\ov: ; Blatiel 4 RAJIV GANDHT UNIVERSITY OF KNOWLEDGE TECHNOLOGIES, BASAR (ALY, 2021-2022) ies & Communication Engincerin Subject Name; DEC Subject Code:ECH101 Date: 22/02/2022 ‘Max Marks: 30 : EISIMTL “Timo: GO Min, SECTION =A (2001) Objective Part _ Note: i) This seetion consists of 10 bits, these could be nsultiple choice, J in the blanks, ora combination of both, and each carziestwo marks. fi) All 10 bits are compulsory, there is NO Choice in Section-A- JL. IEQIXTY)s = 12C9)i¢ then the values of X & ¥ are al B5&7 C785 D.A&S Zevimum number of NAND gatos” are required to implement the - function, f(P,Q, RS) = (P + OR + yD C5 D.6 Ad Ba 3, If C13)x= EA, the possible values of X BY are A.8 & 16 B. 10 & 12 C.9& 13 AB SAL 4. xt — (12)px+ (87); = O Produced decimal roots 8,5 then F=—? AD B.10 eu D.12 5, All the logic gates shown in the igure have 2 propagation delay of 20 ns, Let A= C=Oand B=1aniil dine t= 0, At t= 0, all the inputs ip (Lc. A= C= 1 and B= 0) and remain in that state. For, t> 0, output ZI for a duration (in 1s) of ~ HONS YS ¢————— 6. How many min terms(excluding redundant terms) functionf (v, w.x, y,2) = x-+Jzoriginally have? - A 16 BO C4 : D.32 7." KeMap method of simpliffeation ean be applied when the given function is in? 1 Product of Sum form IL, Sum of Product form UI. Canonical form - IV. any form which of the following is correct? KE only IV * Bonly IIT c1u D.1,1, The subtraction ofa binary number ¥ from another binary number X, done by adding the Ps complement of ¥ to X, result ina binary number without overflow. This implies that the result is ‘A, Negative and is in normal form (J® Negative and is in J's compliment form does. the minimal switching BT.OlL: aul form | \ C. Positive and is in Nor D. Positive and is in 1's compliment fort ” Ba “dass ox sab a +. @ + AB iG + 6G» + BOAABEs Be + ABO=— 10. (X 3)y =G 2)y; how Many ValuesTre possible for "X”--—-—— AL i 22 i G4 a D.7 SECTION =B (10M) Descriptive Part: Note: ; i) This section carries 10 Marks. ii) Two Questions need to be answered ouit of 4 questions asked, Each Question carries 5 Marks, . ic 1) Answer the following questions } a. two switches, one switch being at the ground floor and the-other one at thefirst floor, The bulb can be turned ON and also can’be turned OFF by any one of the™ switches irrespective of the state of the other switch. Determine the logic of switching of the bulb resemblesand draw the switching circuit diagram?[3M] b. Define the following terms?[2M] | ‘ i. Analog, Diserete and Digital signals ii, Why we preter 2°s complement procedure over 1s complement in arithmetic operations. x |. Self-complementary property ~ « . Consensus theorem 2) Design a combinational circuit that accepts a 3-bit number as input and generates an output binary number equal to square of the inns number?[5M] 3) An electric power generating station supplies power to three loads A, B and C. Only.a single generator is required when any one Joad is switched on. When more than one load is on, an auxiliary generator must be started. Design the logic circuit by using NAND ‘gates for the control of switching of the auxiliary generator? [5M] ( : 4) Design a logic circuit that controls an elevator door in a three-stBried building. The circuit hasa controflabile logic signal M, which indicdtés when the elevator is moving (M=1) or stopped (M=0). F;, Fz, and Fs. are floor indicator signals that are normally LOW, and they go HIGH only when the elevator is positioned at the level of that particular floor. For example, when the elevator is lined up with thé second floor, Fy= 1 and I =F = 0, The circuit output is the OPEN signal which is normally LOW and is to go HIGH when the elevator door is to be opened?(SM] THE END—— PTOK RAJLY GANDIIT UNIVERSITY OF KNOWLEDGE TECHNOLOGIES, BASAR (ALY. 2021-2022} Subject Code CLUO1 Subjoct Name:DEC Date:22-04-2022 Max Marks! 60 Exantt ELS1-Regulae Remedial Bigs Time: 20 wl SECTION —A (301 Objective Part: Note: x i) ‘This séetion entries 30 Marks. iy Fifteen Questions uced to be answered out of £5 questions ked; Rach Question earries 2 Marks. There is NO choi O1 A-4-bit numbér is represeated by ABC) with D as LSB. A logic circuit that will produce a‘L? whonever the input is grenter than 0010 butvfes¢ than.1000, The-minimum number of RAND gates required to implement the output logis function is 42. The switching sequence for He Following eireuits is— Fra] ~ oH wut States fe the following eireuit is 03. The niimber of out i] es Bel gS acAU J 6 K inputs ate connected tof, ‘Then-the ouput AH . 04, Ifthe chock signal is 16 Kz: i signal frequency of the following eéunter is ~ OQ a “G LK = Vette fags “Oa a PTORY a a i 4 nents ‘Slave outputs. when the state o 05. Consider the following staten 1. Master.output depends ou the sinve is affected. 2, Change inthe output rere tate of the master is affected TMeane shee poet a se petops {o store 2+bits of information, 4, Master-Slave configuration 5. Master is Negative-cdge trigg 6. Master is Positive-edge triggered fGen iggered. 1d and Slave is Positive-edgo triggere ct and Slave is Negative-cdge triggered, Which of the statements given abovetrelcomet? ni vitauas 06. Toad two mbit santa be required pubes fh adders it 7. chee the sinpifed Boor eqution fora given (X.Y, 2) = Simn(O,3,5,7) LX@Y OZ 2XOYOZ 3BXOV OZ 42XOYOZ ee ie ee costs C. 2&3 * D1L&3 A. Lonly 98. The feure shows the internal schematic of a TTL AND-OR-INVERT (AOI) gate. For the inputs shown in the figure, the output ¥ is —— A B Inputs are Aoating Ad Bt - CAB i D. Data Insufficient. 