1. Class : XII (Nucleus)
Time : 3 hour Max. Marks : 180
INSTRUCTIONS
1. The question paper contain 25 pages and 3-parts. Part-A contains 18 objective question , Part-B contains 6
questions of "Match the Column" type and Part-C contains 12 subjective type questions. All questions are
compulsory.
PART-A
(i) Q.1 to Q.18 have One or More than one is / are correct alternative(s) and carry 4 marks each.
There is NEGATIVE marking. 1 mark will be deducted for eachwrong answer.
PART-B
(iii) Q.1 to Q.6 are"Match the Column" typewhich mayhave oneor more than onematching options and
carry8 marks foreach question. 2 marks will be awarded for each correct match within a question.
There is NEGATIVE marking. 0.5 mark will be deducted for each wrong answer.
PART-C
(iv) Q.1 to Q.12 are "Subjective" questions & carry5 marks.There is NO NEGATIVE marking.Marks
will be awardedonlyif all thecorrect bubbles are filled in your OMR sheet.
2. Indicate the correctanswer for each question byfillingappropriate bubble(s) inyour answer sheet.
3. Use onlyHB pencil fordarkeningthe bubble(s).
4. Use ofCalculator, LogTable, SlideRule and Mobile is not allowed.
5. Theanswer(s)ofthequestionsmustbemarked byshadingthecirclesagainst thequestionbydarkHBpencil
only.
PART TEST-3
PART-B
For example if Correct match
for (A) is P, Q; for (B) is P, R;
for (C) is P and for (D) is S
then the correct method for
filling the bubble is
P Q R S
(A)
(B)
(C)
(D)
PART-C
Ensure that all columns
(4 before decimal and 2 after
decimal) are filled. Answer
having blank column will be
treated as incorrect. Insert
leadingzero(s)ifrequiredafter
rounding the result to 2
decimal places.
e.g. 86 should be filled as
0086.00
.
.
.
.
.
.
.
.
.
.
PART-A
For example if only'B'choice
is correct then, the correct
method for filling the bubble
is
A B C D
For example if only 'B & D'
choices are correct then, the
correct method for filling the
bubbles is
A B C D
The answer of the question
in any other manner (such as
putting , cross , or
partial shading etc.) will
be treated as wrong.
USEFULDATA Atomic Mass:Al=27, Mg=24,Cu= 63.5,Mn=55, Cl = 35.5, O= 16, H =1,P= 31,Ag =108, N =14,Li = 7,
I= 127,Cr=52, K=39,S= 32, Na=23,C=12,Br =80,Fe=56, Ca = 40, Zn= 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207,
He = 4, F=19. Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1.

2. ROUGHWORK
PART - A
Select the correct alternative(s) (choose one or more than one) [4 × 18 = 72]
Q.1 Consider the two concentric conducting loops placed in same plane. There
exists auniform magneticfieldforregion0 <r<r1, withthedirection alongthe
axisofloopsherefieldisincreasingattherate
dt
dB
.IftheresistancesR1&R2
are in the ratio1 : 2, and current in these resistance are I1 & I2 then
(A) I1 = I2  0 (B) I1 = I2 = 0
(C) I1 = –I2  0 (D) I2 = 2I1  0
(Theresistances R1 & R2 liealongcommondiameter)
Q.2 Aconductingwireframeis placedinamagneticfield, whichis directed into
thepaper.The magnetic field is increasing at a constant rate.The directions
of induced currents in wiresAB and CD are
(A)Ato B and C to D (B) B toAand C to D
(C) Ato B and D to C (D) B to Aand D to C
Q.3 AmetalbarABcanslideon twoparallellongthickmetallicrails separatedbya
distance l. A resistance R and an inductance L are connected to the rails as
shown in thefigure.Alongstraight wirecarryinga constant current I0 is placed
intheplaneoftherailsandperpendicularto themas shown.The barABis held
at rest atadistancex0 fromthelongwire.Att =0, itis madetoslideon therails
awayfrom the wire. Find a relation among i, di/dt and d/dt, where i is the
current in the circuit and is the flux of the magnetic fielddue to the long wire
through thecircuit.
(A)
dt
d
+ L
dt
di
– iR = 0 (B) 0
iR
dt
di
L
dt
d




(C) 0
iR
dt
di
L
dt
d




(D) none of these

3. ROUGHWORK
Q.4 Asoundwavefrom stationarysourceoffrequency'f'travelshorizontallyto theright towards avertical
wall.It isreflectedfrom avertical wallsurfacemovingtotheleft withaspeed v0. Thespeed ofsound in
themediumisv.
(A) The number of waves strikingthe wall surface per second is f
v
v
v 0





