Class : XII & XIII
Time : 3 hour
Max. Marks : 297
INSTRUCTIONS
1. The questionpaper contains 99 questions and 24 pages. Eachquestion carry3 marks and all ofthem are
compulsory.There is NEGATIVE marking. 1 mark will be deducted for each wrong answer.
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.
2. Indicate the correct answer(s) for each question byfilling appropriate bubble(s) in your OMR sheet.
3. Use onlyHB pencil fordarkeningthe bubble(s).
4. Use ofCalculator, LogTable, SlideRule andMobile is not allowed.
5. For exampleifonly'B'choice is correct then, thecorrect method for fillingthe bubble is
A B C D
For example if only'B & D'choicesare correct then, thecorrect method for fillingthe bubbles is
A B C D
Theanswerofthequestioninanyothermanner(suchasputting , cross , orpartial shading etc.)
will be treated as wrong.
USEFUL DATA
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, B = 11, Fe = 56, Ca = 40, Zn = 65.4,
Ba = 137,Co = 59, Hg = 200, Pb = 207, He = 4, F=19, Ar = 40
FINAL TEST
PAPER CODE : A
P A P E R - 1

ROUGHWORK
PART-A
Select the correct alternative. (Only one is correct) [99 × 3 = 297]
There is NEGATIVE marking. 1 mark will be deducted for eachwrong answer.
Q.1 Two identical heaters are coated with paint. In 1st case e1 = 1.0 and in 2nd case e2 = 0.5. Both are kept
inidenticalchamberswhichareinsimilarsurroundings.Iftheheatersareswitched on,insteadystate1st
heater has temperature T1 on surface and 1 of its chamber. 2nd heater has temperature T2 on surface
and 2 of its chamber.
(A) 1 = 2; T1 < T2 (B) 1 > 2; T1 = T2 (C) 1 = 2; T1 > T2 (D) 1 < 2; T1 = T2
Q.2 In an optical bench experiment to measure the focal length ofa concave mirror, random error in focal
lengthwillbe
(A)minimum whenu =fandmaximum when u=
(B)minimum whenu=andmaximum when u=f
(C)minimumwhenu =0andmaximum whenu= 2f
(D)minimum whenu =2f andmaximum when u=0
Q.3 Onedigital watch'A'was showing1:12:32 and an old clock'B', not havingsecondshand was showing
1:10, at themoment actual timewas 1:10:15
(A)Ais more precise but less accurate than B (B)Ais less precise but more accurate than B
(C)Ais both more accurate and precise (D) B is both more accurate and precise
Q.4 When beats are produced bytwo progressive waves of nearlythe same frequency, which one of the
followingiscorrect?
(A) theamplitudeof vibrations atanypoint changes simpleharmonicallywith afrequencyequal to the
differenceinfrequenciesofthetwo waves
(B)theparticlesvibratesimpleharmonically,withthefrequencyequaltothedifferenceinthecomponent
frequencies
(C) the frequencyof beats depends on the position, where the observer is
(D) the frequencyof beats changes as the time progresses

ROUGHWORK
Q.5 Microwaves of wavelength  = 5 cm and intensity I0 are split and
recombined bythe metallic mirror system as shown in thefigure. The
intensityofthemicrowaveatthedetectorPisminimumifxis
(A) 0.88 cm (B) 3.54 cm
(C) 3.02 cm (D) 6.04 cm
Q.6 What is the ratio of the acceleration of the ground state electron in a singly ionized helium atom and
doublyionizedlithiumatom?
(A) 2/3 (B) 4/9 (C) 8/27 (D) 1
Q.7 Themass numberofanucleus is
(A)always morethan its atomicnumber
(B)always lessthanits atomicnumber
(C)Sometimes lessthanitsatomicnumber
(D)Sometimes equal toandsometimes morethan its atomicnumber
Q.8 y(x, t) = 2
3
6
)
vt
x
(
10
6
.
1
10
4
.
6






Fora wave motion the disturbance along ydirection is represented by
the above equation. Hereall the parameters are in SIunits. If ydecreases from its maximum value to
onehalf of themaximum value in 2 ×10–3
s,what is thewave velocity?
(A) 20 m/s (B) 4 m/s (C) 4 × 10–3
m/s (D) 20 × 10–3
m/s
Q.9 Whichofthe followingstatementiscorrect isconnection withhydrogen spectrum
(A) Thelongestwavelengthis theBalmerseries is longerthanthelongest wavelengthin Lymanseries
(B)The shortest wavelength in theBalmer series is shorter than the shortest wavelength in the Lyman
series
(C)The longestwavelength inbothBalmerLymanseries areequal
(D) ThelongestwavelengthinBalmerseriesis shorterthanthelongest wavelengthintheLymanseries.

