(DE 101) Total No. of Questions : 9] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) Paper - I : Mathematics - I Time : 03 Hours Maximum Marks : 75
Answer Question No.1 compulsory (15 × 1 = 15) Answer One question from each unit (4 × 15 = 60) Q1) a) Define the degree of a differential equation. dy x b) Find the order of the differential equation y = x + . dx dy / dx c) When do you say that a differential equation is exact?
dy d) What is the integrating factor of the differential equation + py = Q , where P, Q dx are the functions of x. e) When do we say that two family of curves are orthogonal? f) Define correlation. g) Write the equation of regression line of X on Y. h) Write the standard form of Cauchy’s homogeneous linear equation. i) Define the laplace transform of f (t). j) What is the laplace transform of eat tn?
−1 ⎧ s ⎫ L k) Find ⎨ 2 2 ⎬ . ⎩ s − a ⎭ l) State convolution theorem. m) Define the dirac delta function. n) Form the partial differential equation from z = f (x2 – y2) by eliminating the arbitrary function. 2 2 ∂ z ∂ z 2 o) Find the complementary function of 3 x y . 2 − = ∂x ∂x∂y
UNIT - I Q2) a) Obtain the differential equation of all circles of radius a and centre (h, k). dy ycos x++ sin y y b) Solve +=0 dxsin x++ x cos y x OR N-3074 P.T.O. (DE 101)
dy 3 2 Q3) a) Solve + x sin 2 y = x cos y dx b) Find the orthogonal trajectory of the cardioids r = a (1 – cos θ). UNIT - II
2 2 d y dy 2 x 3 x 4 y (1 x ) Q4) a) Solve 2 − + = + . dx dx
b) Solve, by the method of variation of parameters, y′′−+=2logyye ′ x x. OR Q5) a) X is a normal variate with mean 30 and S.D-5, find the probabilities that i) 26 < X < 40, ii) X > 45 and iii) |X – 30| > 5. b) Find the correlation coefficient between x and y from the given data : x :6864755064807540 y :6258684581606848 UNIT - III Q6) a) State and prove the convolution theorem for Laplace transforms.
−1 ⎧ s + 2 ⎫ L b) Find ⎨ 2 ⎬ . ⎩ s + (s +1) (s − 2) ⎭ OR cosat cos bt Q7) a) Find the Laplace transform of − . t
b) Solve y′′−+=+324yyte ′ 3t , when y(0) = 1 and y′(0) = – 1. UNIT - IV Q8) a) Find the differential equation of all planes which are at a constant distance a from the origin.
∂z ∂z b) Solve (mz − ny ) + (nx − lz ) = ly − mx . dx ∂y OR Q9) a) Solve q2 = z2 p2 (1 – p2). b) Solve 2z + p2 + qy + 2y2 = 0 by using Charpit’s method.
llll N-3074 2 (DE 102) Total No. of Questions : 9] [Total No. of Pages : 03 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - II) : MATHEMATICS - II Time : 03 Hours Maximum Marks : 75
Answer Question No.1 compulsory (15 × 1 = 15) Answer ONE question from each unit (4 × 15 = 60)
⎡ 1 ⎤ ⎡ 2 ⎤ Q1) a) Evaluate ⎢− 2⎥ × []4 5 2 × ⎢− 3⎥ × []3 2 . ⎢ ⎥ ⎢ ⎥ ⎣ 3 ⎦ ⎣ 5 ⎦ ⎡1 2⎤ b) Find the eigen values of . ⎣⎢2 4⎦⎥ c) Define Skew-Hermitian matrix. d) State Rolle’s theorem. e) What are the necessary conditions for f (x, y) to have a maximum or a minimum at (a, b). ⎡ cos sin ⎤ f) If A = then find AA'. ⎣⎢− sin cos ⎦⎥ 3 g) If λ1, λ2, λ3 are the eigen values of a matrix A, then what are the eigen values of A . a h) Evaluate ∫ x dx . −a
2 x i) Evaluate ∫∫(x+ y)dxdy . 00 j) Find the directional derivative of f (x, y, z) = xy2 + yz3 at the point (2, –1, 1). k) Find ∇. R if R = xi + y j + z k . ⎛ 1 1 ⎞ l) Find β ⎜ , ⎟ . ⎝ 2 2 ⎠ m) Find the unit normal at (2, –2, 3) to the surface x2y + 2xz = 4. n) State stoke’s theorem. o) Define idemtotent matrix.
