QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6. A Show that B If f ( w = log UNIT I COMPLEX ANALYSIS-I is aalytic everywhere ecept at the origi ad fid is the aalytic fuctio of prove that + log f ( =. A Show that u = + y is Harmoic. B Fid the aalytic fuctio whose imagiary part is e ( y ycos y. A Determie p such that the fuctio f ( = log ( + y + i ta y B Fid all the values of k, such that f ( e ( cos ky+ isi ky dw d.. si +. p. y =. 4. A If f ( = u + iv is a aalytic fuctio of ad if u v= e ( cos y si y, Fid ( i terms of. B Fid a aalytic fuctio whose real part is e ( si y y cos y. 5. A Show that ( = + is ot aalytic aywhere i the comple plae. B Show that + = 4. y y where c cosists of the lie segmets from f 6. A Evaluate the lie itegral ( i = = i c = i d to ad the other from to = i +. cos si B Evaluate d with C : = usig Cauchy s itegral formula. + i 7. A Evaluate B Evaluate c c ( e ( ( d ( 4 where c is the circle = usig Cauchy s itegral formula. d where c is the circle = usig Cauchy s itegral formula. + c 6HS6
QUESTION BANK 8 + i 8. Evaluate ( iy d alog the paths ( i y = ( ii y = 6 9. A Evaluate usig Cauchy s itegral formula si d aroud the circle c B Evaluate c log d (. [M] c : =. where c : = usig Cauchy s itegral formula.. Let C deote the boudary of the square whose sides lie alog the lies = ±, Where c is e cos described i the positive sese, evaluate the itegrals ( i d ( ii c i d ( + 8 c 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT II COMPLEX ANALYSIS-II f = ad the residues at each pole ( ( + B Fid the residue of the fuctio f ( = where c is. [M] + 4. A Determie the poles of the fuctio ( ( = + a at ai i =. A Fid the residues of f ( = at these sigular poits which lie iside the circle = 5 4 B Fid the residues of f ( =. +. A Determie the poles of the fuctio f ( = ad the residues at each pole. B Determie the poles ad residues of ta h. cosa 4. A Evaluate d, a o. + e B Fid the residue of the fuctio f ( = wherec : =. ( 5. Evaluate d =,, a b. [M] a + bcos a + b cos a 6. Show that d =,,( a + acos + a a usig residue theorem. [M] 7. A Fid the biliear trasformatio which maps the poit s (, i, i to the poits(, i, B Fid the biliear trasformatio that maps the poit s (,, i i to the poits + i, i, i i W-plae 8. ABy the trasformatio w =, show that the circles a = c Z-plae correspods to the limacos i the w-plae. B Fid the image of the regio i the -plae betwee the lies trasformatio (a, c beig real i the y = & y = uder the w = e. 6HS6
QUESTION BANK 8 9. AFid the biliear trasformatio which maps the poits (, i, i to the poits (,, i w-plae. B Fid the biliear trasformatio that maps the poit s (, i, i to the poits (, i, i w-plae. A The image of the ifiite strip bouded by = & = uder the trasformatio 4 B Prove that the trasformatio w = si maps the families of lies = y = costat ito two families of cofocal cetral coics. w = cos 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT III. Fid a positive root of = correct to two decimal places by bisectio method., usig bisectio method. [M]. Fid out the square root of 5 give =. e = 7. log ( =.. Fid out the root of the equatio usig false positio method. [M] 4. Fid the root of the equatio usig Regula-falsi method. [M] 5. Fid a real root of the equatio e cos = usig Newto- Raphso method. [M] 6. Usig Newto-Raphso Method A Fid square root of. BFid cube root of 7. [M] 7. From the followig table values of ad y = ta iterpolate values of y whe = =.ad =.8 [M]..5..5. y..5.7.55.9 8. A Usig Newtos forward iterpolatio formula., ad the give table of value...5.7.9 f(..69.5.89.6 Obtai the value of f( whe =.4 B Evaluate f( give f( = 68,9,6at =,7,5 respectively, use Lagrage Iterpolatio. 