1. Class : XIII (Sterling)
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-2
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
bansal classes Page # 2
PART - A
Select the correct alternative(s) (choose one or more than one) [4 × 18 = 72]
Q.1 Standingwaves areproducedonastretchedstringof length Lwith fixed ends.
When there is a node at a distance L/3 from one end, then
(A)minimum andnext highernumberofnodes excludingtheends are2,5 respectively
(B)minimumandnext highernumberofnodes excludingtheends are2, 4 respectively
(C) frequencyproduced maybe V/(3L)
(D) frequencyproducedmaybe 3V/(2L)
[V=velocityofwaves inthestring]
Q.2 Asoundwavefrom stationarysourceoffrequency'f'travelshorizontallyto theright towards avertical
wall. It isreflected from avertical wall surfacemoving to theleft with aspeed 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










3. ROUGHWORK
bansal classes Page # 3
Q.3 Aseriescircuitconsistsofthreeidenticallampsconnectedtoabatteryas shown.
When switchS is closed.
(A)theintensityofbulbAincreases 1.25times ofits initial value
(B)theintensityofbulbBincreases 2.25times ofits initial value
(C) theintensityofbulb Cremains constant
(D)the intensityofbulbAdecreases
25
.
1
1
timesofitsinitial value
Q.4 P–V graph for an ideal gas undergoing polytropic process PVN = constant
is shownhere. Then N is
(A) 1
(B) 2
(C) 1.5
(D) none of these
Q.5 Inthecircuitshown,theamountofcharge that will flowthroughsectionAB
of the connectingwire to the batterywhen the switch S is closed is:
(A) zero
(B) 5 C
(C) 10 C
(D) 20 C
Q.6 CapacitorC isinitiallyuncharged. X isjoined toYfora longtime, during
which H1 heat is produced in resistance R. X is now joined to Z for a long
time,duringwhich H2 heatis producedin R.Then :
(A) H1 = H2
(B) H1 = 2H2
(C)Energysuppliedbycell duringchargingequals 2H2
(D)Energysuppliedbycell duringcharging equals H1 + H2

4. ROUGHWORK
bansal classes Page # 4
Q.7 Forthefollowingcellreaction
2Hg(I) + 2Ag+
(aq) 2Ag(s) + Hg2
+2
(aq) is given that
0
Ag
/
Ag
E  = 0.80 V,
, [Ag+] = 10–3M ;
0
Hg
/
Hg 2
2
E  = 0.785V,
,  
2
2
Hg
= 10–1M
(A) The forwardreaction is spontaneous (B) The backward reaction is spontaneous
(C) Ecell = 1.585 V (D) Ecell = 3.170 V
Q.8 Aspirin decomposes slowlyat room temperature byreacting with water in the atmosphere to produce
acetic acidand salicyclic acid
+ H2O  AcOH +
Considerthefollowinginitialconcentrationandinitial ratedataforthisreaction.
[Aspirin], M [H2O], M Initial rate, Ms–1
0.0100 0.0200 2.4 × 10–13
0.0100 0.0800 9.6 × 10–13
0.0300 0.0200 7.2 × 10–13
0.0200 0.0300 7.2 × 10–13
Which ofthefollowingis thecorrect rate lawforthis reaction?
(A) Rate= K[aspirin] (B) Rate = K[aspirin] [H2O]
(C) Rate = K[H2O] (D) Rate = K[aspirin]2 [H2O]
Q.9 Select the incorrect statement(s):
(A) In 
3
4
PO ion, the P–O bond order is 1.33.
(B) Covalent bond can be formed by overlapping of py
and pz
orbitals
(C) Bond angle in H2
O is lesser than bond angle in OCl2
molecule.
(D) SeF4
and CH4
have same shape.

5. ROUGHWORK
bansal classes Page # 5
Q.10 Which of the following statement (s) is/are incorrect :
(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.
Q.11
)
A
(
12
9H
C 

 
 4
KMnO
)
B
(
4
6
8 O
H
C 
 
 Fe
/
Br2 C8
H5
BrO4
(Only one product)
A is 
(A) (B) (C) (D)
Q.12
2
ZnCl
HCl
HCHO



 
 
A
KCN
.
alc
.
aq

 
 B
PhCHO
)
ii
(
Na
O
H
C
)
i
( 5
2



 


C 

D
2
2
CO
)
ii
(
H
/
O
H
)
i
(




 


