1. Class : XIII (Sterling)
Time : 3 hour Max. Marks : 180
INSTRUCTIONS
1. The question papercontainpages and 3-parts. Part-Acontains 18 objective question , Part-Bcontains 6
questions of"MatchtheColumn" typeand Part-Ccontains12 subjectivetypequestions.Allquestions are
compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS
and Pages. If you found some mistake like missing questions or pages then contact immediately to
the Invigilator.
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-1
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
thebubbleis
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 willbe treated as
incorrect. Insert leading
zero(s) if required after
rounding the result to 2
decimalplaces.
e.g. 86 should befilled as
0086.00
.
.
.
.
.
.
.
.
.
.
PART-A
For example if only 'B'
choice is correct then,
the correct method for
fillingthebubbleis
A B C D
Forexampleifonly'B&
D' choices are correct
then, the correct method
forfillingthebubblesis
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.

2. ROUGHWORK
PART - A
Select the correct alternative(s) (choose one or more than one)
Q.1 AdiscofradiusR rollsonahorizontalsurfacewithlinearvelocityVof centre'O'and angularvelocity
about 'O'. There is a point P on circumference of the disc at angle , which has a
vertical velocity.Here  isequal to
(A)  + sin–1

R
V
(B)


 
R
V
sin
2
1
(C)


 
R
V
cos 1
(D)


 
R
V
cos 1
Q.2 Ahorizontalturntableintheformofadiscofradiusrcarriesafixedsmallgunat
G and rotates with a angular velocityw0 about a vertical axis passing through
thecentreO.Theincrease inangularvelocityof thesystem if the gunfires a
bullet of mass m with a tangential velocity v, w.r.t. the gun is (where I0 is
moment ofinertiaofgunexcludingbullet +table, about O)
(A)
0
I
2
mvr
(B)
r
2
v
(C)
0
I
mvr
2
(D) 2
0 mr
I
mvr

Q.3 Apoint object P of mass m is slipping down on asmooth hemispherical body
of mass M & radius R.The point object is tied to a wallwith light inextensible
string as shown.At a certain instant the speed of hemisphere isV& its
acceleration a (as shownin figure). Then speed Vp &acceleration ap of the
particlehasvalue(neglectfriction)
(A) Vp = V sin 30 (B) Vp = V
(C) ap = a (D) ap =
2
/
1
2
2
2
2
a
2
3
a
R
V























3. ROUGHWORK
For Prob. 4 to 5 (3 Questions)
Considertheshownarrangement.Theblockofmass misreleasedasshown on thesmoothcurvedtrack
of wedge of mass M (=2m). One end of the ideal spring is fixed to the stand 'S' fixed to the ground.
There is no friction between wedge & floor & between block & floor.
Q.4 Ifspringconstant isK, maximumcompressioninthespringwould be
(A)
K
mgh
(B)
K
3
mgh
4
(C)
K
2
mgh
3
(D) none of these
Q.5 Astheblockrebounces from thesprings& climbsup thewedgeagain, themaximum heightattainedby
the block on the wedge would be
(A)
9
h
(B)
3
h
2
(C)
9
h
7
(D) none of these
Q.6 Inyoung'sdoubleslitexperiment,thefringesaredisplacedbyadistancex whenaglassplateofrefractive
index 1.5is introducedinthepathofoneoftheinterferingwave. Whenthis plateis replacedbyanother
plate of thesame thickness, theshift of fringes is (3/2)x. Therefractive index ofthesecond plate is
(A) 1.75 (B) 1.50 (C) 1.25 (D) 1.00
Q.7 Calculatetotalmaximummass(kg)whichcanbeliftedby10identicalballoon(eachhavingvolume82.1
lit. and mass of balloon & gas = 3 kg) at a height 83.14 m at Mars where g = 5 m/s2 & atmosphere
containsonlyAr(At. wt.40).AtMars temperature is 10K and densityofatmosphereat groundlevel is
821
.
0
2
k gm/lit. [Given : e–0.1 = 0.9] (Assume dH = d0
RT
Mgh
e
to be applicable).
(A) 2000 × 0.81–30 (B) 1970 (C) 2000 × 0.9 –30 (D) 2000 × 0.81 – 3