 
(B) The wavelength of the reflectedwave is
f
v
v 0

(C) The frequencyof the reflectedwave is f
v
v
v
v
0
0










(D)The numberofbeatsheardbya stationarylistenerplacedbetween source& thereflecting surfaceis
f
v
v
v
0
0









Q.5 Figureshowsahorizontalmagneticfieldwhichisuniformabovethedottedline
and is zero belowit.Averylong, rectangular, conductingloop of width lmass
m, resistanceR is placed partlyaboveand partlybelow the dottedlinewith the
lower edgeparallel to it. Thevelocitywith which theloop be pushed downward
sothat itmaycontinuetofallwithout anyacceleration
(A) 2
2
B
mgR
l
(B)
R
B
mg
2 (C)
mgR
B 2
2
l
(D)
mg
B 2
2
l
Q.6 Apoint sourceoflight is 60cm from a screen and is kept at thefocus of aconcavemiror which reflects
lightonthescreen.Thefocallengthofthemirroris20cm.Theratioofaverageintensitiesoftheillumination
on the screenwhen the mirror is present and when the mirroris removed is:
(A) 36 : 1 (B) 37 : 1 (C) 49 : 1 (D) 10 : 1

4. ROUGHWORK
Q.7 Considerahypothetical reversiblereaction
2
1
A
A2(g) +
2
3
B2(g) AB
AB3(g), H = –30kJ
If the standard entropies of A2, B2 and AB3 are 80, 60 and 90JK–1 mol–1 respectively, the above
reactionwillbeatequilibriumat
(A) 450 K (B) 750 K (C) 250 K (D) 1500 K
Q.8 The enthalpyof reaction at 273 K is –3.75 kJ. What will be the enthalpyof reaction at 373 K if Cp is
assumed to be zero?
(A) –3075 kJ (B) zero (C) –3.75 ×
273
373
kJ (D) –3.75 kJ
Q.9 Whichofthefollowingstatements is/arecorrect :
(A) Pure silicon can be obtained byreduction of Na2
SiF6
with Na.
(B)Wroughtironis thepurest form of iron.
(C)Quenchingofwrought iron makes it soft whereas steel becomeshard on quenching.
(D) In contact process of manufacture of sulphuric acid NO is used as a catalyst.
Q.10 Whichofthe followingstatement(s)is/areincorrect :
(A) Ni(CO)4
and [Ni(CN)4
]2–
both are d sp2
hybridised
(B) The splitting energyof K3
[VF6
] is greater than that of K3
[V(CN)6
]
(C) Paramagnetic behaviour increases in the order [V(H2
O)6
]3+
< [Ni(H2
O)6
]3+
< [Co(H2
O)6
]3+
(D) [Ti(H2
O)6
]3+
is a colourless species.

5. ROUGHWORK
Q.11 




 
 
O
H
)
ii
(
/
NaHCO
.
aq
)
i
(
3
3
A 

 
 2
2 CS
/
Br
B 


 

O
H
in
Boiled 2
C
Product 'C' is
(A) (B) (C) (D)
Q.12 CH2=CH–



 Li
H
C
H
C
CH
|
|
O
3
—
2 



 
 O
H
by
followed 2 A
A
)
equivalent
1
(
H
O
X
—
2


 


B





 
 3
2 )
OCHMe
(
Al C
(A) compound 'A' is
3
2
2
3
CH
|
OH
CH
CH
CH
CH 


(B) compound 'C' is 3
2
2 CH
CH
CH
CH
CH
|
OH




(C) compound 'B' is 3
2
2 CH
C
CH
CH
CH
||
O




(D) compound 'B' is
H
CH
|
|
O
C
CH
CH
CH
3
2
3 



6. ROUGHWORK
Q.13 Let P & Q are two points denoting the complex number  &  respectively on the complex plane.
Which ofthe followingequations canrepresent the equationsof thecircle passing through P & Q with
least possible area?
(A) 











Z
Z
Arg =
2

(B) Re (Z – )  


Z = 0
(C)
2
Z 
 +
2
Z 
 =
2



(D) Z
Z + 






 


2 Z + 




 


2 Z +   +   = 0
Q.14 The equation to theorthogonal trajectories of the system of parabolas y= ax2 is
(A)
2
2
y
2
x
 = c (B)
2
y
x
2
2
 = c (C)
2
2
y
2
x
 = c (D)
2
y
x
2
2
 = c
Q.15 Considerthefollowingregionsintheplane:
R1 = {(x, y) : 0  x  1 and 0  y  1}
R2 = {(x, y) : x2 + y2  4/3}
The area of the region R1  R2 can be expressed as
9
b
3
a 

