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PART TEST- 1 Class : XII (Nucleus) Time : 3 hour Max. Marks : 300 INSTRUCTIONS 1. The question paper contains TWO PARTS. PART -A (Only one alternative correct) contains 60 questions & each carry 3 Marks. PART - B (One or more alternative correct) contains 24 questions & each carry 5 Marks. 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 for each question by filling appropriate bubble in your answer sheet. 3. Use only HB pencil for darkening the bubble. 4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed. 5. The answer of the questions must be marked by shading the circles against the question by dark HB pencil only. 6. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only. For example if only 'B' choice is correct then, the correct method for filling the bubble is A B C D the wrong method for filling the bubble are (i) A B C D (ii) A B C D (iii) A B C D The answer of the questions in wrong or any other manner will be treated as wrong. USEFUL DATA Atomic weights: 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, Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1 Seelct the correct alternative. Choose only one. cos6x 6 cos4x 15cos2x 10 dy Q.1 If y = cos5x 5cos3x 10cosx , then dx = (A) 2 sinx + cosx (B) –2sinx (C) cos2x (D) sin2x Q.2 If d2x dy 3 dy2 dx + d2y dx2 = K then the value of K is equal to (A) 1 (B) –1 (C) 2 (D) 0 Q.3 If y = at2 + 2bt + c and t = ax2 + 2bx + c, then d 3y dx3 equals (A) 24 a2 (at + b) (B) 24 a (ax + b)2 (C) 24 a (at + b)2 (D) 24 a2 (ax + b) Q.4 If (y2 – 5y + 3) (x2 + x + 1) < 2x for all x R, then the interval in which y lies is 5 5 5 5 2 (A) , (B) (–, –2] (C) 2, 3 (D) (1, 4) Q.5 If x, y, z are in A.P., ax, by, cz are in G.P. and a, b, c are in H.P. then (A) x y = a c (B) x z a c (C) x z b c (D) none of these y x c a z x c a z x c b Q.6 If a + b + c = 3 and a > 0, b > 0, c > 0, then the greatest value of a2b3c2 is (A) 310 ·24 77 (B) 39 ·24 77 (C) 38 ·24 77 (D) none of these ROUGH WORK Q.7 The general value of x satisfying the equation 2cot2x + 2 cotx + 4cosecx + 8 = 0 is π (A) n – 6 π (B) n + 6 π (C) 2n – 6 π (D) 2n + 6 Q.8 If f(x) satisfies the equation for all real x, then f ( x 3) 5 5 f (x 4) 4 6 f ( x 1)(x 2) (x 1) 2 5 = 0 15 (A) f(x) is not periodic

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- Class : XII (Nucleus) Time : 3 hour Max. Marks : 300 INSTRUCTIONS 1. The questionpaper contains TWO PARTS. PART -A (Only one alternative correct) contains 60 questions & each carry3 Marks. PART - B (One or more alternative correct) contains 24 questions &each carry 5 Marks. All of themare compulsory. There is NEGATIVE marking. 1 mark willbe deducted for each wronganswer. 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 for each questionbyfilling appropriate bubble inyour answer sheet. 3. Use onlyHB pencilfor darkening the bubble. 4. Use ofCalculator, Log Table, Slide Rule and Mobile is not allowed. 