ROUGHWORK
Q.10 Imagine that a current is flowing around this test paper in the anticlockwise direction. If an external
magnetic fieldis in +ve x direction, which edge ofthe paper would belifted under the influenceof the
torqueofthemagnetic field?
(A) Top edge (B) bottom edge (C) left edge (D)right edge
Q.11 If an electric dipole is rotating about its center with a uniform angular velocityin the anticlockwise
directioninauniformmagneticfieldwhichisinthedirectionoftheangularvelocity,
(A) net force as well as torque on the dipole is zero
(B) net force as well as torque on the dipole is non zero
(C) net force on the dipole is zero but the net torque on the dipole is non zero
(D) net force on the dipole is not zero but the net torque on the dipole is zero
Q.12 The figure below shows the forces that three charged particles exert on each other.Which of the four
situations showncan be correct.
(I) (II) (III) (IV)
(A) all of the above (B) none of the above (C) II, III (D) II, III & IV
Q.13 Adiverginglens of focal length 10cm is placed10cm in front ofaplanemirror as shownin the figure.
Light from averyfar awaysourcefalls on the lens. The final image isata distance
(A) 20 cm behind the mirror (B) 7.5 cm in front of the mirror
(C) 7.5 cm behind the mirror (D)2.5 cm in front of the mirror

ROUGHWORK
Q.14 Amixtureof4gmheliumand28gmofnitrogenisenclosedinavesselofconstantvolumeat300K.The
quantityofheat absorbedbythemixture to increase rootmean velocityof itsmolecules by50%is (R is
universalgasconstant)
(A) 1500 R (B) 450 R (C) 750 R (D) 3000 R
Q.15 Anopencubicalvesselisstandingonaninclinedplane,angle45°,asseeninfigure. Itswallsarethinand
itiskeptfromslidingdownbyasmallwedge(C).Thevesselisfilledtoitshalfwithmercuryandaniron
sphereisfloatingonthesurfacefrom pointAinthedirectionofpointB.Whendoesthevessel tipover?
(A)When the sphere is atA
(B) When the sphere is at B
(C) When the sphere is at mid point ofAand B
(D) In all thepositions ofthesphere,theprobabilityoftippingis equal
Q.16 Pulldowninthemiddleaheavychain, fixed atbothends, in suchawaythat it formsatriangle.Does the
centre of mass takes up a higher or lower position?
(A) Centre of mass comes down (B) Centre of mass goes up
(C) Centre ofmass remains stationary (D) Cannot be predicted
Q.17 A car follows a truck on a perfectly straight road, both vehicles traveling at 72 km/h speed. What
minimal followingdistanceshould be observed bythe car in order to avoid flying stonesfrom the rear
wheels ofthe truck?
(A) 20 m (B) 10 m (C) 40 m (D) 5 m

ROUGHWORK
Q.18 Figure shows P vs V curve for various processes performed on an ideal gas. All the processes are
polytropic (PVm = constant). For 1, m = –1; for 2, m = 0.5; for 3, m = 1; for 4, m = 1.25 and for 5,
m = .
(A) Molar heat capacity (C) for process 2, C < Cp
(B) Molar heat capacityfor process (1) is
2
C
C v
p 
(C) Molar heat capacity for process 5 is C > Cv
(D)Anypolytropicprocess that lies between 3 & 4 will have positive heat capacity
Q.19 What is fractionof molecule below an altitude h in atmosphere?Assumeuniform gravitational field,
isothermal conditions,mass ofamoleculem, Boltzman constant k,temperatureT.
(A) f = )
kT
/
mgh
(
e (B) f = )
kT
/
mgh
–(
e (C) f = 1 – )
kT
/
mgh
–(
e (D) f = 1 – )
kT
/
mgh
(
e
Q.20
(W) (X) (Y) (Z)
Figure shows four hollow metal spheres each with internal radius a and external radius b. Match each
charge distributionwiththecorrespondingE-fieldgraph.
(I) (II) (III) (IV)
(A) W – II; X – I; Y – III; Z – IV (B) W – III; X – I; Y – II; Z – IV
(C) W – I; X – II; Y – III; Z – IV (D) W – II; X – III; Y – I; Z – IV

