Class : XIII (Sterling)
Time : 3 hour Max. Marks : 216
INSTRUCTIONS
1. The question paper contains 72 questions and 20 pages. Each question carry 3 marks and all of them are
compulsory.There is NEGATIVE marking. 1 mark will be deducted for eachwrong answer.
Please ensure that the Question Paper you have received contains all the QUESTIONS and
Pages. If you find some mistake like missing questions or pages then contact immediately to the
Invigilator.
2. Indicate the correct answer for each question byfilling appropriate bubble in your OMR sheet.
3. Use onlyHB pencil fordarkeningthe bubble.
4. Use ofCalculator, LogTable, SlideRule and Mobile is not allowed.
5. TheanswerofthequestionsmustbemarkedbyshadingthecirclesagainstthequestionbydarkHBpencilonly.
6. The answer(s) ofthe questions must bemarked byshading thecircles against the questionbydark HB
pencilonly.
For exampleifonly'B'choice is correct then, thecorrect method for fillingthe bubble is
A B C D
thewrongmethodfor fillingthebubbleare
(i) A B C D
(ii) A B C D
(iii) A B C D
The answer of the questions inwrong or anyothermanner will be treated as wrong.
USEFUL DATA
Atomic weights: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,
Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1
REVIEW TEST-3
PAPER CODE : A
P
A
P
E
R
-
1

ROUGHWORK
Select the correct alternative. (Only one is correct) [72×3 = 216]
There is NEGATIVE marking. 1 mark will be deducted for eachwrong answer.
Q.1 The area of the region of the plane bounded above bythe graph of x2 + y2 + 6x + 8 = 0 and below by
the graph of y = | x + 3 |, is
(A)
4

(B)
4
2

(C)
2

(D) 
Q.2 Consider straight line ax + by = c where a, b, c  R+ and a, b, c are distinct. This line meets the
coordinate axes at Pand Q respectively. If area of OPQ, 'O' being origin does not depend upon a, b
and c, then
(A) a, b, c are in G.P. (B) a, c, b are in G.P. (C) a, b, c are in A.P. (D) a, c, b are in A.P.
Q.3 If x and y are real numbers and x2 + y2 = 1, then the maximum value of (x + y)2 is
(A) 3 (B) 2 (C) 3/2 (D) 5
Q.4 The value of thedefinite integral 



0
2
a
)
x
1
)(
x
1
(
dx
(a >0) is
(A)
4

(B)
2

(C)  (D) somefunction of a.
Q.5 Let a, b, c are non zero constant number then
r
c
sin
r
b
sin
r
c
cos
r
b
cos
r
a
cos
Lim
r



equals
(A)
bc
2
c
b
a 2
2
2


(B)
bc
2
b
a
c 2
2
2


(C)
bc
2
a
c
b 2
2
2


(D) independent of a, b and c

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Q.6 A curve y = f (x) such that f ''(x) = 4x at each point (x, y) on it and crosses the x-axis at (–2, 0) at an
angle of 45°. The value of f (1), is
(A) – 5 (B) – 15 (C) –
3
55
(D) –
3
35
Q.7 Theminimumvalueofthefunctionf(x)=
x
cos
1
x
sin
2

+
x
sin
1
x
cos
2

+
1
x
sec
x
tan
2

+
1
x
cosec
x
cot
2

as x varies over all numbers inthe largest possible domain of f (x) is
(A) 4 (B) – 2 (C) 0 (D) 2
Q.8 A non zero polynomial with real coefficients has the property that f (x) = f ' (x) · f ''(x). The leading
coefficient of f(x) is
(A)
6
1
(B)
9
1
(C)
12
1
(D)
18
1
Q.9 Let Cn = 



n
1
1
n
1
1
1
dx
)
nx
(
sin
)
nx
(
tan
then n
2
n
C
·
n
Lim


equals
(A) 1 (B) 0 (C) – 1 (D)
2
1
Q.10 Let z1, z2, z3 be complex numbers such that z1 + z2 + z3 = 0 and | z1 | = | z2 | = | z3 | = 1 then
2
3
2
2
2
1 z
z
z 
 , is
(A) greater than zero (B) equal to 3 (C) equal to zero (D) equal to 1

