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1 B.A./B.Com./B.Sc. DEGREE EXAMINATION, MAY (Examination at the end of Final Year) Third Year Paper - II : Science & Civilization (DICS31) Time : 1 Hour 30 Minutes Maximum Marks : 50 Section - A (2 x 13 = 26) Answer any Two of the following in sixty lines 1) Write an account on preparation and types of vaccines. È P Ö " Ç ¼!.À È" ( ¼! # ¾Þ PAà YÞ ( b ßÔÈ" ( YÞ È ½ßÔÈ" # ~È ¼! #È" #2 2) Solar energy is an up growing source of energy - Discuss. Õ ¾Þ Ì! P ~ß«È" #T ~ß«½È".ª¼! ( Ì! P D ÉÈ" ß«'È" #2 3) What is hydrogen bomb? What is the principle involved in the hydrogen bomb? R ~ i Œþ ³ ²( D " YA É(B ¼!.ÀÄ] É ª ÉÈ" ß«'È" #B 4) What is the value of social justice in the modern society. E Þ ( PÞ ßÔÈ".iÈ" #Ä] Õ È".kPÞ ½¼! (È" # ÉÃ(È" à YÞ. d ÉÈ" ß«'È" #2 5) What is satellite? Write about uses and types of satellites. ÌAv RÄ sœý D " YA É(B ÌAv RÄ sœý Hß«¼.YAÃ( ¾Þ PAà YÞ. d ~È ¼! #È" #2 6) Explain the major contribution of modern science to human welfare. E Þ ( PÞ ÌA Ô ¼! ( Éj t à È" à " È". " È" ~ß«YÞ P PÞ ÅY Hß«¼.YAÃ( ~È ¼! #È" #2 7) Write short notes on any THREE of the following: a) Radioactivity. ¾ ¼.»PÞ 2 b) Synthetic detergents. Ô œþ v P u¾ m u(2 c) Geological survey. ry ÛPÞ ßÔ¾ ËÃ(2 Section - B (3 x 4 = 12)

2 d) Steam engine. ÔtÐŒþ$ F i " (2 e) Green Revolution. ß Éß«ÇÈ" È" #2 f) Test tube baby. v ŒÔw u.½»œý ³ 2 g) Pyrethrums. R «~œþ ÐŒþ$2 h) Synthetic fibre. PÞ ~ È" ( ¾Þ Ã(2 i) Pencillin. «ÖÅ Œþ2 Section - C (3 x 4 = 12) Answer all questions 8) Fill in the blanks: a) Compass is used for finding the. PÞ.Öc P ¾Þ PÞ ( È Þ (Þ (¾Þ (2 b) X rays were discovered by. JP Ö¾ à " ( PÞ «v w ". c) Bacteriology means. ³ P w ¼!.Ãk D " YA. d) Chemical responsible for Ozone depletion. Nj] Œþ Ï PÞ ( PA¾Þ Ï È" (¼ (½ ¾Þ Õ ¼! ( " È" #. 9) Choose the correct answer: a) Earth revolves round the sun discovered by!.é( ßÔ.¾Þ (½ a (u(w ß«~! È" (Ï È" # PÞ " (Y " ªÈ ¾Þ (2 i) Kepler ii) Galileo iii) Issac Newton iv) Copernicus.

3 b) SHAR centre is at i) Andhra Pradesh ii) Madhya Pradesh iii) Uttar Pradesh iv) Maharashtra SHAR P ~Þ È" # PÞ Ã ~ß«Ì! È" # i) E ~ Þ ~ß«ÔŒý ii) È" ( Þ ½~ß«ÔŒý iii) H ¾Þ ~ß«ÔŒý iv) È" (ؾAßÑŠ c) The Heart of the computer is i) Keyboard ii) Mouse iii) CPU iv) Printer PÞ ß«Q½u¾ PÞ ( F YÞ ( È" v i) P ³]¾Þ (} ii) È" ŒÔ iii) CPU iv) ~ «u¾ d) Theory of relatively was proposed by i) A. Einstein ii) I.P. Pavlov iii) Ottoham iv) Rutherford Õ «Þ Ô È" # ~ß«b " i) A. L ŒþïÜt Œþ ii) I.P. È" Ä ÐŒþ iii) Nv]wß ÐŒþ$ iv) ¾Þ.œÞ ¾ ß ¾ } 10) Match the following: a) Green house effect i) Health b) Vitamins ii) Alexander flemming c) Coal iii) Methane and CO 2 d) Pencillin iv) Conventional energy a) [ Œþ ß rœô ~ß«È" È" # i) E¾ YÞ ½ b) ÉuÉ( " (Ç ii) DÄ YAm Þ ¾ «ÇÉ( Y c) ³ YÞ (\ iii) É(œ Œþ È" ( ¼! # CO 2 d) «ÔÅ Œ iv) Õ ~ß«¼! ( M " ¾Þ (Ã(