ROUGHWORK
Comprehension (Q.21 to Q.23)
Two particles ofmass m each arerotating parallel to xz planein circle of radius R as shown.
Consider the situation when the particles areat (R, R, 0)and (–R, –R, 0)answer following questions
Q.21 The angular velocityvector of the system of two particles and the total angular momentum of system
about originmakean angleof
(A) 45° (B) 90° (C) 0° (D) 180°
Q.22 What isy-component ofthe totalangularmomentum of thesystem about origin
(A) zero (B)2mvR (C)mvR (D)mvR/2
Q.23 Choose thecorrect statement
(A) The y-component of the total torque actingon thesystem is non-zero
(B) Net force acting on system is non zero
(C) Net torque on the system rotates parallel to xz plane
(D)Total torque acting on thesystem is zero
Q.24 A coil of inductance L = 0.2 H and of resistance R = 62.8  is connected to the mains alternating
voltage of frequency50 Hz. What can be the capacitance ofthe capacitor connected in series with the
coiliftheusefulpowerhastoremain unchanged?
(A) 10 C (B) 50 C (C) 25 C (D) 100 C

ROUGHWORK
Q.25 A neutral particle at rest in a magnetic field decays into two charged particles of different mass. The
energyreleased goes into their kinetic energy.Then what can be the path of the two particles. Neglect
anyinteraction betweenthe twocharges.
(A) (B)
(C) (D)
Q.26 A spherical soap bubble is blown such that its radius increases at a constant rate. Which of following
curves represents power required to increase surface energyof the bubble versus radius of drop.
(A) (B) (C) (D)

ROUGHWORK
Q.27 Alight,rigidsheet oftriangularshapehas acurvedportioncutfromit asshown infigure. Itfloats onthe
surface ofwater. Some soap solutionis dropped over dottedregion. Surface tension ofwater and soap
film areT1
& T2
respectively. T1
= 1.5T2
. Mark correct option.
(A) The frame experiences a net force F = (T1
– T2
)R in y< 0 direction
(B) The frame experiences force F = (T1
– T2
)R in y > 0 direction
(C) The frame experiences force (T1
– T2
)(2–)R in y> 0 direction
(D)Resultantforce on wireframeis zero
Q.28 Astringoflength3Lisfixed at bothends.It resonateswith atuningfork in thirdharmonic.Attimet =0,
astringelementatpositionofantinodeisathalfitspositiveamplitudeandmovingtowardsmeanposition.
Displacement ofastringelement at L/2is givenby
(A) 




 


6
11
t
sin
2
A0
(B) 




 


6
5
t
sin
2
A
3 0
(C) 




 


6
5
t
sin
A0 (D) 




 


6
5
t
sin
2
A0
Q.29 Aprojectileistobeprojectedtowardsenemyterritoryat thesamehorizontallevel.Theinitialvelocityof
the projectile is known to be 100 ± 1 m/s. Initial angle of the projectile is known to be projected
45°  1°. What is the possible rangeof the projectile?
(A) 990 m  R  1010 m (B) 980 m  R  1020 m
(C) 970 m  R  1030 m (D) 930 m  R  970 m

