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REVIEW TEST- 6 PAPER CODE : B INSTRUCTIONS 1. The question paper contains 45 questions and 15 pages. Each question carry 5 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, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207, He = 4, F=19. Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1. Select the correct alternative(s). (One or More than one is/are correct) [45 × 5 = 225] There is NEGATIVE marking. 1 mark will be deducted for each wrong answer. Q.1 The right hand derivative of f (x – 1) = 2x2 – 3x + 1 at x = k where k I, is (A) 4k + 1 (B) 2k + 1 (C) 2k – 1 (D) 4k – 3 5sin3 x cosx Q.2 Which of the following numbers is the maximum value of the function f (x) = (A) 5/8 (B) 3/4 (C) 1 (D) 5/2 tan2 x 1 , x R? Q.3 The equation x3 – 5 3 x = – 4 3 is satisfied by 8 7 17 23 (A) x = cos 18 (B) x = cos 18 (C) x = cos 18 (D) x = cos 18 Q.4 The number 916238457 is an example of nine digit number which contains each of the digit 1 to 9 exactly once. It also has the property that the digit 1 to 5 occur in their natural order, while the digit 1 to 6 do not. Number of such numbers are (A) 2268 (B) 2520 (C) 2975 (D) 1560 v(u z) Q.5 Let u, v, w, z be complex numbers such that | u | < 1, | v | = 1 and w = u z 1 , then (A) | w | 1 | z | 1 (B) | w | 1 | z | 1 (C) | w | 1 | z | 1 (D) | w | 1 | z | 1 x Q.6 A function f (x) satisfies f (x) = sin x + f '(t) (2 sin t – sin2t) dt then f (x) is 0 (A) x 1 sin x (B) sin x 1 sin x (C) 1 cos x cos x (D) tan x 1 sin x ROUGHWORK Q.7 If A and B are different matrices satisfying A3 = B3 and A2B = B2A, then (A) det (A2 + B2) must be zero. (B) det (A – B) must be zero. (C) det (A2 + B2) as well as det (A – B) must be zero. (D) At least one of det (A2 + B2) or det (A – B) must be

- 1. Class : XIII Time : 3 hour Max. Marks : 225 INSTRUCTIONS REVIEW TEST- 6 PAPER CODE : B 1. The question paper contains 45 questions and 15 pages. Each question carry 5 marks and all ofthem are compulsory. There is NEGATIVE marking. 1 markwillbe deducted for eachwrong 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 eachquestionbyfilling appropriate bubble(s) inyour OMR sheet. 3. Use onlyHB pencilfor darkening the bubble(s). 4. Use ofCalculator, Log Table, Slide Rule and Mobile is not allowed. 5. For example ifonly'B' choice is correct then, thecorrect 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 ofthe question in anyother manner (such as putting , cross , or partialshading etc.) willbe 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, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207, He = 4, F=19. Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1.
- 2. ROUGHWORK Select the correct alternative(s). (One or More than one is/are correct) [45 × 5 = 225] There is NEGATIVE marking. 1 markwillbe deducted for eachwrong answer. Q.1 The right hand derivative of f (x – 1) = 2x2 – 3x + 1 at x = k where k I, is (A) 4k + 1 (B) 2k + 1 (C) 2k – 1 (D) 4k – 3 Q.2 Which ofthe following numbers is the maximumvalue ofthe functionf (x) = 1 x tan x cos x sin 5 2 3 , x R? (A) 5/8 (B) 3/4 (C) 1 (D) 5/2 Q.3 The equation x3 – 4 3 x = – 8 3 is satisfied by (A) x = cos 18 5 (B) x = cos 18 7 (C) x = cos 18 17 (D) x = cos 18 23 Q.4 The number 916238457 is an example of nine digit number which contains each of the digit 1 to 9 exactlyonce. It also hasthe propertythat thedigit 1to 5 occur intheirnaturalorder, whilethedigit 1 to 6 do not. Number ofsuch numbers are (A) 2268 (B) 2520 (C) 2975 (D) 1560 Q.5 Let u, v, w, z be complex numbers such that | u | < 1, | v | = 1 and w = 1 z u ) z u ( v , then (A) | w | 1 | z | 1 (B) | w | 1 | z | 1 (C) | w | 1 | z | 1 (D) | w | 1 | z | 1 Q.6 A function f (x) satisfies f (x) = sin x + x 0 ) t ( ' f (2 sin t – sin2t) dt then f (x) is (A) x sin 1 x (B) x sin 1 x sin (C) x cos x cos 1 (D) x sin 1 x tan