9. A Use Newto s Backward iterpolatio formula to fid f( givef(5 =.77, f( =.7 f(5 =.86, f(4 =.794 B Fid the uique polyomial P(X of degree or less such that P( = P( = 7, P4 = 64 usig Lagrage s iterpolatio formula.. A Usig Lagrage s iterpolatio formula, fid the parabola passig through the poits (,,(, ad (,55 B For =,,,,4 ; f(x =,4,5,5,6 fid f( usig forward differece table. 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6. Fit the curve b y = ae to the followig data. UNIT IV X 4 5 6 7 8 Y 5 77 5 6 55 5 [M]. AFit the epoetial curve of the form y = ab for the data X 4 Y 7 7 7 B Fit a straight lie y=a+b from the followig data X 4 Y.8. 4.5 6.. Fit a secod degree polyomial to the followig data by the method of least squares [M] X 4 Y.8..5 6. B Fit a straight lie y=a+b from the followig data X 6 7 7 8 8 8 9 9 Y 5 5 4 5 4 4 4. A Fit a Power curve to the followig data X 4 5 6 Y.98 4.6 5. 6. 6.8 7.5 B Fit a secod degree polyomial to the followig data by the method of least squares X 4 Y 5 8 6HS6
QUESTION BANK 8 b y = ae 5. A Fit the curve of the form X 77 85 9 85 Y.4.4 7.. 9.6 y = ab for B Fit the curve of the form X 4 5 6 Y 8. 5.4. 65. 7.4 6. A Usig Simpso s 8 rule, evaluate + 6 d B Evaluate + d takig h =. usig Trapioidal rule 7. Dividig the rage ito equal parts,fid the value of 8. Evaluate d + i By trapeoidal rule ad Simpso s ii Usig Simpso s 4 9. A Compute 7 B.Fid 8 rule. / rule ad compare the result with actual value. e d by Simpso s rule with subdivisios. si d usig Simpso s rule. [M] log d, usig Trapeoidal rule ad Simpso s rule by sub divisios.. A Evaluate approimately,by Trapioidal rule, ( 4 d by takig =. B Evaluate e d takig h =.5 usig Simpso s rule 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT V. a Tabulate y (., y (., ad y (. usig Taylor s series method give that y = y + ad y( = B Fid the value of y for =.4 by Picard s method give that dy d = +y, y(=. Usig Taylor s series method fid a approimate value of y at =. for the D.E y - y = e, y( =. Compare the umerical solutio obtaied with eact solutio.[m]. ASolve y = + y, give y (= fid y(. ad y(. by Taylor s series method y B Obtai y(. give y =,y(= by Picard s method. y + 4. A Give that dy d =+y ad y ( = compute y(.,y(. usig Picard s method dy y B Solve by Euler s method = give y( = ad fid y(. d 5. AUsig Ruge-Kutta method of secod order, compute y(.5 from y + y = y(=, takig h=.5 B Solve umerically usig Euler s method y ' = y +, y(=. Fid y(. ad y(. 6. AUsig Euler s method, solve umerically the equatio y =+y, y(= B Solve y = y-, y ( = by Picard s method up to the fourth approimatio. Hece fid the value of y (., y (.. 7. A Use Ruge- kutta method to evaluate y(. ad y(. give that y =+y, y(= ' B Solve umerically usig Euler s method y = y +, y( =. Fid y(.ad y(. 6HS6
QUESTION BANK 8 8. AUsig R-K method of 4 th dy y order, solve =, y(= Fid y(. ad y(.4 [6M] d y + BObtai Picard s secod approimate solutio of the iitial value problem dy =, y( = d y + [4M] 9. Usig R-K method of 4 th order fid y(.,y(. ad y(. give that dy = + y, y( = d. AFid y(. ad y(. usig R-K 4 th order formula give that y = -y ad y(= dy B Usig Taylor s series method, solve the equatio = + y d for =.4 give that y = whe =. 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT-I If f( = for all the f( is A Cotiuous at = i B Not Cotiuous at = i C Cotiuous at = D Noe If = + iy the si = A si coshy cos si hy B si coshy + i cos si hy C si coshy + cos si hy D si coshy i cos si hy If f( = is A Aalytic everywhere B ot aalytic everywhere C Not differetiable at = D Noe 4 Cauchy-Riema equatios are A u = v y & u y = v B u = v y & u y = v C u = v & u y = v D u = v y & u y = v 5 The period of si is A B C π D π 6 Fuctios which satisfy Laplacia equatios i a regio are called A aalytic B ot aalytic C Harmoic D Noe 7 A aalytic fuctio with costat modulus is a A costat fuctio B fuctio of C fuctio of y D Noe 8 Imagiary part of cos is A si coshy B si si hy C si hy coshy D cos coshy 9 si i = A isi hy B si hy C icos hy D isi hy The value of k so that + + ky may be harmoic is A B C D oe If w = log is aalytic everywhere ecept at = A B C D If = + iy the cos = A si coshy cos si hy B cos coshy i si si hy C cos coshy + cos si hy D si coshy i cos si hy The value of k so that + ky may be harmoic is A B C D oe 6HS6
