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32. The number of generators of ( ) If E an B are Lebesgue meanlint (Z24, +) is urable, 1 nE E. is xn IS (a)2 (b)6 (c)8 (d)10 '56. im X (b)18 years RagveerChisdaiy form lationand testing L besgue in asurable 43. A Sylow 3-subgroup of a group of LeeladharMndloi (b) Th y u se logical methods of (c)2 1 years (c The farn vM of Lebesgue (b)(a) order 12 has order K.V. Chauda,)indu ive-leductive reasoning to (d)25 years m asurable - ts is an algebra of sets (c)1 (d)0 (c)1 (d)12 (b)3 :29. Under the Right to Education (a)2 arriv at gr neralisations S. Ranianug.un td All fth a1 . Consider an( Z5 Act, elementa ry education 2. Who is selected as the Miss tJnivere (c) The ne icr employ methods of 57. (X tt y) + 70 Given + y') is equal to pt and 20 44 m : means education from fi rst class . rando uza lion in sampling : in 2015? sin{ I x y Then the number of homomorS to (a)AriyauaGuetirus (d) The aria bles and procedures are ' _______.da; then - + ° i) ,X + p Ismip. 20i5 ,. : an . a1. OU C . NIX Olivia Gordai not esc ri- e accura (d)2 (a)! (b)4 (c)5 (c) 0 (b)seventh clans PiaA.Ionso i compl tel3 45. Let Q be the field of rational (d) 1 (a integral i dwergent stics that fiftcs 17. Cond ion or Maria Laigu; a modulo 58. Let a be any element in a (b) Integral is absolutely convergent nurnb:rs and Z2 is na e 3. Who among the following is t1e the e erl enter 2. Then the 'n /0 Boolean al gebra B . If a + S = 1 (c) Integral i not absolutely winner of Ezhuthachan award ii contro s it his or her attempt to 30. Under the Right to Information x3-9x2+Ox+3 and ax = 0,then co vergent Act, disclosure of an information (a)irreducible over Q but reducible their relationship to 2015? ascert (a) x = 1 (d) one of e above on an incident conce rn ing the Sugathakumar; observ d p henomena are called over Z2 x=0 71. f f sati4ies the conditions of economic interest of the state (b)irreducible over both Q and Z2 K. R. Meeia (a) Indep nd entvanables x =a grange's mean value theorem (c)reducible over Q but irreducible (a)is not at all exempted PuthusseryRamachandran (b) l)epe esit variables over Z2 x = a' (b)can made 15 year after the mcid if f' (x) = Ott x'i (a,bJ, then (c) Confo dingvariables MeloorVasudovan (d)reducible over both Q and Z2 59. Which of the following is reflexdent 4. The French open 2015 Womei (d) None o t ese ch of th following is true? 1 -1 Championshipiswonbywhichofth 1&1peso e perimental validity are (c) is no rmally exempted from disive? (a) is constad on Ia, bI closure but can be released 20 46. Let A = 2 2 -1 following player (a) Conte andconstructvalidity (a) 12 (b) is strictl in creasing in [a, b] ~2 3 2 0. (a) Venus William:; years after the incident (b) Statist aIvalidity I? is strictl decreasing in [a b[ (d)is normally exempted from dis- The characteristic polynomial of Ais (c) L' [a, bj (b) SerinaWililairs (c) Intern validity (d) one of th above (a) x+ox+ 8x+4 (c)Simordallalep closure but can be released 15 (d) Inte ialidity, exteriial validity, (d) X1+OX, years after the incident (d) Maria Sharapova statistic validity and const ruct is and q is conjugate 72 im 60 111< p < 8x4 -* z 31. The area of a triangle is equal to: -' 5. Who among the following is the first validity then f ° 0 P that of a square whose side mean- (d) x ~8x+4 Chairman of New Development 19. Qualita ve research focuses on (a) Ip = Eq (a) 0 ures 60 m. Th e side of the trian- 47. The eigen values of the matrix Bank (NDB)? (a) In-dept interview only (b) 1P = li. 1 'I are gle whose corresponding altitude (b) Observ ions only (a) K.V. Kamath (c)lp (d) snot exist (a)1, 4 (b)40 in (a)60 m interie and observations (c)DineshkumarSzarma 61. If