ROUGHWORK
Q.30 AverylongwirecarryingcurrentIisfixedalongx-axis.Anotherparallelfinitewirecarryingacurrentin
theoppositedirectionis kept at adistanced above thewirein xyplane.Thesecond wireisfreeto move
parallel toitself.Theoptionsavailableforits small displacementsarein
(i)+vexdirection (ii)+veydirection (iii)+vezdirection
Takinggravityinnegativeydirection,thenatureofequilibriumofsecondwireis
(A)stableformovement inx direction,unstableformovementinydirection,neutralformovement inz
direction
(B)stableformovementinydirection,unstableformovement inz direction, neutralformovement in x
direction
(C)stableformovement inz direction,unstableformovementin ydirection, neutralformovement in x
direction
(D)stableformovement inydirection,unstableformovementinx direction,neutralformovement inz
direction
Q.31 A sphere of brass released in a long liquid column attains a terminal speed v0. If the terminal speed
attained bythesphere ofmarbleofthesame radius andreleased in thesameliquid is nv0, thenthevalue
ofnwillbe.
Given: Thespecific gravities of brass, marble and the liquidare 8.5, 2.5 and 0.8 respectively.
(A)
17
5
(B)
77
17
(C)
31
11
(D)
5
17
Q.32 Asimplependulumoflength1misallowedtooscillatewithamplitude2°.Itcollides
elasticallywithawall inclinedat1°tothevertical. Itstimeperiod willbe(useg=2)
(A) 2/3 sec (B) 4/3 sec
(C) 2 sec (D) none
Q.33 Aspherical asteroid having the samedensityas that of earth is floating in free space.Asmall pebble is
revolvingaroundtheasteroidunder theinfluenceof gravitynear thesurfaceof theasteroid.What is the
approximate time periodoftheasteroid?
(A) 24 h (B) 365 days (C) 10 min (D) 1 hr 24 min

ROUGHWORK
Q.34 20mlof0.05 M solutionof theconjugate acidof an -amino acid methionine(H2A+)is taken.Thepka
of –COOH group in methionine is 2.8 and pkb ofbasic group is 4.8. Pick out onlyincorrect statement
among thefollowing. [Uselog2= 0.3]
(A) pH oforiginal aminoacidsolutionwas ~ 2.05
(B) pH ofsolution was ~ 2.8 when 10 ml 0.05 M NaOH solution is added to original solution
(C) pH of solution is ~ 6when 20 ml 0.05 M NaOH solution is added to original solution
(D) pH ofsolution is 3.8 when20 ml 0.05 M NaOH solution is added to original solution
Q.35 Whichofthe followingcompound(s)will givebluecolourwhenit is converted intoLassaigne's extract
and FeSO4 is added followed byFeCl3.
(I) (II) (III) CH3–NMe2 (IV) NH2–NH2
(A) IIIonly (B) II & III (C) II, III & IV (D) I, II, III & IV
Q.36 ZnO shows yellow colour on Heatingdue to
(A)d–d transition (B) C–T spectra
(C)Higher polarisation causedbyZn2+ ion (D) F– centres
Q.37 Thedecomposition of N2O5 inchloroform was followedbymeasuringthevolumeof O2 gas evolved :
2N2O5 (CCl4) 2N2O4 (CCl4) + O2(g). The maximum volume of O2 gas obtained was 100 cm3. In
500 minutes, 90 cm3 of O2 were evolved. The first order rate constant (in min–1) for the rate of
disappearance of N2O5 is
(A)
500
303
.
2
(B)
500
303
.
2
log
90
100
(C)
500
303
.
2
log
100
90
(D)
500
10
100


ROUGHWORK
Q.38 What will be the order of rotation barriers about C–N bond among these compounds ?
(I) CH3–CH2–NH2 (II) (III)
(A) I > II > III (B) I < II < III (C) II > III > I (D) III > I > II
Q.39 Complex compound [Cr(NCS)(NH3)5] [ZnCl4] will be
(A)Colourless&diamagnetic
(B) Greencoloured& diamagnetic
(C) Green coloured& shows coordinationisomerism
(D)Diamagnetic&showslinkageisomerism
Q.40 The vapour pressureofpure perflourocyclohexane (C6F12)aregiven bythefollowingequations:
Solid C6F12 : log10 p(mm Hg) = 8.68 –
T
1890
Liquid C6F12 : log10 p(mm Hg) = 7.60 –
T
1530
Themolarenthalpyoffusionofsolid C6F12 is approximately
(A) 1658 cal (B) 360 cal (C) 3420 cal (D) 720 cal
Q.41 + HNO3 + H2SO4  Product.
Productis:
(A) (B) (C) (D) Both B & C