QUESTION BANK 8 4 If f( is aalytic fuctio i a simply coected domai D&C is ay simple Curve the f(zd = A B C D oe 5 The curves u(, y = C ad v(, y = C are orthogoal if u + iv is A aalytic B ot aalytic C Harmoic D Noe 6 If u + iv is aalytic the v iu is A aalytic B ot aalytic C Harmoic D Noe 7 A harmoic fuctio is that which is A Harmoic B ot aalytic C aalytic D Noe 8 A aalytic fuctio with costat imagiary part is A costat B aalytic C Harmoic D Noe 9 If f( is aalytic ad equals u(, y + iv(, y the f ( = A u + iv B v y iv C v y + iv D oe cos i = A isi hy B si hy C icos hy D cos hy The period of si is A B C π D π Lt f eists the that limit is If ( A Not uique B Uique C Twice D Noe Solutio set of si = is A = B = + D Noe = C ( 4 If = + iy the cos = A cos B si C cos D Noe 5 Imagiary part of si = A si coshy B si si hy C si hy coshy D cos sih y f = is 6 If ( A Aalytic everywhere B ot aalytic everywhere C Not differetiable at = D Noe 7 Arg is A Differetial i every domai B Not differetial ay where C Differetial oly at origi D Noe 8 Polar form of Cauchy-Riema equatios are r u = v, r vr = u B r ur = v, r vr = u = v, r v = u D r u = v, r v u A r u r C 9 If f ( r r r r = = is A Not differetiable at = B ot aalytic everywhere C Aalytic everywhere D Noe 6HS6
QUESTION BANK 8 Real part of cos is A si coshy B si si hy C si hy coshy D cos coshy The period of ta is A B C π D π If f ( = Re( is A aalytic B ot aalytic C ot differetiable D Noe A poit at which f( fails to be aalytic is called A Sigular poit of f( B ull poit of f( C No-Sigular poit of f( D oe 4 If f ( = sih is A ot aalytic everywhere B Aalytic everywhere C Not differetiable at = D Noe 5 The period of the fuctio is A B C π D π si = e i 6 If = + iy the A B si C cos D Noe 7 Solutio set of cos = is A = B = + D Noe si = C ( y 8 + = sih sih A B - C D y 9 If si ( + i = + iy the + = si cos A B - C D 4 If e = A B e C D e 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE Subject with Code : ENGINEERING MATHEMATICS (6HS6 Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 Lt If ( a f UNIT-II COMPLEX ANALYSIS-II does ot eist the is sgularity = a A Pole B Removable C Isolated essetial D Noe The fuctio has a isolated sigularity at = A B C D Noe The limit poit of a sequece of poles of a fuctio f( is A Pole B Removable C Isolated essetial D Noe e 4 The value of d, C : = is c ( A B C D Noe e 5 The pole of f( = e is ((+ A, B, C, D, 6 The pole of f( = is ( ( A, B, C, D, + 7 The pole of f( = is ( ( A, B, C, D, 8 The residue of f( = at the pole = i is ( +4 i A i B i C i D i 9 The residue of f( = 4 at the pole = is A 4 B 4i C 4 D 4 A pole of order is called A Simple B Not simple C Isolated D Noe Lt f = the If ( a = a eists is A Pole B Removable C Isolated D Noe 6HS6
