Karnataka High Court
Mrs G Hemalatha W/O K Sudhakar vs The Registrar Rajiv Gandhi University ... on 1 September, 2010
Author: Anand Byrareddy
Bench: Anand Byrareddy
IN THE HIGH COURT 01+" KARNATAKA CTRCUIT BENCH AT GULBARGA, t DATED THIS THE 1st DAY OI.+T$E>')'F'1'E§»IV1"'B'A'}§§}j'x: f BEFORE-., t E M THE HoN'BLE MR_JUsT:'oE_ANAN'D tt w.P.No.4T041/2oos (EDN--ADM1TT BETVVEEN I ._V_Raj'ohug:35S4 1OV3;~-- ---------- : Petitioner S. Roja Advocate) I. The' Registrar, xx = Health Sciences, Mrs. G. Hema1at_ha,_ . _ - W/o. K. Occ:Stud¢1Tt;"Age.,:.';'33 R/o. H.No.' 4w--1;¢_;2, am A Anantapur_'d'istrio:£.,~_ '' Andhra Prad€vs_h,«VV 7 . V Now restidihg a'1:-.AV " W C /0. Bheemarma K.M.; Colony, Mahtralaya Road, ' < Rajiir Gandhi University 401 'T' Block, Jayanagar, Bangalore-41. Z 2. The Principal, Navodaya College of Nursing, Navodaya Education Complex, Navodaya Nagar, Mantraiayam Road Raiehur -- 584 103 3. The Secretary, Indian Nursing Council. Combined Councils Building. Kottur Road, Temple Land, j New Delhi -- 110 002. A 2: Respondents», .'
[By Shri. Veeresh 13. Patil, Adv_ocateA.fo'r R-- :2 id Shri. S.S. Haveri, Advocatefor R~3r. . V Respondent No.2 s'erved}_ j, u i This writ p'e,tition"'is filed under Articles 226 and 227 of the constitution' of i'--ndia"prayirig'=to..quash the impugned coininunieafion 'dated: .__2Qi1;1;'.:2;OO8i issued by the first respondent' No'--.,Aic2;/Ami/M.sc. (N) 2008-09 Vide AnnexVu--r--e.--G";~«. = V l 'Writ on for preliminary hearing in 'B' gr0up,_this_ day, p_th_e"'court made the fo1loWing:--
d'bRDER petition coming on for preliminary hearing isveonsidered for final disposal, having regard to the faetsand circumstances of the case. 2:'. Heard the learned counsel for the petitioner 'and'the learned counsel for the respondents. é had already paid her examination fees for the second year examination, she was also permitted to take tvheusecond year examination, as well.
7. The question that wou1d:_-arise' 't7oi*..consid;;r:é::tion of this court is whether the 'petitioner was,:'i'1:.dvee§i .€1igib1§' to take the PG course, as 64.71% as against the i. _
8. V counsel for the petitioner. on the text book titled Numerical Analysis" by S.S. Sastry and-.piacVes__re'lian'ce4 on the foiiowing extract therein:
1,3 AND THEIR COMPUTATIONS 'Ti'i1ere are two kinds of numbers, exact _ numbers. Examples of exact numizas are 1, 2, 3, ....,1/2, 3/2, ./'Q, 7:, "e,V__i'etc., written in this manner. Approximate A it numbers are those that represent the numbers A to a certain degree of accuracy. Thus, an é approximate Value of it is 8.1416, or if we desire a better approximation, it is 314159265. But we cannot write the exact Value of 7: .
The digits that are used to .
number are called sign;'fcant_....d.igits=..::or significantfgures. Thus, theiinumbers' 0.66667 and 4.0687 contiaini'-._1fi\'1re1s'igriificaiit'~.,vn"' digits each. The '1n'umber"
however, only two signi_ii'c,ai11t_V diigits, and 3, since the zeros *-the position of the decimal point.-1' numbers 0.00 145,. j0.00o;,12i5 ' 0000145 all have three In case; of ambiguity, the be used. For e5gaih'p1éf,,p,1:; 11jj1u§nb;e1¥125,600, the number of uncertain, whereas the number's 2V.5(3V'§:"1.(:j"=-, 2.560 x 104 and 2.5600 x Q1104 have ~~three, :four and five significant digits, ' 1. respeictively.
