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

2. ROUGHWORK Select the correct alternative. (Only one is correct) [72×3 = 216] There is NEGATIVE marking. 1 markwillbe deducted for eachwrong answer. Q.1 I alternativelytossa fair coinandthrow a fair dieuntilI, either tossa head or throwa 2. IfItoss the coin first, the probabilitythat I throw a 2 before I toss a head, is (A) 1/7 (B) 7/12 (C) 5/12 (D) 5/7 Q.2 LetA, B, C, D be (not necessarilysquare) realmatrices 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. Q.3 The area ofthe region ofthe plane bounded above bythe graphof x2 + y2 + 6x + 8 = 0 and below by the graph of y = | x + 3 |, is (A) 4  (B) 4 2  (C) 2  (D)  Q.4 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. Ifarea 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 inA.P. (D) a, c, b are inA.P. Q.5 If x and y are realnumbers and x2 + y2 = 1, then the maximum value of(x + y)2 is (A) 3 (B) 2 (C) 3/2 (D) 5
3. ROUGHWORK Q.6 The value ofthe definite integral     0 2 a ) x 1 )( x 1 ( dx (a >0) is (A) 4  (B) 2  (C)  (D) some functionofa. Q.7 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 ofa, b and c Q.8 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.9 The minimumvalue ofthefunctionf (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 in the largest possible domain of f (x) is (A) 4 (B) – 2 (C) 0 (D) 2 Q.10 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
4. ROUGHWORK Q.11 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.12 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) greaterthanzero (B) equalto 3 (C) equalto zero (D) equalto 1 Q.13 Number ofrectangleswith sides parallelto the coordinate axes whose vertices are allofthe form(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.14 Number of roots ofthe function f (x) = 3 ) 1 x ( 1  – 3x + sin x is (A) 0 (B) 1 (C) 2 (D) more than 2 Q.15 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 by x – 1 then p(2) is (A) 3 (B) 6 (C) – 3 (D) – 6 Q.16 Let f (x) be a function that has a continuous derivative on[a, b], f (a) and f (b) have opposite signs, 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
5. ROUGHWORK Q.17 Whichofthefollowing definite integralhasa positive value? (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.18 Let set A consists of 5 elements and set B consists of 3 elements. Number of functions that can be defined fromAto B whichare neither injective nor surjective, is (A) 99 (B) 93 (C) 123 (D) none Q.19 Acircle with centerAand radius 7 is tangent to the sides ofan angle of 60°.Alarger circle withcenterB is tangent to the sides oftheangle and to the first circle. The radius ofthelarger circle is (A) 3 30 (B) 21 (C) 3 20 (D) 30 Q.20 The value ofthe scalar     s r · q p       canbe expressed in the determinant formas (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.21 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
6. ROUGHWORK Q.22 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.23 A, B and C are distinct positive integers, less than or equalto 10. The arithmetic mean ofAand B is 9. The geometric mean ofAand C is 2 6 . The harmonic mean of B and C is (A) 19 9 9 (B) 9 8 8 (C) 19 7 2 (D) 17 8 2 Q.24 If x is real and 4y2 + 4xy+ x + 6 = 0, then the complete set of values ofx 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
7. ROUGHWORK Q.25 Which ofthe following compound haspyramidalgeometry? (A) B(CH3)3 (B) (CH3)3C (C) (CH3)3N (D) BF3 Q.26 20 mlof0.2 M – NaOH and 40 ml0.1 M – H2SO4 are mixed together in a flask & volume made up to 250 ml. The pH oftheresultant solution is (A) 5 (B) 6 (C) 8 (D) noneofthese Q.27 Whichofthefollowingis incorrect statement (A) I3 – is linear in shape and consist 22 valence electrons (B) HNCO and N3 – is linear in shape (C) hydroxylamine is more nucleophilicthanNH3 (D)AlN is more ionic than MgO Q.28 For thefollowing reaction CH3–CH2 – Cl + NaOH  CH3–CH2–OH+NaCl Ifthe reagent is NaOH the best solvent is (A) water (B) C2H5OH + H2O (C) C2H5OH (D) onlyNaOH Q.29 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 inpure state (D)AgI2 – is unstable whileAgF2 – is stable compound Q.30 Organic compound(A) reacts withalc. KOH and gives (B), whichontreatment withNaOEt isomerizes to (C). Compound (C), on treatment with OsO4 followed byHIO4 results CH3CH=O only. Select the incorrect statement. If (A) is a monohalogen 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 withNaI/acetone according to first order rate kinetics.