ROUGHWORK
Q.11 Numberof rectangleswith sides parallel to the coordinateaxes whose verticesare all of theform (a, b)
with a and b integers such that 0  a, b  n, is (n  N)
(A)
4
)
1
n
(
n 2
2

(B)
4
n
)
1
n
( 2
2

(C)
4
)
1
n
( 2

(D) n2
Q.12 Number of roots of the function f (x) = 3
)
1
x
(
1

– 3x + sin x is
(A) 0 (B) 1 (C) 2 (D) more than 2
Q.13 If p (x) = ax2 + bx + c leaves a remainder of 4 when divided by x, a remainder of 3 when divided by
x + 1, and a remainder of 1 when divided byx – 1 then p(2) is
(A) 3 (B) 6 (C) – 3 (D) – 6
Q.14 Let f (x) bea function that has a continuous derivative on [a, b], f (a) and f (b)have oppositesigns, and
f ' (x)  0 for all numbers x between a and b, (a < x < b). Number of solutions does the equation
f (x) = 0 have (a < x < b).
(A) 1 (B) 0 (C) 2 (D) cannot be determined
Q.15 Whichofthefollowingdefiniteintegralhasapositivevalue?
(A) 



3
2
0
dx
)
x
3
sin( (B) 


0
3
2
dx
)
x
3
sin( (C) 



0
2
3
dx
)
x
3
sin( (D) 




2
3
0
dx
)
x
3
sin(
Q.16 Let set Aconsists of 5 elements and set B consists of 3 elements. Number of functions that can be
defined fromAtoBwhichareneitherinjectivenorsurjective,is
(A) 99 (B) 93 (C) 123 (D) none

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Q.17 Acirclewith centerAandradius 7 is tangent to thesides ofan angle of
60°.AlargercirclewithcenterBis tangent tothesides oftheangleand
to the first circle. The radius of thelarger circle is
(A) 3
30 (B) 21
(C) 3
20 (D) 30
Q.18 The value of the scalar    
s
r
·
q
p





 canbe expressed in thedeterminant form as
(A)
s
·
p
r
·
p
s
·
q
r
·
q








(B)
r
·
q
s
·
q
s
·
p
r
·
p








(C)
s
·
p
r
·
q
s
·
q
r
·
p








(D) s
·
q
r
·
q
s
·
p
r
·
p 







Q.19 If
x
1
0
1
x
1
0
1
x
n
·
x
Lim
x





l = – 5, where , ,  are finite real numbers then
(A)  = 2,  = 1,   R (B)  = 2,  = 2,  = 5
(C)   R,  = 1,   R (D)   R,  = 1,  = 5
Q.20 If f (x, y) = sin–1( | x | + | y | ), then the area of the domain of f, is
(A) 2 (B) 2
2 (C) 4 (D) 1
Q.21 A, B and C are distinct positiveintegers, less than or equal to 10.The arithmeticmean ofAand B is 9.
The geometric mean ofAand C is 2
6 . The harmonic mean of Band C is
(A)
19
9
9 (B)
9
8
8 (C)
19
7
2 (D)
17
8
2

ROUGHWORK
Q.22 If x is real and 4y2 + 4xy+ x + 6 = 0, then the complete set of values of x for which yis real, is
(A) x  2 or x  3 (B) x  – 2 or x  3
(C) – 3  x  2 (D) x  – 3 or x  2
Q.23 Ialternativelytoss afaircoinandthrow a fairdieuntil I, eithertoss ahead or throwa 2. If Itoss thecoin
first, the probabilitythat Ithrow a 2 before I toss a head, is
(A) 1/7 (B) 7/12 (C) 5/12 (D) 5/7
Q.24 LetA, B, C, D be (not necessarilysquare) real matrices such that
AT = BCD; BT = CDA; CT = DAB and DT = ABC
for the matrix S =ABCD, consider the two statements.
I S3 = S
II S2 = S4
(A) II is true but not I (B) I is true but not II
(C) both I and II are true (D) both I and II are false.