4 B.A. DEGREE EXAMINATION, MAY (Examination at the end of Third Year) Part - II : MATHEMATICS Paper - III : Rings and Linear Algebra (DBMAT 31) Time : 03 Hours Maximum Marks : 100 SECTION-A Answer all questions. (8 x 5 = 40) Each question carries 5 marks. 1) Prove that intersection of two ideals of a ring R is an ideal of R. R È" ü! ( ¼ #PÞ S ¾ Þ ( L ¼! (Ã(Ö,EÞ ¾AÐÃ(- e Þ " 0 R È" ü!. P L ¼! (Ä DÈ" ' ( Þ a.ß«2 2) If are two polynomials over a ring R, then prove that R È" ü! ( R «¾Þ Ëb ß«² " ¾ Þ ( ²ß (ß«Þ (Ã( RÄ 0 D ¾Þ. «a 2 3) Express the vector as a linear combination of the vectors e 1 = (1, 1, 1), e 2 = (1, 2, 3) and e 3 = (2, 1, 1) ßÔ ¼.YÞ YA ~È ¼! ( 2 ßÔ Ì! " ( e 1 = (1, 1, 1), e 2 = (1, 2, 3) È" ( ¼! # e 3 = (2, 1, 1) ßÔ Ì! à ²#n 4) Find the null space, range, rank and nullity of the transformation T : R 2 R 2 defined by T(x, y) =. T : R 2 R 2 ²#n ß«È" ¾Þ " T(x, y) = D ¾Þ Ëb Ô T ¼ #PÞ S Ì!. ½ ¾AÚ! È" #0 È ½ «0 ß«È" ¾Þ " P v 0 ß«È" ¾Þ " Ì!. " ½ à " ( PÞ " (P S 2 5) Find the inverse of the matrix of A =. R «È".~ PÞ A ¼ #PÞ S ÉÄ]È" ( È".~ PÞ " ( PÞ " (P S 2

5 6) Show that are the eigen values of the matrix A =. R «È".~ PÞ A ¼ #PÞ S Ä Þ Ï PÞ ÉÃ(È" Ã( Ã( D a.ß«2 7) State and prove Cauchy-Schwarz inequality. P Ñ * Õ S ˾ m DßÔÈ". " " ( ~ß«È" b b0 ¾Þ. «a (È" #2 8) Find a unit vector orthogonal to (4, 2, 3) in R 3 (R). R 3 (R) Ä] (4, 2, 3) ßÔ Ì! PÞ ( à ² YA H ¼! $ sœý ßÔ Ì! " ( PÞ " (P S 2 SECTION-B Answer all questions. (4 x 15 = 60) Each question carries 15 marks. 9) a) i) If A and B are two ideals of a ring R, then prove that A+B is an ideal of R containing both A and B. È" ü! (È" # R Ä] A, B Ã( ¾ Þ ( EÞ ¾Þ ÐÈ" #þ # " A+B ßÔÉ( A, B à " ( PÞ ÅZ¼! # " ª EÞ ¾Þ ÐÈ" ( a.ß«'è" #2 ii) If in Z 5 [x] find i) and ii). Z 5 [x] Ä] D¾ # " i) ii) à " ( PÞ " (P S 2 Ã( ²ß (ß«Þ (Ã( OR b) i) Prove that Q is a field. Q MPÞ ~ D a.ß«2 ii) Show that is a prime ideal of Z[x] but not a maximal ideal of Z[x]. Z[x] Ä] MPÞ ~ß«" EÞ ¾Þ ÐÈ" # DÈ" ' ( Þ 0 D PÞ È" ( EÞ ¾Þ ÐÈ" # PAÞ a.ß«2