09. The number of one's present in the binary representation of (15256) + (5x16) -3=—~ AD B.8 C7 D. InsufficietData (or) Invalid 10. A shift register with the serial output connected back to the serial input is ——-~ A. Feedback shift register B, Shift Register Counter C. Universal Shift register D. Serial to Parallel converter 11. Assertion (A): Master-Slave JK flip-flop is free from Race-around condition, Reason (R) : Master-Slave uses two JK flip-flops A Both ‘A a Rare truc and R is the correct explanation of A, B. Both A & R are true but R is NOT the correct C. Ais true but Ris false, saplation oh D, Ais false but Ris true, 412. Which of the followirig Mlip-fiop is used as a Inteh? ADK FlipFlop BARS Hip-Fop C.D Plip-Flo TE Blip-F 13. A 4-bit right shift register is initialized to value 1000 for (QsQ2 ® an. eo puts Sent aorta Oa Rethough ‘vo XOR gates as shown below, The value at D after 3 Lo eG PTOAd Bl C. Can't detexmine since datw insufficient. D, Nowe af the options 14, A Mod-f counter on be obtained fom which of the circuits 4, hit Twisted Ring Counter Select the cowuters froma the above codes ALR B2&3 Cs D.1,2.3.4 15. A.3-bit Gray counter is ased to control the dudput of the mitiplexer as shows in the figure below, The inidsl state of the counter is 000, The outpul ig pulled high when nuultigleser is no¢ enabled. The output of the circuit follows the sequence: +5y Acta, 1, 1.1, 1a 1, 1, Ie B. Lo, Jy hy da Ls 15a 1 Ge Ly Toy My Tig Ine Ly By D. Tp, Wi, Las Uy Tos Fes Bs SECTION -B'(36M) Deseriptive Part: Note: f) This section carries 30 Marks, 3) Questions siced tu beinsweved outt of six questions asked, Each Question 1 Marks. : 1) Design BCD subtraetor by using 4-bit binary adders with nent skotohes? (LOM 2) Design 3-bit Binary. to. Gray code converter by using Decader & Eneader only? [10M 3). ioe dqbilUniversal Shift Register which consists of Lefi shiét, Right shift & Paralte] Loading operations by using 47 Mux- aud Suitable Mp-flops with mcot sketches? 1004] 3 4) Eiye soldiets, a, B, C, D, B volunteer to perform an important military task iF theiv following conditions are satisficd: Fither A or B ur bath must go. ) Either C or E, but iiot buth, inust ge. ) Either both Aanid C ga or neither goes. iv) If’) goes, then E must alsa #0, VEC goes, then A and D must also 26, »T.ODefine the variables A, B, C, D, E such thot an wmprimed variable will mean that the convesponding gakier lias. been solected to. go. Determine the expression which specifies the combinations of the valunteers whu ean get the'aséignment?[ LOM) 5) Binary message bity are coming sesially, They ave to be inken in blocks of four binary digits 5 &z 8) Ap and coded into Tbil binary. word.as yay’ @y Ap Cz-Cy.cy, Where ca, cyand Cy satisfy the following equations, [10M] ash art ast & ah ark agt cy yt 4 ng a5 y the complete ingic cirenit for generalibg cx, csand tgiving the of S/P (Sotial tu el) converter and parily generator circuits, Bxplain.the working of the circuit, TL 3f-an additional panity.bi Cp is'to be’ generated making total number of bits ina block ¢part 1) equal (o eight so thar number of 1's in the block are even, given the logic eireuit for generation of Cy usiag minimum nomber of E-OR’s, WT. Ifthe 7-paralfel bits:generated ia ppart-Lare to bie transmitted serially give the details of the P/S (parallel to serial) eonyerter suo ihat 7-bit word i accommadaded over the ariginalty'4-bic word duration. 6) Reduce the’ following ‘state diagram and also write the reduced stato table. There aré infinite mumber of input sequeners that can be considcrcil. Cousider fhe input sequence 01010110100 starting from the initial stute ‘a’? [10R] XstudentD: Iq )16 1 Subject Name: Dis ’ RAJIY GANDUL UNLVERSITY OF KNOWLEDGE TECHNOLOGIES, BASAR (AY, 2021-2022) BRANCH: ECL al Blectronic circuits Subject Code: EC1101 Exum: MT 2 PAPER Date: 12/04/2022 Max Marks: 30 ‘Time: 60 minutes secTion-a 2X10=20marks NOTE: Auswer ALL questions aud cach question carries hyo marks 1, On aK. FLIP-FLOP When isthe flip-flop i @ Hold Condition 2. How many AND gates are required for a 81 multi iplexer? a2 bb 8 a5 3, The circuit'shows in figure below generates the fiction of 25 aX €y2tY , | k eo ann Baa bo oO oa ~~ ORV bY 4, In &:1 multipléxér is ned to implement the logicd! funotion Yas shown The output ¥ js given as ae {=D,b=D] . 5. Whal input should be given to “S” when SR flip~ (lop is converted to JE flip — flop? i ajyKQ 55.0 »)K.Q ALO Page 1 of,6. Draw the functional table for T-flip flop-~----- 7, Consider the following combinational function block involving four Boolean variables.x,y,a,b whore x,u,b are inputs and y is the oulputitx,y,a,b) if (x is 1) y=a; else y =b; Which one of the following digital logic blocks is the most suitable for implementing the function? a.Full adder Ss af A tulti iplexer b Priority encoder .Elip-flop 8.A negative edge-triggercd FLIP-FLOP changes state at the fi ,_ stock pulse. 9.1n Sofial Shifting method, Data shifting occu... : zone bit ata time o. Simultaneously b.Twe bit at a time d-Three bit ata time 10. The himbcr of logic gates and the way of their interconnections dan be classified as, ogical networ! ce.Cireuit network ‘b.syslem network : d,Gate nebwork SECTION-B NOTE: Answer any. TWO questions and each question carries five marks Realize the following fimction, x1 MUX F(A,B,C} = £(0,1,3,4.3) .Design a BCD adder with neat Circuit representation. [243M] -LDesigh a left shift register and-explain its operation with aa, Example. . . iiDesign a3 bit Even parity generator, [32M] 3.i Explain about Race Around condition and conditiong to avoid it. ii.Convert SR to T Mlipflop [342M] 4iDesigh a 1-bit Digital Comparaior. [3M} ii. Obtain sum expression of haif adder using 2*] noux, [2] Page % of 2RAJIY GANDHLE UNIVERSITY. OF KNOWLEDGE‘ (Academic Year 2021-2022) ECHNOLOGIES, BASAR Subject Name: Engineating Graphics Subject Coder CEI701 Date: 02-05-2022 Max. Marks; 25 Exam: B1SIMT3 Time: 90 Minutes. | This question paper consists af two sections ane 10 questions SECTION. Jnstructions (9 answer the questions from Section -A Answer ALL questions from Scetion-A. Eacli questiow earvies { mark Indicate the question numbier VERY CLEARLY on drawing shéet. 1. A right ciccular cone when cut by # plane parallel to Hs geagrator, the curve obtained isa 2) Ellipse b) parabola ©) hyperbola d) circle 2. Which of the following applications hyperbolic cucve is insett? a) ‘Solar eblectar “by Cooling tower “GFlamp tetigctors 4) ménumnenis 3. The curve traced out.by, 4 point on the cizcumfacence ofa ciccle which zolls en-another cirele with internal contact is . %) Epicyeioid —“ b)HYjpneyclold —a)aycloid. 