5. Theanswerofthequestionsmustbemarkedbyshadingthecirclesagainst thequestionbydarkHBpencilonly. 6. The answer(s) ofthe questions must be marked byshading the circles against the questionbydark HB pencilonly. For example ifonly'B' choice is correct then, thecorrect method for filling the bubble is A B C D the wrong method for filling thebubble are (i) A B C D (ii) A B C D (iii) A B C D The answer ofthe questions inwrong or anyother manner willbe treated as wrong. USEFUL DATA Atomic weights: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, Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1 PART TEST-1 O B J EC T I V E
- ROUGH WORK Seelct the correct alternative. Choose only one. Q.1 If y = cos cos cos cos cos cos 6 6 4 15 2 10 5 5 3 10 x x x x x x , then dy dx = (A) 2 sinx + cosx (B) –2sinx (C) cos2x (D)sin2x Q.2 If d x dy dy dx 2 2 3 + d y dx 2 2 = K then the value of K is equal to (A) 1 (B) –1 (C) 2 (D) 0 Q.3 If y = at2 + 2bt + c and t = ax2 + 2bx + c, then d y dx 3 3 equals (A) 24 a2 (at + b) (B) 24 a (ax + b)2 (C) 24 a (at + b)2 (D) 24 a2 (ax + b) Q.4 If (y2 – 5y+ 3) (x2 + x + 1) < 2x for all x R, then the interval in which ylies is (A) 2 5 5 , 2 5 5 (B) (–, –2] (C) 3 2 , 2 (D) (1, 4) Q.5 If x, y, z are inA.P., ax, by, cz are in G.P. and a, b, c are in H.P. then (A) x y y x = a c c a (B) a c c a x z z x (C) b c c b x z z x (D) noneofthese Q.6 If a + b + c = 3 and a > 0, b > 0, c > 0, then the greatest value of a2 b3 c2 is (A) 7 4 10 7 2 · 3 (B) 7 4 9 7 2 · 3 (C) 7 4 8 7 2 · 3 (D) noneofthese
- ROUGH WORK Q.7 The generalvalue ofx satisfying the equation 2cot2 x+ 2 3 cotx + 4cosecx + 8 = 0 is (A) n – 6 (B) n + 6 (C) 2n – 6 (D) 2n + 6 Q.8 Iff(x)satisfies the equation 15 6 5 5 4 5 ) 1 ( ) 2 )( 1 ( ) 4 ( ) 3 ( 2 x x x f x f x f = 0 for allrealx, then (A) f(x) is not periodic (B) f(x) isperiodic withperiod 7 (C) f(x) is periodic with period 1 (D) f(x) is anodd function Q.9 Ifxi = aibici where i= 1, 2, 3 are three digit positive numbers suchthat each xi is a multiple of19, then for some integer n, A = 3 2 1 3 2 1 3 2 1 c c c b b b a a a is ofthe form of (A) 19n (B) 19n + 1 (C) 19n + 2 (D) 19n + 3 Q.10 The derivate oftan–1 x x 1 1 w.r.t. sin–1 x is (A) 1 (B) 2 1 (C) – 2 1 (D) none
- ROUGH WORK Q.11 If y = (1 – x)– e–x x 1 then (A) (1– x) y + (1–x)y – y = 0 (B) (1– x) y – (1+x)y – y = 0 (C) (1– x) y + (1+x)y – y = 0 (D) (1– x) y + (1+ x)y + y = 0 Q.12 Iff(x) =[n+ psinx] 0 < x<, where nis integer &pis prime, [ ] denotesGIF thenno. ofpoints at which the functionis nondifferetiable (A) 2p – 1 (B) p – 1 (C) p (D) 2p + 1 Q.13 Let f(x) is defined in [–2, 2] by 2 0 1 , 4 min 0 2 1 , 4 max ) ( 2 2 2 2 x x x x x x x f Thenf(x) is (A) Continuity&differentiabilityat allpoints (B) disc at 1 point &non differentiabilityat more than 1 point (C) nondifferentiabilityat more than1 point &continuityat allpoints (D) none Q.14 Let f(x) is 2 1 sin101 x x where [x] denotes step up function then f(x) is (A) both odd as well as even (B) neither odd nor even (C) odd function (D) evenfunction Q.15 Let and be the roots of function f(x) = x3 + x2 – 5x – 1 = 0. Then [] + [] + [], where [ ] denotes GIF = (A) 1 (B) –2 (C) –3 (D) 4
