 3 z < 0.5): 0.1915. .,,,", ,{07 Marks) Eleven students were given a test in statistics. They were provided additional coaching and then a second test of equal difficulty- was held at the end of coaching. Marks scored by then in the two tests are given belo ven I II t9 24 19 22 t8 20 20 20 23 20 t7 Do the marks give evidence that the student have benefited by extra coaching? Given t005(10) :2.228. Test the hypothesis at 5Yo level of significance. (07 Marks) Test Test 23 20 19 21 *8ri<** 2 of2 18 20 22 18 t7 23 t6
3. 3. MATDTP4Ol USN Fourth Semester B.E. Degree Examination, Dec.2013/Jan.2\$t4 Advanced Mathematics - ll Max. Marks:100 Time: 3 hrs. Note: Answer any () o o * g .= o o ! Eg cEe 76 -o0 coo an 2 a. Find the equation of the plane through the points c. b0i ccd -o >! e 3o aLE LO )E >- (! -^o eoo o= so tr> ^-o 5e Z ! o -2) and perpendicular to (07 Marks) x-2:,u-l _r-3 end x+i_>-3_z-1 (07 Marks) 0 (07 Marks) ii) (2a+ 36) x (a +,::,45) (07 Marks) b. c. rr a' b. c. a'.1 O o (l; -2,2) (-3, l, are coplanar. Prove the following: , i) (34 - 26) x 1-la + 2b-; = l4(A + 6) U< - (06 Marks) c. a. -_I {*i=, Find the sine of the angle between d = 2il2 j_+ k jrLb = 2i 1- 12ka Find the value of ), if the vectors a = 4r+ 6j+ 2k, b=3i +10j +5k and c ^X 'ii + a' b. a6 tro. o." o theplane2x-y-z+6:0" t22*1 'od 3A OE I Find the angle between the following lines: oE -o UO Prove that the equation of the plane in the intercept form is b. tso ;:r questions. I a. Prove that sin' cr + sin' B + sin' y = 2. (06 Marks) b. If 11; ml, n1 and 1.2, mz, fl2 are direction cosines of two lines then pxove that the angle (07 Marks) between,,them is cos 0: l-J-zt m1m2 * nrflz. : ,,ir c. Find the equation of the plane through the interaction of the pl4nes'2x + 3y - z : 5 and (07Marks) x-2y -32= - 8, also perpendicularto the plane x +y -z:2. I .: FIVEfull a. b. c. E d. (06lVlarks) =-41+5J+i[- ' = 5(a + 6) along the curve i = (t' -4O1+(t2 +at)j+(8t2-.3t3;[. nina the velocity (06 Marks) and acceleration at t : 1 and also find their magnitude. ., :4 at the point (- 1 , -1 , 2). nind,ihe unit normal vector to the surface xy3 z2 :_ (07 Marks) (07Marks) Findthedirectionalderivative ofx2yz3 at(1, 1, 1)inthedirectionof i+j+2k A particle rr,lclVes {,; (06 Marks) Find div F and curl F, where F = xti + ytj + zt[ . ,,"'l Prove that curl grad Q : 0. (oiiMarks) Find the constants a,b, c such that the vectorF =(x* y +az)i+(x+ cy +22)k+(bx+ 2y -r)j (07 Marks) is irrotational. Find the Laplace transform of the following: sin 4t cos3t cos hat t e-t sin t 1 - cost GENTH'al LlElgi&RY 20 Marks)
4. 4. MATDIP4Ol 7 Find the inverse Laplace transform of a' - /s+1 '"1r r.,J s+l - __-:_ b. (06 Marks) (07 Marks) s'+2s+2 t' (o7ilIarks; G+1)G{2X,L:5 ., ",{}1* , 8 a. tr;'@g ,,.,. Laplce transforms, solve the differential equation subjectEffi-the conditions y(0) b. : :0. y'(0) gy-*x **r=sint, dt dt Given that x : 1, yffiwhen t : 0. Solve the siffilppeous equations Lfl./ {furgl. dt'- 6y dt , =5e" (10 Marks) =9oF\$, using Laplace transforms. ,.ftrI* (lo Marks) 4 d,. **{<i<{< ," , " ... q t:: ti' ' ; "'* ,,*;t i: ::: :: - I :: '!i;-,::' i" {;lli};,.., ::::. ::" ' .{ }. _r*!#U '' ',,,"""""",,,,':1 , . ,,,-, =.= , .:::: q tl, '{+,t t- ,,1' : ta..""':':""""' '"' -.::::- '::::, ' 2 of2 u-
5. 5. 10cY42 USN Fourth Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4 Goncrete Technology Max. Marks:100 Time: 3 hrs. Note: Answer FIVEfull questions, selecting atlesst TWO questions from each part. PART _ A () o o 1 a. a b. What are Boughe's compounds in cement? Explain the role of each compound in strength (10 Marks) gaining and hardening process. of flow,lt"Jlr.u, Exp14,,1\$he process of "Dry Process" of manufacturing cement with a help () o 3e =h 3 ool =ca .