ROUGHWORK
Q.25 Whichofthefollowingisincorrectstatement
(A) I3
– is linear in shape and consist 22 valence electrons
(B) HNCO and N3
– is linear in shape
(C)hydroxylamineis morenucleophilicthan NH3
(D)AlN is more ionic than MgO
Q.26 Forthefollowingreaction
CH3–CH2 – Cl + NaOH  CH3–CH2–OH+NaCl
If thereagent is NaOH the best solvent is
(A) water (B) C2H5OH + H2O (C) C2H5OH (D) onlyNaOH
Q.27 Select thecorrect statement
(A) bond energy of N  N << P  P
(B) bond energy of P – P < N – N
(C)Ti(H2O)3
+3 is a coloured compound in pure state
(D)AgI2
– is unstable whileAgF2
– is stable compound
Q.28 Organiccompound(A)reacts withalc.KOHandgives (B),whichon treatmentwithNaOEt isomerizes
to (C). Compound (C), on treatment with OsO4 followed byHIO4 results CH3CH=O only. Select the
incorrect statement.If (A)is amonohalogen hydrocarbon with molecularweight is 92.5.
(A) (A) gives yellow ppt. withAgNO3
(B) (A) do not give anyppt. withAgNO3 in NH3
(C) (C) gives brown ppt. withAgNO3/NH3
(D) (A) reacts with NaI/acetone according to first order rate kinetics.
Q.29 If R–isomer have –ve rotation and S-isomer have +ve rotation, select the correct statement about the
mixture ofR andS 2–bromobutane, specificrotationofmixture is +18.40 andspecificrotationofR–2–
bromobutane is –230 then select the incorrect statement
(A) S–isomer has 23% specific rotation (B) 80% excess of S over R isomer
(C)R-isomerhas composition 10% only (D) None of these

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Q.30 When2–chlorobutanereactswithNaOHinpresenceofethylalcoholand water,ratekineticsofreaction
follows
(A) (B)
(C) (D)
Q.31 


H major product is
(A) (B) (C) (D)

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Q.32 Chirapos was developedbyprofessor Kagan &has founduseful applications in asymmetricsynthesis.
Usingfischerprojectionshownbelow,whichiscorrectstatement aboutconfigurationofthechiraposein
terms ofR/S notation.
(A) It is 2R, 3R molecule (B) It is 2S, 3R, molecule
(C) It is 2S, 3S molecule (D) It is 2R, 3S molecule
Q.33 Inthefollowingreaction
Product is
(A) (B) (C) (D)

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Q.34 Select theincorrect statement
(A)Al3+ on treatment with aq. Na2S givesAl(OH)3
(B) Cr3+ on treatment with aq. Na2S gives Cr(OH)3
(C) Cr(OH)3 dissolvedin basic solution ofbrominewater
(D)When mixture ofAgCl, Hg2Cl2 is treated with NH3 and resultant is filtered, black residue consist
HgNH2Cl,Hg, only
Q.35 For the reactions
I AcOH
NaOAc

 

II AcOH
NaOAc

 

Select thecorrect statement
(A) rate of Ist reaction is 1011 times faster than trans IInd
(B) rate of IInd reaction is 1011 times faster than trans Ist
(C) rate of Ist reaction and IInd reaction are equal
(D)reactionnot possible
Q.36 Theequilibriumconstant fortheionizationofR–NH2(aq)inwateras
R–NH2(g) + H2O(l)  R–NH2(aq) R–NH3
+(aq) + OH–(aq)
is 8 × 10–6 at 25°C. Find the pH of a solution at equilibrium with pressureof R–NH2(g) is 0.5 atm.
Assume Henry's Law, at equilibrium PA = K[A]; where K =1.[Take log 2.82 = 0.45]
(A) 12.3 (B)  11.3 (C)  11.45 (D) None