ROUGHWORK
Q.42 Whichofthefollowingis correct.
(A) F2 has higherdissociation energythan Cl2
(B)Fhas higherelectronaffinitythanCl
(C) HF is stronger acid than HCl
(D)Boilingpoint increases downthegroup inhalogens
Q.43 3
H
N

– CH(R)– CO2H has its Ka1 = 10–7. The isoelectric point of the -amino acid occur at pH = 8.2
hence pKa2 of the conjugate acid of -amino acid is equal to
(A) 9.4 (B) 1.2 (C) 7.6 (D) 2.4
Q.44 Theproduct ofI– with 
4
MnO inalkalinemedium is
(A) I2 (B) 
3
IO (C) IO– (D) 
4
IO
Q.45 Whichofthe followingwill racemizeinpresenceofacidorbaseimpuritiesinaqueousmedium.
(A)
Cl
O
|
|
|
Ph
C
C
Me
|
CH3


 (B)
D
O
|
|
|
CH
C
CH
C
Me
|
H
3
2 



(C) (D)
3
3
2
CH
O
|
|
|
CH
CH
C
C
Ph
|
H





ROUGHWORK
Q.46 (X) + K2CO3 + Air 
 
Heat (Y)
(Y) + Cl2  (Z) Pink
Whichofthefollowingiscorrect?
(A) X = black, MnO2 , Y = Blue, K2CrO4, Z = KMnO4
(B) X = green, Cr2O3, Y = Yellow, K2CrO4 , Z = K2Cr2O7
(C) X = black, MnO2 Y = green , K2MnO4, Z = KMnO4
(D) X = black, Bi2O3, Y= colourless KBiO2, Z = KBiO3
Q.47 Writecorrect order of stability
(A) I > II > III > IV (B) III > II > I > IV (C) III > I > II > IV (D) III > II > IV > I
Q.48 The structure of diborane (B2H6)contains
(A) Four (2C–2e–) bonds and two (2C–3e–) bonds
(B) Two (2C–2e–) bonds and two (3C–2e–) bonds
(C) Four (2C–2e–) bonds and four (3C– 2e–) bonds
(D) None
Q.49 This question consist of two statements each, printed as assertion and reason, while answering this
question youare required to chooseanyone of thefollowing responses.
(A) If both assertion and reason are true and the reason is a correct explanation of assertion.
(B) If both assertion and reason are true but reason is not a correct explanation of assertion.
(C) If assertionis true but thereason is false.
(D) If assertion is false but thereason is true.
Assertion : Me MgBr give CH4 with acetone.
Reason :  – H of carbonyl compounds are active (acidic).

ROUGHWORK
Q.50 Nitrogen dioxide cannot be obtained from
(A) Cu(NO3)2 (B) Hg(NO3)2 (C) NaNO3 (D)AgNO3
Q.51 PhCHO&HCHOwillbehavedifferentlywithwhichofthefollowingreagents
(A)Tollen's Reagent (B)FehlingSolution (C)Schiff'sreagent (D) NaBH4
Q.52 The oxide does not have coordinate bond is
(A) N2O (B) NO (C) N2O5 (D) NO2
Q.53 & are:
(A)chainisomers (B)positionalisomers (C)conformers (D)enantiomers
Q.54 FeSO4 is a verygood absorber for NO, the new compound formed by this process is found to contain
number ofunpairedelectrons
(A) 4 (B) 5 (C) 3 (D) 6
Q.55 Most stableformofethyleneglycol is:
(A)anti (B)gauche (C)fullyeclipsed (D)partiallyeclipsed
Q.56 Theformation of 
4
PH is difficultcompared to 
4
NH because
(A)lonepairofphosphorus isopticallyinert
(B) lone pairof phosphorus resides at almost pure p-orbital
(C) lone pair of phosphorus resides at sp3 orbital
(D) lone pairof phosphorus resides at almost pure s-orbital
Q.57 Whichofthe followingheptanols arechiral 1-heptanol, 2-heptanol, 3-heptanol, 4-heptanol.
(A)All arechiral (B) 2-heptanol and 3-heptanol
(C) 2-heptanol, 3-heptanol & 4-heptanol (D) 3-heptanol and 4-heptanol