- 3. ROUGHWORK Q.7 IfAand B are different matrices satisfyingA3 = B3 andA2B = B2A, then (A) det (A2 + B2) must be zero. (B) det (A – B) must be zero. (C) det (A2 + B2) as wellas det (A – B) must be zero. (D)At least one of det (A2 + B2) or det (A– B) must be zero. Q.8 Suppose we are given a point Pon theArgand plane represented by the complex number Z, moving anticlockwise along the circle with | z | = 2 from the point of complex number 2 + 0i to 0 + 2i. If = 2 Z 1 Z then the path described by Q which represents the complex number is (A) a line withgradient 1/3 passingthrough the origin. (B) a circle (C) a segment ofline 4x – 3 =0 with y varying from [0, 1/4] (D) a line 4x – 3 = 0 with y varying from [0, ) Q.9 Ifthe linepassing through(–2, 1, b) and (4, 1, 2) is perpendicular to the vector k̂ 2 j ˆ 3 î andisparallel to the plane containing the vectors k̂ c î and k̂ b j ˆ c thenthe ordered pair (b, c) is (A) 2 1 , 1 (B) (1, – 6) (C) (– 1, 0) (D) 2 1 , 1 Q.10 Acommitteeofthree persons isto be randomlyselectedfroma group ofthree menand two womenand the chair person willbe randomlyselected fromthe committee. The probabilitythat thecommittee will have exactlytwo women and one man, and that the chair person willbe a woman, is (A) 5 1 (B) 15 8 (C) 3 2 (D) 10 3
- 4. ROUGHWORK Q.11 A circle having centre (0, k) with k > 6 is tangent to the lines pair x2 – y2 = 0 and y = 6. The radius of the circle is (A) 6( 2 – 1) (B) 12 (C) 2 6 (D) 2 6 + 6 Q.12 The functiondefined as f (x) = n Lim 1 x if x 1 1 1 x 0 if x 1 0 x if x cos n n n n 2 . Which ofthe following does not hold good? (A) continuous at x = 0 but discontinuous at x= 1. (B) continuous at x = 1 but discontinuous at x= 0. (C) continuous both at x = 1 and x = 0. (D) discontinuous bothat x = 1 and x = 0. Q.13 The ends A and B of a rod of length 5 are sliding along the curve y = 2x2. Let xA and xB be the x-coordinate oftheends.At the moment whenAis at (0, 0) andB is at (1, 2)the derivative A B dx dx has the value equalto (A) 1/3 (B) 1/5 (C) 1/8 (D) 1/9 Q.14 Which ofthefollowing function(s) satisfythehypothesis ofRolle's theoreminthe stated interval? (A) f (x) = 1 – x2/3 in [–1, 1] (B) f (x) = 6 x x in [–6, 0] (C) f (x) = (x – 1)–2 in [0, 2] (D) f (x) = x3 – 3x2 + 2x + 5 in [0, 2] Q.15 The line which contains all points (x, y, z) which are of the form (x, y, z) = (2, –2, 5) + (1, –3, 2) intersects theplane 2x– 3y+ 4z = 163 at Pand intersects theYZ plane at Q. Ifthe distance PQ is b a where a, b are relatively prime and a > 3 then (a + b) equals (A) 23 (B) 95 (C) 27 (D) none
- 5. ROUGHWORK Take g = 10 m/s2 where ever required. Q.16 In the diagramshown, insteadystate (A) Charge on 1 f capacitor is 1 C (B) Charge on 2 f capacitor is 2 C (C) Charge on 3 fis zero (D) Potentialdifference across 2fcapacitor is 2 volt Q.17 A particle ofmass 'm' is projected with velocityu at an angle '' withthe horizontal. The coefficient of restitution foranyofits impact withthe smooth groundis e. (A)Totaltimetakenbythe particle before it stops moving verticallyis e 1 g sin u 2 (B) Total horizontaldistance moved inthe time beforeit stops moving verticallyis ) e 1 ( g 2 2 sin u2 (C)Average force on the particle over the time intervalin whichit makes first 'n'impacts with ground equals 2 mg (1 – e) directed upwards. (D) Average force on the particle over the time interval in which it makes first 'n' impact equals 2 mg (1 – e) directed downwards Q.18 The time period of a particle executing SHM is T. There is a point P, at a distance x from the mean position O. When the particle passes P towards OP (moving away from mean position O), it has speed V then find the time in which it return to P again (A) T (B) x 2 VT tan T 1 (C) Tsin–1 x VT (D) x 2 VT cot 2 T 1