- ROUGH WORK Q.16 The summation ofnon real roots of the equation x4 + 3x3 – 2x2 + 3x + 1 = 0 is (A) 1 (B) – 1 (C) 0 (D) – 3 Q.17 The valueofthe determinant cos( ) cos( ) cos( ) sin( ) sin( ) sin( ) sin( ) sin( ) sin( ) x A x B x C x A x B x C B C C A A B is (A) –[sin2(A– B) + sin2(B – C) + sin2(C –A) ] (B) sin2(A+B) + sin2 (B+C) + sin2 (C+A) (C) O (D) None Q.18 If every solution of the equation 3 cos2x – cos x – 1 = 0 is a solution of the equation a cos22x + bcos2x – 1 = 0. Then the value of (a + b) is equal to (A) 5 (B) 9 (C) 13 (D) 14 Q.19 n n n n n Lim 1 sin 1 where Q (A) 1 (B) – (C) e1– (D) e1+ Q.20 Iff (x) = cosec–1(cosecx)and cosec(cosec–1x) are equalfunctions thenmaximumrange ofvaluesofxis (A) 2 , 1 1 , 2 (B) 2 , 0 0 , 2 (C) , 1 1 , (D) 1 , 0 0 , 1
- ROUGH WORK Q21. Amixture gives three precipitates X, Y, and Z when NH4OH is added in presence ofNH4Cl. For the separationofthesefollowing scheme is followed. Filtrate P, Q, and R are respectively. (A)Al(OH)3, Fe(OH)3, Cr(OH)3 (B) Fe(OH)3,Al(OH)3, Cr(OH)3 (C) Al(OH)3, Na2CrO4, Fe(OH)3 (D) NaAlO2, Na2CrO4, FeCl3 Q22. What volume of 0.2M Ba(MnO4)2 solutionis required for complete oxidation of 25g of89.6% pure FeCr2O4 in acidic medium. (Given Fe = 56, Cr = 52, Ba = 137, Mn = 55, O = 16) (A) 400 ml (B) 200 ml (C) 350 ml (D) None ofthese Q23. Consider the reaction Whichofthefollowing is true forYand Z. (A) Y is CF2 = CCl2 and Z is OEt CCl CF | 2 3 (B) Y is CF3-CHCl2 and Z is CF2 = CCl2 (C) Y is CF3 – CDCl2 and Z is CF2 = CCl2 (D) Y is CF2 = CCl2 and Z is CF3 – CDCl2
- ROUGH WORK Q24. Column I (Species) Column(II) (Hybridisation) (I) PCl5 (P) sp2 (II) BrF5 (Q) sp3 (III) NO2 – (R) sp3d2 (IV) SO3 2– (S) sp3d Choose the correct alternative. I II III IV I II III IV (A) P S R Q (B) R S Q P (C) R S P Q (D) S R P Q Q25. Which ofthe following statement is correct about O2, O2 +, O2 – and O2 2– (A) Bond order ofO2 is greater than O2 + whereas less than O2 – and O2 2– and both are paramagnetic. (B) Bond order of O2 2– is less than that of O2 + whereas greater than that of O2 and O2 – and O2 2– is diamagnetic and O2, O2 + and O2 – are paramagnetic. (C) Bond order ofO2 + is greater than that ofO2, O2 – and O2 2–, except O2 2– whichis diamagnetic, all other are paramagnetic. (D) None ofthese Q26. The magnitic moment oftwo ions Mx+ and My+ ofanelement M (Z = 26) is foundto be 5.916 B. M. If x> ythenwhich ofthe following statement is correct (A) My+ is more stable than Mx+ (B) Mx+ is more stable than My+ (C) Bothare equallystable (D) None ofthese Q27. Consider thefollowing molecules. (I) (II) (III) (IV) PBr3Cl2 (A) = 0 for I, II and III only (B) = 0 for II and III only (C) = 0 for II, III and IV only (D) = 0 for allthe four. .