6 10) a) i) Prove that a non-empty subset W(F) of a vector space V(F) is a subspace of V iff and. V(F) MPÞ ßÔ ÌA ¾AÚ! È" #2 W(F) Ì!. ½ ¾Þ ßÔÉ( 2 V Ä] W MPÞ H ¾AÚ! PAÈ" v P EÈ" Ì! ½PÞ ß«¾A½ß«¼! (È" ( È" ( ¼! # D a.ß«2 ii) Define a linear transformation of a vector space U(F) into a vector space V(F). Is the mapping T : R 3 R 2 defined by T is a linear transformation. ßÔ ÌA ¾AÚ! È" # U(F) " ( V(F) " PÞ ( ²#n ß«È" ¾Þ " " ( ¾Þ Ëb a 2 T : R 3 R 2 ~ß«È (¼! ( T D¾ # ²#n ß«È" ¾Þ " È" (È" ' ( B OR b) i) If α, β, γ are linearly independent vectors of V(R), then show that α+β, β+γ, γ+α are also linearly independent. V(R) ¼ #PÞ S α, β, γ Ã( ²#n Õ Ë ~ ½ ßÔ Ì! þ # α+β, β+γ, γ+α Ã( PÞ. ²#n Õ Ë ~ ½Ã a.ß«2 ii) Let U(F) and V(F) be two vector spaces and T : U V is a onto linear transformation N is the Null space of T. Then prove that. T : U V MPÞ ßÔ ÌA ¾AÚ Ã ²#n ß«È" ¾Þ " N, T à ¼ #PÞ S Ì!. ½ ¾AÚ! È" # U(F) È" ( ¼! # V(F) D¾ # " D a.ß«2 1 2 = ) a) i) Reduce the matrix A 2 1 into Echelon form and hence find its 8 7 rank. R «A È".~ PÞ " ( È" Q½ÁÞ ¾Þ.ß«Ä] P È". d0 E È".~ PÞ ¼ #PÞ S P v PÞ " (P S

7 ii) Find the eigen values and eigen vectors of the matrix of A =. R «A È".~ PÞ PÞ ( Ä Þ Ï PÞ ÉÃ(È" Ã( È" ( ¼! # Ä Þ Ï PÞ ßÔ Ì! Ã( PÞ " (P S 2 OR b) i) If A =, verify Cayley-Hamilton theorem and hence find? R «A È".~ PÞ PÞ ( P Æ*ØÉ(Ãw Ô ª ßÔ a. Þ 0 " ( " ( PÞ " (P S 2 ii) If A =, test A for diagonalizability. R «A È".~ PÞ PÞ ( ÉPÞ À ¼! ( " ( ß«À a 2 12) a) i) In an inner product space V(F), then prove that for all. V(F) D D ¾Þ Ã»ê ¾AÚ! Ä] " PÞ ( D a.ß«2 ii) In an inner product space R 3 (R), obtain an orthonormal basis from the basis using Gram-Schmidts process. R 3 (R) D D ¾Þ Ã»ê ¾AÚ! È" #Ä] D E«é¾Þ " ( D à ² E«é¾A ª YAÐŒþ$* Ô»sŒý ß«Þ Ä] ¾A²uw 2 OR b) i) State and prove Triangle inequality. ~! (i DßÔÈ". " " ( ~ß«È" b b0 ¾Þ. «a (È" #2 ii) Define self adjoint, unitary, normal and orthogonal operators and prove that if T 1 and T 2 are two self-adjoint operators on a inner product space V. Then prove that T 1 +T 2, T 1 T 2 and at 1 are also self adjoint. Õ Ë " (² Þ 0 à ²0 D à ²0 KP ¼! (0 ß«È" ¾Þ " à " ( ¾Þ Ëb a 2 È" ( ¼! # V D D ¾Þ Ã»ê ¾AÚ! È" # R «T 1 È" ( ¼! # T 2 Ã( ¾ Þ ( Õ Ë " (² Þ ß«È" ¾Þ " RÄ T 1 +T 2, T 1 T 2 È" ( ¼! # at 1 Õ Ë " (² Þ ß«È" ¾Þ " à a.ß«2 Ã( PÞ.yé

