TRB PG இயற்பியல் வினாக்கள் குறித்து சென்னை உயர்நீதிமன்றம் அளித்த தீர்ப்பின் முக்கிய பகுதிகள்
Prayer in all the WPs:- Writ Petition has been filed under Article 226 of the Constitution of India for issuance of Writ of Certiorarified Mandamus calling for the Provisional Selection List for the direct recruitment for the Post of Graduate Assistants in Government Higher Secondary Schools 2012-2013 for the subject of Physics on the file of the respondent and quash the same as illegal and direct the respondent to evaluate and provide marks for the entire 150 questions in the Written Examination dated 21.7.2013 conducted by the respondent and consequently allot correct marks for the error in Question No.63 and consider the petitioner for recruitment of Post Graduate Assistants (Physics) within the stipulated time by this Honourable Court.
Petitioners : Mr.R.Prabhakaran
For Respondent : Mr.D.Krishnakumar
Special Government Pleader
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C O M M O N O R D E R
Since common issues are involved in all these writ petitions, the same were heard together and they are disposed of by means of this common order.
2. These writ petitions have been listed before me as a specially ordered case on the orders of the Hon'ble the Acting Chief Justice dated 25.06.2014.
3. The Teachers Recruitment Board conducted exam for Post Graduate Assistants / Physical Education Director Gr.-I Examination - 2013. The petitioners participated in the said examination. Their Roll Numbers are 13PG13040524, 13PG18040235 and 13PG15040073 respectively. The question papers were in four series. The questions were of objective type. The petitioners were supplied with 'C' and 'D' series question papers respectively. They had secured 100, 101 and 101 marks respectively. According to the petitioners, for question Nos.31, 78, 86 and 88 though they had answered rightly, they have not been awarded each one mark to the said questions.
4. I have heard the learned counsel appearing for the petitioners and the learned Special Government Pleader appearing for the respondent as well as perused the records carefully.
5. It is brought to my notice by the learned Special Government Pleader appearing for the respondent that the correctness of the question No.88 in 'D' series has been decided by this Court in an earlier writ petition in W.P.No.29346 of 2013 dated 03.07.2014. In view of the said admitted position, the said question is not taken up for adjudication in these writ petitions.
6. Question No.31 in 'D' series reads as follows:
Q.No.31. Express 7x4-9x2+2 in terms of Legendre Polynomials. Given P2(x) = = (3x2-1), P3(x)=5x2-3x/2 and P4(x) = 1/8 (35x4-30x2+3)
(A) 8P4(x)-P2(x)+P0(x)
(B) 2/5 (4P4(x)-5P2(x) + P0(x))
(C) 8/5(P4(x)-4P3(x)+2P2(x)-P0(x)
(D) 1/7 (P4(x)-2P3(x) + 2P2(x)-P0(x)
7. According to TRB the question itself is wrong and therefore the same was omitted from valuation. But, according to the petitioners, option 'B' is the right answer.
8. Today, three experts in the Physics subject are present before this Court who are (1) Dr.A.Subbiah Pandi, Associate Professor, Department of Physics, Presidency College, Chennai, (2) Dr.K.Chitra, Associate Professor, Department of Physics, Bharathi Women's College, Chennai and (3) Dr.B.Uma Maheswari, Associate Professor, Department of Physics, Bharathi Women's College, Chennai. This Court had the benefit of hearing them also. The experts would explain to me that the basic equation is as follows:
Pn(x) = 1/2n n! ??(x) = 1/2n n! dny/dxn = 1/2nn! dn/dxn (x2-1)n "
In this formula 'n' is substituted by 0, 1, 2, 3..... and if 'n' is zero, as per the formula the deduced answer will be one. If 'n' is 1 then the deduced answer is 'x'. If 'n' is 2 then the deduced answer will be 1/2(3x2-1). If 'n' is 3 then the deduced answer will be 5x3-3x/2. But in this question, the 'n' value has been given as 0, 1, 2, 3 and 4. So far as the deduced value when 'n' is 2, it has been correctly given as = (3x2-1). Similarly when 'n' is 4 value of deduced answer is correct. But so far as the value of 'n' as 3 is concerned, in the question itself the deduced answer is wrong i.e. instead of 5x3-3x/2 it has been mentioned as 5x2-3x/2. Therefore, this question was deleted by the TRB.
9. The experts produced a standard text book known as 'Mathematical Physics' authored by Satya Prakash. I am able to understand that when 'n' value is given as 3 the deduced answer should be 5x3-3x/2, but since it has been given as 5x2-3x/2 the question itself is wrong and it may be true that option 'B' can be deduced by applying the above deduced values, but that cannot be correct because it is the standard formula that if 'n' is substituted by 3 then the deduced answer must be 5x3-3x/2. Therefore, I agree with the experts and I hold that the TRB was right in deleting the question from valuation.