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Q.37 Whichstatement(s)is/aretrueabout therelation betweenthefollowing compounds?
(a) (b) (c)
(I) a and b are tautomers (II) b and c are resonating structures
(III) a and c are resonating structures (IV) a and c are tautomers
(A) I & III (B) II & IV (C) I, II & III (D) I & IV
Q.38 Arrangethefollowingcarbocationsintheincreasingorderoftheirstability.
(I) (II) (III)
(A) I > II > III (B) I > II = III (C) I > III > II (D) III > I > II
Q.39 Whichstatementaboutthefollowingequilibriumis/aretrue?
Ph3C–H +


K
O
Me 

K
C
Ph3 + MeOH
(I) The reactionfavours the product formation.
(II)Ph3CK is the dominant anionicspecies in this reaction.
(III) Methanol is the weaker acid in this reaction.
(IV) Thereactionfavours thereactant formation.
(A) I & II (B) I, II & III (C) IV only (D) III & IV

ROUGHWORK
Q.40 Which one of following carbonyl compound when treated with dilute acid forms the most stable
carbocation?
(A) 3
3 CH
C
CH
||
O

 (B) (C) (D) 5
6
5
6 H
C
C
H
C
||
O


Q.41 Correct order ofheat of combustion is:
(p) 1,3-Pentadiene (q) 1,3-Butadiene
(r)2,3-Dimethyl-1,3-butadiene (s) Propadiene
(A) s > q > p > r (B) s > r > q > p (C) r > p > q > s (D) s > r > p > q
Q.42 Writecorrect orderofreactivityoffollowinghalogenderivatives.
(I) (II) CH2=CH–Cl (III) Et3C–Cl (IV) PhCH2Cl (V) Ph3C–Cl
(A) I > V > IV > III > II (B) V > IV > I > III > II
(C) V > I > IV > III> II (D) I > V > III > IV > II
Q.43 Correctorderofnucleophilicityoffollowinganionsinpolarproticsolventis:
(A)

3
CH >
-
2
NH >

OH >

F (B)

3
CH <
-
2
NH <

OH <

F
(C)

3
CH =
-
2
NH =

OH =

F (D)

3
CH >

F >

OH >
-
2
NH

ROUGHWORK
Q.44 NO2 isinvolvedintheformationof smogand acidrain.Areaction that is important in theformation of
NO2 is
O3(g) + NO(g) O2(g) + NO2(g) K = 6 × 1034
If the air over a section of Pooja Towers contained 1.0 × 10–6M O3, 1.0 × 10–5M NO, 2.5 × 10–4M
NO2 and 8.2 × 10–3M O2, what can we conclude
(A) there will be a tendencyto form more NO and O3
(B) there will be a tendencyto form more NO2 and O2
(C) There will be a tendencyto form more NO2 and O3
(D)Therewill be no tendencyforchangebecause thereaction is at equilibrium
Q.45 Theequilibrium SO2Cl2(g) SO2(g)+ Cl2(g) is attained at 250C in aclosed container and Helium
is introduced.Whichofthefollowingstatementis correct
(1) The concentrations of SO2, Cl2 and SO2Cl2 change
(2)Morechlorine is formed
(3) Concentration of SO2 is reduced
(4) More SO2Cl2 is formed
(A) 1, 2, 3 (B) 2, 3, 4 (C) 3, 4 (D) none of these
Q.46 In the system LaCl3(s) + H2O(g) + heat LaClO(s) + 2HCl (g) equilibrium is established. More
water vapour is added to re-establish the equilibrium. The pressure of water vapour is doubled. The
factor bywhich pressure of HCl is changed is
(A) 2 (B) 2 (C) 3 (D) none of these
Q.47 Whichofthefollowingcompoundhaspyramidalgeometry?
(A) B(CH3)3 (B) (CH3)3C (C) (CH3)3N (D) BF3
Q.48 20 ml of0.2 M – NaOHand 40 ml 0.1 M – H2SO4 are mixed together in a flask & volume made up to
250 ml.The pHof theresultant solutionis
(A) 5 (B) 6 (C) 8 (D) none of these