8. ROUGHWORK Q.31 IfR–isomer have –ve rotation and S-isomer have +ve rotation, select the correct statement about the mixture ofRand S 2–bromobutane, specific rotationofmixture is +18.40 and specific rotationofR–2– bromobutane is –230 then select the incorrect statement (A) S–isomer has23% specific rotation (B) 80% excess of S over R isomer (C) R-isomer has composition 10% only (D) None ofthese Q.32 When2–chlorobutanereactswithNaOH inpresence ofethylalcoholand water, rate kineticsofreaction follows (A) (B) (C) (D) Q.33    H major product is (A) (B) (C) (D)
9. ROUGHWORK Q.34 Chirapos was developed byprofessor Kagan &has found usefulapplications inasymmetric synthesis. Using fischer projectionshownbelow, whichiscorrect statement about configurationofthe chirapose in 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.35 Inthefollowingreaction Product is (A) (B) (C) (D)
10. ROUGHWORK Q.36 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 dissolved in basic solution ofbromine water (D) When mixture ofAgCl, Hg2Cl2 istreated withNH3 and resultant is filtered, blackresidue consist HgNH2Cl, Hg, only Q.37 For the reactions I AcOH NaOAc     II AcOH NaOAc     Select thecorrect statement (A) rate ofIst reaction is 1011 times fasterthan trans IInd (B) rate ofIInd reaction is 1011 times faster thantrans Ist (C) rate ofIst reaction and IInd reaction are equal (D) reactionnot possible Q.38 The equilibriumconstant for the ionizationofR–NH2(aq) inwater as R–NH2(g) + H2O(l)  R–NH2(aq) R–NH3 +(aq) + OH–(aq) is 8 × 10–6 at 25°C. Find the pH ofa solutionat equilibrium with pressure ofR–NH2(g) is 0.5 atm. Assume Henry's Law, at equilibriumPA = 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.39 Whichstatement(s) is/are true about the relationbetweenthe following 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.40 Arrange the followingcarbocations inthe increasing orderoftheir stability. (I) (II) (III) (A) I > II > III (B) I > II = III (C) I > III > II (D) III > I > II Q.41 Whichstatementabout the following equilibriumis/are true? Ph3C–H +   K O Me   K C Ph3 + MeOH (I) The reactionfavours the product formation. (II) Ph3CK is the dominant anionic species in this reaction. (III) Methanolis the weaker acidinthis reaction. (IV) The reactionfavours the reactant formation. (A) I & II (B) I, II & III (C) IV only (D) III & IV
12. ROUGHWORK Q.42 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.43 Correct order ofheat ofcombustionis: (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.44 Write correct order ofreactivityoffollowing halogenderivatives. (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.45 Correct orderofnucleophilicityoffollowinganions in polar proticsolvent is: (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.46 NO2 isinvolved in the formationofsmog and acid rain.Areaction that is important in the formation 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 willbe a tendencyto formmore NO and O3 (B) there will be a tendency to formmore NO2 and O2 (C) There will be a tendency to form more NO2 and O3 (D) There willbe no tendencyfor change because the reaction is at equilibrium Q.47 The equilibriumSO2Cl2(g) SO2(g) + Cl2(g) is attained at 250C in a closed container and Helium is introduced. Whichofthe following statement is correct (1) The concentrations of SO2, Cl2 and SO2Cl2 change (2) More chlorine is formed (3) Concentration ofSO2 is reduced (4) More SO2Cl2 is formed (A) 1, 2, 3 (B) 2, 3, 4 (C) 3, 4 (D) noneofthese Q.48 In the system LaCl3(s) + H2O(g) + heat LaClO(s) + 2HCl (g) equilibriumis established. More water vapour is added to re-establish the equilibrium. The pressure of water vapour is doubled. The factor bywhich pressure ofHClis changed is (A) 2 (B) 2 (C) 3 (D) noneofthese