8 B.A. DEGREE EXAMINATION, MAY (Examination at the end of Third Year) Part - II : MATHEMATICS Paper - IV : Numerical Analysis (DBMAT 32) Time : 03 Hours Maximum Marks : 100 SECTION-A Answer all questions. (8 x 5 = 40) All questions carry equal marks. 1) Evaluate i) ii) ÉÃ(È" à " ( ¾A²u(wÈ" #2 2) Construct the Newton s backward difference table from the following of x and R «ß«v wpþ Ä] x È" ( ¼! # ÉÃ(È" à " ( ".½u ŒþÞ* ¾ YÞ È" ( " Þ ß«v wpþ " ( PÞ uw 2 3) Derive Bessel s Interpolation formula. ³ ÔÌŒýÞ D ¾ ËÌ! " ßÔ.~ È" # " ( ¾A²u(wÈ" #2 4) Use Stirling s formula to find given that y 1 = 5225; y 6 = 4316; y 11 = 3256; y 16 = 1926; y 21 = 306 R «ÉÃ(È" " ( ²v w Ôw Ç Y Ö ßÔ.~ È" # éë¾a ÉÃ(È" " ( PÞ " (P S 2 1 5) Evaluate 0 x 3 dx with five-subintervals by using Trapezoidal rule. 1 ~v «j ¾ # Þ ÌŒý ¼! (È" (È" # éë¾a 0 6) Derive Simpson s rule. x 3 dx ÉÃ(È" " ( 9 Hß«*D ¾Aà PÞ " (P S 2 Ô ß«Ö ŒþÖ ¼! (È" (È" # " ( ¾A²u(wÈ" #2

9 7) Solve the equation graphical method. YA PÞ ÌŒý ß«Þ éë¾a ßÔÊ(PÞ ¾Þ Ï ª Õ a 2 8) Solve the following system of equations by using matrix inverse method. x 1 + x 2 + x 3 = 6; x 1 + 2x 2 + 3x 3 = 14; R «ßÔÊ(PÞ ¾Þ Ï È" #à È" ½È" ßÔŸ " ( È".~ PÞ ÉÄ]È" ( ß«Þ éë¾a Õ a 2 SECTION-B Answer all questions. (4 x 15 = 60) All questions carry equal marks. 9) a) i) Derive Lagrange s Interpolation formula. Ä YA k D ¾ ËÌ! " ßÔ.~ é ª ¾A²u(wÈ" #2 ii) Find f (10), given that at x =1, 7, 15 respectively, by using Lagrange s interpolation. f (10) ÉÃ(È" " ( Ä YA k D ¾ ËÌ! " ß«Þ éë¾a PÞ " (Y " (È" #0 Fa du x =1, 7, 15 à È" Þ. OR b) i) By means of Lagrange s interpolation formula prove that Ä YA k D ¾ ËÌ! " ßÔ.~ È" # " ( ²v w D ¾Þ. «a (È" #2 ii) Construct the forward and backward difference tables from the following of x and y x y R «ß«v wpþ Ä] x È" ( ¼! # y ÉÃ(È" à " ( Hß«¼.Z b ß«'¾ YÞ È" ( " È" ( ¼! # ¾ YÞ È" ( " Þ ß«v wpþ à " ( PÞ uw 2

10 10) a) Find e 1.17 by using Gauss forward interpolation formula from the following table x y R «ß«v wpþ " ( 0 YAŒÔ ß«'¾ YÞ È" ( " D ¾ ËÌ! " ßÔ.~ é ª Hß«¼.Z b e 1.17 ÉÃ(È" " ( PÞ " (Y " (È" #2 OR b) Find cos, using Gauss backward interpolation formula from the following table x y R «ß«v wpþ " ( cos " ( YAŒÔ* ¾ YÞ È" ( " ß«Þ éë¾a PÞ " (P S 2 11) a) i) Evaluate from the following table of data at and x = 0 x y R «ß«v wpþ " ( 0 È" ( ¼! # x = 0 È" Þ ÉÃ(È" " ( PÞ " (P S 2