- 6. ROUGHWORK Q.19 Whichofthe following is sufficient conditionfor finding theelectric flux E througha closed surface? (A) Ifthe magnitude of E is known everywhere on the surface (B) Ifthe totalcharge inside the surface is specified (C) Ifthe totalcharge outside the surface is specified (D) Onlyifthe location ofeachpoint charge inside the surface is specified Q.20 The spring is compressed bya distance a and released. The block again comes to rest when the spring is elongated bya distance b. During this process (A) work done by the spring on the block = 2 1 k(a2 + b2) (B) work done bythe spring on the block = 2 1 k(a2 – b2) (C) coefficient offriction= mg 2 ) b a ( k (D) coefficient offriction = mg 2 ) b a ( k Q.21 The electric potentialdue to aninfinite thinnonconducting sheet ofpositive chargedensityat a point located at a perpendicular distance Z fromthe sheet is (Assume V0 to be the potentialat the surface of sheet): (A) V0 (B) 0 0 Z V (C) V0 + 0 2 Z (D) V0 – 0 2 Z
- 7. ROUGHWORK Q.22 The figure shows, two point charges q1 = 2Q(>0) and q2 = –Q. The charges divide theline joining them in three parts I, II and III (A) Region III has a localmaxima ofelectric field (B) Region I has a localminima ofelectric field (C) Equilibriumpositionfor a test charge liesin regionII (D) The equilibriumfor constrained motionalongthe line joining thecharges is stable fora negative test charge Q.23 In displacement method, the distance between object and screen is 96 cm. The ratio oflength oftwo images formed bya convex lens placed between them is 4.84. (A) Ratio ofthe length ofobject to the lengthofshorter image is 11/5 (B) Distance between the two positions ofthe lens is 36 cm (C) Focallength of the lens is 22.5 cm (D) Distanceofthe lens fromthe shorter image is 30 cm Q.34 The net rate ofheat loss bya hot bodydepends upon. (A) temperature ofbody (B)temperatureofsurroundings (C) materialofthe body (D) natureofthe surface Q.25 Amanofmass M is carrying a ballofthe mass M/2. Themanis initially inthestate ofrest ata distance D fromfixed verticalwall. Hethrowsthe ballalong the floor towards the wallwith a velocityV with respect to earth at t = 0. As a result of throwing, the man also starts moving backwards. The ballrebounds elasticallyfromthe wall. The manfinally collects theball.Assuming friction to be absent. (A) The velocityofthe man + ballsystemafter the man has collected the ballis 3 V 2 (B) Linear impulse byballonman is 3 MV
- 8. ROUGHWORK (C) Linear impulse by ballon man is 6 MV (D) He catches the ball again at t = V D 4 Q.26 Two identicalblocks each ofmass 2M are joined bymeans of a light springofspring constant k.AmanofmassM is standing on one of the block as shown in the diagram. If man jumps horizontallywith a velocityV relative to block and horizontal surface issmooth, then (A) the maximumcompressionin the spring is 3 V k M 2 (B) man landsat horizontaldistance g h 2 V frominitialposition ofthe block (C) right blockloses contact withwallwhenthe elongationinspring is maximum (D) velocityofcentre ofmass oftwo blocks after 2M loses contact withwallis 6 V
- 9. ROUGHWORK Q.27 Acapacitorofcapacitance Cischargedto apotentialdifferenceV0. Thechargingbatteryis disconnected and thecapacitor is connected to a uncharged capacitor ofunknowncapacitance Cx. The finalpotential difference across the combinationisV, after the switchS is closed, then: (A) Cx = V V V C 0 (B) Finalenergystored is 2 1 CV0V (C) Heat generated in the circuit is 2 V V CV 0 0 (D) Heat generated in the circuit is 2 V CV0 Q.28 An ideal gas has molar heat capacity at constant pressure Cp = 5R/2. The gas is kept in a cylindrical vessel fitted with a piston which is free to move. Side walls of the container and the piston are non conducting. Mass ofthe frictionless piston is 9 kg. Initial volume of the gas is 0.0027 m3 and cross- section area ofthe piston is 0.09 m2. Theinitialtemperature ofthe gas is 300 K.Atmospheric pressure P0 = 1.05 × 105 N/m2.An amount of2.5 × 104 J ofheat energy is supplied to the gas bya heating coil, then (A) Initial pressure of the gas is 1.06 × 105 N/m2 (B) Finaltemperature ofthe gas is 1000 K (C) Final pressure of the gas is 1.06 × 105 N/m2 (D) Work done by gas is 9.94 × 103 J