4) involute 4 A bypocycloid having-diametér of ihe rolling citele one-half that of the generating circle resembles a) Straight line by circle Sheliipse ——d) None of these 5. The front view of a point ig 50mm above ihe reference Jine and top view ts 20 mm helow the front view. The point lies in a) First angle bysccondangle ——_¢) thiril angle ) fourth angle 1 : PT.d az 2 360 Zi Pe - : Answer any Four Questions from Section-I ft awing sheet. Indicate the question number VERY. CLEARLY on drayying shee ide circle ameter Fa 6. Draw an epioysldid ofa circle of 40 mm diameter which rolls ottiéide a circle of (20. mm diameter iT . (6M) 1 one revolution, 7. Caristruct an ellipse when the distinee of its focus fiom its directrix is 50 mm and cecentricity is 2/3. Also, draw a tangent and a normal (0 the ellipse at ¢-point 70 mm away from the directrix. (Sy 8, Draw the oxthographie projections of the following points, Distance hetween projectors js 30 mm. _ (6M) 8) point T is in HLP. and. 30 mm behind the V.P. b) Point U is in V_P. and 40 nim bélow HP. 'e) Point Vis in V.P. and 35 mm-above H. 1d) Paine W is in H.P, and 48 mm ia font of VA e) Point X is 29 mm above HP, and 30 mm in front of V,P, 9. A line LM 70 tam long , hasits end L- i0.mm above the HLP,-and 15 mm in front of V.P. is top view aiid front view measures 60 mm and-40 mm respectively. Draw the projection of the line and its inclinations with ILP. and V.P. (5M) 10. A pentagon ABCDE of side 30min has its side AB in the V.P. and inclined at 30° to the ELP. and the comer is 15 mm above the ELP. and comer D is 30mm in front of the V.P. Draw the projections of the plane sind find its'iiclinations with the V.P, 6504) a Ay fe wt ¥ i" yor - 5 {MTL RANY GASDRU UNIVERSITY OF KNOWLEDGE TECUNULOGIES, BASAR (A. 2021-2023) Computer Science and Engineering Departmen, Subject Nantes Progeumuritng for problem solving Subject code: C5101 Dates 2402/2022 Time: | hows Exom: El_SEMI (CSB,ECE & BE) Ma Mavic: 20 Answer all the yuestions, each question carzjes 1 mak (@0"1=20NIneks) 1. with 9 bits sigued integer range ie atin Sl b, 512 to HST 255 ta #256 1: «256 t0 +255 2: which of the following number is used fir represen ing addeess of a variable a. signed integer unsigned integer. both signed add Unsigasd integer d. None. 4. Which of the [ollowing option is eotieot for Moat dita (ype 4 After fractional poine it hotds upto 4 ‘b: Aftcr fimetiona! point it holds upto’s di ¢. Aflerfinctional poincit lolds upte 6 digits After fteciional point it hells upla I2 digits 4, Which of the following identifier is eqrrecl for Jong, integer a Ye bh 0.466 a %e 5. Which of the Tollowing function is dotined in “stdio.t" hone fe spring), —bseonif) both pintif) asd geang) 4 note a thy'sbove &, predict ontpu of the following © program . ; inuaraint float x=3.5855; int yotaths; ined" 36d" y)i : return O; }- 2355 b.35 a4 a3 4. predict outpal of the Pollowing ¢ program int main { int aSiike eoty FH; iH; printed, You, 2d, Yad" aAd.K); setum OF i a 44,54 d4.4.44 oAhSd a 4344 &. what fs the output of the folloveing o program? fat ving { Sint nde jetesnd Drinaftd" J); romm Bt 1 a5 ba 24,5 454 9.-what willbe the output of the following e program? int soning) { int x=L2.y3naxtys i peincit ised 2): v rena 0; As b.zd 26 i, Compilation error AX 10, what wil! be The ouipat of the following © program? lest int maint iat inta=4 i iffarddetb<3). pooilt"Tiue"}; bse prinett"Palso")s yerarn 11; s Tac b, False cc. both True and False d, None HH which of the following is an assignment operator ine ae be oF a. 12. hat will be the output of the following c program? int maing}{ forint { printf"); 3 ream 0; + b.H printed ford tiie .o. H printed for timed, None a. H printed for infinite times 13. what will be ouput of Uie following ¢ pragram? int maint { fit x=2; switeht vase 1: prinef(" 1"); case 2: 1 printi(! case: prinlt?3"); default; eid relura 0; 3 21334 bad ©2334 42341 14, which of the fallowing Joop executed atleast ane time evereloop condition is false afar loop 6. While teop e-dawhileloop — «l, Nenu of the option 15, wal will be the outpet of the following ¢ program? int main(}{ int x; fore lyecopeht) ifte—4) contre;Lo printt"%d "x); } i return 0; } 2.12345 b1234 1236 1235 16, what will be the output of the following ¢ program? int mainO{ float x=3.55 swviteh(s){ case } retum 0; } a123 9 b32t e12 4. Compilation error 17. which of the following option is correct for printing the variable address a, printf(*%ou" &evariable) b. printf"%u'" variable) «, printf(%t',evariable) 4. printi("%E" variable) 18: which of the following option is correct about the loop? 2. using loop we can avoid rewritting the block of code again and again in the program bb. Joop repeates until the loop condition is false ¢. both option a and option b are corvect d. none of the above 19; Which of the following is not a keyword in C programming? a. void b. switch default add 20. how many bits in 1 kilo bytes(1KB) a. 1024 bits b, 1023 bits, 0, 8192 bits 4. 8191 bits Section-II Answer any two questions, cach question carries 5 marks 15*2=10Marks] 1. a) Write in detail about the switch statement with an example [2.5 Marks] ') Write in detail about if-else and nested if-else stalements with an examples [2.5 Marks] 2. Write a ¢ program to read floating point number as input fiom user Keyboard and convert this fleating point number into integer umber. Read second input as integer number from user Keyboard, Compare converted integer with second input integer if conveted integer value is greater than second input integer then print CSE, If lesser then print ECE'and if both are equal then print EEE, [5 Marks} 3, Write in detail about the loops with an examples {5 Marks] 4, Write a ¢ program to find given number is palindrome or not 15 Macks}Ne cea s Bl4ilsy RAJLV GANDHS UNIVERSLI'Y OF KNOWLEDGE TECHNOLOGIES, DASAR i (A.