- ROUGH WORK Q28. Whichofthefollowing statements is correct (A) Powerfulnucleophile increases the rate ofSN2 however it decreases the rate ofSN1 reaction. (B) InEimechanismeliminationaccordingto saytzeff. (C) Rate ofsolvolysis of is more then that of (D) None is correct Q29. O H II NaHCO aq I 3 3 ) ( ) ( A O H Br 2 2 B (white ppt. of B) Compound 'B' is (A) (B) (C) (D)
- ROUGH WORK Q30. 3 2 HNO HNO A O H KOH 2 / B O H Br 2 2 C DMF SOCl / 2 D H O H NaOH 2 G MeI II NaH I ) ( ) ( F O CO CF 2 3 ) ( E H is usedfor the preparation of"Antileuckemiadrug" H is (A) (B) (C) (D)
- ROUGH WORK Q31. PhLi C9H11N PhLi X 'X' can be (A) (B) (C) (D) Q32. ne diazometha N CH 2 2 X + Y Y Both X andYare functionalisomers. Both X &Yare (A) & (B) & (C) & (D) &
- ROUGH WORK Q33. Anidealgasissubjectedto thechangeaccording to thegivencurve, showing thedependenceofpressure on absolutetemperature for constant moles. When the gas is being heated (A) compressiontakes place (B) expansiontakes place (C) can't say (D) neither compressionnor expansion Q34. Inthe followingseries ofelectronicallysaturatedand isoelectric ions, the observedX–O bond distances have beendetermined: Ion X–O Bond length(Å) SiO4 4– 1.63 PO4 3– 1.54 SO4 2– 1.49 ClO4 – 1.46 The order of p–d bond character (A) SiO4 4– > PO4 3– > SO4 2– > ClO4 – (B) SiO4 4– > ClO4 – > SO4 4– > PO4 3– (C) ClO4 – > SO4 2– > PO4 3– > SiO4 4– (D) ClO4 – > PO4 3– > SO4 2– > SiO4 2– For Question No. 35 - 36 For two gasesA& B, Pv/sV isothermare drawn at TKas shown. TA &TB are criticaltemperatures of Aand B respectively. Q35. Whichofthefollowing is TRUE? (A) TA < T < TB (B) TA > T > TB (C) TA > TB > T (D) None ofthe above
- ROUGH WORK Q36. The correct statement(s) is (are) (I) Pressure correctiontermwillbe more negligible for gas Bat T K. (II) The curve for gas B willbe of same shape as for gasAifT > TB (III) gasAwill show same Pv/s V curve as ofgas 'B' ifT > TA (A) III only (B) II and III (C) II only (D)all Q37. The correct order ofatomic orbitals in terms ofenergybetween 8s and 8p orbitalare (A) 7d, 6f (B) 5g, 6f, 7d (C) 6d, 7f (D) 4h, 5g, 6f, 7d Q38. The bond lengthofthe S–O bond is maximumin which ofthe following compound. SOBr2, SOCl2, SOF2 (A) SOCl2 (B) SOBr2 (C) SOF2 (D)Allhave same length Q.39 For reversible system X(g) Y(g) + Z(g), a quantity of X was heated at constant pressure P at a certain temperature. Theequilibriumpartialpressure ofX was found to beP/7. What is the value ofKp at giventemperature (A) 6P/7 (B) 9P/7 (C) 36P/7 (D) 6P Q.40 Whichofthe following graphscorrectlyrepresents the variationof = V dP dV T / withPfor anideal gas at constant temperature (A) (B) (C) (D)
- ROUGH WORK Q.41 Atube oflength L isfilled completelywithanincompressible liquid ofmassM and closed at bothends. The tube isthenrotated ina horizontalplane about one ofits endswitha uniformangular velocity.The force exerted bythe liquid at the other end is: (A) ML2/2 (B) ML2 (C) ML2/4 (D) ML22/2 Q.42 Ablock ofmass 15kg isresting ona roughinclinedplane as showninthe figure. The block is tied up bya horizontalstring whichhas a tension of50 N. The friction force betweenthe surfaces ofcontact is (g = 10m/s2) (A) 2 50 N (B) 2 100 N (C) 50 N (D) noneofthese Q.43 Asimple pendulumconsists ofa smallwoodenbobofmassm andlight string oflengthl.Abullet ofmass m1 is firedhorizontallytowards the pendulumwitha speed v1 . Thebullet emerges out ofthebob witha speed v1/3 and the bob just completes motion along a verticalcircle. Then v1 is : (A) gl m m 5 1 (B) gl m m 5 2 3 1 (C) gl m m 5 3 2 1 (D) gl m m 1 Q.44 Particles P and Q ofmasses 20 gmand 40 gmrespectivelyare projected from the positions Aand B on the ground. The initial velocities of P and Q make angles of450 and 1350 respectivelywiththe horizontalas showninthe figure. Each particle has an initial speed of49 m/sec. The separationAB is 245 m. Both particles travelin the same verticalplane and undergo acollision.After the collisionPretraces its path. The position ofQ fromAwhen it hitsthe ground is: (A) 245m (B) 3 245 m (C) 2 245 m (D) 2 245 m