- 10. ROUGHWORK Q.29 Theaccompanying figureshowstwo concentric conductingthinsphericalshells isolated fromeachother. The smaller shellhas radius band net charge +Q. The larger shellhas radius 2b and net charge –Q. IfR is the distance fromthe commoncenter, (A) the highest electricfield magnitude E occurs immediatelyoutside thesmaller shell(R~b) (B) the highest electricfield magnitude E occurs immediatelyoutside the larger shell(R~2b) (C)At R = b potentialis maximum (D)At R = 0 potentialis maximum Q.30 Auniformbar oflength 6a and mass 8mlies on a smooth horizontaltable. Two point masses mand 2m moving in the same horizontal plane with speeds 2v, and v, respectively, strike the bar (as shown in figure)andstickto the bar aftercollision. Denotingangular velocity,totalenergyand velocityofcentreof massby , E and Vc respectively, we have after collision (A) Vc = 0 (B) = a 5 v 3 (C) = a 5 v (D) E = 5 mv 3 2
- 11. ROUGHWORK Q.31 Whichoffollowingreactionproduct is Diastereomer. (A) 4 2 CCl Br (B) H ) ii ( NaCN ) i ( (C) 4 CCl HBr (D) Et | Ph CH CH CH CH3 peroxide HCl Q.32 Select thecorrect statement (A) Resonance energyis temperature dependent (B) 4d &5d series metals forms low spin complex (C) Cisplatinexpress geometricalisomerism (D) Benzene reacts with CrCl3 andforms organometallic compound Q.33 Whichamong thefollowing are correctlymatched (A) 3 2 NH / NaNH (B) 2 2 ZnCl HCl O C H (C) O Ac HNO 2 3 (D) 3 3 NO C CH || O
- 12. ROUGHWORK Q.34 The correct order ofenergies ofd-orbitals ofmetalionin a square planar complex is (A) dxy = dyz = dzx > 2 2 y x d = 2 z d (B) 2 2 y x d = 2 z d > dxy = dyz = dzx (C) 2 2 y x d > 2 z d > dxy > dyz = dzx (D) 2 2 y x d > dxy > 2 z d > dzx = dyz Q.35 Inthegivenreaction: [X] [X]is: (A) 2 moles (B) (C) one mole (D)Allofthese Q.36 Select thecorrect statement (A) [Fe(NO)(H2O)5]SO4 is coloured because ofd–d transition (B) [Fe(NO)(H2O)5]SO4 is coloured because of charge transfer (C) [Fe(NO)(H2O)5]SO4 is brown ring (D) [Fe(NO)(H2O)5]SO4 is high spin complex Q.37 Select thecorrect statement(s): (A)G > 0 for oxidation-reduction reaction (Redox) performedinelectrolytic cell (B) The rate constantsofthe forward &reverse reactions are equalat chemicalequilibrium. (C) Molarconductivityfor a strong electrolyte increases as theelectrolyte concentration increases. (D) Ac 228 89 is a member of 4n + 3 series.
- 13. ROUGHWORK Q.38 (A) NaOH Reactant (A) is (A) 3 5 2 3 CH C ) CH ( C CH | | | | O O (B) H C ) CH ( C CH | | | | O O 4 2 3 (C) H C ) CH ( C H | | | | O O 5 2 (D) OH CH ) CH ( C CH | | O 2 4 2 3 Q.39 Saturated solutionofSO2 is heated at 150°C ina closed container. The product obtained is treated with BaCl2 solution. What is/are the most suitable observation(s) (A) No ppt. (B) whiteturbidity (C) evolutionofSO2 (D) The turbiditybecomes white ppt Q.40 3 2 3 CH CH C CH | | O 2 2N CH A (Major) H CO CH 3 3 B (Major) Product B is: (A) 3 2 2 3 CH CH CH C O CH | | O (B) 3 2 2 3 CH CH CH O C CH | | O (C) 3 2 2 3 CH CH O C CH CH | | O (D) 3 2 3 CH CH O C CH | | O Q.41 Which reactionis(are) possible (A) MgCl2 + NaNO3 (B) BaSO4 + HCl (C) ZnSO4 + BaS (D) BaCO3 + CH3COOH
- 14. ROUGHWORK Q.42 5 PCl (A) Identifyproduct (A). Name ofthe reaction. (A) C NH | | O Cl, Beckmann rearrangement (B) NH C | | O Cl, Hoffmannbromamide reaction (C) C NH | | O Cl, Hoffmannbromamide reaction (D) NH C | | O Cl, Beckmannrearrangement Q.43 Which ofthe following complex are coloured (A) MnO4 – (B) CrO4 2– (C) Cr2O7 2– (D) MnO4 2– Q.44 Compound (X) C4 H8 O, whichgives2,4-Dinitrophenylhydrazine derivative andnegative haloformtest. (A) 3 2 3 CH CH C CH | | O (B) 3 3 CH | CHO CH CH (C) (D) CH3 – CH2 – CH2 – CHO
- 15. ROUGHWORK Q.45 Which ofthefollowing statements is/aretrue (A) In Ferrocyanide ion, the effective atomic number is 36 (B) Chelating ligandsare atleast bidentate ligands (C) – ] ) NH ( ) CN ( CrCl [ 2 3 2 2 and [CrCl3(NH3)3] both have d2sp3 hybridisation (D)As the number ofrings incomplex increases, stabilityofcomplex(chelate) also increases