"=._Vin*..numerica1 computations, we come across numbers, which have large number of digits, and it will be necessary to cut them to a 3 usable number of figures. This process is called rounding off. It is usual to round-off numbers according to the following rule: To round-off a number to n signii'ic'aI.iLt_"v., digits, discard all digits to the right of ~ digit, and if this discarded number ..':~.. b
(a) less than half a unit in the nth digit unaltered; _ V _ V fb) greater than half a the rjalaee, increase the
(c) exactly half a unit piaeevtiiiiicrease the nth digit leave it . 0 A _ The to be correct to n. ;Signifieant fi'gures..¢--' Eicarilple Eifi'ie'4'nuInbers given below are 5 ~rounded--o':Tf to four significant figures:
1.6583 to 1.658 30.0567 to 30.06 0.859378 to 0.8594 3.14159 to 3.142 In hand computations, the rounjdetofif error can be reduced by carrying -5 computations to more significant. at each step of the computation»; "A usefti1.ifu1e .is":7 at each step of the corn.putation,.
one more significant lthatvgiyen in the data, perfornijthe'_l'1a;stl"o--p'eration and then round--off. However, l..r_nolst.-'éllilrripiiters allow more nmnber vpiigiures than are usuagiy-.,.;_ec;i:-i'red:.:_inl' e_ng'ine_eri_ng computations. which allow a plrecisionp Qf::'.Slgf1lfiC3.1'lt figures in the range of to 10-39. Arithmetic carried out 'this precision is called single precisioni-arithrnetic, and several computers iriiplernent double precision arithmetic, which l'co'ul.d lhbelkused in problems requiring greater accur'7a:t:. Usually, the double precision 2 .arithn1etic is carried out to 15 decimals with a l " range of about 10-308 to 10303. In MATLAB, there is a provision to use doubie precision arithmetic.
E 'l V' "'-.pet'i-tiorrer would to be considered as having obtained secured more than 54.50% and hence, Cfreliance on an unreported decision of this court in the 10 In addition to the round--off error discussed above, there is another type of error which be caused by using approximate computations, M such as one that arises ' ~ a truncated infinite series istised. of error is called truncation naturally associated _ pro_b1em'~ convergence. 'l'1uncattioi1..p er-14¢;-, __ in . can be evaluated and often to make it as smairas _possi'ole;--.._'$'e'ctions 1.4 and 1.5 will be devoted fV>vdis,:§:'1}é4.si_§.n of these errors", A A it I Furtlier;-"12_e" the above View of the 1eamed"au'thlo,r_ viréjn'}d"'clearlfldernonstrate that the rule of Inathernatieal in so far as rounding--o.ff the numbers "co'ncerned,V'if applied in the case on hand, the would appropriate direction.
The learned counsel would also seek to place é 11 case of Shri. Rajeev M. -vs- The Registrar, Viswesvaraya Technological University, Belgaum (W..P.No.51369/2004) disposed of on 15.OS3.20O{)'V,'i',\:.2'_1}herein the facts were, that the petitioner therein graduate and the aggregate percentage of by him was 49.88% in the for d' admission to the M.C.A €'our_se. "The vmarksv..preS£cI'ibed* was 50% in the qualifying the present case on hand, he was ineligible. In that circumstance, the approached this court, this placing dreliance on several judgmer1t.s _o'f.. t'he~1sS__.11pre11i:e Court ~hamely:
Va) = 'Iviv/'S§:'j'Motiia!:_:Padampat Sugar Mills Co. Ltd., --
vs; iFh€'V"St'a:.-tat!/T'. of Uttar Pradesh {AIR 1979 sc- 62111 V {ii}. nRajend'r'a"V Prasad Mathur --vs-- Karnataka T _ '_*UA:n--i_versity [AIR 1986 SC--1448], i" {iii'}"..v.V'\:..P¥g:.VV'vSadh€ --vs-- University of Mysore and " -v"ar1otherin (1987) 4 sec 537, Kum. D.H. Samudhayatha --Vs-- Viswesaraiah Technological University (VTU] and another (ER. 2003 KARgO2), 12 This court has held that the petitioner therein having completed two years of studies and when he wasflon the verge of completing the course. And this permitted him to pursue the studies directed the University to annourice;_the' resul.ts- ofVthe'V:.firlst '' year and having allowed <the_V student' toicompulete Vthieii course, equity demanded petitionfierttherein be permitted to comp1ete""theeohugrsrell also taking note of the fact thatrthhe of the need to strictly adh*ere__ prescribed in acadeni-icV,rri'attel*s§ the authorities acted belatedly for the student to pursue the studies. over 'tWo._p1*elcious years, there would not have been. any occa'sion_.«to strain the strict adherence to prescriptions by informing the petitioner that he vvasnot. eligible to pursue the course, for no fault of his. l<._The leariaed counsel would thus contend that the petition xibieipaliowed as both law and equity demand it. 2 13
10. While the learned counsel for the respondents would vehemently oppose the present writ petition and submit that the matter is squarely covered by a decision of T this court in the case of Miss. N. Gayath;ratn:::¢7 Rajiv Gandhi University of HeaE~tli'j:~..:$e£ences, represented by its Registrar ' 224-9) and would further vsu--bmit2't,hat.V tlie'reyjVVar3iotheri' unreported judgments of similar question was considered.' the above cited reported judgme11t__ dpecilsion cited by the petitioner, further submit that inathematics as regards 'rounding 4' the academic standards prescribedlibpy v.the._tJniVe:,rsities would have to be strictly ~=.,adh'ei:cd_:'1o.: As"«..for«'instance if a student who secures entitled to be graded as having secured a the requirement is 60%, to be so graded. 5 14
11. The marks secured by the petitioner in the case on hand in her qualifying examination is 54.71%, which is less than 55%, by reference to any Voi*'.,:i"3'<z,1ale of Mathematics as regards 'rounding--off of :..v:tiie eligibility criteria cannot be watered dov_v*n.~- of the petitioner being entitled,' -the"'rule'<:;jiof 'rounding--off of the number_s,.._is
12. In the lighti"g.of"--_g_tli1e, contentions, the question that would for-.fconsidieration, as already stated is:
has secured 54.710/o her'titialifirinigTexarnination and who has been p'er_r'niptted_iby'.th'e.__':authorities to pursue the Post _ _VGraduate,coui*_se"'in M.Sc (Nursing) is enabled to that she, has secured 55%?"