10. Next is Question No.78 in 'D' series which reads as follows:
Q.No.78. Total energy of perfect Bore-Einstein gas is :
(A) E=3/2 nkT [1 - A/25/2 A2/35/2 - ....]
(B) E=1/2 nkT [1 - A/25/2 A2/35/2 - ....]
(C) E=3/2 nkT [1 + A/25/2 + A2/35/2 + ....]
(D) E=1/2 nkT [1 + A/25/2 + A2/35/2 + ....]
11. According to TRB, they have deleted the said question from valuation because none of the option is correct. But, according to the petitioners, option 'A' is the right answer.
12. The petitioners would rely on a text book known as 'Statistical Mechanics authored by Gupta and Kumar, wherein, option 'A' has been shown as the correct answer.
13. But the experts present before this Court has referred to the Standard text book titled Thermodynamics and an Introduction to Thermostatistics by Herbert B.Callen, wherein, it is stated that the question should have contained the temperature status. If the temperature is greater than the critical temperature then the answer would be one thing and if the temperature is less than the critical temperature than the answer would be different. Since the temperature is not given in the question, the question has to be deleted. But the experts would fairly concede that in all the books authored by Indian authors including the book authored by Gupta and Kumar the temperature is not at all taken into effect.
14. In my view, for having read the books authored by Indian authors, the petitioners who have answered option 'A' need not be penalised. In such view of the matter, the deletion of this question from valuation is not correct and therefore the TRB should revalue Question No.78 in 'D' series and award one mark to all the candidates who have answered option 'A' as the right answer.
15. The next is Question No.86 in 'D' series which reads as follows:
Q.No.86. The binding energy of an ?-particle is :
(A) 2.031882 u (B) 3.031882 u
(C) 4.031882 u (D) 5.031882 u
16. According to TRB all the answers given are wrong and therefore the question has been omitted from valuation. But, according to the petitioners, option 'C' is the right answer.
17. The petitioners would rely on a textbook titled Modern Physics authored by Mr.R.Murugeshan and another, wherein at page 387, it is stated as follows:
"Calculate the binding energy of an ?-particle and express the result both in MeV and joules:
Solution: Mass of 2 protons + 2 neutrons = (2x1.007276 + 2x1.008665)u
= 4.031882u
Mass of the ?-particle = 4.001506u
Mass defect ?m = 4.031882 4.001506)u = 0.030376u
` B.E.=(0.030376x931.3)MeV = 28.29 MeV.
= 45.32 x 10-13J "
18. It is the admitted case that total mass of helium is 4.031882u, but according to the formula, binding energy is to be calculated by deducting the mass of the alpha particle and then applying the formula. The formula for calculating binding energy per neculon is equal to mass defect and 931.3 MeV. As per the calculation made, the binding energy of ?-particle must be 28.29 MeV. But all the four options given refers only to the total mass of ?-particle. Thus, no option refers to binding energy and therefore no option is the right answer. But the petitioner would state that binding energy is directly proportionate to the mass of helium and therefore option 'C' should be taken as the correct answer.
19. In my considered opinion it is not possible because there is a vast difference between mass value and binding energy. From mass value binding energy has to be calculated after deducting the mass of the alpha particle and therefore the question in my considered opinion is wrong. As has been stated by the experts the question is wrong. Therefore, I agree with the experts and I hold that the TRB was right in deleting the question from valuation.
20. At this juncture, I have to say that the power of this Court to interfere with the decision of experts in respect of key answers has been elaborately dealt with in a number of judgments of the Hon'ble Supreme Court, about which, I need not elaborate. I deem it suffice to refer to the judgment of the Hon'ble Supreme Court in Kanpur University Vs. Samir Gupta, reported in 1983 (4) SCC 309, wherein, the Hon'ble Supreme Court has held that if the key answer is demonstrably wrong, then only this Court has got power to interfere with the same. Applying the said decision, we have to examine this case as to whether the key answer set by the respondents is demonstrably wrong. Here, in this case, the petitioner is not able to demonstrate that the key answer pertaining to question No.31 is wrong.
21. The challenge to other questions are not pressed by the petitioners.
22. In view of all the above, the writ petitions are disposed of on the following terms.
(i) The challenge made to Question Nos.31 and 86 in 'D' series are rejected.
(ii) It is directed that TRB should revalue all the answer sheets of the candidates and award one mark to those candidate who have answered option 'A' as the right answer for Question No.78 in 'D' series. Thus the challenge to this question succeeds.
The interim orders already granted are hereby vacated. Consequently, the connected miscellaneous petitions are closed. No costs.
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