S is a non-empty set of real 73. e radius oconvergence of the (b)-1, 2 (c)80 m (d)90 m (d) Harshit Saumitiwa (d) Docume t analysis only numbers, then Do er series 6. The scheme Project Arrow is 20. Proba ilitv based sampling: 32. The heiaht of an are of a circle is (c)0, 5 (a) InI S = Sup S - 00 10cm and its diameter is 12.5 cm. (d)Cannot be dete rm ined related to which among the method• 2 (2-3i)" is following term? The chord of the are is of length 48. Let V be a finite dimensional (b) Ini S = -Sup (-8) (a)Stratifle sam pli ng be the identity vector space, I (n! (c) Inf S = Sup (-S) Medicine (b)Purposi sampling (a)1 0 cm 0 transformation on V , then the (b)12 cm (d) lnf S = -Sup S Postal Dartment (c)Random tampling null space of! is Telephone department d)Judgem nt sampling (c)8 cm 62. Every infinite set has (a) 1 (a)(0) I. The cas known as 'Privy Purse (d)l 1 cm Infrastructure facility (a) an uncountable subset (b) 0 (b)) 7.ln20l5 which among the following crop Case is 33. A sphere of radius 4cm is carved (c)v (b) a countable subset (c) ,!from a homogeneous sphere of (d)None of the above in Kerala get the Baumasuchika... a)R.C. Coor er v. Union of India (c) both countable and uncountable (d) title? radius 8 cm and mass 160 g. The 49. If V is a vector space with dim b)Ashok Ku ar Yadav v. Hatyana subsets 74. A etion is . In be harmonic if mass of the smaller sphere is (a) Pokkali Rice C) West Be. al v. Nripendra Nath V =n , then the dimension of the (d) none of the above (a)80 g (b)60 g (b) Vazhakulazn Pinapple d)Madhav I an Scindia v UoI hyperspace of V is 12 5' 63. A real valued function / has dis- (a) (c) Wayanad Gadhak.isala Rice (d)20 g 12. In which of the followi ng cases (c)40 g (a)n + Vs continuity of the second kind atx (d) Changalikodan did the preme Court declare 34. A pendulum swings through an (b)n-1 = a if 8. In 2015 which among the following Salwa Jis in as unconstitutionangl e of 30 and describes an are (c)n+1 a alL / (a +) exist only (b) =0 (d)0 film won 8.8 cm in length. Th e length of the title al? a (a exist o nl y ay / -) : 50. Let V be a vector space of all Suvamachalcoram in Kerala ()Kihoto Ho lohan v. Zachillu the pendulum is (Use = 22 ) Neither! (a +) nor! (a -) exist: 15u + hu 2x2 matrices over!?. Let The the v. Jharkhand International Film Festival? (b)Pratap Si = 0 (c) linear mapping T:v -*v such Both! (a +) and! (a -) exist ox TY (a) Shadow behind the moon ()Nandini I ndar s Chattisgarh a8.8 cm T(A) that = AB-BA where B = 64. For the sequence {x,,) , wherex (b)Ottal (4)Pooranv tateofU.P (b)16.8cm (d) = 0 12 1 Then the nulli ofT is = (-lfn, the [jx,, is (c)OzhivuDivasalheKali 2. No law rit de by the Parliament ax Oy ! (c)124 cm 31Lo (d)Jalalsstoiy and havin g extra-territorial oper(d)lo. 2 cm (a)l (b)2 (d)4 (c)3 0 9. The American pacecraft New ation will b deemed 35. A solid cube is cut into two ! SI. Banach space is a Horizon is launched to study which (a)invalid log zdz where c cuboids of equal voluntes. Th e ! (a)Complete normed vector space 75. Th e alue of among the followi ng planet? (b void ! (d) ratio of the total surface area of! (b)Normed vector space J (a) Moon (b) Pluto (c constitubio al 65. Every open set of real numbe rs is is the u t circle is the given cube to that of one of (c)Complete vector space (c)Mars (d)Venus (d valid the union of the cuboids is (b) 2n (a) iti (d)None of the above 10. Which among th e following 24 A legislati Bill which contains (a)2: 1 (b)3 :2 ! 52. Which of the following is t rue? (a) countable collection of disjoint (c) 4 iti (d) 0 Constitutional Amendment Act is nly provisi ndealingwith giving closed intervals (d)4 :3 ! 