GATE 2012, Question Paper, Download, Answer key, pdf file 12 february

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GATE2012 Official Published AnswerKey - Paper:Physics
1 (A) 2 (C) 3 (A) 4 (C) 5. Marks to All 6 (A) 7 (B) 8 (D) 9 (C) 10 (A)
11 (A) 12 (C) 13 (D) 14 (B) 15. Marks to All 16 (C) 17 (B) 18 (B) 19 (D) 20 (A)
21 (D) 22 (B) 23 (D) 24 (D) 25 (C) 26 (A) 27 (C) 28 (A) 29 (B) 30 (C)
31 (D) 32 (A) 33 (B) 34 (A) 35 (D) 36 (C) 37 (A) 38 (C) 39 (B) 40 (D)
41 (B) 42 (B) 43 (C) 44 (D) 45 (D) 46 (B) 47 (A) 48 (C) 49 (D) 50 (A)
51 (A) 52 (C) 53 (B) 54 (B) 55 (B) 56 (D) 57 (A) 58 (B) 59 (A)
60 Marks to All 61 (C) 62 (B) 63 (B) 64 (D) 65 (A)

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70 comments :

vbk5mnnit12 February, 2012
Here are my answers
QS. - 1 Ans B (Linearly dependent)
2 - C
3 - B
4 - C
5 - C
6 - A
7 - A Not Sure
8 - D
9 - C
10 - B
11 - C
12 - C
13 - D Not Sure
14 - B Not Sure
15 - B
16 - A
17 - B
18 - B
19 - D Not Sure
20 - A
21 - D not sure
22 - A not sure
23 - A
24 - D
25 - B not sure
vbk5mnnit12 February, 2012
26 - B Not Sure
27 - C
28 - A
29 - B
30 - C
31 - B
32 - A Not Sure
33 - B
34 - D
35 - C
36 - A Not Sure
37 - A
38 - C
39 - B
40 - D
41 - C Not Sure
42 - B
43 - A Not Sure
44 - D Not Sure
45 - D
46 - A Not Sure
47 - A
48 - A Not Sure
49 - C Not Sure
50 - D Not Sure
51 - C Not Sure
52 - C
53 - A
54 - B
55 - B
56 - A Not Sure
57 - A
58 - B
59 - A
60 - B
61 - C
62 - B
63 - B
64 - D Not Sure
65 A
Anonymous12 February, 2012
mention the Set Code guys . I means these answers are for Set A, B, C or D.
Anonymous12 February, 2012
@vbk5mnnit
CORRECTION TO THE ABOVE ANSWERS
5-D
11-A
13-A
14-B
16-C
21-D
22-A
25-C
26-A
31-D
32-A
35-B
36-C
46-D
47-D
48-C
49-C
50-A
raj13 February, 2012
regarding the vectors a and b
i think they are linearly independent
bcoz u cannot write one in terms of other
So the answer should be (A)
MOHIT SHARMA IIT@KGP13 February, 2012
1 B 21 A 31 D 41 D 51 A 61 C
2 C 22 C 32 A 42 A 52 C 62 B
3 B 23 A 33 A 43 B 53 A 63 B
4 C 24 B 34 D 44 D 54 B 64 D
5 D 25 B 35 C 45 B 55 B 65 A
6 A 26 C 36 A 46 C 56 A
7 A 27 B 37 C 47 A 57 A
8 D 28 B 38 A 48 C 58 B
9 C 29 D 39 B 49 B 59 A
10 D 30 A 40 C 50 D 60 B
please check these key for gate 2012 physics these are correct

by; Mohit Sharma
iit kharagpur
MOHIT SHARMA IIT@KGP13 February, 2012
please check these answer for gate 2012 physics
by; MOhit Sharma IIT Kharagpur

1 B
2 C
3 B
4 C
5 D
6 A
7 A
8 D
9 C
10 D

21 A
22 C
23 A
24 B
25 B
26 C
27 B
28 B
29 D
30 A

31 D
32 A
33 A
34 D
35 C
36 A
37 C
38 A
39 B
40 C

41 D
42 A
43 B
44 D
45 B
46 C
47 A
48 C
49 B
50 D

51 A
52 C
53 A
54 B
55 B
56 A
57 A
58 B
59 A
60 B

61 C
62 B
63 B
64 D
65 A
Anonymous13 February, 2012
@ mohit sharma
dear cross check your some of the answers
like for 30-will be C others
30-c,33-b,35-d,38-c and some others like for 37,40,42 and some others
Anonymous13 February, 2012
@MOHIT SHARMA IIT@KGP

do you have solutions for questions 11-20??
raj13 February, 2012
Try to explain the answer and not just simply putting the answer.