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Q.49 Two isochoric cooling processAB and CDare shown in P-Vdiagram for the same gas. In which case
heat lostwill bemore.
(A)AB (B) same in both cases (C) CD (D) can't say
Q.50 PVversusTgraphofequal masses ofH2, Heand CO2 isshowninfigure. Choosethecorrect alternative
(A) 3 corresponds to H2, 2 to He and 1 to CO2
(B) 1 corresponds to He, 2 to H2 and 3 to CO2
(C) 1 corresponds to He, 3 to H2 and 2 to CO2
(D) 1 corresponds to CO2, 2 to H2 and 3 to He
Q.51 Two smooth cylindrical bars weighing W each lie next to each other in contact.Asimilar third bar is
placed overthetwobars asshownin figure. Neglectingfriction, theminimum horizontalforceon each
lower barnecessaryto keep them together is
(A) W/2 (B) W (C) W/ 3 (D) W/(2 3 )

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Q.52 A possible means for makingan aeroplaneinvisible to radar is to coat the plane with an anti reflective
polymer. If the radar waves have a wavelength of 3.0 cm and refractive index of polymer is n = 1.50.
Thenwhatwillbetheminimumthicknessofcoating(hererefractiveindexofaeroplanematerialishigher
thanpolymer)
(A) 0.5 cm (B) 1.0 cm (C) 0.25 cm (D) 1.25 cm
Q.53 Ariver is flowing with velocity2 m/s.Aboat is moving downstream.Velocityof boat in still water is
3 m/s. A person standing on boat throws a ball vertically upwards w.r.t himself with a velocity of
10m/s.At the topmost point, thevelocityofball w.r.t manstandingon boat, w.r.t riverand w.r.t ground
respectivelyis
(A) 5, 3, 0 m/s (B) 0, 3, 5 m/s (C) 0, 5, 3 m/s (D) none of these
Q.54 An object starts moving at an angle of 45° with the principal axis as shown in the figure in front of a
biconvexlensoffocal length+10cm.Ifdenotestheangleatwhichimagestartstomovewithprincipal
axisthen
(A)  =
4
3
(B)  =
2

(C)  =
4

(D)  = –
4

For Problems 55 to 56
Parallellightbeamofwavelength500nmfallsontwonarrowslit inYDSE
at angle = 300 as shown in figure. The distance between slit d=25×10–4
cm. On lower slit a transparent material of thickness t = 15 × 10–3 cm is
placed. Therefractive index of transparent material =7/6. The
interference pattern appears on screen at distance D (D >> d), then
Q.55 Thecentral maximawilloccuronscreen
(A) below point O (B) above point O
(C) at point O (D)data's areinsufficient to decide

ROUGHWORK
Q.56 How manynumber of fringes will pass through from point  = 0 (point 0). If we remove transparent
materialfromthelowerslit?
(A) 50 (B) 25 (C) 12 (D) none of these
Q.57 Aconcavemirror ofradius ofcurvature40 cm formsan image ofan object placed on theprincipal axis
at a distance 45 cm in front of it. Now if thesystem is completelyimmersed in water ( =1.33) then
(A)theimagewill shift towardsthe mirror
(B)themagnificationwillreduce
(C)theimagewillshiftawayfromthemirrorandmagnificationwillincrease.
(D)thepositionoftheimageandmagnificationwillnotchange.
Q.58 Imagine a hypothetical material whose average temperature coefficient of linear expansion is 0.1 /°C.
Findthefractionalincreaseintheareaofathinsquareplateofabovematerialwhentemperatureincrease
by 10°C.
(A) 1 (B) 2 (C) 3 (D) None
Q.59 A particle of mass m is projected at an angle of 60° with a velocityof
20 m/s relative to the ground from a plank of same mass m which is
placedonsmoothsurface.Initiallyplankwasatrest.Theminimumlength
of theplank for which theball will fall on theplank itself is(g = 10 m/s2)
(A) 3
40 m (B) 3
20 m (C) 3
10 m (D) 3
60 m
Q.60 Amanslowlypullsabucket of waterfrom awell ofdepthh. Ifthemass oftheuniform ropeand bucket
full of water are m and M respectively.The valueof work done bythe man is
(A) (m+M) gh (B) 