, where a and b are integers. Then the
value of (a + b) equals
(A) 2 (B) 3 (C) 4 (D) 5

7. ROUGHWORK
Q.16 Imagine that you have two thumbtacks placed at two points,Aand B. If the ends of a fixed length of
string are fastened to the thumbtacks and the string is drawn taut with a pencil, the path traced by the
pencilwillbeanellipse.Thebest waytomaximisetheareasurroundedbytheellipsewithafixedlength
ofstringoccurs when
I thetwopointsAand Bhavethemaximum distance between them.
II two pointsAand B coincide.
III Aand B are placed vertically.
IV The areais always same regardless of the location ofAand B.
(A) I (B) II (C) III (D) IV
Q.17 Consider the expansion, (a1 + a2 + a3 + ....... + ap)n where nN and n  p. The correct statements are
(A) number of different terms in the expansion is, n +p  1C n
(B) co-efficient ofany term in which none of the variables a1 , a2 , ...... , ap occur more than once
is 'n'
(C) co-efficient of anyterm in which none of the variables a1 , a2 , ...... , ap occur more than once
is n!
(D) Number of terms in which none of the variables a1 , a2 , ...... , ap occur more than once is 





n
p
.
Q.18 The probabilitythat apositivetwodigit numberselectedat random hasits tens digit at least three more
thenitsunitdigitis
(A) 14/45 (B) 7/45 (C) 36/45 (D) 1/6

8. ROUGHWORK
PART - B
MATCH THE COLUMN [8 × 6 = 48]
INSTRUCTIONS:
Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some
entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries
ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II.
Q1. A rod abof length L = 1m & resistanceR = 1 ismovingwithconstantvelocity
V= 1m/sbyapplyingexternal forcealongthe longconducting rails. The
conducting rails are placed in the same plane of longcurrent carrying wire
having current I= 1A. Neglect theresistance of rails
ColumnI ColumnII
(A) emf inducedinrod is (P)
2
0
2








 2
2
n
l
(B)inducedcurrent in rod is (Q)


2
0
ln 2
(C) external horizontal force(F)applied (R)


4
0
ln 4
on the rod is
(D) rate of work done byexternal agent is (S)
2
0
2
n
4








l
Q.2 ColumnI ColumnII
(A)Wavesinsolids (P)Transverseonly
(B)Electromagneticwaves (Q) Can betransverseorlongitudinal
(C)Longitudinalwaves (R) Require amedium to propagate
(D) Pressure waves (S) Must be elastic parameters dependent

9. ROUGHWORK
Q.3 Column I ColumnII
(Compound) (DissolvesIn)
(A)Ag2
O (P)Aqueous NH3
(B)Ag2
S (Q) KCN
(C)AgCl (R) HNO3
(D)Ag2
CrO4
(S) Na2
S2
O3
Q.4 ColumnI ColumnII
(A) 


 


O
H
,
O
H 3
2
(P)
(B)




 

O
H
)
iii
(
CO
)
ii
(
Ether
,
Mg
)
i
(
3
2 (Q)
(C) +H2C=O+HCl+ZnCl2A (R) &
C 

 
 3
)
OEt
(
Al
B
Compound 'C' is
(D)
4
CCl
NBS

 
 [X ] 


 

COK
)
CH
( 3
3 [Y] Z (S) 2
CH
O
C
|
|
O


Compound 'Z' is

10. ROUGHWORK
Q.5. Column–I Column–II
(A) Thedifferentialequationofallparabolashaving (P) 1
theiraxisofsymmetrycoincidingwiththeaxisof
x has its degree
(B) Thedifferentialequationof all parabolaseachof (Q) 2
which has a latus rectum '4a' & whose axes are
parallel to x-axis is of degree
(C) Degree ofthe differential equation y= a  
a
x
e
1 
 , (R) 3
a being the parameter is
(D) The polynomial f (x) satisfies the condition f (x + 1) = (S) does not exist
x2 + 4x. The area enclosed by y = f (x – 1) and the
curve x2 + y = 0, is
k
2
16
where k is

11. ROUGHWORK
Q.6 Column–I Column–II
(A) The name of the conic represented bythe (P) Ellipse
equation px + qy = 1, where p, q  R,
p, q > 0 is
(B) Two parabola y2 = 4a (x – 1), and x2 = 4a(y – 2) (Q) Circle
always touch each other. 1 and 2 being variable
parameters. Then, their points of contact lie on a
(C) If parabolaof latus-rectum l, touchesa fixed equal (R) parabola
parabola, theaxes of the two curves beingparallel,
thenthe locusofthevertex of themovingcurveis
(D) From a point P tangents are drawnto the parabola (S) hyperbola
y2 = 4ax. If the chord of contact of these tangents
touches the rectangular hyperbola x2 – y2 = a2, then
thelocus of P is