N-3075 P.T.O. (DE 102) UNIT - I Q2) a) Solve the equations 3x + y + 2z = 3, 2x – 3y – z = – 3, x + 2y + z = 4 by determinants. b) Using the Gauss-Jordan method, find the inverse of the matrix. ⎡ 1 1 3 ⎤ ⎢ 1 3 − 3⎥ ⎢ ⎥ ⎣− 2 − 4 − 4⎦ OR Q3) a) Test for consistency and solve the equations 2x – 3y + 7z = 5, 3x + y – 3z = 13, 2x + 19y – 47z = 32. ⎡1 3 7⎤ b) Find the characteristic equation of the matrix A = ⎢4 2 3⎥ . Show that the equation ⎢ ⎥ ⎣1 2 1⎦ is satisfied by A and hence obtain the inverse of the given matrix. UNIT - II 1 Q4) a) If x is positive, show that x > log (1 + x) > x – x2. 2 324 x 22xx b) Using Maclaurin’s theorem show that exxcos=+ 1 − − + ...... 3! 4! OR Q5) a) Expand ex in powers of (x – 1) upto 4 terms. b) Find the volume of the greatest rectangular parallelo piped that can be inscribed in the 2 2 2 x y z 1 ellipsoid 2 + 2 + 2 = . a b c UNIT - III
Q6) a) Evaluate ∫∫ xy dx dy , where A is the domain bounded by x - axis, ordinate x = 2a A and the curve x2 = 4ay.
∞∞ −+()xy22 b) Evaluate ∫∫edxdy by changing to polar coordinates. Hence show that 00
∞ 2 ∫e−x dx= . 0 2 OR
N-3075 2 (DE 102)
16 2 Q7) a) Show that the area between the parabolas y2 = 4ax and x2 = 4ay is a . 3
1 dx b) Express ∫ interms of gamma function. 4 0 1− x
UNIT - IV
2 n n−2 Q8) a) Show that ∇ (r ) = n (n +1) r .
b) If F = 3xyi – y2 j , evaluate ∫ F.dR, where c is the curve in the xy - plane y = 2x2 from (0, 0) to (1, 2). OR
22 Q9) Verify Green’s theorem for ∫ ⎡⎤(xy++ y) dx x dx , where C is bounded by y = x and y = x2. c ⎣⎦
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N-3075 3 (DE 103) Total No. of Questions : 5] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - III) : PHYSICS Time : 03 Hours Maximum Marks : 75 Answer Question No. 1 compulsory. Answer one question from each unit. All questions carry equal marks.
Q1) a) Define harmonic wave and write its two characteristics. b) Write about double refraction. c) State and explain Gauss Law. d) Discuss the Faraday’s laws of electromagnetic induction. e) Write the properties of matter waves. f) Write the differences between spontaneous and stimulated emission. g) Explain photovoltaic effect.
UNIT - I
Q2) a) Derive the equation of state of SHM discuss in detail the formation of Lissajous figures from simple harmonic waves. OR b) Write the principle of diffraction. Describe an experiment to determine dispersion and resolving power of a grating.
UNIT - II
Q3) a) State and explain Biot - Savart’s law and derive the expression for B due to circular loop. OR b) Define Hall effect and obtain an expressive for Hall coefficient and describe an experiment to determine it experimentally.
N-3076 P.T.O. (DE 103)
UNIT - III
Q4) a) Explain the Debroglie concept of matter waves. Describe Devison - Germer experiment to demonstrate the existence of matter waves. OR b) Explain intrinsic and extrinsic semiconductors with suitable examples. Write the distinction between metals, insulation and semiconductors.