14. ROUGHWORK Q.49 A smallobject placed ona rotatinghorizontalturntable just slips when it isplaced at a distanceof4 cm fromthe axis ofrotation. Ifthe angular velocity ofthe turn table is doubled, the object slips when its distance fromtheaxis ofrotation is (A) 8 cm (B) 4 cm (C) 2 cm (D) 1 cm Q.50 Asmallblock of mass mis released fromAinside the frictionless circular groove of radius 2 m onan inclined plane as shown in figure. The contact force between the block and inclined plane at point B is (A) 28 mg (B) 2.5 mg (C) 2 28 mg (D) 18.5 mg Q.51 Two isochoric cooling processAB and CD are shown in P-V diagramfor the same gas. In which case heat lost willbe more. (A)AB (B) same in both cases (C) CD (D) can't say Q.52 PV versusT graphofequalmasses ofH2, He and CO2 isshowninfigure. Choose thecorrect 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
15. ROUGHWORK Q.53 Two smooth cylindricalbars weighing W each lie next to each other in contact. Asimilar third bar is placed over the two bars as showninfigure. Neglecting friction, the minimumhorizontalforce oneach lower bar necessaryto keep themtogether is (A) W/2 (B) W (C) W/ 3 (D) W/(2 3 ) Q.54 A possible means for making an aeroplane invisible to radar is to coat the plane withan anti reflective polymer. Ifthe radar waves have a wavelength of3.0 cm and refractive index ofpolymer is n= 1.50. Thenwhatwillbethe minimumthickness ofcoating (hererefractive indexofaeroplanematerialis higher thanpolymer) (A) 0.5 cm (B) 1.0 cm (C) 0.25 cm (D) 1.25 cm Q.55 Ariver is flowing with velocity2 m/s.Aboat is moving downstream. Velocityofboat in stillwater is 3 m/s. A person standing on boat throws a ball vertically upwards w.r.t himself with a velocity of 10 m/s.At the top most point, the velocityofballw.r.t manstandingonboat, 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) noneofthese Q.56 An object starts moving at an angle of 45° with the principal axis as shown in the figure in front of a biconvexlensoffocallength+10cm. If denotesthe angle at whichimage starts to movewithprincipal axisthen (A)  = 4 3 (B)  = 2  (C)  = 4  (D)  = – 4 
16. ROUGHWORK For Problems 57 to 58 Parallellight beamofwavelength500 nmfalls ontwo narrowslit inYDSE at angle  = 300 as shownin figure. The distance between slit d=25×10–4 cm. On lower slit a transparent materialofthickness t = 15 × 10–3 cmis placed. The refractive index oftransparent material = 7/6. The interference patternappears on screen at distance D (D >> d), then Q.57 The centralmaximawilloccur onscreen (A) below point O (B) above point O (C) at point O (D) data's are insufficient to decide Q.58 How many number of fringes will pass through from point  = 0 (point 0). Ifwe remove transparent materialfromthe lower slit? (A) 50 (B) 25 (C) 12 (D) noneofthese Q.59 A concave mirror ofradius ofcurvature 40 cmformsanimage ofanobject placed on theprincipalaxis at a distance 45 cmin front ofit. Now ifthe systemis completelyimmersed in water ( = 1.33) then (A) the image willshift towardsthe mirror (B)themagnificationwillreduce (C) theimage willshift awayfromthe mirror and magnificationwillincrease. (D) the positionofthe image and magnificationwillnot change. Q.60 Imagine a hypotheticalmaterialwhose average temperature coefficient oflinear expansionis 0.1 /°C. Findthe fractionalincreaseinthe areaofathinsquareplate ofabove materialwhentemperature increase by 10°C. (A) 1 (B) 2 (C) 3 (D) None