4. ROUGHWORK
Q.8 How manymg of quick lime is required to remove hardness of 1 kg of hard water having 366 ppm of
HCO3
– and contains Ca2+ as the only cation
(A) 72 mg (B) 84 mg (C) 168 mg (D) 170 mg
Q.9 A 10 litre box contains O3 and O2 at equilibrium at 2000K. Kp = 4.17 × 1014 for 2O3 3O2.
Assume that 3
2 O
O P
P  and if total pressureis 7.33 atm, then partial pressure of O3 will be
(A) 9.71 × 10–5 atm (B) 9.71 × 10–7 atm
(C) 9.71 × 10–6 atm (D) 9.71 × 10–2 atm
Q.10 

 
 KOH
Br2
If the reactant is (d) (dextrorotatory) then in final product 
(A)inversionofconfigurationtakes place
(B)racemisationtakes place
(C)retentionofconfigurationtakes place
(D) none of the above
Q.11 Select the correct statement(s)
If S = f (E, V, n1, n2) &A= f (T, V, n1, n2)
(A) S is equal to f (E, V, n1, n2) (B) S is equal to f (E, V, n1, n2)
(C) Ais equal to f (T, V, n1, n2) (D) Ais equal to f (E, V, n1, n2)

5. ROUGHWORK
Q.12
Compound Bhas a neutralisationequivalent112. G is adichloro alkane.
(A) A = , B = , C = , E = ; F =
& G = ClCH2CH2CH2CH2Cl
(B) A = , B = , C = , E =
& G = ClCH2CH2CH2CH2CH2Cl
(C) A = , B = , C = , E = , F =
& G = ClCH2CH2CH2CH2CH2Cl
(D) A = , B = , C = ;
E = ; F = & G = ClCH2CH2CH2CH2CH2Cl

6. ROUGHWORK
Q.13 Whichofthefollowingstatement(s)is/arefalse
(A) If a, b and c are positive numbers not equal to 1 and a < b, then logac < logbc.
(B) The equation x2 – b = 0 has a real solution for x for any real number b.
(C) The sequence an defined byan = 3(0.2)–n is a geometric sequence.
(D) cos(cos(x)) < 1/2,  x  R
Q.14 Let f (x)= x –
x
1
thenwhich one ofthe following statement are incorrect
(A)Functionis invertible ifdefined from R – {0} R.
(B) f (x1) > f (x2),  x1 > x2 and x1 ,x2  0.
(C) Graphof the function has exactlyone asymptote.
(D) Functionis one-oneineverycontinuous interval [a, b]defined on one sideof origin.
Q.15 If f (x) = 


 
0
x
if
2
}
0
{
)
1
,
1
(
x
,
x
1
sec
x
tan
x 1
1





 

, then f '(0) is
(A) equal to – 1 (B) equal to 0 (C) equal to 1 (D)nonexistent
Q.16 If a,b are positive realnumbers suchthat a– b =2,then the smallest valueof the constant Lfor which
bx
x
ax
x 2
2


 < L for all x > 0, is
(A) 1/2 (B) 2
1 (C) 1 (D) 2
Q.17 If K R0 then det. {adj (KIn)} is equal to
(A) Kn – 1 (B) Kn(n – 1) (C) Kn (D) K
Q.18 Let f(x)is
2
1
sin101








x
x
where [x] denotes step up function then f(x) is
(A) both odd as well as even (B) neitherodd nor even
(C)odd function (D)evenfunction