UNIT - IV
Q5) a) Explain population inversion. Write the working of GaAs Laser. Discuss the advantages of lasers over normal light in fibre optics and holography. OR b) Write the principle and working of photodiode and phototransistor and draw its characteristic curves.
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N-3076 2 DE104 Total No. of Questions : 5] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - IV) : CHEMISTRY Time : 03 Hours Maximum Marks : 75
Answer Question No. 1 compulsory (15) Answer ONE question from each unit (4 x 15 = 60)
Q1) a) Write the coagulation method for purification of water. b) Explain electrolysis of water. c) What is meant by softening of water? d) What are semiconductors? e) What is meant by condensation polymerisation? f) How do you prepare PVC? g) What is meant by Vulcanization? h) Define electrode potential. i) Give the significance of electrochemical series. j) What are the applications of secondary batteries? k) Define liquid crystals. l) What is cathodic protection? m) What is meant by Sacrificial anode? n) What are corrosion inhibitors?
UNIT - I Q2) a) How do you estimate hardness of water using EDTA method? b) Explain the process of demineralisation of water. OR a) Explain the role of sterilization and disintection in purification of water. b) Give the principle and applications of reverse osmosis. UNIT - II
Q3) a) Explain metallic bonding in solids. b) Give the band theory of solids.
N-3077 P.T.O. DE104 OR a) Give the mechanism of condensation polymerisation with an example. b) Distinguish between thermoplastic and thermosetting plastics. UNIT - III
Q4) a) Give the preparation and applications of BuNa-S Rubber. b) How can you determine pH using glass electrode? OR a) Write a note on electrochemistry of lithium batteries based on organic solvents.
b) Give the concept of H2 – O2 alkaline fuel cell.
UNIT - IV
Q5) a) Write a note on galvanic and microbiological corrosions. b) Explain the principle, surface preparation and applications of electroplating. OR a) Explain the electrochemical theory of corrosion. b) Explain the use of various liquid crystals in information technology.
ZZZ
N-3077 2 (DE105)
Total No. of Questions : 5] [Total No. of Pages : 03 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - V) : ENGLISH Time : 03 Hours Maximum Marks : 75
Q1) Correct the errors in the following sentences : (15 × 1 = 15) a) Have you met our professor in computer science? b) We are trying to change this house for the last three years. c) She is more intelligent than him. d) Each of the boys were interviewed by the principal. e) She does all the work except to wash the dishes. f) I am thinking to write my autobiography. g) The bride, loaded with presents, smiled at the guests. h) He should be returnning soon, isn’t it? i) Though Rani worked very hardly, she failed. j) She is too good. k) Don’t worry; I already informed her about that. l) He orders me as though I am his assistant. m) I can’t cope up with this problem. n) Let us discuss on the matter. o) The whole city was affected for the storm.
Q2) a) Read the following passage and answer the questions that follow: (5 × 2 = 10) Years ago an expert on automation, sir Leon Bagrit said that in future, computers would be developed which would be small enough to carry in the pocket. Ordinary people would then be able to use them to obtain valuable information. Computers could be plugged into a national network and be used like radios. For instance, people going on holiday could be informed about weather conditions, can drivers; can be given alternative routes when there are traffic jams. It will also be possible to make tiny translating machines. It is impossible to assess the importance of a machine of this sort, for many international unisunderstandings are caused simply through on failure to understand each other. Thus computers are the most efficient servants man has ever had and there is no limit to the way they can be used to improve our lives. i) How would the future computers be developed? ii) How would computers help can drivers? iii) What does ‘efficient servants’ mean? iv) How can computers help in bringing the countries of the world together? v) What does the automation expert say of computers? N-3078 P.T.O. (DE105) b) Bring out the differences of meaning of any FIVE of the following pairs of words and use them in sentences of your own. (5 × 1 = 5) i) Affect - Effect ii) Ancient - Antique iii) Bridal - Bridle iv) Council - Counsel v) Dual - Duel vi) Emigrate - Immigrate vii) Fain - Feign viii) Metal - Mettle ix) Popular - Populous x) Wave - Waive
Q3) a) Write a paragraph on any ONE of the following: (1 × 6 = 6) i) Terrorism ii) Women reservation b) i) Write a letter to the town rationing officer, applying for a ration card. (1 × 5 = 5) OR ii) Write a letter to the editor of a news paper on the need for repairing the roads of your town. c) Give the meaning and use them in your sentences any EIGHT of the following idiomatic expressions. (8 × ½ = 4) i) To read between the lines ii) At the Right of iii) Vexed with iv) Cut back v) Run after vi) A fly in the ointment vii) To smell a rat viii) To lose heart ix) A month of sundays x) As tough as nails.