= 2a. b. 3 a. a-.1 nbo Yo otr b. -O o> o2 Define water cement ratio, and how this w/c ratio will have influence on workability of fresh concrete. ::: ,. ,, 4 a. b. ,, (10 Marks) What are admixtures? Why ihey..ale used in ttle,,manufacture of concrete? Explain any three (10 Marks) admixtures used in concrete manufacture. ',,,,, '''i ni'"; o= oO (10 Marks) What are the physical requirements of good fine and coarse aggre\$ates? Define "Grading of aggregates", what is the importance of.grading of aggregates in the (10 Marks) manufacture of quality concrete. ''. tt"'' Write notes on i) Segregation - .. " "t"' ii) Bleeding. (10 Marks) What are the filed tests condtrCted on quality of cement at site of construction. (10 Marks) boe ",,,, PART a6 -e) 5-E s5. =:! o'' 5 a. b. A,i related with compressive strength of .,,i ,, r (10 Marks) tr. ttt Define: . ,',ll' i) i) iD tr< z it concrete? Write shoft notes on =o EL o '''"' ':::::""" ""' i,.,.*- 6 a., Fxplain the relation between the modulus of elasticity and compressiv tr> -61 ,,' Define "Tensile "strength of concrete". How is Flex\$ml'strength ii) Cofuressive strength iii) : Sptit tensile strength. o= !o v, boo co! o= o. ;i ,,' -B 7a. b. 8 a. b. r1r1'.. , (10 Marks) th of concrete. : Factors affecting the shrinkage Factors affecting creep. What are the factors contributing to cracks in concrete? Explain the significance of durability of concrete in its affecting the durability of concrete. a i !l (lo Marks) the factors (10 Marks) Define nominal mix, and its types, explain the importance of design mix in the RCC design (10 Marks) of structural members. Write step by step procedure for I.S method of mix design (preferably flow chart) (10 Marks)
6. 6. l0cv43 USN Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l4 Structural Analysr's - I Time: 3 hrs. Max. Marks:100 Note: 7, Answer FIVEfull questions, selecting ot least TWO questions from each part. 2. Assume any missing data suitably. o o o L a I PART _ A b. between determinate a.rd indeterminate structures with examples. (06 Marks) Determine the static and kinematic indeterminacy for the structures shown in Fig.Q1(b). c. ; Fig.Ql(b) Write strain energy expressions fbr 4xrql, shear bending and twisting. a.: Distinguish C) = () 3e bo69 =n -bo troo .= c I hoo yo ol -O o> o :] a= oc) 2 a. (10 Marks) (04 Marks) Determine slope and deflection at the free end for the cantilever beam shown in Fig.Q2(a), (10 Marks) using moment area method. botr 26 6L= 5u aX 66x\$"r* oi b. o= dtE @ Fig.Q2(a) Fig"Q2(b) , Deterftine the slopes of support and deflection under the load ror the ,bea* Fig.Q2(b), using conjugate beam method. i,?"#Lil !o 5." ^: 3a. ia0 .-c 6= go =(€ tr> =o 5L J< f, .i ,,, 'o (06 Marks) State and prove Maxwell's reciprocal theorem. point C of the Using the method of virtual work determine the horizontal displacement of a (14 Marks) frame shown in Fig.Q3(b). Take E :2x10s N/mm2 and I :4x106 mma. I o o '7 (n o ,kN Fie.Q3(b) a*r^ Fig.Q4 -n
7. 7. 10cv43 Determine the vertical and horizontal deflections at point C of the truss as shown in Fig.Q4, using unit load method. Area of cross section of all the members is 6x10-a m'. Take E:200 GPa. (20 Marks) PART _ B 3a. A three hinged parabolic arch is loaded as shown in Fig.Q5(a). Determine the B.M- at loaded points. lookN h6" b. 6a. b. (10 Marks) lSoLrJ -'l t+u -aw Fie.Q5(at =l Fie.e6(a) A flexible suspenSioa cable of weight 0.0075 kN/m hangs between two vertical walls 60 m apart, the left end being attached to the wall at a point 10 m below the right end. A concentrated load of I kN is attached to the cable in such a manner that the point of attachment of the load is 20 mhorizontal from the left and wall and 5 m below the left hand support. Show that maximum tension occurs at the right hand support and find its value. A cantilever beam of constant flexural rigidity is propped at its free end to the level of fixed end. Determine the reaction of the prop when the beam carries udl over the entire span. Hence draw BMD and SFD. Fig.Q6(a). (10 Marks) Determine the fixed end moments or support moments for the beam loaded as shown in Fie.Q6(b). , (to Marks) Fie.Q6(b) Fig.e7(b) a. Derive the generalized Clapeyron's theorem of three moments. (06 Marks) , b. Analyze the continuous beam ABC shown in Fig.Q7(b), using Clapeyron's thoorem of three rnbments. Hence draw BMD and SFD. Also sketch elastic curve. (14 Marks) Find the horizontal thrust for the two hinged parabolic arch as shown in Fig.Q8. The moment of inertia at any section is I. secO, wheie 0 is the slope at section and I. is M.I. at the crown. Neglect the effect of rib shortening. Draw BMD. (20 Marks) Fig.Q8 *ri<*ri<* 2of?-