E 

HBr
F
(A) Compound D is
(B) Compound Ais
(C) Compound F is
(D) Compound F is

6. ROUGHWORK
bansal classes Page # 6
Q.13 You are given an unlimited supplyof each of the digits 1, 2, 3 or 4. Using only these four digits, you
constructn digitnumbers. Such n digitnumbers will be calledLE GITIMATE if itcontains the digit
1 either aneven number times ornot at all. Numberof n digitlegitimate numbers are
(A) 2n + 1 (B) 2n + 1 + 2 (C) 2n + 2 + 4 (D) 2n – 1(2n + 1)
Q.14 Whichofthefollowingstatements arecorrect?
(A) Number of words that can be formed with 6 onlyof the letters of the word "CENTRIFUGAL" if
each word must contain all the vowels is 3 · 7!
(B) There are 15 balls of which some are white and the rest black. If the number of ways in which the
balls can bearranged in a row, is maximum than the number of white balls must be equal to 7 or 8.
Assume balls of the same colour to be alike.
(C)Thereare12things, 4alikeofonekind, 5alikeofanotherkindandtherestarealldifferent. Thetotal
number ofcombinations is 240.
(D) Number of selections that can be made of 6 letters from the word "COMMITTEE" is 35.
Q.15 Given three points P1, P2 and P3 with position vectors k̂
ĵ
î
2
r1 



; ĵ
3
î
r2 


and k̂
3
ĵ
î
r3 



respectively.Equation ofalineorthogonalto theplanecontainingthesepoints and passingthrough the
centroid P0 of the triangle P1P2P3, is
(A)  
k̂
2
j
ˆ
3
î
4
3
1
r 



+ )
k̂
2
j
ˆ
3
î
14
( 


(B) k̂
3
2
j
ˆ
î
3
4
r 



+ )
k̂
2
j
ˆ
3
î
14
( 


(C) k̂
2
j
ˆ
3
î
4
r 



+ )
k̂
2
j
ˆ
3
î
14
( 


(D)  
k̂
2
ĵ
3
î
4
3
1
r 



+ )
k̂
2
j
ˆ
3
î
10
( 



7. ROUGHWORK
bansal classes Page # 7
Q.16 Evaluate  








3
0
2
1
2
dx
x
1
x
2
·sin
x
1
1
=
(A)
72
7 2

(B)
16
2

(C)
9
2

(D) none
Q.17 Which of the followingis always true about a function f(x) on theinterval [a, b] = {x |a < x <b|}?
(A) If f (x) > 0 on [a, b], then 
 
b
a
b
a
dx
)
x
(
dx
)
x
( 2
f
f
(B) If f (x) is increasing on [a, b] then f 2(x) is increasing on [a, b]
(C) If f (x) attains a minimum at c where a < c < b, then f ' (c) = 0
(D) none
Q.18 Let 




dx
e
2
x
=  and f (t) = 




dx
e
2
x
t
, (t > 0)
(A) f (x) is equal to
x

(B)f(x)is monotonicdecreasing
(C) if area bounded by y = f (x), x = 2, x = 16 and y = c is minimum then c =
3

(D) equation of normal to curve y = f (x) at x =  is y – 1 = 2(x – )

8. ROUGHWORK
bansal classes Page # 8
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. Athinunchargedsphericalconductingshellofradius'R'isshowninfigure.
Two point charges +q and –2q are fixed at pointA(inside shell) & point B
outsideshellasshown infigure
ColumnI Column II
(A) Electricpotential at 'O' (P) –
R
Kq
(B) Electric potential at 'O' due to charge (Q) +
R
Kq
induced on inner surface of shell
(C) Electric fieldstrength at 'O' (R) can becalculated easily
(D) Electricfield strength at 'O'due to (S) can not be calculated easily
charge on outer surface of shell
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
bansal classes Page # 9
Q.3 ColumnI ColumnII
(A)Dithionousacid (P) S–O–S bond is not present
(B)Thiosulphuricacid (Q)All S atom in the molecule has oxidation state +3
(C) Caro's acid (R)Acidic strength of all Hatoms present in the
molecule is different
(D)Pyrosulphuricacid (S) at least one S atom has oxidation state +6 in molecule
Q.4 Column I Column II
(A) CH3
–CN + HCl +AlCl3
(P)
(B) +AlCl3 (Q)
(C)
3
2
3
CO
Na
.
aq
of
presence
in
POCl
PhNMeCHO





 
 
(R)
(D) 



 
 
H
)
ii
(
H
O
O
H
)
i
( 2
2
(S)

10. ROUGHWORK
bansal classes Page # 10
Q.5. ColumnI ColumnII
(A) P(m, n) (where m, n  N) is anypoint in the interior of (P) 20
the quadrilateral formed bythe pair of lines xy= 0 &
8x2 + 5y2 + 14xy – 48x – 30y + 40 = 0 the possible
number of positions of the point P is
(B) The graph of y = x + k intersect the graph of (x–3)2 + (y + 2)2 (Q) 4
= 50 in one or more points if and only if a < k < b then b–a is
(C) If a