ROUGHWORK
Q.58 What products areformedduring, the electrolysis of a concentrated aqueous solution of NaCl?
(I) Cl2 (g) (II) NaOH (aq) (III) H2 (g)
(A) Ionly (B) I & II only (C) I & III only (D) I, II & III
Q.59 Predict themajorproductP infollowingreaction:
HCl
NaNO2


 
 P
(A) (B)
(C) (D)
Q.60 The product Octalone is obtained byMichael addition followed byaldol condensation of reactants R
and S in presence of a base. S gives positiveiodoform test.
R + S 
 
 
,
B
Octalone
R andS are respectively:
(A) + CH3–CH=O (B) +
O
|
|
H
C
CH
CH2 


(C) +
O
|
|
CH
C
CH
CH 3
2 

 (D) +
O
|
|
CH
C
CH
CH 3
2
3 



ROUGHWORK
Question No. 61 & 62 (2 questions)
Q.61 StepC(refining)involvedinpurificationofPbmetal
(A)Distillation (B)Bessemerization
(C)Cupelation (D)Electrolyticrefining
Q.62 Whichofthefollowingmetalsareobtained byautoreduction method:
Pb, Mn, Cu, Cr, Fe,Al.
(A) Cu, Fe (B) Cu, Pb, Mn (C) Mn, Cr, Pb (D) Pb, Cu
Q.63 Thiscompoundonozonolysisgiveswhich ofthefollowingcompounds
(I) (II)
O
O
|
|
|
|
CHO
C
CH
C
C
OHC
|
|
O
2 




(III)
CHO
|
CHO (IV)
O
|
|
O
CH
CH
C
C
OHC
|
|
O
2 




(A) I, II, III & IV (B) I, III, IV (C) I, II, III (D) I, II, IV

ROUGHWORK
Q.64 In the reaction;
OH
CH
ONa
CH
3
3


 
 ; the product is
(A) (B) (C) (D)
Q.65 ThecorrectIUPAC name of thefollowing compound is:
O
C
H
OH
|
|
CHO
CH
CH
C
O 2






(A)3,3-diformyl propanoic acid (B)3-formyl-4-oxo-butanoic acid
(C) 3,3-dioxo propanoic acid (D) 3,3-dicarbaldehyde propanoic acid
Q.66 CH2=CH–CH2–CH2–CCH )
eq
1
(
HBr

 
 Product is
(A) BrCH2–CH2–CH2–CH2–CCH (B) CH2=CH–CH2–CH2–CH = CH–Br
(C)
Br
|
CH
C
CH
CH
CH
CH 2
2
2
2 



 (D)
Br
|
CH
C
CH
CH
CH
CH 2
2
3 





ROUGHWORK
Q.67 Let f (x) = ax7 + bx3 + cx – 5, where a, b and c are constants. If f (–7) = 7, then f (7) equals
(A) –17 (B) –7 (C) 14 (D) 21
Q.68 For f (x) = sin 










 

2
x
2
cos , then the f ' 




 

4
(A) – cos 1 (B) 1 (C) – 2 (D) 0
Q.69 If x and yare real numbers such that x2 + y2 = 8, The maximum possible value of x – y, is
(A) 2 (B) 4 (C) 2 (D) 2
2
Q.70 A plane passes through the point P(4, 0, 0) and Q(0, 0, 4) and is parallel to the y-axis. The distance of
theplanefromtheoriginis
(A) 2 (B) 4 (C) 2 (D) 2
2
Q.71 Let f (x)becontinuous anddifferentiablefunctionforall reals.
f (x + y) = f (x) – 3xy + f (y). If
h
)
h
(
Lim
0
h
f

= 7, then the value of f ' (x) is
(A) – 3x (B) 7 (C) – 3x + 7 (D) 2 f (x) + 7
Q.72 For b> a >1, the area enclosed bythe curve y= ln x, yaxis and the straight lines y = ln a and y= ln b is
(A) b – a (B) b(ln b – 1) – a(ln a – 1)
(C) (ln a)(b – a) (D) (ln b)(ln a)
Q.73 The set ofpositive values of nfor which
n
2
30
cos
1
i
2
30
cos
1