QUESTION BANK 8 If Lt f ( a eists fiitely the = a is sgularity A Pole B Removable C Isolated D Noe The value of + c d d, C : = is A B C D Noe e f = is ( + 4 ( + A,-4 B,4 C,-4 D -4,- e f = at the pole = is ( + 4 4 The pole of ( 5 The residue of ( A 6 If 4 f ( has a simple pole at = a B 4 C the ( = = a A B Lt ( + a f ( a i 4 D -4 Re s f C Lt ( a f ( a D Noe 7 Is cross ratio of four poits ivariat uder the trasformatio is A Biliear B Iverse Biliear C coformal D Noe 8 The image of the lie y = c uder the mappig w = si is A Parabola B ellipse C Hyperbola D Noe 9 The cross ratio of the four poits,,, 4 is ( ( 4 ( ( ( 4 ( 4 A B C D Noe ( ( 4 ( ( 4 ( ( The biliear trasformatio maps iverse poits of a circle ito A Iverse poits B costat C sigular poit D Noe The image of the lie y = c uder the mappig w = cos is A Parabola B ellipse C Hyperbola D Noe The type of sigularity of the fuctio e at = i is A Simple pole B Not simple pole C Isolated essetial D Noe si At = f ( = has a sigularity at which is called A Simple pole B Not simple pole C Isolated essetial D Removable 4 The residue of e f ( = at the pole = is ( A B - C D Noe 4 6HS6
QUESTION BANK 8 = k w = si 5 The image of the lie uder the mappig is A Parabola B ellipse C Hyperbola D Noe 6 The pole of f ( = is ( + 4 ( A,-4 B,4 C,-4 D -4,- 7 Uder the trasformatio is coformal everywhere ecept at A Etire w-plae B Origi C Ifiite strip D Noe w = 8 The type of sigularity of the fuctio si at = is A Simple pole B Isolated essetial C Not simple pole D Noe si 9 f ( = has a sigularity at which is called A Simple pole B Not simple pole C Isolated essetial D Removable The image of the lie is A Parabola B ellipse C Hyperbola D Noe The pole of f ( = is ( + 4 ( + A,-4 B,4 C,-4 D -4,- If ( has a simple pole at = a the Re s f ( = f = = k uder the mappig = a w = cos A B Lt ( + a f ( If ( f has a simple pole at = a the s f ( = = A B Lt ( + f ( d 4 The value of d, 5 5 The residue of ( c C Lt ( a f ( a D Noe Re C Lt ( f ( D Noe C : = is i A B C D Noe f = at the pole = ia is + a ia ia ia A B C D 6 The pole of f ( = is + A i B,i C D Noe + 7 The pole of is 4 c ( ( d A,4,- B,-4, C,4, D,-4,- a 6HS6
QUESTION BANK 8 a + b 8 The biliear trasformatio w = is coformal if c + d A ad bc B ad bc = C ab cd = D ab cd 9 The pole of f ( = is + 4 A B,i C D Noe i 4 If ad bc = the b = a d c the every poit of -plae is a A Iverse poits B Critical poits C sigular poit D Noe SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (OBJECTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year &Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT-III Eample of a trascedetal equatio A. f ( = log. = B. f ( = = C. f ( = + 7 = D. Noe If first two approimatio ad are roots of 9 + = are ad by Bisectio method the is A..5 B..5 C..5 D..5 Eample of a algebraic equatio A. f ( = log. = B. f ( = = C. f ( = ta + = D. Noe 4 I case of Bisectio method, the covergece is A. liear B. C. very slow D. quadratic 5 Bisectio method is used for A. Solutio of algebraic or trascedetal equatio B. Itegratio of a fuctio C. Differetial of a fuctio D. Solutio of a fuctio 6 For ------------ method of solutio of equatios of the form f( = approimatio is to be very close to the root ad f ( A. Bolao B. Newto-Raphso C.Secet D. Chord 7 If the two roots are & of 4 = by Bisectio method the is A..5 B..5 C..5 D..5 6HS6
QUESTION BANK 8 8 Eample of a trascedetal equatio A. f ( = c e + c e B. f ( = + 7 = C. f ( = + 5 7 = = D. Noe 9 If first two approimatio ad are roots of log 7 = are.5 ad 4 by Bisectio method the is A..75 B..75 C..75 D. 4.75 If first two approimatio ad are roots of 9 + = are ad by Bisectio method the is A..5 B..5 C..5 D..5 If first two approimatio ad are roots of 4 = are ad by Bisectio method the is A..5 B..5 C..5 D..5 The order of covergece i Newto-Raphso method is A. B. C. D. The Newto-Raphso method fails whe A. f ( is egative B. f ( is ero C. f ( is too large D. Never fails 4 I case of Bisectio method, the covergece is A. liear B. C. very slow D. quadratic 5 Uder the coditios that f(a ad f(b have opposite sigs ad a<b, the first approimatio of oe of the roots f(=, by Regula-Falsi method is give by af ( a bf ( b af ( b bf ( a A. = B. = f ( a f ( b f ( b f ( a af ( a + bf ( b af ( b bf ( a C. = D. = f ( a + f ( b f ( b + f ( a 6 For ------------ method of solutio of equatios of the form f( = approimatio be very close to the root ad f ( A. Bolao B. Newto-Raphso C.Secet D. Chord 7 I the bisectio method of solutio of a equatio of the form f( = the covergece of the sequece of midpoits to a root of f( = i a iterval (a,b where f(af(b< is A. Assured ad very fast B. Not assured but very fast C. Assured but very slow D. Idepedet o the sequece of poit 8 Newto-Raphso method is used for A. Solutio of algebraic or trascedetal equatio B. Itegratio of a fuctio C. Differetial of a fuctio D. Solutio of a fuctio 9 I the method of False positio for solutio of a equatio of the form f( = the covergece of the sequece iterates to a root of f( = is A. Assured ad very fast B. Not assured but very fast C. Assured but slow D. Idepedet o the sequece of poit is to 6HS6
QUESTION BANK 8. I Newto Raphso method we approimate the graph of f by suitable A. Chords B.Tagets C. Secats D. Parallel Newto s iterative formula for fidig a root of f( = is f ( f ( A. + = + B. + = f f ( f ( f ( C. + = + D. + = f ( f ( Newto-Raphso method is also called A. Method of taget B. Method of false positio C. Method of chord D. Method of secats Amog the method of solutio of equatio of the form f( = the oe which is used commoly for its simplicity ad great speed is ---method A. Secat B. Regula falsi C. Newto Rasphso D. Bolao 4 The Regula Falsi method is related to at a poit of the curve A. Chord B. Ordiate C. Abscissa D. Taget 5 The Newto Raphso method is related to at a poit of the curve A. Chord B. Ordiate C. Abscissa D. Taget 6 Newto s iterative formula for fidig the square root of a positive umber N is N N A. = i+ B. i i+ = i + i i N N C. = i+ i D. i+ = i + i i 7 Newto s iterative formula for fidig the reciprocal of a umber N is N N A. = + B. + = C. + = ( N D. + = ( + N 8 Regula- falsi method is used for A. Solutio of algebraic or trascedetal equatio B. Itegratio of a fuctio C. Differetial of a fuctio D. Solutio of a fuctio 9 The cube root of 4 by Newto s formula takig = is A..889 B..889 C.5.889 D.4.889 The square root of 5 by Newto s formula takig = 6 is A.7.96 B.5.96 C.6.96 D.4.96 If first two approimatio ad are roots of e = are ad by Regula-falsi method the is A..575 B..575 C..7575 D..5575 If first two approimatio ad are roots of 4 = are ad by Regula-falsi method the is A.4.666 B..666 C..666 D..666 ( 6HS6
QUESTION BANK 8 Newto s iterative formula for fidig the pth root of a positive umber N is A. N = ( + + p p p ( N + = p p p C. N ( + = p p p ( N + = p p 4 The geeral iteratio formula of the Regula Falsi method is + A. + = + f ( B. + = + f ( f f ( f f ( ( ( C. = f ( D. = f ( + f ( f ( + =.64 f ( + f ( 5 If first approimatio root of 5 + = is the by Newto-Raphso method is A.4.6565 B..6565 C..6565 D..6565 6 Newto s iterative formula to fid the value of N is N N A. = + + B. + = N N C. = + D. + = 7 If first approimatio root of = is =. 8 the by Newto-Raphso method is A..5 B..5 C..5 D..5 8 Newto s iterative formula to fid the value of N is N N A. = + + B. + = N N C. = + D. + = + 9 6. If first two approimatio ad are roots of log 7 = are.5 ad 4 by Regula- Falsi method the is A..7888 B..7888 C..7888 D. 4.7888 4 If first approimatio root of cos = is =. 