 M
2
m
gh (C) 




 
2
M
m
gh (D) None of the above

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Q.61 Ifthemassofblockis1kgandahorizontalforceof 3
10 Nisapplied
horizontallyontheblockasshowninthefigure. Thefrictionalforce
actingonthe block is
(A) zero (B)
3
10
N (C)
3
20
N (D) 5 N
Q.62 Abeaker contains 200 g of water.The water equivalent of beaker is 20 gm.The initial temperature of
water in the beaker is 20°C. If 440 g of hot water at 92°C is poured in, then the final temperature, will
be nearest to: (neglect heat loss)
(A) 58°C (B) 68°C (C) 73°C (D) none
Q.63 The frictionforceactingbetweensurfaces in contact in theadjoining figureis best represented by
(A) (B)
(C) (D)
Q.64 Twoparticles havingpositionvectors m
)
ĵ
5
î
3
(
r1 


and m
)
ĵ
3
î
5
(
r2 



aremovingwith velocities
)
ĵ
3
î
4
(
v1 


m/s and )
ĵ
7
î
a
(
v2 


m/s. If theycollide after 2 sec, the value of 'a' is
(A) 2 (B) 4 (C) 6 (D) 8

ROUGHWORK
Q.65 Inthebalancemachineshowninthefigure,whicharmwillmovedownward
after thesystem is released(assumingstring, arm of balancemachineand
thepulleytobelight)
(A)left (B)right
(C)remainsstationary (D) none of these
Q.66 Apointmoves onacircleof radius2meteranditsspeeddependson thedistancecoveredas v = S
 .
Thenthetimetakenbytheparticleinmakingthefull circleis
(A) 2 sec. (B) 3 sec. (C) 4 sec. (D) none
Q.67 Aplanemirroroflength2miskeptalongtheliney=–xasshowninthe
figure.Aninsecthavingvelocityof î
4 cm/sismovingalong thex-axis
from faraway.Thetimespanforwhichtheinsectcanseeitsimagewill
be
(A) 50 sec (B) 25 sec
(C) 2
25 sec (D) 2
50 sec
Q.68 The Potential EnergyUvs x curvefor aparticleis shown in figure.
Thentheconservative force(F)vs xcurvewill be:
(A) (B) (C) (D)

ROUGHWORK
Q.69 Aconverging beamof rays is incidentona divergingthin lens.Having passed through thelens the rays
intersect at apoint 15 cm fromthelens.Iflensisremoved thepoint wheretherays meet willmove5 cm
closertothemounting that holds thelens. Thefocal lengthoflens is
(A) f = 10 cm (B) f = 15 cm (C) f = 30 cm (D) f = 40 cm
Q.70 Twoparticles tiedtodifferentlight stringsarewhirledin ahorizontalcircleas shown infigure.Theratio
of length ofthestrings (L2/L1)sothat theycompletetheircircular path with equaltimeperiod is
(A)
2
3
(B)
3
2
(C) 1 (D) none of these
Q.71 Asmall objectplacedonarotatinghorizontal turntable justslips when it isplaced at adistanceof4 cm
from the axis of rotation. If the angular velocity of the turn table is doubled, the object slips when its
distancefrom theaxis ofrotationis
(A) 8 cm (B) 4 cm (C) 2 cm (D) 1 cm
Q.72 Asmall block of mass m is released fromAinside the frictionless circular groove of radius 2 m on an
inclined planeas shown infigure. Thecontact force between the blockand inclined plane at point B is
(A) 28 mg (B) 2.5 mg
(C)
2
28
mg (D) 18.5 mg

ROUGHWORK