7. ROUGHWORK
PART - B
MATCH THE COLUMN
INSTRUCTIONS:
Column-Iand column-IIcontainsfour entries each. Entries ofcolumn-Iareto bematchedwith some
entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries
ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II.
Q.1 Inthefigureshowntwoidentical smallcharged balls havingmassmand charge
'q'aresuspendedwith thehelpoftwolight inextensiblesilk stringseach oflength
'l'.At equilibrium theangularseparationbetween thestrings is ''
ColumnI Column II
(A) If  is verysmall then charge'q'is (P) 3/2
proportional to
(B)TensionTinstringisproportional to (Q) l
(C) Ifsystem is taken ina satellite. Then (R) 
tension T is proportional to
(D)Angularseparationbetweenthe charges (S) l–2
(at equalibrium)in thesatellite is
Q.2 In thefigure shown,upperblockis given a velocity6m/s & lower
blocka velocity3m/s. Whenrelative motionbetweenthem stops
(Here block 2 Kg is verylong)
ColumnI ColumnII
(A)Work done byfriction on 1 kg block (P) 3 Joule
(B)Work done byfriction on 2 kg block (Q)negative
(C) Net work done by friction (R)positive
(D) Loss in K.E. of system (2kg + 1kg block) (S) 7 Joule

8. ROUGHWORK
Q.3 Matchthefollowing
ColumnI ColumnII
(A) Canaryyellowprecipitate with (NH4)2MoO4 (P) NO3
–
(B) Brownringtest (Q) NO2
–
(C)Acidradical whichevolves gas with conc. HCl (R) AsO4
3–
(D)Acidradical whichgives gas withdil. H2SO4 (S) PO4
3–
Q.4 Matchthefollowing
List I List II
(A) 
 
CuCl (P)Freeradical mechanism
(B) CH3–CH=CH2 (Q) Non Classical Carbocation
 Cl2/
Cl
|
CH
CH
CH 2
2 

(C) CH3–CH=CH2 


 
 Cu
/
Zn
/
I
CH 2
2 (R) Carbenoid
(D) CH3–CH=CH2 





 

OH
/
NaBH
)
ii
(
O
H
/
)
OAc
(
Hg
)
i
(
4
2
2
(S)Through carbocation

9. ROUGHWORK
Q.5. Column–I Column–II
(A) Numberofrealsolution(s)oftheequation (P) 2
   2
2
2
2
5
1
2
2
x
x
x




(B) The range of the function f(x) = tan–1
x
x


1
1
– tan–1x (Q) 1
consists ofhowmanyelements
(C) TheintegralvalueofxintheDomainofdefinitionof (R) 0
the function f (x) = log 1
9
3
·
10 1
x
2
x

 
 + )
x
1
(
cos 1


(D) Value ofthe expression
 
0
0
0
0
4
1 78
sin
66
sin
42
sin
6
sin
log
(S) 3
is
Q.6 Column–I Column–II
(A) If
2
2
y
x  =
)
x
/
y
(
tan 1
ae

, a > 0, assuming (P)
5
2

y > 0, then, y'' (0) = –
2
/
e
a
K 

where K is
(B) If y = sin–1
2
x
1
x
2

then
dx
dy
at x = –2 (Q) 2
(C) If 2
0
x x
x
cos
B
x
sin
A
x
2
sin
4
Lim




(R) 5
exist thenA–B
(D) If f(x) = [2 + 3sinx] 0 < x <  where [ ] denotes (S) –4
GIFthenno.ofpoints at whichfunction is non
differentiable

10. PART - C
Q.1 A force F acts on a uniform rectangular cabinet weighing 400 N as shown in
figure.Thecabinetslides withconstant speedwhenaforceF=200Nisapplied
at height h = 0.4 m at angle 370 from horizontal.At what distancex (in cm),
from edgeA,the resultant normal reactionacts on cabinet
(sin370 = 3/5)

11. Q.2 Asmall ball of mass m is suspendedbyastiff massless rodof length l.Asmall
bulletofsamemassm strikes theballhorizontallywithvelocityV&emerges with
velocity
2
V
horizontally.Ifaftercollisionballis justabletoswingthrougha
a complete circle, then find the force (in newton) applied byhinge on the rod
immediatelyaftercollision(herecollisiontimeisnegligible)(Herem=1kg,
g = 10m/s, l = 1m)

12. Q.3 Whenthegapbetweentwoidenticalconcavethinlens(=3/2,f=10cm)placedincontactis filledwith
certain liquid, the image of an object placed at 15 cm from lens shifts away from the lens by5/4 cm.
What is the R.I. of the liquid ?