12. PART - C
Q.1 InaLloydmirrorinterferenceexperiment asshown inthefigure,thesource(S)
and the screen are separated by a distance of 1 m. At a certain position of
source the fringewidthis 1/4mm andbymoving the sourceawayfrom the
mirror alongthelineABby0.6 mm the fringe width changed to 1/6 mm. What is
the wavelength (in Å) of light used? [5]

13. Q.2 Findthemagnitudeofmagneticfield(inT)atOofthecoordinatesystemifthe
wirecarryingcurrent i =8A hasshapeshowninfigure.Theradiusofthecurve
part is R = 10 cm, the linear parts of the wire verylong (here  = 3.14)
[5]

14. Q.3 In the circuit E = 50.0 V, R = 250 and C = 0.50 F, the switch S
is closed for a long time. After the switch is opened, the voltage
across thecapacitor is measured . It is found that maximum potential
difference across capacitor is 150 V. What is the inductance L of
ideal inductor? (in Henery) [5]

15. Q.4 Findthevoltage(inKV)appliedtoanX-raytubewithNickel(Z=28)asatargetmaterial,ifwavelength
difference between the K line & cut off wavelength of continuous X-rayspectrum is equal to 84 pm
(here ionisation energyof H–atom 13.6 e.v & hc = 12420 ev Å) [5]

16. Q.5 One hunter is out on a day in early Spring when the air temperature is –100C and the atmospheric
pressureis1atm.Duetotheintense physical activityofhunting,thehunter's averagebreathingrateover
a six hour period is 15 breaths per minute and each breath has a volume of 0.62 Lat body temperature
(370C). The air inhaled is warmedto bodytemperature onthe wayof thelungs. How much heat is lost
in the process of breathing during this six hour period? The specific heat capacity of air at constant
pressure is approximately30JK–1 mol–1. Notethat air maybetreated as an ideal gas.(Take R = 0.08 lit
atm K–1) Report your answer in kJ. [5]

17. Q.6 A 0.347 g of a metal (A) was dissolved in dil. HNO3
. This solution gave a red colouration to Bunsen
flameandonevaporationgave0.747gofmetaloxide(B).(A)alsoreactedwith N2
formingacompound
(C) and with H2
, it forms (D). On reacting 0.1590 g of (D) with H2
O, a gas (E) was evolved and a
sparinglysolublecompound(F)formed,whichgaveastronglybasicsolutionandrequired200mlof0.1
M HCl to neutralise it. (D) when treated with Lewis acid (G), forms a well known powerful reducing
agent (H). Deduce the molar mass of (H) if (G) dissolves in excess of NaOH but does not dissolve in
excess of aqueous NH3
. [5]

18. Q.7 Hydrocarbon (A) of M.F. C8
H16
reacts with O3
/Ph3
Pyield twomoles of B(C4
H8
O). Bis oxidized to C
andthentreatedwith PCl5
togive D.Don treatement with hydroxylaminegavea compound(E) which
gives redcolouration to Ferric chloride solution. When (E) is treatedwith strong HCl it gave (F) with
evolution of CO2
. (F)on treatment with HNO2
gavea compound which gave ayellow precipitate with
NaOI. What is the molecular weight ofF (in gm). [5]

19. Q.8 1342gram of1.0 molal sucrose(M.W. =342)solutionin wateriscooled to –3.00C.What weightofice
(in gm) would be separated out at this temperature? Given that the amount of icethat separates out on
cooling a solution containing50g of glycol (OH–CH2–CH2–OH) in 0.2 kg waterto –100C is 50 g.
[5]

20. Q.9 Let Z = 18 + 26i where Z0 = x0 + iy0 (x0, y0  R) is the cube root of Z having least positive
argument. Find the value of x0y0(x0 + y0). [5]

21. Q.10 A dieis weighted such that theprobabilityofrollingan n is proportional to n2 (n= 1, 2,3, 4, 5,6).The
die is rolled twice, yielding the numbers a and b. The probability that a < b in lowest form is
q
p
where p + q = [5]

22. Q.11 If the expression z5 – 32 canbe factorised intolinear and quadratic factors over real coefficients as
(z5 – 32) = (z – 2)(z2 – pz + 4)(z2 – qz + 4) then find the value of (p2 + 2p). [5]

23. Q.12 A movable parabola touches the x and the y-axes at (1, 0) and (0, 1). The locus of the focus of the
parabola is ax2–ax + ay2 – ay + 1 = 0 where a is. [5]