¥.2021-22) Ss Cumunion for. ECE and CSE / Subjects Lined Algebra, Subject Cod TALIOI ‘Time: 60 Minutes Max Marks: Dater 23-02-2022 Rexam B151_ MTL Nato; Caloulators are NOT allowed. ‘This Question Paper Consisis of Sectlon~A and Seetlou-B Section-A Objective and Svetion-B Deseriplivs. Becton’, Answer all the questions. Sn ‘This section consists of 20 questions each carries ONE sack. 2OxK1=20 1. Let be the veolor space of functions f1R B. IEW, = €fGe: f(=x) = FGI and Wy = (FG: f(—2) = Fx), then which of the following is TRUE? de Doth Wand Wo ure subspare-of ¥ BW, is subspace of V, but 1¥ is not C. We is subspace of 7, but IY, isnot D. neither #7; nor HW subspaces of Y 2, Tet B= [ajs) be the vestor space of all 1x n matrices over roa! mumbers, Then whieh of the following got is NOT a subspace of V2 j AL fay € Ray =—ay) B. [ay € Bay = Ofori > sf} FE eg Ring Bay} Day € Bay > 8} 3. For what valuo of ke, the sot (4%, 1, 0). (Life, 13 (0, 1.0) linearly dependent? & 0 : B-1 GA D2 4. Which if the following statement is TRUE? . cae ‘A. Alincarly independent set in a vector space V spans a.vector space V. B. Asset contains zero vector is linéarly independent, Ci Union of twe subspaces ofa vector space is also a subspace, 2 Move of the above sintement is uc. 5, JEW. is a subspace of a vector space V, then A dimw=dim¥ BdmW dimv &. Tredimension of the vootor space ¥ ofall symmetric matrices of aides 3°% 3 sith reel entries and trace equal to zero is AB PS 06 D9 2. Let TrR? SR" be the near transformation defined by Tepe yt 2 ¥ 2X, Sem By + 22). Then kernel of Tis {8} SSO —— CEL) D. LS{(0A,1). (0,1, 29} 8 Lot P:R" + B? bea linear transformation and nullity of ?"is 2. Then rank of T is At B.S ne DA ‘b. LetT:R? +R? he'the linear transformation defined by “He,y,2) = (eens 6 —y sin 8,sin a + y cus 8, 2)."thon T is : ACTL Be onto _ Peat be an nk Dy nuither 1-1 noronte 10, The coontinate veotor of (4,3,9} relative to the basis ((1,0,1), (2.1.2). (1,2. 2 8 A. (2-610) B.t-6,114) €.2,64) ED) LcLet ¥ be the veclar space af all real polynomial of degree at most 2: Define 7:¥ ty Tip) = 2p. Therpauix of 7 sith standard basis is Page 1of2. oo 0 0 10 o1 0 f 3 ( ok 4 “Flo 0 2 c a0 2 BE) “Eid cbt: i following is TRUE? 2 12. Which of the following 15 TRI Peace then deta < js odd order skew-symmel d Me nad Baro nex n maces, then (AB) = Aree. . G. Mattix multiplication is commutative. D. If A js Hermitian mat ix, then GA) is al ond AB = BA = @, then (A+ ©. Nilpotent Js Henmitiun sunlsise is 13.1. A and B are idempotent matsices BM ogc yt Tdempotcnt —-B. Involuntwy The diagonal elements of Skew-Hennition matrix are a. i “« . o * B. Real C. purely imaginary 0 or purely imaginary 13 2 15. Leta [e 1 sme acen ni oo 1 B.-8 C4 8. r AL4 16, Ts the set (x.y, 2)? 4-3? + 2? = 2027} subspace of R°(R)? TEnot, give the rcason. 17. Let¥ be the.veclor space of all polynomials over real: numbecs-whose degree less-than or equal fo n- Then dim(V) tt 18, Let W, and We be’ subspaces of a vector space RS(R). If dim i, W2=5, Then dim W102 4 1 TBP e ig.a linear mapping such thal T(1,2) = (1,1) and 7(2,3) = (0, 1), then 7 1 dimW, = 2 and dim(W4 + na) = 20, Determinant ofan Orthogonal mateix is__ Je Section-B Answer any TWO questions from the following. Each question earries FIVE marks. 2x5=10 1 . m 7 ¥ : i ae a) Find basis and dimension of the subspace W = (Gvsy. Dix + 2y z= 0} at feabe space RR). b) Show that thie set {1-+.2x ++ «?, 3 4 x?, x + x?) fonn a basis for P,(Q). oa % [243] a) State Rank-Nullity theorem. 8) Let Ts Maya) F(R} defined by 1 ([@ 4) Het @+elx t+ (a+b)x? +023. Then Tis inventble or not? Tfinvertible, then find it N 12 3. Let T:R? R® be a finear: transform. Let A = /9. i be the matrix of T with respeot ‘to the “1 3 orciored biases By © (C1,2), (-2, 19} and B, = (C,—- 1.1), 12,8 : 12), (2, = (G,-1-D, (2,3), (1, 0,29). The i 4 transfocmation 7 relative (o the bases 2 and a 2.3). om The Pea te as : a 23 = , E [243] a Leas [pp ]aide=[2, 3] then find AB by using row method of matrix multiplication 1 2-38 4459 . b) Bxpress.the matrix A=j67+6 OG 4-5] as the Hermitic , Si] a es of Hermitian and. Skow-Herinttion matrices. Pace 2 of 2IY S. ayn ANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGIES, BASAR(A.Y. 2021-2022) PX? SuBIecT: CALCULUS [ECE & CBE) : SURIECT COPE: MALLIZ scnantee iD DATE 24/02/2023 Biaie! adnan Hour SECTION-A Ansiver all questions. Each question cares two Marks feo x2 = 20) Note: Write.the answers 11 sedetly at one place, 1. Which of the following statementis FALSE? Ay ‘Limi 1 wy at ) “Limit of a sequence (2) uaF B) Lf Sy = ("+ 6) ,then the sequence (§,) convergent to 5 C} Upper bound of sequence 2191817 ........18% b} Lower bound of sequence (1+(-1)")",_, re Wis 0 2. A sequence is said to be an oscillate-finitely sequence if it is A) unbounded and not divergent 8) bounded and not convergent ©) Neither convergent nor divergent 0) bounded and soi divergent a s.=Ea -2Y then the sequence (5,,) A) Monotonic increasing’ 8} divergent) Manotonic deeredsing p) Oscillatory nf . 4 tin EY = ; 2 oo a ayo a3 q } 8 5. The sequence. (iq), where Sy = aiesagier convergent to ; = A) 30 a) 15 gq. .# » ot 6, For the series Bf Gs A) itisdivergent by nth term divargdnt test b) It is convergent by combination of comparisan test and, Geometric sories test Gc} tei convergent by alternating series text 5 ; D) It is convergent by combination of limit comparison test and P- series test i 7, Tor whet volves of p, the series ifaa 2a; convergent? A) -25ps2 8} p< cg pee of p> is «. sum ofthe sore of 2+) +@) +) : ae a3 a 2 a=9, For the series DResear A) It isdivergent by ntlr fer divergent test 8) This divergeut by Ratio’s test anette ¢)" itis convergent by alternating series test B} tis convergent by integral test sos, = Fe, $4 =ea GES then which one of the following staternent is TRUE? A) Both 5, and 5, ave absolutely convergent 8) 5, 3s absolutely convergent and S,.is conditionally converg ©) Sy is conditionally convergent and S; is absolutely convergent D) Both’ S, and &, are conditionally convergent mvergent SECTION-B Answer any two'ef the fotlowing questions. {2x8=10) 1. a} Prove tat (ay) = f252].n = 1.2). is Monotonic Increasing vequcnce. Bt a Prove thaé lim laser ato Lwin 2, a) Determine whether the sequence (a,} SM 1 Find lim au 3 al ts convergent and find its swrn SM b) Determine.whel ies 2 sy" i ) ther thie series 24 ) tee ig cénvergent or divergent 2M 4, Test thie convergence of the series P=," SM End of the Question paper! Baber)v4, RAJIY GANDHI UNIVERSITY OF KNOWLEDGE TECHNGLOGIES, Basan Pa wey ai (ay. 2021-2022) Subject: CALCULUS[EOE & CSI) ExamcEASIM72 Date: 13/04/2022 DN: BiANIG| Duratlon:60 Min Sub Code: MAI102 . Max Marks: 30 SECTION-A Answer all questions. Each.questian carries two Marks (10 *2=20) Note: Write the answers In erderly at ane place Which of the following function given below satisfies all the conditions of Rolle’s Theorem Pyar ig | By fide belvxe (01) are [dy Di) f(z) = e%sine VE pA 9. Maclaurin Series of f(z) =cos*x at a= Dts . rainagt5 eye cot ; ey a) costes ESE BI costs 1+ TS ty 25. poe, foarte exe s ayaa OC cates tag Bl wre a 3. The first three nen ere terms of the Taylor's series of the function f(x}.