76. Thei age of ti unit circle id = (c)4 :1 ! (a)All normed spaces are inner related to the Land Boundary f a g rantee by the 36. What is the value of ! (b) uncountable collection of dis- : 1 und r the tm jsformation w = ! product spaces Agreement between India and 'overnm tnt 01 India is (b)AlI inner product spaces are joint closed intervals 2z+z is 1 Bangladesh? (a) inancialI B 1 ? normed spaces (c) coun ta ble collection of disjoint Circi 1 (a) 100 (b) 119 (c) 110 (d) 112 (b) Money Bil ! (c)All inner product spaces are ! open intervals Strai line ! 5+j11. Th e best teacher is one who is (c) rdinary Bil Banach spaces Para It (d) uncoun table collection of dis5F___ capableof--------. (d) I of the a ye . ! ! (d)AlI inner product spaces are ! joint open intervals Cardi id giringagood result : -25. The tot il mber of Ministers : : Hubert spaces . ! 77- If " 15 11 set, T a collection of ! 66. A set E is nowhere dense if inspiring the udents'to learn i eluding th Prime Minister in ! ! all sub ! 53. Banach space is a H ilbert space if rof X t it (X,T)is +429 closure of B contains non-empty (b) (a)Pythagorean theorem holds (e) completing the topic in time t e Coundl f Ministe rs should (a) .(a)Diseree 2 . . 2 open se 5 : (b)Projection theorem holds (d) helping the students in preparing per- : : not ex eec : fl isc e closure of E contains no non,.. (c)Parallelogram law holds notes c ntoftlite t tal members of the td) Thvnsl -5±'29 ! (d)None of the above empty open sets ! ! 12. Learning by Doing principle is I use of Ithe eople. ! (c) (d)7 2 ! 54. If T is a bounded linear operator ! (c) closure of £ contains empty (d) None the abov reflectedin------. (a)1 : 78. Let X I Y are t000gical spaces. : on a Hilbert space H, which of the : open set (a) Realism (b) Icealism (b)2 37. 21000000 mO(l 7 is Th e func i onf is a lomeomorphism following is not t rue? (c) Pragmatism (d)Nnturalism (c)lt) .d,noneoftheabove . (A\A . ''2 if -' : (a)T is normal if T is self-adjoint 13. In inducth reasoning, one (d)Nne oft a ote 6i. If ft and fit are two real-valued (a) f:X -> is a bije4tive function 38. Whens° + 5x - -3 is divid- (b)Tis normal ifTis unita ry proceeds from amount of fine 26. The mamat bounded functions defi ned on [a, ed by x-e 2, the remainder is ! ! (c)T is self-adjoint if T is normal ! ! (b)f is co nuous particular to gieral tht can be imposed on the ! (a)0 (b)l ! bJ then for every partition p on (d)None of the above general to particular reponde;ittw violates aprotec- (c)2 (c)f*Y is cont uous [a, b] (d)3 55. Th e equation of the normal at rational to empirical tidn ord er I sued under the 39. A tree with 7 vertices has the point (® sec® ,b tan® ) on (a) (J(p, /1 +f) = U(p, ft)-i- (J(p, f2 (d) All oft above none of these Vomen from: edges. Prtectio x2 y. . (b)U(p,f+f2~U(p,fI)+U(p,f2 79. Eve ry ompact subset of a ! the hyperbola b2 =1 is 14. Which of the followingisaprojective Donestic %iol cc Act is (a)8 (b)7 Hausdo space is U(p, ft +f2 ~ fJp, /1)9 U(p, ! aid forteaching? (a)Tes Thousand upees ! (c)5 (d)6 ! (a) Closed ! ! (d) None of the above (a) Still model (b) Working model (b)F4ty Thousan Rupees 40. The number of distinct spanning (a) sec® - tan 0 =1 68. If f:[a, bJ - R is continuous and (b) Open se a b (c) Charts (d) Slides (c)Thnty '1?housa d Rupees : trees ofK4 is : : . . : Null set monotonicfunction then ! ! ! (a)16 (b) 12 (c)32 (d)8 15. The most significant system of (d)Noe oft hese ! td' N f he above is Riemann integrable on [a, b] f evaluationis --------. 27. etionsil Pa ks are notified 41. If the identity element e i S (b) sec® + tfle =1 The ord( and degxe of the difb a exists in a sentigroup (5, i), then / is not Riemann integrable Formative evaluation un4er ferntial quation ! itisa ! ! [a,b[ Summative evaluation (a)ln4'an F wests ct ax by (a)Group (c)®-=a2+b2 is Riemann integrable on!? Cont in uous and comprehensive (b)Foiest.0 )nserv lonAct f is dx dx21 (b)Groupoid None of the above evaluation -(c)Enironntent P ection Act ! (c)Monoid ax by ! ! 69. Which of the followi ng is true? ! (a) 1 4 Continuous evaluation (d)Wi1i Life Prote tion Act • )2,4 , (d)None of the above , (d)ij +j=a-+b, (a) The set [0, 1 [is not countable 16. Characteristics of descriptive 28. Th mm imum e of a donor of , )3,4 3:1