Again can someone explain why a and b were linearly dependent.
Anonymous13 February, 2012
@MOHIT SHARMA IIT@KGP.. mention the set for which you have given the answers
Aditya13 February, 2012
I think raj is right.. Should be independent..
1} A
Neethal13 February, 2012
can i get the answer for 26
Anonymous13 February, 2012
1 have answer is A correct. i have solution it is linearly independent. have anyone of solution 5 1nd 24 question correctly
s.p.raj13 February, 2012
dear sharma, check your ans. i thought there are more wrong
MOHIT SHARMA IIT@KGP13 February, 2012
correction
Answer 1. (A)
Two vectors u and v are linearly independent if the only numbers x and y satisfying xu+yv=0 are x=y=0. If we let and there
dterment should not be zero.
Anonymous13 February, 2012
Vbk5nnit answers are more reliable..
Arpan kumar nayak iitkgp13 February, 2012
1-A
because a1k1+a2k2=0 and a1=0 also.
4-C
Id.c=2Ipeak/3.14
5-A
E=h2(nx2+ny2)/8ma2.here nx=ny=1
we get than A is correct.
8-D
9-A
12-C
resistivity=1/ne*mobility.
14-B
15-B
19-D
B=del cross A
E=-grad phhi- delA/del T
20-A
23-C
24-C
E=(n+1/2hw). here n=0 for ground state
25-C
independent component=n(n+1)/2. here n=3
26-A
28-A
29-B
30-C
33-B
35-C
40-B
42-B
43-B
44-A
48-C
E=-crossH/2m(d2/dx2shai
49-A
54-A
55-D
60-A
63-B
65-A
Arpan kumar nayak iitkgp13 February, 2012
plz chk my result and tell if you get somthing wrong after searching book.
Anonymous13 February, 2012
Any guess about this years cut off marks????
Aditya13 February, 2012
@arpan please explain how B is correct for question 40..
Anonymous13 February, 2012
@raj
yes u are right . they are independent..
Raj Nair14 February, 2012
Answers with my explanations(verified from relevant books)

*************************************************************
1) As already said a and b should be linearly independent
Answer = A
*************************************************************
2) the MI of rod when the axis passing through the centre and perp to the rod is given by:

I=(M*l^2)/12

In our case M = M1+M2 and l = 2L so I = (M1+M2)(2L)^2/12 = (M1+M2)L^2/3
Answer = C
*************************************************************
3) This is striaght forward the time average of the cos function gives the 1/2 factor

Answer = B
*************************************************************
6) Check wiki
http://en.wikipedia.org/wiki/Compressibility

Answer = A
**************************************************************
7) The formula comes out to be
DeltaE = g *mu * B
where DeltaE = difference in energy , g = landeg factor ,mu=bohr magneton , B=applied mag field

So all we have to do is find the g factor for the given state of sodium Na

Now g = 1 + (j(j+1) + s(s+1) - l(l+1)) / 2 j(j+1)

when u put l=0(bcoz given state is s) , s=1/2(bcoz 2s+1=2) and j = 1/2

we get g = 1 + 1 = 2

Answer = 2*mu*B = B

******************************************************************

8)The fermi energy is given by the formula

Ef = some constant * n^(2/3)

also Ef = 1/2 * m * vf^2 were vf = fermi velocity

from the above two relation we get that fermi velocity = vf = some constant * n^(1/3)

Answer = D

*****************************************************************************

9) this can found by elimination method

proton = baryon = bound state of three quarks
=not a fundamental particle bcoz its made from quarks = A) and B) are wrong
meson = bound staet of quark-antiquark
= not a fundamental particle bcoz its made from quarks = D) is wrong

Answer = C
*******************************************************************************
14) http://en.wikipedia.org/wiki/Orbital_eccentricity