= logs, abo = Lis A) Gee DEG TPS" Bl Gedo tP eat? oC) Gem Ee pee |B) Gop Teo 4, ES = Gam de, 5, f° Ede, then which of the following i TRUE ¢ ‘A. Both S, & §, are Divergents a B. 4, Convergent & 5; Divergent C,. 5; Divergent. Sy Convergent D. Roth S$, 8S, are Convergents g. [far sind dx = 5 = Ax B) o-x Clog oa 8. If ge gged athen Al itis convergent by ca: B) It is divergent by Comparison Test C) This coniétgent by Comparison Test D) itis divergent by combination of Comparison Tes! snbination of Comparison Test & P-Integral Test + 8; Peintegral Test tte a: US wee A) Convergent -3 C} Convergent to 0 B) Convergent to3 1B) Divergent to. P.T.0 Page Lof 27 SePAD TAIN ee Y) 8. lime 409 ape § does not exist Aa Bo G 38 2B Ai ! } 2422 then = 9.Ifx = ey = e*cos3t,z = 0 singeand x= x” +’ A) Bet B) tet C) de® D) Be 10. Maximum and Minimum values of f(x, are A) 68 and 0 B}68and-68 —¢) O and -68 D) 64 and -64 SECTION-B Answer any two of the following questions 'y) = 5x —3y, subject to x? + y? = 136 (2*5=10) 1 ‘a) State cauchy’s mean value theorem and verify this theorem for the function — f(x) = e*, g(x). = e~* on [a,b] b) Find M wirin series for f(x) = sinx at x 0.By using this find Maclaurin series for f(x) = sin (x?) atx = 0 2 a) Evaluate [f aekg ae b) Evaluate Si resseay a) Prove that {[°3-" dy = b) Evaluate ff x3(1~ vx) ax = e az az Sap) thon prove that #28 42 = aan End of the Question paper Page.2 of 2 3M 2M 3M 2M 3M 2M SMAX RAJIV GANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGINS,BASAR (AY. 2021 ~ 2023) Common ior CI und CSE Subject: Linear Algebra Subj de Baer 13/04/2008 ener 00 Daten Exam BLS1M‘e-IL 5 NOPEx(i) Scientific caleulatars arc NOT allowed } This question paper consists of Section-A and Section-B . Gi) Section-A Objective and Section-B Descriptive. Sectlon-A, Apswer all the questions. This séction consists of 20 questions each carries ONE mark. 2 x1=20 1. Which fo the following is TRUE? AL (A+B)! = 4-14 87 if A ond B are invertible matrices. B. Any square matrix caw be transformed into fdéntity mattis using elementary row operations. ©. A and AP have the same inill space. P.1E.A =A", thien the row.spece of A equals.columa space. 2, Let Abe a square matrix af order n whidlvis both Heritian:and Unitary matrix. Then A is A. Tdempotent matrix —_B, Involutory matrix 6. Nilpotent-maceix 1D. Permutation matsix 3, Let A be an 4x4 matelx with ronkfA) = 1. 16s lhwear system AX = 1 inconsistent, then raidk of augmented mateix [A : bis Ad BQ a3 Ded 1-2 5 -3 a tet Ae]2 3 1 —4). Then dimeusion of left nall space of A is 3.8 +3 = ALO Bl G2 D:3 5. Consider the polynomial f(x) = Sx -l 2 in P(e) with the inner produat < f,g >=fy {(e)gwlitx. Then Wilas As nv . 0.39 dD. va Let R",n 2 2 be equipped with standard innior-praduct. Lett, Raycom ty bem columal veetors foriiiang an orthonormal basis of RY. Let A be the mx m matrix formed by the column vectors 01, as --5 Un: ‘Then AAzaAt BL A= A? Cathe Ant D. Jal =1 1 Consider the eet Wi +2 {(1,1, 1)" (E, -L,0Y"} is sulaspace of Re, TF (a, 8,7)" € WA, then + At y= AO Bl Oe Da 8. TE the projection of (3,4, 4)" oubis dee Fine tseoupl (2,2, 1), then the Length uf ereor veelor is AWE B. va G2 pve 4, Let P be the projection matihx for-any subspace. ‘Shen which of the following s FALSE? AcP's PT B. pia P O, venk(P) = 2 DP iPaP-i 10.-The best line y = ma +¢ to, the points (0,6), (1,0), (2,0) ts Ape dat5 Boys 32-8 Gy Se Deys $245ce eae ? LL, Which of the following ‘stitement is TRUE for a moti Ade ae a8? ‘A. z(2? — 1) can be characteristic polynomial of. Ay if Ais ‘Gain a 3, ale — Ife + 1) eon bo charncieristle pelyromial of a 1A is Orthogent. ©. 2(a? +1) ean be cliacactesisti polynomial of Ay if! is ‘Unitary. D. ef ean be characteristic polyoemial af A, if A Is Nilpoteh 20, The trace and determinant of 8 mulrix A= Be al ara respectively 2 and —3, Then determinant of aay 22, A Sis AA 38 B. -36 O.48 D.-18 13, Let A be « Skow-Hermitian matrix of ordor 3.qthem whish of the following set denotes the eigenvalucs of AT . . A {L4-) B. {01,3} © (24, 0,28} D {4 17) 22 21° 14, The trace of the matrix [0 2 3 | is oo 8 ae B22 +3 c. 439 18. Lek A be an 3 3 zeal matrix whose eigenvalues ate 1,2,3. H some 8,c€ R, ad 2454 + cla, then (a, 2,¢) eqtials to AL (6-6, 11) 'B. (6,6, —11) ©. (6, -14,8) D. (6, 11,6) 16. Let A be en 5x 5 matrix whose eigeuvalugs we 1,3,3,3 aud-4, Then A will (A-3)) 17. Let A = laghearay = 0 oF 1.983, Day = IW) end Dg aay = 1 LF aP +8 (iagonaliva ble tf rank of hen munaber of such mstvices are 18, Por what-values ofa and 6 the system’ of linear equations + 29-+3z =D, ‘has unique solution. |, 2a + by +62 = 0 125 19. Let A= |2 3. «then basis of [R(A)}E is fu aed 20. For the mate A= | 2 ID, goomotrie multiplicity corresponding to eigenvalue 2 is, 1k 2, Section-B Answer any TWO questions from the following. Hach question carries FIVE. marks. % ‘1 vie oe sees phernrelhe mail ( 2 eae ws, i 2 3 2, Brpress the iuateix ]—1 0 3) i QFefactorization. o 2 3 4 1 4, Using: Cayley-Huiluan theoren, ful invernd of tlie mars | 2 2} RAJIV GANDHI UNIVERSITY OF KNOWLEDGE 1 ECHNOLOGIES, BASAR = M79 : ~ GAY, 2021-2009) Nam P Conspurer Scionce atid Engineering Departeiont Subject Name Programing for problem solv ‘Subject code: (patel 042002 pene ane Timeliee # gym El_SEMI (CSBECE & ERE} Max furl: 30 Section-J Answer sll-the questions, ench question carries 1 maxi (20% 1=20Ma¥ce) 1, Which of the follow.ng fnstion is used fo find die first occurrence of a given string ink anothecsring? sh are b) suche) c}atmsergy sisted) 2 What is the maxirvum nuniber of ebsraeters that ean be etd in the siting varinible eher Line[40]? O38 6/39 40 aad 3. What will bethe omput of the following C code? Finclude int matat) { , int *pir, a= 20; per aa spit pirs3; . print Helin", } 223 e) error 20 a) None 4, How is an array initialized in C langage? 