13. Q.4 Considertheshownidentical arrangements inwhichauniform
rod (length l, mass M)is suspended bymeans ofa ideal spring
andastring.It is given thattherodis perfectlyhorizontal in the
shownequilibriumposition.Assumethatthestringiscutin
arrangement (i) & springis cut in arrangement (ii). If a1 & a2
be the values of acceleration of centreof mass of rod in (i) & (ii)
respectively,immediatelyafterthestring/springis cut,thenfinda1/a2 .

14. Q.5 1.0gofamixturecontainingSb2O3 andSb2O5 andsomeinert impurities required 100ml0.01 Niodine
fortitration.Theresultingsolutionis thenacidifiedandexcessofKIwasadded.Theliberated I2 required
100 ml 0.02 M Na2S2O3·5H2O for complete reaction. Calculate the % of Sb2O5 in the mixture. The
reactions are [at. wt. Sb = 122]
Sb2O3 + 2I2 + 2H2O  Sb2O5 + 4H+ + 4I–
Sb2O5 + 4H+ + 4I–  Sb2O3 + 2I2 + 2H2O

15. Q.6 Aballooncontaining1moleairat 1 atminitiallyis filled furtherwithairtill pressure increasesto 3 atm.
The initial diameter of the balloonis 1 m and the pressure at eachstate is proportion to diameter of the
balloon.Ifballoonwillburst whenpressureincreasesto7 atm.Calculatethenumberofmolesofairthat
must be addedafterinitial condition toburst theballoon.

16. Q.7 Thekeyreactioninthemanufactureofsyntheticcryolightforaluminiumelectrolysisis
HF(g) + Al(OH)3 (s) + NaOH (aq)  Na3AlF6(aq) + H2O(l)
Assuminga96%yieldofdried,crystallized product, whatmass (inkg)ofcryolitecanbeobtainedfrom
the reaction of 351 kg ofAl(OH)3, 1.10 m3 of 50.0% by mass aqueous NaOH (d = 1.50 g/mL), and
225 m3 of gaseous HF at 312.08 kPa and 87oC? (assume that the ideal gas law holds)
[Given: Al = 27, O = 16, H = 1, Na = 23, F = 19, R = 8.3 JK–1 mol–1]

17. Q.8 The vapour pressure of water at 300 K is 25 torr. If the standard state pressure is defined as 1 bar (750
torr) estimate the G° [inkJ/mol] for the process.
H2O (l)  H2O (g) at 300 K
(Neglect variation of H and S with pressure for liquid)
Use [R = 8.314 JK–1 mol–1 ; X
og
X
n
l
l
= 2.3, log 3 = 0.48]

18. Q.9 Thenumberofpositiveintegral solutions oftheequation
1
z
yz
xz
z
y
1
y
xy
z
x
y
x
1
x
3
2
2
2
3
2
2
2
3



=30 is:

19. Q.10 In a triangleABC with altitudeAD,  BAC = 450, DB = 3 and CD = 2. The area of the triangleABC
is

20. Q.11 Asequenceofequilateraltriangleisdrawn.Thealtitude ofeachis 3 timesthealtitudeofthepreceding
traingle,thedifferencebetweenthe areaofthefirst triangleandthesixthtriangleis 3
968 square unit.
Theperimeterofthefirsttriangleis.

21. Q.12 Findtheintegralvalueofaforwhich theequation
(x2 + x + 2)2 – (a – 3) (x2 + x + 2) (x2 + x + 1) + (a – 4) (x2 + x + 1)2 = 0
has at least one real root.