Answeer = B

********************************************************************************
10)For GM counter B) is wrong bcoz particle type cannot be identified
C) is wrong bcoz info of energy is lost
D) is wrong bcoz oprating vol is definetly not in few volts its around 300 volts or so

Answer = A

**************************************************************************************

16) The energy difference for raman rot spectra is given by = B(4J+6) were B=rotational constant

first stoke/anti-stoke line appear at 6B from the centre and the rest are seprated by 4B

S0 12.96 = 6B
B = 2.16

Answer = C
*****************************************************************************************

18) the given spatial part of wavefunction is symmetric so the spin part has to be anti-symmetric

answer = B

******************************************************************************************
19) use B= del cross A and E = -Del phi - dA/dt

answer = D

******************************************************************************************
20) A

21) either C or D not 100% sure

25) symmetric component = n(n+1)/2 = 3(3+1)/2 = 6

answer = C
********************************************************************************************
Do reply if u find any mistake.
Anonymous14 February, 2012
@ Mr Sharma, there are some wrong answer in ur soln. 29-B, since the sum of eigen values is equal to the sum of principal diagonal.
Physics Lover14 February, 2012
I think answer for 24 is D.
In the truncated harmonic potential only even numbers are permissible for n.(Because hermite polynolial should vanish at x=0). ie, E=(2n+1+1/2).
Neethal14 February, 2012
@Raj Nair

in question no 7, they have asked for the difference in the energy of levels from the original one in the presence of magnetic field. so it should be muB*B no. the difference between the splitted energy levels between will be 2*muB*B. am i right?
MOHIT SHARMA IIT@KGP14 February, 2012
@Arpan kumar nayak iitkgp
arpan please check again (40-D) we both checked this with text book and please check this reference once again (http://hyperphysics.phy-astr.gsu.edu/hbase/hydwf.html#c1) and (44-D) because if we expend e^1/z the we get series 1+1/z+.... then we can solve it by normal method and we will get 2*pie*i so answer is D.
Physics Lover14 February, 2012
@Raj,

I've a doubt your ans qn no 3.

They asked to find time averaged energy density associated with electric field.

Energy density = 1/2*(epsilon)*E^2

Here E=E0 Cos(wt-kz)

ie, Energy density =1/2*(epsilon)*E0^2*Cos^2(wt-kz)

On taking time average,
Energy density=1/4(epsilon)E0^2.

then (A)'ll be the answer.

(I think so,may be wrong)
abhinav14 February, 2012
friends any guesses about this year cutt off marks..
Anonymous14 February, 2012
50-A
group velocity is derivative of \omega. so first derivative will give cos. but first brillouin zone boundary condition make it as cos(90). so answer is zero.
Raj Nair15 February, 2012
@Physics Lover

Actually the time average of cos^2 gives 1/2 factor.

This is nicely explained in griffiths ch 9 pg 381.look at the footnote of that page.

or check the link below for the screenshot of that page.

http://imageshack.us/photo/my-images/638/83949441.png/
Raj Nair15 February, 2012
@Neethal

yes u r right

DeltaE = 2*bohr magneton * B

So answer is option B
Raj Nair15 February, 2012
@MOHIT SHARMA IIT@KGP

I agree with u on 44-D

as already explained
The residue of exp(1/z) at 0 is by definition the coefficient of
1/z in the Laurent expansion of exp(1/z) about 0. We have
exp(1/z) = 1 + 1/z + (1/z)^2/2! + ...,
so the residue is 1.

So answer is 2*pi*i*residue = 2*pi*i
Raj Nair15 February, 2012
@Anonymous

yes u r right.

frist derivative gives cos(k*a/2)
also for first BZ k=pi/a
S0 v=cos(pi/2)=0

Answer 50)A
Raj Nair15 February, 2012
@MOHIT SHARMA IIT@KGP

also 40)D is right.

the radial pbb density will have a mixima.
prashant15 February, 2012
@Physics Lover

it is right
Saurabh Sahu & Bindesh Shukla from Gorakhpur15 February, 2012
Saurabh Sahu & Bindesh Shukla says