12,3} ojint af] [1.2.3] none aint a={ 1,23} byiatal 5, Which header fite should ba’ inchided! te use factions like sfen() anc strcmp()? a) stdiah 6) stdibb e)string.t nonerent 9-2 function, what solually gots passed? y if you Foss an arey'aBan TENT a)Valuc of clensenls ‘in array. by) First element of the array 0) Base address af the anioy g)Addross ofthe last coment oF anny 4, Sine of the army need not to be specified, when + a} tis a formal parameter i) Ilis asdeclarntriow ch Initiatiztton is par of definition AJAl of these §, What is the cutgut of the below progtann void myshowrCint 9; ‘yoid ming { int o=10; prioulf"¥id ", 3); rnyshowi (tea); prin". + void myshow(inl "k) { #20; I 4) 1010 1020 <) 2020 4) Compiler error og. th tie absence of « exit condition ins eoursive function, he Folfowing error is given. 3} kun.time error a} Compile time eerer, e) Logical exor 4) No error 10, Wharis the output of he following? sineludessidiok> jiat abatn) { printi(" Hello” maint): return OF } 2) Heliais printed atce 2)0 in chimed ) Hella js not printed at all 6) Melle infinite number of times TL Whereis the outpnt af the below program? voiul main { int af] = 11.2,3,4.5}, "ps B =D ‘printf("96d ", p)s pia ‘printe{nved ", #7); 1| | 22 23 2d &) none 12. Suppose weave a one dimensional army, named ‘x’, which contains 10 integers. Which of the {allowing is the correct way (0 allocate memory dynamically to the array ‘x’ using malloc| a) x=({nt)malioe(10); 1b) x=(int*)matloc(10,sizeofCint)); <¢) x-malloc(int 10,sizeoflint); 4) x=(jnt"}mallo<(10*sizeofGind); 13. If malloc) and calloc() are not type casted; the default return type is . a) void* b) void** ) int* ‘d) ehar* 14; The_____finetion returns the number of characters that are present before the terminating mull character. a) strength) b) sttlenQ 6) strlent) @) stechro, 15. what is the output? d#include int main) { int a[5] = {5, 1, 15, 20, 25}; inti, j, m; i=+afl]: j= oli printf("%d, %d", i, j); return 0; } 022 3 216 4) None 16. arguments passed to’a function cail is known as a)formel — b)funetion arguments cJactual arguments d)none 17. Choose a correct statement about C language arrays, a) An aitay size'can not changed once itis created, b) Array element value can be changed any number of tines ‘ €) To access Nth element of ari array students, use students{n-{] as the sitting index is 0, all a,b,c are correct @) only aand ¢J8. what syill be dic autpat of the following ¢ progrim? Hinelude int Fianotint int); int main} int a=3.h=t) print{"¥4a" fane(a,b)); } int fane(inta, int hy ite rein 0; iff return a, Tetum a+ funcfa,bel}s} 4723 6) 22 24 @uone 19. malloc is available in whieh liboary ajstdlibh b)stdiof — gjetypeh. a) stringh 20; what is the ouput of the below program? void main() a)S75 777 SIF Scction-IL Answer any two questions, ench question carries § inarks \ drone (5*2=10Marks} 1 write a program to rend 10 fntegers ,store it in an array and count the positive number S, Nepative ‘numbers, evew and odd in ai aay(SM) 2. a)Weite a program io print the Fibonavoi series usiog recurdion(3M) Hywhat is difference between scan) and wets) *how to wead the niuitple lines nist 0g using scani(}2(2M} 3. Explain the call by vilue and call by reference with example (Si) 4. Define malloe() arid caljoct}thaw the memory is allocated Explain with expuaple 2(5M4) iynamicelly using callne(yé RAJEY GANDHI UNIVERSITY OF KNOWLEDGE 1 ECHNOLOGIES, BASAR (ALY, 2021-2022) ; cment : Départanent of Manag i Go BONS Tite: | Hour, (8.40 - 9.30AM) Max Marks: 30 Subject Namo: Constiuution of India Date: 11-04-2022 7 yeu: B1 Som! CSE, ECE_MT2 PART I: Answer any (2) Tro Quesiions 5*2=L0 Marks 1. ‘Write and explain all the articles in right to expality. 2. Classify the directive pfineiples and write and explain at least one article for each category. Write and explain any two criticisms of the directive principles. 3. Write down all the fundemental dutics. 4, Write and explain the powers and: funetions of the president, PART I: Miateb the List I with List IL If Marks 1 Ht A, Right to Constitutionst remedies 1, 26 13, Right iW Education 2A C. Probibition of Eniployment of Children in Factories BAQA D. Equality before Law 4.24 E. Freedom to manage religious affairs 5.A:32 PART Ii: Answer the following mutiple-choiee questions 10 Marks L. Fundemental sighs are borrowed ftom which of the following Covistitutiois: @ USSR BUS ¢. France d. Ireland 2. The Right to Equality are mentioned in \ a Al-18 b. A 15622, ©, A 23-24 oO. A 25-28 \ 3+ Articles 26-51 in the indian Gunstitution are relaced to which of the following. Fundamental Rights ¢. Directive Principles of State Policy b. Unfon Executive d. Fundamental Duties 4. Port A of the Constitution desis with which of the following, a. Fundamental Rights ¢. Directive Principles of State Follcy b. Union Executive d, Fundamental Duties 8. Who is the supreme Commander of the defence forcas af india, 2 Frimelinster b.President ¢. Governor d, Defence ministerpig -RASIY GANDHT UNIVERSITY OF KNOWLEDGE TECHNGLO GIES, BASAR *) (acy, 292-7022) Exam:€1S2_EST(REG) Subject: CALCULUSIEGE & OSE] (en paul] Duration: 2 hrs so Date: 27/04/2022 Bla Sub Code: Mya1192/ 13111102 Mark: SECTION-A Answer lh questions. Each question eartles two Matks {45x 2=30) nNoter Write the answers it ordoriy at one place 4, Witieh of the following statement is FALSE? A} Limit of a sequence & ase ByITS, = oer then the sequence ‘(Gy is-divergent : Q] The ante is said to be, ‘an ogcillateHinitely if it js"bounded and not convergent, D) Every convergent sequence is bounded 2. 185, = oar fs w.saguence, ten TimeaSn = . ai a) oo a 3 pp 2 3. For whatvalues of x, the seriee.2., Ee convergent? N zerse Bo or Arey r(2 ‘ls Ga Oo Raete=pe2 py 12. fF 4 sine xcoste de = Nom Bs oak aj 13, Ilnz =x? +5? then Xzy +. Als By tain! Gate Date 44. If fy,2) = ie Pt a aye, = ofy = cost, = C7 thon fate =0 is Ay 2 3 Qa Ds Fe 2? with constraint + y = 4, then Which one ofthe following is TRUE? AL Maximum 16, minimus’ 8} Maximunn't6; atinirium 4 ©) Maximum 16, Minimum —16 0) Maximum 4, Minium 0 P-n0. Page 20f 3 ser oY ayProw 18 y P co a 9 38: 20.Answer any THREE of the following: questions. 16. Fra 20. a) SECTION-B (3 %10 = 30) a) Prove that (a,) = Ese = 1,2,..is Monotonic Increasing sequence. 4M B) Prove that limyses [gear weetv web gee] #2 3M a 6) Find tinpse [SI am wis convergent and find its sum, 5M a) Prove that the series 2+ b) ‘Test for the convergence of the seiies DAMES an 5M a) State Lagrange mican value theorem and verify this theorem for the function f(x) = (@— D(x -2)@— 3) on [0.4] 5M b) Find Taylor series for ((@) = 2 atx=2 eM a) Bvaluate [°.