Q4) a) Write a brief report to the district education officer on child drop out in rural areas. (1 × 10 = 10) b) Give one word substitutions for the following explanations. (10 × ½ = 5) i) A person who believes in God ii) Killing one’s father. iii) One who eats indiscriminately and in large quantities. iv) Saying things in a round about way. v) A person with strange and peculiar habits vi) Someone who loves collecting stamps. vii) One who dedicates one’s life to a selfless pursuit. viii) A particular method used to achieve something. ix) Easily convineed, cheated and gulled. x) One who totally abstains from drinking.
Q5) a) Write a small essay on any one of the following : (1 × 5 = 5) i) Globalization ii) Pollution b) Expand ONE of the following: (1 × 5 = 5) i) Rome is not built in a day. ii) Variety is the spice of life.
N-3078 2 (DE105) c) Write antonyms of the following words: (5 × ½ = 2½) i) Ripe ii) Trivial iii) Upright iv) Miser v) Idealistic d) Write synonyms of the following words : (5 × ½ = 2½) i) Prudent ii) Insane iii) Giggle iv) Deny v) Brisk TTT
N-3078 3 (DE 106) Total No. of Questions : 9] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - VI) : COMPUTER PROGRAMMING Time : 03 Hours Maximum Marks : 75
Answer Question No. 1 compulsory. Answer ONE question from each unit.
Q1) a) Size of character data type. b) Bit wise operators. c) Define operator precedence. d) Define type casting. e) Write syntax for nested if-else. f) ‘Continue’ statement. g) Syntax for do-while. h) Initialisation of array. i) What is pointer? j) List two string handling functions. k) Calloc ( ) function. l) What is return type of main ( ) function? m) List two file processing functions. n) What is structure? o) What are command line arguments?
UNIT - I
Q2) a) Explain about logical and bitwise operators in C. b) Write C program to comparision of three numbers. OR Q3) a) Explain about data types in C. b) Write a ‘C’ program to perform various arithmetic operations by using switch statement?
N-3079 P.T.O. (DE 106) UNIT - II
Q4) a) Explain looping structures in C language. b) Write a C program to check given number is palindrome or not. OR Q5) a) Write about call by value and call by reference function in C. b) Write a C program to find the factorial of given number using recursion.
UNIT - III
Q6) Define array. Explain about declaration and initialization of one dimensional and two dimensional array with examples?
OR Q7) Explain about various string handling functions.
UNIT - IV
Q8) What is file? Write the syntax for creating file. Explain about various file operations. OR Q9) a) Differentiate structures and unions with example. b) Create structure for maintaining the employ details.
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N-3079 2 (DE 107)
Total No. of Questions : 9] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - VII) : ENGINEERING MECHANICS Time : 03 Hours Maximum Marks : 75
Answer Question No. 1 compulsory and one question from each unit. All question carry equal marks.