5 the by Newto-Raphso method is A..554 B..554 C..554 D..4 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 +. The ( th A Polyomial of. The UNIT IV order differece of a polyomial of th th degree is degree B polyomial of first degree C costat D Zero th order differece of a polyomial of ( th th degree is A Polyomial of degree B costat C polyomial of first degree DNoe. While evaluatig a defiite itegral by Trapeoidal rule, the accuracy ca be icreased by takig umber of subitervals. A Larger Bsmaller C Medium DNoe 4. I Simpso s /8 rule the umber of subitervals should be A Eve B Odd C Multiples of 8 D Multiples of 5.. I Simpso s / rule the umber of subitervals should be A Eve B Multiples of C Odd D Noe 6. The followig formula is used for uequal itervals of values A Newto s forward BLagrage s C Newto s backward DNoe 7. The priciple of least squares states that A Sum of residuals is miimum B Sum of residuals is maimum C Sum of squares of the residuals is miimum D Noe 8. If y = a + a the secod ormal equatio by least square method is_ A y = a + a B y = a + a C y = a + a D Noe 9. If y=6.77,y= l(y the Y= A.845 B.845 C.845 D.845. If y=4.77,y= l(y the Y= A.4 B.45 C.459 D Noe. If y=8.,y= logy the Y= A.99 B 9.9 C.99 D Noe. If y = a + b the first ormal equatio by least square method is A y = a + b B y = a + b C y = a + b D Noe 6HS6
QUESTION BANK 8. If y = a + b + c the secod ormal equatio by least square method is A y = a + b + c B y = a + b + c C y = a + b + c D y = a + b + c 4. If y = a + b + c the third ormal equatio by least square method is A y = a + b + c B y = a + b + c = a + b + c y = a + b + c C y D 5. I Simpso s rule state that b f ( a A [( y + y + ( y + y +... + y ] d = h B h [( y y + ( y + y +... + y ] C h [( y + y + ( y + y4 +... + 4( y + y +...] + D Noe 6. The value of / ( + d by Simpso s / rule(take =4 is A.69 B.5 C -.69 D Noe 7. If y = a + b + c the secod ormal equatio by least square method is A y = a + b + c B = + + y a b c C y = a + b + c D y = a + b + c 8. If i = 5, yi =, i yi =, i = 55, = 4 ad y = a + a The A. B.5 C. D 9. If y = a + a + a the secod ormal equatio by least square method is A y = a + a + a C y = a + a + a = 5, yi =, i yi =, i = 55, 4 B y = a + a + a D y = a + a + a. If i = 5 ad y = a + a The a = A. B.5 C. D. The Epoetial curve is.. b A y = a b B y = a C b y = ae D Noe. The power curve is.. b b A y = a B y = ab C y = a D Noe. If y = a + b the secod ormal equatio by least square method is A y = a + b B y = a + b C y = a + b D Noe 4. If y = a + b the first ormal equatio by least square method is A y = a + b B y = a + b C y = a + b D Noe a = 6HS6
QUESTION BANK 8 5. I Simpso s /8 rule the umber of subitervals should be A Eve B Odd C Multiples of D Noe b 6. By Trapeoidal rule, f ( d = a h A [( y + y + ( y + y +... + y ] h C [( y y + ( y + y +... + y ] h B [( y + y ( y + y +... + y ] h D [( y y ( y + y +... + y ] 7. I Simpso s rule state that b f ( a d = A h [( y + y + ( y + y4 +... + 4( y + y +...] B h [( y + y + ( y + y +... + y ] h C [( y + y + ( y + y +... + y ] D Noe 8. I the geeral quadrature formula = gives A Trapeoidal rule B Simpso s rule C Simpso s rule D Weddle s rule 9. The value of / d by Trapeoidal rule(take =4 is A.69 B.5 C -.69 D Noe d. The value of + by Simpso s rule (take =4 is A.6854 B.7854 C.8854 D.9854. The value of / ( d by Simpso s / rule(take =4 is A.69 B.5 C -.69 D Noe. The value of d by Trapeoidal rule (take =4 is A.5 B.5 C.5 D.5. Equatio of the straight is A y = a b B y = a b C y = a + b D b y = a the first ormal equatio is 8 y = a + b 4. If log y = (=No.of poits give A a + b B log a + b C a + b log D log a + b log 6HS6
QUESTION BANK 8 b 5. I Simpso s rule state that f ( 8 d = a A h [( y y + ( y + y + y... + y + ( y + y + y... + y + 4 6 9 8 B h [( y + y + ( y + y4 +... + 4( y + y +...] C h [( y + y + ( y + y4 +... + 4( y + y +...] D Noe 6. If y=9.,y= logy the Y= A.9685 B.9685 C.9685 D.9685 7. 7. I simpso s rule the umber of sub itervals should be A eve Bodd Cmultiple of D Noe 8. I simpso s rule the umber of ordiates should be ` [ ] A Eve B odd C multiple of D Noe 9. I simpso s 8 rule the umber of sub itervals should be A Eve B odd C multiple of D Noe 4. The value of / ( + d by simpso s / rule(take =4 is A.69 B.589 C.456 D 56 6HS6