 




isreal, is
(A) 4, 8, 12,  (B) 6, 12, 18,  (C) 8, 16, 24,  (D) 12, 24, 36, 

ROUGHWORK
Q.74 PointsAandB areselectedonthegraphofx2 +2y=0sothatthetriangleABOisequilateral.Thelength
of the sideof thetriangle is ('O'is the origin)
(A) 3
4 (B)
3
4
(C)
3
4
(D) 3
2
Q.75 If f (x) is continuous and differentiable over [–2, 5] and – 4  f ' (x)  3 for all x in (–2, 5) then the
greatest possible value of f (5) – f (–2) is
(A) 7 (B) 9 (C) 15 (D) 21
Q.76 The graph of f (x) =
20
x5
–
12
x4
+ 5 has
(A)norelativeextrema, onepointof inflection.
(B)tworelativemaxima,onerelativeminimum,twopointsofinflection.
(C)onerelativemaximum,onerelativeminimum,onepointofinflection.
(D)onerelativemaximum,onerelativeminimum,twopointofinflection.
Q.77 Minimum value of 






2
A
tan
3
2
A
cot
2
1
whereA (0, 180°) occurs whenAequals
(A) 60° (B) 90° (C) 120° (D) 150°
Q.78 Let k be an integer and p is a prime such that the quadratic equation x2 + kx + p = 0 has two distinct
positive integer solutions. Thevalue of (k+ p)equals
(A) – 1 (B) 0 (C) 3 (D) 6
Q.79 Consider the particle travellingclockwiseon the elliptical path
25
y
100
x 2
2
 =1. The particleleaves the
orbitat thepoint (–8, 3)andtravels inastraightlinetangent to theellipse.Atwhat pointwill theparticle
cross the y-axis?
(A) 





3
25
,
0 (B) 






3
25
,
0 (C) (0, 9) (D) 





3
7
,
0

ROUGHWORK
Q.80 Thesolutionof thedifferential equation, ex(x +1)dx +(yey –xex)dy=0 with initial condition f (0) = 0,
is
(A) xex + 2y2ey = 0 (B) 2xex + y2ey = 0 (C) xex – 2y2ey = 0 (D) 2xex – y2ey = 0
Q.81 The valueof the expression, cos 35° +cos 125° + 2 sin 185°(sin 130° + sin140°) when simplified is
(A) positive andgreater than(1/2) (B) negative and less than (– 1/2)
(C) 1/2 (D) zero
Q.82 f (x) = 1
x
4 2
5 
. How manyof the following are true?
I The domain of f is | x | 
2
1
II The range of f (x) is y  1
III Thegraphoff (x)is symmetricabout the y-axis.
IV f(x)hasnocritical points.
V The graph of f (x) never decreases.
(A) one (B) two (C) three (D)four
Q.83 IfA= 





 1
x
tan
x
tan
1
thenlet usdefineafunction f(x)=det.(ATA–1)thenwhichofthefollowingcan
not be the value of  
 
 


 


 

times
n
)
x
(
f
.
..........
f
f
f
f is (n  2)
(A) f n(x) (B) 1 (C) f n – 1(x) (D) n f (x)
Q.84 The equations of L1 and L2 are y= mx and y= nx, respectively. Suppose L1 makes twice as large of an
angle withthe horizontal (measured counterclockwisefrom the positive x-axis)as does L2 andthat L1
has 4 times the slope of L2. If L1 is not horizontal, then the value of the product (mn) equals
(A)
2
2
(B) –
2
2
(C) 2 (D) –2

ROUGHWORK
Q.85 Three balls marked 1, 2 and 3are placed in anurn. One ball is drawn, its number is recorded, then the
ballisreturnedtotheurn.This process isrepeated andthenrepeated oncemore,and each ballis equally
likelytobedrawnon eachoccasion. Ifthesumofthenumbersrecordedis 6,theprobabilitythat theball
numbered 2 was drawn at all the three occassions, is
(A)
27
1
(B)
7
1
(C)
6
1
(D)
3
1
Q.86 Number of integral values ofx the inequality 







1
x
2007
x
2
log10  0 holds true, is
(A) 1004 (B) 1005 (C) 2007 (D) 2008
Q.87 Let f bea one-to-one continuous function such that f (2) =3 and f (5) =7. Given 
5
2
dx
)
x
(
f =17, then
thevalueofthedefiniteintegral 

