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FINAL TEST Class : XII & XIII Time : 3 hour Max. Marks : 297 PAPER CODE : A INSTRUCTIONS 1. The question paper contains 99 questions and 24 pages. Each question carry 3 marks and all of them 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 by filling appropriate bubble(s) in your OMR sheet. 3. Use only HB pencil for darkening the bubble(s). 4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed. 5. 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. 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 PART-A Select the correct alternative. (Only one is correct) [99 × 3 = 297] There is NEGATIVE marking. 1 mark will be deducted for each wrong 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 in identical chambers which are in similar surroundings. If the heaters are switched on, in steady state 1st 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 of a concave mirror, random error in focal length will be (A) minimum when u = f and maximum when u = (B) minimum when u = and maximum when u = f (C) minimum when u = 0 and maximum when u = 2f (D) minimum when u = 2f and maximum when u = 0 Q.3 One digital watch 'A' was showing 1:12:32 and an old clock 'B', not having seconds hand was showing 1:10, at the moment actual time was 1:10:15 (A) A is more precise but less accurate than B (B) A is less precise but more accurate than B (C) A is both more accurate and precise (D) B is both more accurate and precise Q.4 When beats are produced by two progressive waves of nearly the same frequency, which one of the following is correct? (A) the amplitude of vibrations at any point changes simple harmonically with a frequency equal to the difference in frequencies of the two waves (B) the particles vibrate simple harmonically, with the frequency equal to the difference in the component frequencies (C) the frequency of beats depends

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- 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–CCH ) eq 1 ( HBr Product is (A) BrCH2–CH2–CH2–CH2–CCH (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

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