1- A
2- C
3- B
4- C
5-
6- A
8- D
9- C
11- D
13- B
14- B
17- B
18- B
19- D
23- B
25- B
27- C
29- B
30- C
34- D
35- D
39- B
40- D
42- B
43- A
47- A
49- D
50- D
54- A
55- A
56- A
57- A
58- B
59- A
60- A
61- C
62- A
63- B
65- A
Anonymous15 February, 2012
@Arpan kumar nayak iitkgp
sir plz correct the answer of q.54
ans54=b
sonam15 February, 2012
@Raj Nair
in q.25 independent components are asked. so plz check ur ans.are independent and symmetric components are same???
Anonymous15 February, 2012
@Physics Lover
agree with u that answer of q.24=d
vardhan16 February, 2012
sir how it is b?if we take b option for Q.54,then we will get wrong answer for Lagrangian equation.pls justify ur answer
Physics Lover17 February, 2012
@raj nair, abt no. 3

I've seen that.
But that is the energy density for electric and magnetic field combined.They are asking about the energy density associated with electric field only. In an EM wave electric and magnetic field contributes 1/4*(epsilon)*E^2 each and final energy density'll be 1/2*(epsilon)*E^2.

And answer for 40 can never be D.
If you put r/a=0 in the given equation for P(r) is not zero.The answer is C i think.
Raj Nair17 February, 2012
@Physics Lover

Regarding the energy density store in EM fields

for electric field it is (1/2)epsilon E^2
for magnetic field it is (1/2)B^2/mu

thats why the total is written as u=1/2(epsilon E^2+B^2/mo)

Even if we assume what u r saying is correct then how do get the factor 1/4
Raj Nair17 February, 2012
For q)34 why answer is D)

i think it should be A)

any explanations

I think D) is wrong bcoz quarks do interact through weak interactions.

From wiki "A quark of one flavor can transform into a quark of another flavor only through the weak interaction, one of the four fundamental interactions in particle physics......."
Physics Lover17 February, 2012
@Raj Nair

Yes for electric field it is 1/2*epsilon*E^2.

What is E here?

E=E0 Cos(wt-kz)

Substitute and take time average.

that'll add an additional 1/2 to the eqution.
Physics Lover17 February, 2012
@Raj Nair

But i think in the hyperphysics link,the graph is not similar to ours for it plots the derivative of probability density.

The probability density is P(r)=1/(4*Pi*a^3)exp[-2r/a0]

when r/a0=0,

P(r)=1/4*Pi*a0^3 which is nonzero.

In the option D, P(r)=0 for r/a0=0

Also I can't understand how this can be approximated to function of the form x^2 exp[-2x] when a0 is a constant,not variable here.

Can you pls explain these?
Physics Lover17 February, 2012
Can anybody tell me the answers for 20,33 and 43 with explanation?
Raj Nair18 February, 2012
@Physics Lover

If u look in griffiths ch 9 eq 9.55

it says that u = epsilon E^2

and that the electric and magnetic contributions are equal

im not sure now but i think vector E is to be substitued in equation 9.55 which is epsilon E^2
Raj Nair18 February, 2012
@Physics Lover

first have a look at this link

http://www.physicsforums.com/showthread.php?t=49807

Actually P(r) = r^2*Exp[-r] where i have not included the constants

but the point is that we do have a variable r^2(coming from the volume element) multiplied by the exponential so the function goes to zero as r goes to zero.

So the answer is D)
Raj Nair18 February, 2012
@Physics Lover
For 20) answr is A)

becoz the voltage at the inverting terminal is +1V becoz of the voltage divider connected.

so as soon as the voltage at the non-inverting terminal(vin) goes above +1V the output will go into positive saturation(+10V)

So this happens only in option A)
Anonymous18 February, 2012
correct answers
1-b
2-c
3-a
4-c (2*10/pi)
5-d

6-a
7-b
8-d
9-c (elementary particles, all other not)
10-doubt

11-a (use reflectivity equation with n=3/2)
12-c (conductivity 0.288, take invesrse)
13-a (for 2D kinetic energy Kb T, but here K.E=1/2 mv^2=1/2 m(Vx^2+Vy^2). Since they asked mean (1/2) of velocity square answer is a
13-a
14-b
15-b

16-c (first raman line 6B)
17-b
18-b
19-d
20-doubt

21-d (properties of nuclear force)
22-a
23-
24-
25-c

26-a
27-
28-a
29-b
30-c

31-d
32-a
33-c
34-d
35-b

36-c
37-(a or c)
38-c
39-b
40-d

41-
42-b
43-
44-d
45-d
46-
47-a

48-c (free space-V=0)
49-d (for real part wave function and its conjugate are same)
50-a