7
3
1
dx
)
x
(
f equals
(A) 10 (B) 11 (C) 12 (D) 13
Q.88 Tworays with commonend point 'O'forms a 30° angle.PointAlies on oneray, point B on theotherray
andAB =1.Themaximum possible lengthof OB is
(A) 3 (B)
3
4
(C) 2 (D)
2
1
3 
Q.89 Suppose that thequadraticfunction f (x) =ax2 +bx + c is non-negativeontheinterval [–1, 1]. Then the
area under the graph of f over the interval [–1, 1] and the x-axis is given bythe formula
(A) A = f (–1) + f (1) (B) A= 













2
1
2
1
f
f
(C) A = )]
1
(
)
0
(
2
)
1
(
[
2
1
f
f
f 

 (D) A= )]
1
(
)
0
(
4
)
1
(
[
3
1
f
f
f 



ROUGHWORK
Q.90 Let F1, F2 are the foci of the hyperbola
9
y
16
x 2
2
 =1 and F3, F4 are the foci of its conjugate hyperbola.
If eH and eC aretheir eccentricities respectivelythenthe statement which holdstrue is
(A) Theirequations oftheasymptotes are different.
(B) eH > eC
(C)Area of the quadrilateral formed bytheir foci is 50 sq. units.
(D)Theirauxillarycircleswillhavethesameequation.
Q.91 Consider the two functions f (x) = x2 + 2bx + 1 and g(x) = 2a(x + b), where the variable x and the
constants aandbarereal numbers.Each suchpair oftheconstants aandb maybeconsideredas apoint
(a, b) in an ab – plane. Let S be the set of such points (a, b) for which the graphs of y = f (x) and
y = g (x) do not intersect (in the xy– plane.). The area of S is
(A) 1 (B)  (C) 4 (D) 4
Q.92 Let 0 =
33
32
32
23
22
21
13
12
11
a
a
a
a
a
a
a
a
a
and let 1 denote the determinant formed bythe cofactors of elements of
0 and 2 denote the determinant formed by the cofactor at 1 and so on n denotes the determinant
formed bythe cofactors at n – 1 then the determinant value of n is
(A) n
2
0
 (B)
n
2
0
 (C)
2
n
0
 (D) 2
0

Q.93 The polynomial P(x) = x3 + ax2 + bx + c has the propertythat the mean of its zeroes, the product of its
zeroes,andthesumofitscoefficientsareallequal.Ifthey-interceptofthegraph ofy=P(x)is 2,thenthe
value of b is
(A) – 11 (B) – 9 (C) 1 (D) 5
Q.94 If 

2006
10
k
10
k
C simplifies to nCp where p is prime then (n + p) has the value equal to
(A) 2017 (B) 2018 (C) 2019 (D) 2020

ROUGHWORK
Q.95 The number of three elements sets of positive integers {a, b, c} such that a × b × c = 2310, is
(A) 40 (B) 30 (C) 25 (D) 15
Q.96 Let u = dx
x
sin
3
2
cos
2
/
0
2







 
and v = dx
x
sin
3
cos
2
/
0







 
, then the relation between u and v is
(A) 2u = v (B) 2u = 3v (C) u = v (D) u = 2v
Q.97 In thefiguregiven, two circleswith centresC1 and C2 are35units apart, i.e. C1C2 =35. Theradii of the
circles with centres C1 and C2 are 12 and 9 respectively. If Pis theintersection of C1C2 and a common
internaltangent to the circles, then l(C1P)equals
(A) 18 (B) 20
(C) 12 (D) 15
Q.98 Let Z = 

2007
1
k
k
ki , then Re(Z) + Im(Z) equals (where i = 1
 )
(A) 0 (B) 2007 (C) – 2008 (D) 3012
Q.99 Position vectorsofthefour angularpoints ofatetrahedronABCDareA(3, –2, 1); B(3, 1,5); C(4, 0, 3)
and D(1, 0, 0).Acute angle between the plane facesADC andABC is
(A) tan–1 





2
5
(B) cos–1 





5
2
(C) cosec–1 





2
5
(D) cot–1 





2
3