11 ii) State and prove Taylor s series method. v þ Ì Ï Ô é é ª ~ß«È" b b0 ¾Þ. «a (È" #2 OR b) i) Find and at x = 1.6 from the following table x y R «ß«v wpþ " ( È" ( ¼! # ÉÃ(È" à " ( x = 1.6 È" Þ PÞ " (P S 2 π ii) Evaluate 2 cosθ d θ, taking by using Trapezoidal rule. 0 ~v «j ¾ # Þ ÌŒý Ô é È" # " ( Hß«¼.Z b YA šßô(p 2 π 0 cosθ d θ " ( ¾A²u(wÈ" #2 12) a) i) Use the method of Newton s Raphson method to find a real root of the equation x sin x + cos x = 0. x sin x + cos x = 0 ßÔÊ(PÞ ¾Þ Ï È" # " PÞ ( ÐéßÔ È" È" $Ä ª ".½u Œþ*¾Aß«Ö Œþ ßß«Þ éë¾a PÞ " (P S 2 ii) Solve the following system of equations by using Factorization method 2x 1 3x x 3 = 3 ; x 1 4x 2 + 2x 3 = 20 ; 5x 1 2x 2 + x 3 = 12 R «ßÔÊ(PÞ ¾Þ Ï È" #à È" ½È" ßÔ " ( PA¾Þ Ï PÞ ß«Þ éë¾a Õ a 2 OR b) i) Find an appropriate root of x 3 + x 1 = 0 near x = 1 by using Regula-Falsi method. ¾ YÞ (Ä * ÅÖ ß«Þ éë¾a x 3 + x 1 = 0 ßÔÊ(PÞ ¾Þ Ï PÞ ( ÐéßÔ È" È" $ÃÈ" # x = 1 Þ YÞ \¾Þ YA PÞ " (P S 2 ii) Solve the following system of equations by using Gauss-Elimination method 4x 1 + x 2 + x 3 = 4 x 1 + 4x 2 2x 3 = 4 3x 1 + 2x 2 4x 3 = 6 R «ßÔÊ(PÞ ¾Þ Ï Ã È" ½È" ßÔŸPÞ ( YAŒÔ* ÅZ ß«' ß«Þ éë¾a Õ a 2

12 Time : 03 Hours (DSENG 31) B.A. DEGREE EXAMINATION, MAY (Examination at the end of Third Year) PART II : ENGLISH Paper - III : Drama and Fiction Maximum Marks:100 1) Answer any ONE of the following in about 400 words. (20) a) Give a general estimate of Milton as a poet. b) Milton s Samson Agonistes is a classical tragedy. Discuss. c) Dalila is an embodiment of Female Frailty. Discuss. 2) Answer any ONE of the following in about 400 words. (20) a) Write a note on the greatness of Shakespeare as a dramatist. b) Discuss A Midsummer- Night s Dream as a comedy which blends love intrigue, fairy magic and farce. c) Sketch the character of Hermia. 3) Answer any ONE of the following in about 400 words. (20) a) What was Bernard Shaw s contribution to English Drama? b) Bring out the theme of the play The Apple Cart. c) Justify The Apple Cart as a political satire. 4) Answer any TWO of the following in about 400 words choosing ONE from each section: (2 10=20) SECTION-A a) Comment on the title of the novel, The Financial Expert. b) Sketch the character of Dr. Pal.

13 SECTION-B a) Draw a brief character sketch of Dr. Primrose. b) Write a note on the structure of the novel, The Vicar of Wake field. 5) Annotate any four of the following choosing any two from each section: (4 5=20) SECTION-A a) Love looks not with the eyes, but with the mind. b) The lunatic, the lover, and the poet are of imagination all compact. c) The iron tongue of midnight; hath told twelve Lovers, to bed; tis almost fairy time. d) Never anything can be a miss when simpleness and duty tender. SECTION-B a) Of what now I suffer, She was not the prime cause, but I myself. b) The sun to me is dark. And silent as the moon. c) These are thy wanton arts. And arts of everywoman false like thee. d) Wisest men have erred, and by had woman deceived.

14 (DSENG 32) Time : 03 Hours B.A. DEGREE EXAMINATION, MAY (Examination at the end of Third Year) Part II : ENGLISH Paper - IV : Language and Literature Maximum Marks:100 1) Answer any ONE of the following in about 300 words. (20) a) Bring out the characteristic features of the Neo-classical Age. b) What are the features of Shakespearean Age. c) Explain the salient traits of the Age of Milton. 2) Answer any ONE of the following in about 300 words. (20) a) Discuss the characteristics of the Age of Wordsworth. b) Describe the general characteristics of the Victorian Age. c) Discuss the special features of the Age of Hardy. 3) Critically comment on the achievements of any TWO of the following in 150 words each. (2 10=20) a) Chaucer b) Pope c) Charles Dickens d) Keats. 4) Answer any two of the following in about 300 words. (2 12=24) a) Write an essay on the Indo-European family of languages and the place of English in it? b) Discuss the chief characteristics of Middle English.