—Sdx 5M b) Evaluate [Pots de . 5M a) Find Maximum ,Minimum and saddle points of Fy) = 2x3 + 2y3 — 9x? + By? — 12y 4M xy b) Show that f(x,y) = ae G0) # ©) 5. Nor continuo 4 us at (0,0) 3M 0, Gy) = (0,0) #2 ¢} i w= tant (4), then prove that x24 yt =), Sey = sind 3M sere ax CO). a} Prove that { TF a LO) SM b) Test for the cony Qf the 3 ergence of the series Sig SM - End of the Question paper Page 3 of 3_ RASIY GANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGIES, BASAR : (A.¥. 2021-2022) ' Depiirtwent of Management Subject Name: Constitution of India Subject Cade: BMO005 Date: 20-04-2022". : Time: 2 ours Beam: El Semi CSE, BCE 2Seml CHEM_REG Max Marks: 60 PARTE: Answer ony Wy ‘THREE ‘quan 5410-30 Marks ail Ris along with their articles. 2. Write dow ill ths fees ofthe onstitation aud Features Borrowed. °5, “Waite dala dhs powers of Pes AB he Waite and expla any! 16 pitecvePrnceles of state policy. Googe Wake texto ie Preémble-an explain any fivekey words. 6.. Write down all thé Fundamental Duties. '§ Marks 1 1:24 Janmary 1950 2.22 July 1947 . 26 January 1930 26 Tanuary 1950 5:26 November 1949 “BL Natioial Azthdn sind Song-adopted on ? cominensemeat of thé Co , 8 Marks B a, Artiolg S1A, b. Articletg - ” . “Artiste 394, : - e 1. Freedom af Speech 2°2. Equal Justice and Fee legal aid 43. Constitutional Remedics 4. Right to Education 5, Fundamental Duties Poge $08210 Marks PART Il Answer the following muitipie-choiee questZons : in tation is divided into Le nee ae wna ehsers Sp C24 chopiers 5 paris D. 2ehaptets I2.parls 2 The tenure of the Prine Manistor an Presiles! of hugia Respectively’ A, Sand 6years B, 4 and Gyoals C. Sand Syears D. 6 and 6 years , satan 3, Which articles of the Constitution abolishes Untouchability and Titles respectively? A, Article 18 and 19 B, Article 15 and 16 .C. Article 14-and 15 D. Articlé 17 and 18 | 4. Jn Which part the Funda mental rights and Duties are provided respectively? A. Part IL and I B, Part Land IV-A © Part V and VI D, Part. 1 ond ID 5, Wher were the Fundamcatal Duties of the Indinn citizens incorporated iu the constitution? A, 1952 B. 1976 6.1979 _D, 1981 & ow many meinbers are wowinated by the prosident inthe Lok Subba sind Rajya Sabha A.2and 12 een 15 C2 sel D. Sani 5 7 Who is the Prime Minister of Iudia before wad aéter Charan Singht A. Chandra Sekhar and Jndira Gandhi B, Indira Gandbi and Deva Gowda D, Morarji Desai and Indira Gandhi ©. Rajiv Gandhi and PV Narasimha Reo &. Which of the following Articles contain Directive Prineiples of State Policy? A. 30 to 49 B.3610,51 ~ 6.42 t0 56 1.28 t0 48 9, Which of the following Telugu person, became the president of Tudia? ‘APY Narasimha Rao 'B.Venkaialt Naidu CK Keshava Rao D. Nealam Sanjeeva Reddy ci. avbieb ofthe fellawing word is nataddel Co the Preamble by the 42 Constitafional amendment A. Sovereign 8B. Sociatist CeSecular Da lntegity 10 Marks PART IV: Fill in the blanks 1. Number of Lok Sabha MP Seats 2, In india Number of States are, ‘two Committees related to Fundantental Duties ee and Chief Justice of Telangana High Couct__- ‘Chairman of Rajya Sabha, langana ___-Rajya Sabha MP Seats and Union Territories are - Name of Chief Justice of India ‘Name of the Governor of Telangana Number of MLA Seats in Telangatia are, ‘Telangana Assembly Speaker's Name's, dhu Schome is related to which part'of dl and as a President, ‘pedkar Jayanti is eclcbrated on MLC seais are Council Cliuirman’s Nome is ‘Dalitha Ban: ho Constitution amount givenis_ “Minimum age to contest as a Seepanch __ __ Am Se RS 10: National Voters Day is celebrated on Page2of2RAJIV GAND ‘ HI UNIVERSITY OF KNOWLENGE ‘TECHNOLOGIES, BASAR Q, (AY. 2021 - 2022) : / Commen for Zick and GSE ‘ subject: Linear Algebra fe Sue: nea Subject ode: MALO Exam: EISIEST [Peg/teni] Mew ax Markse Bist NOTE:(i} Scientific calculators are NOY allowed, a) This question paper consists of Section-A and Suction-B . (ii) Sestion-A Descriptive and Section-B Objective. Section Answer any '‘ITIREE questions from the following, 3x10=30 Zach question carries TEN marks, [5+5] a) IT. BA. 2B defined as T(x, 75, 29, %4} = (or + 22d.+ 23, 0) — Te, 250" +.03 — az), then find the basis for null space and range space of P. Hence verfy rankc-nullity thearént, . 1 2 : b} Let T: P(e) + fale) be a Incar transformation, Let A = [ & i be the mutrix representation of the” ed oh Tinear transfotmatign with respect to ihe ordered basis, {1 + 2,2} in i{x) and {I = 2, fis Py(@). Then, find the lingar transformation 7. ‘ 2, [545] 112 tm oO a}LetA= {1 2 af. Then find invertible mauices Pond Q such that Pag = |B a: 23 5 Wat By bas = fb BE Far what valués of & and ys the system of linear equations x-+y+2 = 6,2+2y+ have () no solution, @) # unique solution wud Gi) an infinite nany solutions, 3. 15+5] “1205 8 . . aera] 2 3 4 7] .Uhendind R(A),CCA) RCA) and (OCA) 4, 3 1-1 5 B) Find the projection of (1,2, -1)” onto ehe subspace HW’ = {62,y, 2)" BS 222+ 4-7 =.0} 6 RS. [545] 4, a) Using Gram-Schriidt incdiod, find’an orthonormal set Ln &* containing the veeror (1, —1,1)7. b} Stace Cayley-Hamilon theorum, using thi theorem find the matrix A°—SA 4 7°38 AL bAtt Red. 3 BAP tae, a= la 1 |. 11I 8) Reduce the quadeatie forts 9,340) = u+-O4/4-8ic! « Dry- Zpcto the canonieal fora by an ontoy transformation, ra it 1) Find the singulae-value decomposition of the matrix 4 s ft | , tit 6. B iy a} Find the matrix A whose gigenvalites Li, 2and covresponding eigenvectors are (15,107 4,1, Ot respectively: 122 ) Find the Jordan. canonical farni of the matrix A= a 2 uz. aes Scetion-A Aaswer all the Questions, Hack one carries TWO marks, Bxaay 1. The dimension of the real vector space ¥ ofall skewrsymme trix matrices of. onder d 4 ig 2. Tf the set ((2—1,2), (2,42), (0,2,3]} is basis for e¥(}, chen #. 