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# MCP-13th Paper-1 Code-A.pdf

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MCP- 13th Paper-1 Code-B.pdf
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### MCP-13th Paper-1 Code-A.pdf

2. 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
3. ROUGHWORK 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
4. 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
5. ROUGHWORK 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
6. 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.
7. 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
8. ROUGHWORK Q.30 When2–chlorobutanereactswithNaOHinpresenceofethylalcoholand water,ratekineticsofreaction follows (A) (B) (C) (D) Q.31    H major product is (A) (B) (C) (D)
9. ROUGHWORK 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)
10. ROUGHWORK 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
11. ROUGHWORK 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
12. 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
13. 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
14. ROUGHWORK 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 )
15. ROUGHWORK 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
16. 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
17. ROUGHWORK 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
18. 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)
19. 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
20. ROUGHWORK
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