-fI_'o~rr>1«.,,iti1e authority cited by the counsel for the pet.itionerA,7}j_ following passage from the New Encyclopaedia Britannica, 1501 edition, under the chapter g 15 "Numerical Analysis" at page--38 of volume 25 is illuminating:
" H _ Most problems involve infinite sets' values, each of which can potentiallyrequire-in ' an infinite number of __,digits _--'for'* representation. Digital comp11.ltation,,'eith'er____ A' human, mechanical.,o_r electronic, its': very nature, finite: it"vi.nV*olves it numerical values, fiof is represented in '-alifinite "of;vdigi.ts. These two approxirnations«.of'v.infin'ite' Vdnantities by finite Q1'ies:_lead__ to of error in _.round--off and tr1.1if1_ca.t:i'oii--:Iierror; Aijnnrrierical analyst is 'interestedinwdeterrrriniiig the size of possible errors in Analystists try to find _ _bou1l'1"ds"onV'Verrors"nor estimates of errors. A 'pound is «.a____y1-ialue that the analyst can gnaraiitee the error will not exceed. An a value that the analyst believes is. ifapproximation of the error (error estimates typically vary from the true error ll a factor of 2). The word error is unfortunate because it suggests a mistake 5 16 or sin. l2ound--off and truncation errors are unavoidable: the job of the numerical analyst is to find out how to compute accurately and efficiently in their presence» Finite-precision errors: rot2'1_1"d-:o,iff:i' The precision of a value number of digits used iniiits :_1'*e}3rese.r1Atation;-3____é It is typically between seven" 0' digits, depending on and calculation,--.- FiniAte";§r_eci'sion n'ie'ansV.v*i:hat most Values caiinlot be exactly, but that there is..s.o_Ir1e' error in the compu;ted':,approxin1atio1j:;' example, if 4/ 3 :l§5"y'._f'i:ijJe"significant decimal {the most"; accurate possible :':,_1sing; -digits}',._Ttii.e1*eis a round--off error of o;0,ooo333§'. 10 - 4, as illustrated V. _belo\if: ' 0' 3 ..... .. Decimal representation " -- fizalue 1.3333333...
5--di'git representation 1.3333 r_ound'--off error 0.0000333... "Ail; calculation are subject to the effects of round--off errors. Round~off errors, which 5 17 are proportional to the size of the value containing the error when a fixed number significant digits is used, can be as large 5 in the first neglected place or the last retained place. when added to a much smal1eIj:'val'_ue,:v off can be large re1a'£i,Ve tO:4tlf1Q5".5.II1al1,'§j3.F.l, ' For example, if 23,4516-.is added to in five digits, the a round-off errorfinf 23,456 is subtracted frorn the result is
11. arithmetic.
(23.4se r:j.to..s;s;..23.45e 1 1.0, which has anti:-errorii place. After the :,:additio1fi. wasflless than onewhalf in the - but the subtraction ren2o_VtredV'the._V "t3..1.~i"ee leading digits, 234, umoving" 'error to the third place. "phenomenon is called cancellation. cause errors but makes the sizefloi' errors already introduced larger "relative to the computed result. Thus, although round-off errors are small, their effect in the final answer can be large, so that one of the tasks of the numerical analyst is to degse or modify 19 certainly be that it is 55%. Therefore, there is no hesitation in holding that notwithstanding the_4"'*a.sutnct eligibility ' criteria and the mandate prescribed by the University, would be and that this court ought not iri'ter:fere..fi r'u_Ies:_*of . academic standards wouldinot. be 'deistroyed Ai.ii;;3z_..x(irtue treating the percentage of petitionelt as 55% in her as against 54.71%. Therefore, circumstances of the case on the authorities is therefore,..not~5_in rules of Mathematics as regards numbers' and therefore, the percentagVe'--..ofv. 5' secured by the petitioner in her e_xa1ninati.oi"1 shall be construed as 55% and she 'eligible for admission to the PG Course. she has already completed the examination "abut the:. results are Withheld, the same may be "'-aiinottnced. g