2 ag 3 As | 3-1 0], thendct{-g4et) x “Ff 4 8 : 2 ~ 3 “saya « )testeiuecta 10 1 5. In BY, Tet the jtiner product bac By >= y Ac wih A= {2 4 4 ‘Thon with this inner produce tke angie between the vectors ¢1, 1)7 and COs it 4 latAe |2 3 6. In, with standard inner product eoorcinate vector of (44) with respect to thie orthogonal basis {0h “1.0, 4,0, 91), 10,3, 5} OF R) is % Hlyenvalues of Hermitian matrte are _. G «2 2 ‘ 8 weae| 5) Lf then dimension ofan space of comespondtng edgematue 218 2 arg 3. Thein s i ‘p28 — nyey 15+ SER OF etic fom.) way pag? ban? BEI — Page 2{Sh vot a be 24% 4 and having a minimal polynomial 38~ 9? +24—2= 0. Then the cota number ef Jordan Tioga] blocks in the JCF of A corresponding to al! cigenvalues-are —seu—e Ly 7 RP it! fs linear transformation defined ae T(u, yz) = (ehyuo at Het vw), then the matrix of Towith respect to the standard basis is Ba 4 i : D3, 0 11 Lad 10 -¥ efor. p. {1 2 0 oi 4 oid 1D, Let A be a 5 x 7 matrix and whose rank Ly 3. Then nullity of 4 is AQ 3.2 c3 Da =30 43. Which of the four subipaces ofA vontains de error vector ¢? A Nay B. NCAT) & Ol) paar —1and 2, Then 14, Lot A be 98% 3 matrix with cigenvalues 1, B, Ab— Ais non-singwlar A. AP + Ais nonsingular D. AP 24 is non-singular G. AP 2A js non-singular Us. Let Abe att ve x1 matrix, Then which of the following is FALSE? AL AAT and ATA are diggonalizable. B. AAT and ATA have same characteristic polynomial. c. Aa and A7A are symneizic matrices. 1, None of the above. AprowthbaauND OF THE PABERAHHA HI Page 3Ne Siibject! Communi “pete: 18-04-2022 BAILY GANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGIES, RASAR (A. ¥, 2021-2022) DEPARTMENT OF ENGLISH ion Skills Thno: thour Mas binds m: EI-CS/-S1-FST (BCE & CSR) Reg ® REDL The question puper comtains thu sections. Section A consists of 20 Questions cand cach qiestion earrtes One Mark Section B consists of Six Questions, attemyn any Three. Bach question eaprics Ten Marks. sEgnON 30x1=30 Answer ail tite questions, bL 7 Identify the word which is MOT an absteret noun. 2) Happiness b) Sadness 2} Joyfilness: Identify the FALSE Statement. 2) Common noua: refers to every persoa af thing’o! b) Common nona: can be 2 countable and ancountable noun. . . , ¢) Common foun: can talk about rdaerete now, abstract noun, rhaterial noun und. collective noun’: 4) Common noun: represents ‘substance’ of which things-are made. ‘ Find out the Object Pronoyns. 2) J, we, you, he, she, itand thiey c) My, oun, your, his, her, its and their Identify the Reflexive Pronaun. 7 al by me * c) ming dy myself - Find out the ‘Third Person Plural fiom he, given pronouns. a) We By You s) They d) Your Identify the’ Demonstrative Pronouns. . 4), Anybody, nobody, somebody; everybody. . b) This, that, these, those o) Myself, yourself, eutselves, themselves: d) Mine, yours, lors, theles “Pind cut an appropriate definition'of Indefinite Pronoun. 2). ‘Indefinite pronovn: to refer to people or things without saying exactly who or What they are. D) Indefinite pronoun: used lo point to spevifie people or things within a sentence, ¢} Indefinite pronoun: when the action is dong by the subject turns back (reflects) upon the subject. d) indefinite pronoun: used.in the object refers to the samy person or thing denoted by the subject Choose the corréct stalement from the following. a) Acelative pronoun is a word that introduess a dependent (or relative} clause and connects it to an dy Gold Fthe same class. b) Me, es you, tim her, it aid them, &) Mine, oivss, Yours, his, leis, ‘and theirs ‘dependent clause, 6) Arelutive pronoun is one which is used to refer to nouns mentioadd previously, whether they are peopte, places, things, animals, or 3deas. ©) Relative pranonhs can be used to join two simple sentences. 4) which, thal, Whose, whoever, whomever, who, and whorn ire called relative pronouns. ¢) All the above are correct.9. Identify the correct type of adjective of the underlined word. A Title knowledge is @ dangerous thing. a) Adjective of quantity b) Adjective of quality ©) Descriptive adjective d) Numeral adjective 10. Find out the correct definition of an adjective. a) An adjective is a word used to add something to the meaning of @ noun or, pronoun. b) An adjective. describes or modifies noun/s and pronoun/s. in a,sentence.. It, normally indie, quality, size, shape, duration, feelings, and more about a noun or pronoun. 3 ¢) Adjectives usually provide relevant information about the nouns/pronouns 4). Articles and some other words like articles—no, some, any, much; many, few, a fev, litte, Tittle, ete. also function like adjectives. ¢) All the above are correct. ' Correct the mistakes in the following sentences, 11, One of my classmate is an engineer. : “ 12. One must finish his task in time. 13. Mathematics are a difficult subject. 14, Each of the six boys in the class has finished their task. 15. Ram is elder than ail other boys of this class, 16, Either Ramesh or are to do this work. 17. Each boy and every git] were given reward. 18. Mvall friends are cricket players. 19. The Wings of Fire is. autobiographical work of Dr. A.PJ. Abdul Kalam. 20. All Indians must respect cach other, , Read the passage carefully and choose the sie leas ainswer. a The habit of reading is one of the greatest resources of mankind; and we enjoy reading books that belong to us much more than if they are borrowed. A borrowed book is like a guest ini the house; it must be treated with punctiliousness, with certain considerate formality. You must see that it sustains no damage; it must not suffer while under your roof. You cannot leave it carelessly, you cannot mark it, ‘you carinot tum down the pages, and you cannot tse it familiarly. But your own books belong fo you; ‘You treat them with that affectionate intimacy that annihilates formality. Books are for use, not for show, A good reastn for marking favourite pages in books is that this practigé enables you to remember mofe easily the significant sayings, to refer fo them quickly. Everyone Should begin collecting a private library’ youth; one should have one's own Bookshelves, which should ould be fice and accessible to the hand as well as to the not have doors, lass windows, or keys; they sl "aye. Books are of thé people, by the people and forthe people. Literature isan iminortal pad of storys it is the best and most enduring part of personality. : 21. The above passage is about : ; a), books b) games o)jokes 4) magie 22: What is te meaning of punctiliousness? * 6) very dull a) Very neglect 6) very laxy _o) very careful 23, According to the passage, books are more enjoyable when they are a) in book-shops b) borrowed 6) in the library ——_d) personal posstisions 2