17. ROUGHWORK Q.61 A particle ofmass m is projected at an angle of60° with a velocityof 20 m/s relative to the ground from a plank of same mass m which is placedonsmoothsurface. Initiallyplankwasatrest. Theminimumlength ofthe plank for which the ballwillfallon the plank itselfis (g = 10 m/s2) (A) 3 40 m (B) 3 20 m (C) 3 10 m (D) 3 60 m Q.62 Amanslowlypulls a bucket ofwater fromawellofdepthh. Ifthe mass ofthe uniformropeand bucket fullofwater are mand M respectively. The value ofwork done bythe man is (A) (m+M) gh (B)        M 2 m gh (C)        2 M m gh (D) None ofthe above Q.63 Ifthe mass ofblock is 1 kg and ahorizontalforce of 3 10 Nis applied horizontallyonthe block as showninthe figure. Thefrictionalforce acting onthe block is (A) zero (B) 3 10 N (C) 3 20 N (D) 5 N Q.64 Abeaker contains 200 g of water. The water equivalent of beaker is 20 gm. The initialtemperature of water in the beaker is 20°C. If440 g ofhot water at 92°C is poured in, then the finaltemperature, will be nearest to: (neglect heat loss) (A) 58°C (B) 68°C (C) 73°C (D) none
18. ROUGHWORK Q.65 The frictionforce acting between surfaces incontact in the adjoining figure is best represented by (A) (B) (C) (D) Q.66 Two particles havingpositionvectors m ) ĵ 5 î 3 ( r1    and m ) ĵ 3 î 5 ( r2     are moving with velocities ) j ˆ 3 î 4 ( v1    m/s and ) ĵ 7 î a ( v2    m/s. Iftheycollide after 2 sec, the value of'a' is (A) 2 (B) 4 (C) 6 (D) 8 Q.67 Inthebalancemachineshowninthefigure, whicharmwillmovedownward after thesystemis released (assuming string, armofbalance machine and the pulleyto be light) (A) left (B)right (C) remains stationary (D) noneofthese Q.68 Apoint moves onacircleofradius 2 meterand itsspeed dependsonthe distancecoveredas v = S  . Thenthetime takenbythe particle in making the fullcircle is (A) 2 sec. (B) 3 sec. (C) 4 sec. (D) none
19. ROUGHWORK Q.69 Aplane mirroroflength2 mis kept along the liney= –xasshowninthe figure.An insect having velocityof î 4 cm/s ismoving along the x-axis fromfar away. The time spanfor which the insect cansee its image will be (A) 50 sec (B) 25 sec (C) 2 25 sec (D) 2 50 sec Q.70 The PotentialEnergyU vs x curvefor a particle is shown infigure. Then the conservativeforce (F) vs xcurve willbe: (A) (B) (C) (D) Q.71 A converging beamofrays is incident on a diverging thinlens. Having passed through thelens the rays intersect at apoint 15 cmfromthe lens. Iflensis removed the point wherethe rays meet willmove 5 cm closer to the mounting that holds thelens. The focallengthoflens is (A) f = 10 cm (B) f = 15 cm (C) f = 30 cm (D) f = 40 cm Q.72 Two particles tiedto different light stringsare whirled in a horizontalcircle as showninfigure.The ratio oflength ofthe strings (L2/L1) so that theycomplete their circular path with equaltime period is (A) 2 3 (B) 3 2 (C) 1 (D) noneofthese
20. ROUGHWORK
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