QUESTION BANK 8 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayaavaam Road 5758 QUESTION BANK (DESCRIPTIVE Subject with Code : (6HS6 Course & Brach: B.Tech AG Year & Sem: II-B.Tech& I-Sem Regulatio: R6 UNIT V Successive approimatios are used i A Mile s method B Picard s method C Taylor series method D oe Which of the followig i a step by step method: A Taylor s series B Adam s bashforth CPicard s D oe Ruge-kutta method is self startig method: A true B false C we ca t say D oe 4 The secod order Ruga-kutta formula is A Euler s method B Newto s method C Modified Euler s method D oe 5 Euler s th term formula is A y = y + hf(, y B y + = y + hf(, y C y = y + hf(, y D oe 6 Which of the followig is best for solvig iitial value problems. A Euler s method B Modified Euler s method C Taylor s series method D Ruge-kutta method of order 4 7 To obtai reasoable accuracy value i Euler s method, we have to h value is A Small B large C D oe 8 If coditios are specified at the iitial poit, the it is called A Iitial value problem B fial value problem C Boudary value problem D Noe 9 If coditios are specified at two or more poits, the it is called A Iitial value problem B fial value problem C Boudary value problem D Noe The first order Ruga-kutta formula is A Euler s method B Newto s method C Modified Euler s method D Noe The secod order Ruge-Kutta formula is y = A y +(k + k B y - (k + k C y + (k + k D y - (k + k The th differece of a th degree polyomial is A Costat B Zero C oe D Noe Successive approimatios used i method A Euler s B Taylor s C Picard s D R-K 6HS6
QUESTION BANK 8 4 The taylor s for f( =log (+ is A - + -. B + -. C Both a ad b D Noe 5 Solvey = + y, y( =, fid y = y(. by usig Euler s method A. B.6 C. D.86 6 The R-K method is a.. method A Picard s method B Euler s method C Mile s method D self- startig method 7 Usig Euler s method y = y y+ A. B. C. D. 8 Usig Euler s method y = y y+, y(= ad h=.give y=., y(= the the picard s method the value of y ( = A +log(+ B -+log(+ C +log(+ D Noe 9 If dy d y ( is A.95 B.95 C.95 D Noe Euler s first approimatio formula is A y = y + hf(, y B y = y + hf(, y C y = y + hf(, y D y = y + hf(, y Secod order R-K Method formula is A y = y + (k + k B y = y + (k 4 + 4k + k C y = y + 6 (k + k D y = y + (k + k dy The itegratig factor of y = d A e B e C D e The secod order Ruge-Kutta formula is y = A y +(k + k B y - (k + k C y + (k + k D y - (k + k 4 Usig Euler s method y = y,y(= ad h=.give y=. y+ A. B. C. D. 5 Ruge-kutta method is self startig method: A False B we ca t say C True D Noe dy 6 The itegratig factor of + y = d A e B e C e D e 7 Usig Euler s method y = y,y(= ad h=.give y=. y+ A. B. C. D. 8 If dy = -y ad y(= the by Picard s method the value of d y ( is A.95 B -.95 C.95 D Noe ' 9 If y = y, y( = by Euler s method the value of y(. is A.9 B. C - D -.9 e 6HS6
dy d If = + y, y( = A + + the by Picard s method the value of B C + QUESTION BANK 8 y ( is dy y The itegratig factor of + = d A B log C D dy y th If =, y( =,ad h=. the the value of i 4 order R-K method is d y + A B. C. D. Usig Euler s method y = y,y(= ad h=. give y=. y+ A. B. C. D. dy 4 If = y, y( =, the by Picard s method the value of y ( is. d + + k A B C D + + dy y 5 The itegratig factor of = d A B C D 6 The Third order R-K formula is.. A y = y + ( k + k + k B y = y + ( k 4k + k 6 6 C y = y + ( k + 4k + k D y = y + ( k + k + 4k 6 6 7 Usig Euler s method y = y y+,y(= ad h=.4give y=. A.4 B.4 C.4 D.4 8 If dy = -y ad y(= the by Picard s method the value of d y (. is A.7 B -.7 C.8 D Noe y = y, y = by Euler s method the value of (. ' 9 If ( y is A.9 B. C - D dy = + y, y =, the by Picard s method the value of y ( is. d A + B + C + + D + + 4 If ( D + e e 6HS6