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HSST Mathematics, Online Examination
PAPER
88. The solution of the integral (b) T 2(1 cos )+ g (1+ cos p) (b) 1 (c) 1 W11Y)=( 7 1 X) :?Hp)+X(p). equation (c) 2 (1—cos)—g(1+cos) (c) i! 2 (b)2x4 ..x (d) 22(1—cos)—g(1+cos) (d)x2 (c) y=c (d) x)6)(a)d (1)(x)—xi 4 (d) (fX)= f ("1 X) 82 The general solution of (d) x = 0 93 L (s'+a2) ] ' .85. The general solution of the wave, is 96. The only idempotent t-conorm is. 100. Let X be a non empty compact Hausdorif space. If eveiy point of (a) algebraic sum + -_! = 0 mis of the form is — 1 equat.ion ?? isa limit point ofX, then o (b) drastic union (h) tanx (a) --(1 - cosat) .— —c OX (a) cosx a(a) Xis disjoint (c) standard fuzzy union (d) secx (c) sinx u =f(x + iy) —g(x — iy) (b) Xis countable yx,t) x+ct)qs x— (a) (d) bounded sum !1L = 4) t) 89. The minimizing curve must satis(b) u =fx — iy) —g(x — iy) (c) Xis uncountable 97 Usmg fuzzy arithmetic fe a differential equation called u =f(x + zy) + q(x — 1 y) (b) y(x 1) f(x+ct) . one o e a oe operations on mtervals (4,lo]/[l,21 is (a) Lagrange's equation a =f(x — iy) + g(x + iy) fix—ct) (c) x a(a) 4,5j (b) Euler-Lagrange equation 83. The partial differential equation ' — [2,10) ANSWER KEY (c) Gauss equation formed by eliminating the arbi- (d) No general solution exists (d) —2- sizi :at (c) [ 2,8] a 86. Stirling's form ula is the IA, 2C, 3C, 413, 5A, 6B, 71), (d) None of the above trarv of Gauas forward and backsard 90 A solid figure of revolution for a Ans (a) The language generated by the 8B 9B 10A 11B 12C 1 3A function fromz =f() ormu Se. X : given surface area, has maximum urammar G = (S) ( a bi S P) 14D, 15C, 16B 17A 18D 19C 20A, (a) Arithmetic mean 94. e'd.x is . volume is in the case of w ere is.gwen y is jo (b) Geometric mean (a) a circle (b a s here + (a x —0 —),A is 28B, 29D, 30C, 31C, 32A, 331), 34B, / ox 0 Y — (c) Harmonic mean (d) a parabola (c) an ellipse 35B, 36A, 37C, 38B, 39D, 40A, 41C, (b) (d) None of the above 91. A rigid body movi ng in space (a) I OVOI 2 2 42C, 43B, 441), 45A, 46C, 47C, 48A, 87. The interpolating polynomial of + with one point fixed has degree of =0 {a"'bn~O' bx 0 Y 49B, 50A, 51A, 52B, 53C, MC, 55D, the highest degree which correfreedom (d) (a'2b°;n~O) (d) r (c) sponds the functional values (a) 3 99.Whichof the followingisnottrue 56D, 57D, 58D, 59A, 60A, 61B, 62B, (b) 1 95. Using Fourier series, representf(—l)=9, f(0) 5, f(2)= 3, (c) 6 (d) 9 =0 y in the derivative of a smooth vec- 63C, 64D, 65C, 66B, 67B, 68A, 69D, Ox + Oy f(5)=15 is 92. A particle of unit mass is moving mgx in th e mt,erval I -ititI the tor fieldX? 70B, 71A, 72D, 73D, 74B, 75B, 761), e series under gravitational field, along (a) M . + I') = X+ 1.7 (a) x3 +x2 + 2x + 5 + L o. 77A, 78D, 79A, 80C, 81C, 82C, 831), Ox OV (b) x2 -3x+ 5 + —+ is 84B 85A, 86A 87B 88C 89B 90B (b) (JX) = ( , f) co f 5 7 ~ ~4x- ~5x +5 .84. The orthogonal traiectory of the (e) 91A, 92C, 93A, 94C, 95D, 96C, 97B, motion is family of curves x y2 = k is : (d) x+5 f(p)(+X) (l +cos)—g(l—cos) (a) 0 98A, 99D, 100C (a) 81. The value of Wronskian W(x, x2 , X43) is (a)2x2 (c)2x:)
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