51-b (square \omega and integrate both side from -pi/a to +pi/a)
52-
53-
54-b
55-b

56-
57
58-b
59-q
60-b

61-
62-b
63-b
64-
65-a
DINESH IIT BOMBAY20 February, 2012
for linearly indepdent vectors p*vector a +q*vector b =0 where p and q should be zero explicitly.so answer A is correct for question 1.
DINESH IIT BOMBAY20 February, 2012
HERE 1/2 FACTOR WE ARE GETTING FROM ENERGY DENSITY FORMULA AND WE HAVE TO GET AVERAGE SO 1/2 FACTOR WILL COME OUT FROM AVERAGE OF COSINE SQUARED.
Anonymous20 February, 2012
can anyone explain me the question (62) an automobile plant ........
Anonymous21 February, 2012
in question no. 62,
suppose total 100 shock obsorbers company has to buy.then 60 will be supplied by X and 40 by Y.
(.40*72)/100=.288
(.60*96)/100 =.576
then probabilty is .288/(.577+.288) =.334
so, ans is B
Anonymous21 February, 2012
plz explain the answer to q. no. 38
Anonymous22 February, 2012
ans to Q.38 is C because
Z = ge^-β€
acc. to Question
Z = 1 + 2e^(-β€) + e^(-2β€)
where g is the degeneracy factor,
can u plz explain me ans to q. 35 and 36
Anonymous22 February, 2012
@Anonymous but according to the question of probability the question ask us to calculate the probability of finding the reliable shock absorber which are made by Y from all (i.e. we have to include the probability of getting non reliable also) so the answer is 0.288
Anonymous23 February, 2012
U r right.
But .288 represents the shock obsorbers which are reliable. so probability is number of reliable shock obsorbers divide by the total number of reliable cases.

I think so........
Anonymous23 February, 2012
@Anonymous my friend I would like to correct you...... the question nowhere ask us to pick the shock absorber from the reliable one.... it ask us to pick the shock absorber randomly.... so there is probability of getting non reliable shock absorber also...
Anonymous24 February, 2012
Read the end line of question 62.
THE probability that a randomly chosen shock obsorber,which is found to be reliable, is made by Y is.....
just a human27 February, 2012
@MOHIT SHARMA IIT@KGP
its(40) a standard ques wid standard fig...nd 1 basic thing prob f electron in nucleus shud b zero
Anonymous29 February, 2012
hello .. any idea abt dis years cutoff for ph??
Anonymous01 March, 2012
how acc. To ur own explanatin answr of q 38 is corect.its d instead c.
Anonymous12 March, 2012
@Anonymous

explanation of q. no. 38 is-------

you know the partion function given by-:
Z=sigma*g*exp(-beta*E(energy))
here g is called degeneracy.

and sigma run from 1 to 3 bcoz three energy levels are given i.e
0, e , 2e.so

Z=1*exp(-beta*0)+2exp(-beta*e)+1*exp(-beta*2e)
here 2 is multiplied in second term bcoz in question says that the energy level 'e' are two fold degenerated i.e the degeneracy g=2.

so- Z=1+2exp(-beta*e)+exp(-beta*2e)

so- Z=(1+exp(-beta*e))^2

so answer is-- 38-C.
Anonymous12 March, 2012
@DINESH IIT BOMBAY

my dear Dinesh--

Ans. 3-B

please see the below notes of chapter-9 of quantum mechanics by David j Grifith.
Anonymous12 March, 2012
@Anonymous

explanation of q.no.-35 is---

both move in same direction so first find relative velocity i.e-
(2c/3)-(c/2)
c/6
then put this velocity c/6 in length conraction formula you get
ans. 35-D
pravati13 March, 2012
hiii, arpan. your ans of question 24 is wrong.it wil b (D).As it is unsymmetrical .ground state energy wl b 3/2 hcros omega.so first e.state wl 7/2 hcros omega
S01 March, 2015
GATE 2012 Answer Key

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GATE 2012, Question Paper, Download, Answer key, pdf file 12 february - Comment the description of Answers

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