Q1) (15 × 1 = 15) a) What is Mechanics. b) System of co-planer forces. c) Principle of transmissibility. d) Define a truss. e) Laws of dry friction. f) moment of force about a point. g) Scalar product of two vectors. h) Equilibrium of rigid body in 3 -d. i) State principle of virtual work. j) Polar moment of Inevtia. k) Newton’s Second law of motion. l) State of principle of Impulse. m) State parallel axis theorem. n) What do you understand by potential energy? o) Draw the displacement - time curve for linear motion.
UNIT - I Q2) Determine the magnitude and direction of the resultant of the system of forces shown in the fig. 1.
OR Q3) A pull of 180 N applied upward at 30º to a rough horizontal plane was required to just move a body resting on the plane while a push of 220 N applied along the same line of action was required to just move the same body downwards. Determine the weight of the body and the co-efficient of friction. N-3080 P.T.O. (DE 107)
UNIT - II
Q4) Determine the centroid of area shown in fig:2.
All dimension are in mm.
OR Q5) Derive the expressions for moment of inertia of a) Traiangle about the base. b) Semicircle about the diametral axis.
UNIT - III
Q6) A uniform ladder of weight 600 N rests against a smoth vertical wall and a rough horizontal floor making an angle of 45º with the horizontal. Find the force of friction at the floor using the method of virtual work.
OR Q7) A small stal ball is shot vertically upwards from the top of a building 25 m above the ground with an initial velocity of 18 m/sec. a) In what time, it will reach the maxi height. b) How high above the building will the ball rise.
UNIT - IV
Q8) A pump lifts 40m3 of water to a height 50 m and delivers it with a velocity of 5 m/ sec. What is the amount of energy spent during this process? If the job is done in half an hour. What is the input power of the pump which has an overall efficiency of 70%? OR Q9) The rotation of a fly wheel is governed by the equation W = 3t2 – 2t + 2 where W is in radiouss / Second and t in seconds. After one second from the start the angular displacement was 4 radious. Determine the angular displacement. Angular velocity and angular acceleration of the fly wheel when t = 3 seconds. TTT N-3080 2 (DE 108)
Total No. of Questions : 10] [Total No. of Pages : 02 B.Tech. DEGREE EXAMINATION, MAY - 2013 (Examination at the end of First Year) (Paper - VIII) : ENGINEERING GRAPHICS Time : 03 Hours Maximum Marks : 75
Answer one question from each unit
UNIT - I
1 Q1) Construct a diagonal scale of to show metres and long enough to measure 500m. 4000 Mark a distance of 290m on the scale. OR Q2) The major and minor axes of an ellipse are 125 mm and 100 mm respectively. Draw half of the curve by concentric circles method and remaining half of the curve by oblong method?
UNIT - II
Q3) A line AB, 70 mm long is inclined at 45º to the H.P. and 30º to the V.P. Its end A is on the H.P. and 25 mm infront of the V.P. Draw its projections. OR Q4) A regular pentagon of 30 side is resting on one of its edges on the H.P. which is inclind at 45º to the V.P. Its surface is inclind at 30º to the H.P. Draw its projections.
UNIT - III
Q5) A square pyramid, base 35 mm side and axis 80 mm long has a triangular face on the H.P. and the vertical plane containing the axis makes an angle of 45º with the V.P. Draw its projections. OR Q6) A cube of edge 50 mm is resting on the H.P. on one of its faces with a vertical face inclined at 30º to the V.P. It is cut by section plane perpendicular to the V.P and inclined 45º to the H.P. The section plane intersects the axis at 45 mm from the base. Draw the projections.
N-3081 P.T.O. (DE 108) UNIT - IV Q7) Draw the development of truncated pentagonal prism.
OR Q8) A triangular prism, base 70 side, resting on one of its bases on the H.P. with a face perpendicular to the V.P is pentreted by a horizontal traingular prism of base 40 mm side. The axes of the two solids intersects each other and a plane passing through them is parallel to the V.P. Draw the line of intersection.
UNIT - V
Q9) Draw the Isometric projection of the fig.1 shown below. (Sphere is resting on square prism)
OR Q10) Draw the top view, Front view and left side view of the fig. 2.
TTT N-3081 2