, b

and c

are threemutuallyperpendicular unit vectors and (R) 12
d

is unit vector which makes equal angle with c
and
b
,
a



then
2
d
c
b
a






 = p + q r where q, r and p are three consecutive
natural numbers then find the value of p + q + r
(D)Abscissa andordinates of n given points areinAPwith first term a (S) 9
and common difference 1 and 2 respectively. If algebraic sum of
perpendiculars from these given points on a variable line which
always passes through the point 





11
,
2
13
is zero, then a + n =

11. ROUGHWORK
bansal classes Page # 11
Q.6 ColumnI ColumnII
(A) The value of
 






n
4
r
1
r
2
n
n
4
r
3
r
n
Lim =
q
p
(P) 2
in its lowest form where p + q =
(B) No.ofintegral values of a forwhichthe cubic (Q) 0
f(x) = x3 + ax + 2 is non monotonic and has
exactly one real root.
(C) The radicalcentreof three circles is at the origin. (R) 1
The equations of two of the circles are x2 + y2 = 1
and x2 + y2 + 4x + 4y – 1 = 0. If the equation of
third circle passes through the point (1, 1) and (–2, 1)
is x2 + y2 + 2gx + 2fy + c = 0 then f – c =
(D) If x2
+ y2
+ z2
– 2xyz = 1 , then the value of (S) 11
2
2
2
z
1
dz
y
1
dy
x
1
dx






12. PART - C
Q.1 Two ideal springs of force constant K1 and K2 and block A of mass m are
arranged in thefigure. Thestringpassing over two massless pulleys P1 & P2 is
massless&inextensible. Thenfindtheangularfrequency(in rad/s)ofnatural
oscillation of blockA(here K1 = K2 = 8000 N–m, m = 0.2 kg) [5]

13. Q.2 A metal sphere of radius a is surrounded bya concentric metal spherical shell of radius b (b > a). The
spacebetweenthespheresis filledwithmaterial whoseelectrical conductivityvaries withtheelectric
field strength E according to the relation  = KE where K is constant. A potential difference V is
maintained between inner sphere and outer shell. Then find thecurrent (in ampere) between the inner
sphere &outer shell. [Here K = 7 × 10–2 ohm–1 volt–1, V = 20 volts, b = ea (e : exponential) &  = 22/7] [5]

14. Q.3 In the given figure, a string of linear mass density 3 × 10–2 kg/m and
length L = 1 m, is stretched by a force F = (3 – kt) N, where k is a
constant andtis time insec.At thetimet =0,apulseisgenerated at the
end P of the string. Findthe value of k (in N/s) if thevalue of force
becomes zero as the pulse reaches point Q. [5]

15. Q.4 3 moles of an ideal gas 






2
R
7
CP at pressure PA and temperature T
TA is isothermally expanded to
twice its volume. It is then compressed at constant pressure to its original volume. Finallythe gas is
compressedatconstant volume toitsoriginal pressurePA. Calculatethenetwork done(injoule)bygas
(here TA = 4000K; ln2 = 0.693, R = 8.31 J/mole0K) [5]

16. Q.5 Anorganiccompoundgives substitutionaswellaseliminationaccordingtothefollowingreaction
OH
R


 +
whendextrorotatorysample,heatedwithexcessalkylalcoholthenangleofrotationobservedatfollowing
intervals
t(sec) 0 3 
Angleofrotation(deg) 450 250 50
Calculate the angle of rotation after10 sec. (take log 2 = 0.3) [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 At 270
C the emf ofthe cell Pb |PbCl2
||AgCl |Agis 0.42Vand its temperature coefficient is
p
dT
dE






=
–4.2×10–4
V/K.Calculatethe modulus of heat offormation ofAgCl (s)in Kcal if theheat offormation
of PbCl2
is –85.09 Kcal. (Use 1 cal = 4.2 J) [5]

20. Q.9 Number of eight digit numbers which can be formed using the digits 1, 3, 4, 5, 6, 7, 8, 9 (without
repetition) if eachnumberhas to be divisibleby275 is [5]

21. Q.10 The least integral value of a for which the function f(x) =
3
x
3
a
+ (a + 2)x2 + (a – 1)x + 2 possess a
negativepointofminimum. [5]

22. Q.11 Let c
and
b
,
a



bethreenon-coplanarunitvectorsequallyinclinedto oneanotherat anacuteangle.If
c
b
b
a






 = c
r
b
q
a
p




 , then p2 + q2/cos + r2 is equal to. [5]

23. Q.12 Equation ofstraight linemeetingthe circle x2 + y2 = 9intwo points at equal distances of 5from a point
(x1, y1) on the circumference ofthe circle is given byxx1 + yy1 +
q
p
= 0.Where p + q = (no.
q
p
is in its
lowestform) [5]