- ROUGH WORK Q.45 Auniformrodofmass M islying inthe stateofrest onaroughhorizontalplane. The rod being rotated in vertical plane very slowly by the help of a variable force F always perpendicular to the lengthofthe rod such that rod can rotate about the point O without anyangular acceleration. The maximumvalue of static frictionforce acting at the point O isequalto (A) Mg (B) 2 Mg (C) 4 Mg (D) none Q.46 Asoliduniformsphere is rollingwithout slipping onafrictionless surface, showninfigure with a translationalvelocityvm/s. Ifit is to climb on the inclined surface thenv should be: (A) > gh 7 10 (B) > gh 2 (C) 2gh (D) 7 10 gh For Problem 47 to 49 Aboat ofmass M sails with velocityv0 iˆ.At t = 0, its engine stops, and at the same time a ballofmass m(m< < M) is thrown from the boat with initial velocityu ĵ . Here x - direction is horizontaland yis vertically up. The water exerts a friction drag force proportional to the boat's velocity (v), so that i Kv F ˆ , where Kis positive constant. The acceleration ofthe boat canbe written as: i M Kv a ˆ or i M Kv dt dv ˆ i Ce v M Kt ˆ /
- ROUGH WORK Where C isa constant emerging dueto integrating. Now assumethat ballis observedfromthe reference frameofboat (X'Y'). The originofthisreference framecoincidedwiththestaticframe (XY)at t =0. The accelerationoftheballinthe referenceframe ofboat canbewritten as j a i a a y x ˆ ' ˆ ' ' and inthe static frame it canbe written as j a i a a y x ˆ ˆ . Q.47 The value ofconstant C is (A) v0/2 (B) v0 (C) v0(M/m) (D) v0 (m/M) Q.48 Values ofax and ax' respectivelyare: (A) ax = 0; ax' = M Kt e M Kv / 0 (B) ax = 0; ax' = M Kt e M Kv / 0 (C) ax = ax' = M Kt e M Kv / 0 (D) ax = 0; ax' = M Kt e M Kv / 0 Q.49 The horizontalcomponent ofball's velocityas seenfromthe boat willbe: (A) v0e–Kt/M (B) v0 (C) v0eKt/M (D) v0(1 – e–Kt/M) Q.50 Aconcave anda convexlens havingthe focallengthof20 cm&10cmrespectivelyand areput inmutual contact to formlens combination. Thecombinationis usedto see anobject 5cmhighkept at 20 cmfrom the lens combination.As compared to the object, the image willbe (A) realmagnified and inverted (B) real, smaller and errect (C) virtual, smaller and errect (D) noneofthese Q.51 Whenthe plane surface ofplano-convex lensis silvered, the lens behaves like a concavemirror offocal length30cm, but whentheconvexsurface is silvered, it behaves like aconcave mirror offocallength10 cm. Therefractive index ofmaterialoflens is (A) 3 4 (B) 2 (C) 2 3 (D) 1.5
- ROUGH WORK Q.52 One face of a prism of refractive angle 300 and ref. index 2 is silvered. At what angle(i)must arayoflight fallonthe unsilveredfacesothat after refraction into the prismand reflectionat the silvered surface it retraces its path (A) 300 (B) 450 (C) 600 (D) none Q.53 The distance between an object and screen is d. Aconvex lens of focallength f is placed between the object and the screen. Ifmis the transverse magnificationofimage then (A) f = 2 1 m md (B) f = 2 1 m m d (C) f = m md 1 (D) f = m m 2 1 d Q.54 Ablock of 4 kg is placed on a plank having mass 8 kg. Aforce F = 20 N is applied on plank. Then find the frictionforce between 4 kg block and plank. Here coefficient offriction between 4 kg & 8 kg is = 0.4 (g = 10m/s2) (A) 3 10 N (B) 16 N (C) 3 20 N (D)zero Q.55 The diagramshows a thinuniformsemicircular disc ofmass M and radius R. What is the moment ofinertia ofdisc about an axis in the plane ofdisc (showninfigure) (A) 3 MR2 (B) 4 MR2 (C) MR2 (D) none Q56. Adisk rollswithout sliding ona horizontalsurface. Iftherelative velocitybetween the pair of point A1B1, A2B2 andA3B3 are V1, V2 and V3 respectively then (A) V1 = V2 = V3 (B) V1 > V2 > V3 (C) V1 < V2 < V3 (D) Data's are insufficient to decide