15 c) English is an International language. Discuss. d) Explain the origin of the English Language. 5) Define and illustrate any FOUR of the following. (4 4=16) a) Simile b) Personification c) Hyperbole d) Oxymoran e) Irony f) Antithesis g) Paradox h) Apostrophe.

16 B.A. DEGREE EXAMINATION, MAY (Examination at the end of Final Year) (DBSTT 31) STATISTICS Paper III: Applied Statistics Time : 03 Hours Maximum Marks : 100 Answer any Four of the following. (4x20=80) SECTION -A 1) a) Explain simple random sampling? And also show that in SRSWOR V(y) = 2 N-n s. N n b) Explain systematic sampling? 2) a) Explain two-way classification? b) Explain the basic principles of experimental designs. 3) a) Describe layout of RBD, give its merits and demerits and also uses. b) Describe the LSD, give its merits and Demerits and uses of LSD. 4) a) Explain the construction of np chart and its uses. b) Explain the construction of C chart and its applications. 5) a) Define vital statistics and its uses and also sources of vital statistics. b) Explain Reproduction rates (NRR & GRR). 6) a) Describe the functions and organizations of NSSO. b) Explain the various standardized death rates.

17 7) a) Define Time series, give its uses and also explain components of Time series. b) Explain the ratio to meaning average method. 8) a) Explain the various sample index numbers and weighted index numbers. b) Explain base shifting, splicing. SECTION B (10x2=20) Answer the following questions. 9) a) Pilot survey. b) Optimum allocations. c) Assumptions and uses of AWOVA. d) Layout of LSD. e) P chart. f) Mortality rates. g) CSO h) Uses of Time series. i) Cost of living Index number. j) Fisher Index number is idea/i.n. E E E

18 B.A. DEGREE EXAMINATION, MAY (Examination at the end of Final Year) STATISTICS (DBSTT 32) Paper IV: Operations Research, Computer Programming and Numerical Analysis Time : 03 Hours Maximum Marks : 100 SECTION -A (4x20=80) Answer any Four questions. All questions carry equal marks. 1) a) What is meant by Transportation problem solve the following transportation problem. To From A B C Supply I II III Demand b) Explain assignment problem? Give its mathematical formulation. Explain Hungarian method. 2) a) Explain the Linear programming problem and also graphical method solution to LPP. b) Solve the following LPP by simplex method Min Z = 4x 1 + x 2 Subject to 3x 1 + x 2 = 3 4x 1 + 3x 2 6 x 1 + 2x 2 3 x 1, x 2 0

19 3) a) Explain 2 x 2, 2 x n game theory. b) Solve the following game through graphical solution. Competitor B B B B A Competitor A A ) a) Explain the following: i) OMR ii) Visual display unit iii) Disk iv) Analogue computer b) Explain the statements: i) GOTO ii) IF-THEN iii) FOR-NEXT iv) DIM Functions and matrix operations 5) a) Define interpolation, its assumption and uses. Also estimate the population for the year Year x: Population y: (in lakhs) b) Estimate the value of x = 656, by using Lagranges formula. x: log 10 x: ) a) Derive general quadrature formula. 1 b) Using Trapezoidal rule and Simpson 1/3 rule to find 1 + x dx taking h= 0.1.

20 7) a) i) Using Newton s Raphson method find the root of the equation x 3 + x 2 1 = 0 ii) Using Regula Falsi method find the root of the equation x 3-5x + 3 = 0. b) Use Gauss elimination method to solve 5x 1 - x 2-2x 3 = 142 x 1-3x 2 - x 3 = -30 2x 1 - x 2-3x 3 = 5 8) a) How do you handle in the data in Excel? Explain various editing techniques in Excel. b) Explain the steps to find mean and variance of set of observations using Excel. SECTION B (10x2=20) Answer all the questions. 9) a) Operations Research, scope, limitation, uses. b) Sequencing problem. c) Formulation of LPP. d) Define Merge and burst events. e) Newton s divided formula. f) Weddle s rule. g) Gauss seidal method. h) Numerical differentiation. i) Copy and paste data Random data files. j) PERT and CPM. E E E