- ROUGH WORK Q57. Aparticle is projected towards a fixed wallfrompointA(at a distance 'x' fromthe wall) and collides elastically. IfR = horizontalrange inabsence ofwallthentotaltime offlight willbe minimumif (A) x = R/2 (B) x= R/ 2 (C) x = 2 R (D) independent ofx Q58. Two ends ofa helicaluniformspring offorce constant K and mass M are projected withvelocityV initsnaturalstate (as shownin figure). The maximumextensioninspring willbe (A)V K m (B) V K m 3 (C) K m 2 (D) V K m 6 Q59. A particle P with a mass 2.0 kg has position vector r = 3.0 m and velocity = 4.0 m/s as shown. It is accelerated bythe force F= 2.0 N.Allthree vectors lie ina common plane. The angular momentum vector about origin O is (A) 12 kgm2 /s out of the plane ofthe figure (B) 12 kg m2 /s into the plane of the figure (C) zero (D) 24 kgm2 /s out of the plane ofthe figure Q60. A small bead of mass m moving with velocity v gets threaded on a stationarysemicircular ring of mass mand radius R kept on a smooth horizontaltable. The ring can freelyrotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity ofthe system? (A) v/R (B) 2v/R (C) v/2R (D) 3v/R
- ROUGH WORK More than one alternative(s) Q.1 Whichofthefollowing statements are correct? (A) IfAis a nonsingular matrix of order n then |adjA| = |A|n (B) IfAis a nonsingular matrix oforder n then 2 ) 1 ( | | | ) ( | n A A adj adj (C) adj (KA) = Kn - 1 (adj A) (D) maximumno. ofdistinct entries ina symmetric matrixoforder nis 2 ) 1 ( n n . Q.2 If x satisfies log2x + logx2 = 4, then log2x can be equalto (A) tan 12 (B) cot 12 (C) tan 8 (D) cot 8 Q.3 Value of the expression log1/2(sin6° · sin 42° · sin45° · sin 66°· sin 78°) (A) lies between 4 and 5 (B) is rationalwhichis not integral (C) isirrationalwhich is a simple surd (D) is irrationalwhichis amixed surd. Q.4 In a triangleABC, altitude fromits vertex meet the opposite sides in D, E and F. Thenthe perimeter of the triangleDEF, is (A) 2 R 4 abc (B) R 2 (C) r ) c b a ( R (D) R rs 2 where is the area ofthetriangleABC and allother symbols have their usualmeaning. Q.5 Let x1, x2 are the roots ofthe quadratic equation x2 + ax+ b = 0 where a and bare complex quantities and | x1 | = | x2 | = 1. If y1 and y2 are the roots of the quadratic equation y2 + | a |y + | b | = 0 then (A) y1y2 = 1 (B) | a | 2 (C) | y1 + y2 | 2 (D) | y1 | and | y2 | are reciprocal of each other
- ROUGH WORK Q.6 Which ofthefollowing statements are correct (A) If y = xn (acos(lnx) + bsin(lnx)) and x2D2y + (1 – 2n)x Dy + Ky = 0 then the value of K is 1 + n2 (B) Let f(x) = cot–1 (x2 + 4x +2 – ) be a function defined R 2 , 0 then complete set ofvalues of for which f(x) is onto is 2 17 1 . (C) Iff(x) = x x x | | log ] 1 [ where [ ] denotes step up function thenrange offis singleton (D) The range ofthe function f(x) = tan–1 x x 1 1 – tan–1x consists ofone element Q.7 The realsolution ofthe equation 2 2 2 2 5 1 2 2 x x x is (A) Naturalnumberbut not prime (B) Compositenaturalnumber (C) Rationalnumber (D) Integer Q.8 Iff(x) = n n n n n n n x x x x b x a x Limit 1 tan sec 1 sin sin is continuous at x= 1 thenwhich ofthefollowing relations are incorrect (A) a + b = 0 (B) a – b = 0 (C) a + b = 1 (D) a + b = –1
- ROUGH WORK Q9. In which ofthe following case configurationabout chiralC* is retained : (A) NaH X Br CH3 Y (B) 2 SOCl X Na MeO Y (C) 3 PCl X Na MeO Y (D) MeOH H / Q10. X A A O H by followed MgBr CH eq 3 3 . 1 [X] willbe (A) + H + (B) Ph–CH2–Br (C) HCN (D)
- ROUGH WORK Q11. In a mass spectrometry experiment, various ions H+, Li+, O2+ & 3 N were projected with a same velocityintoa same magneticfieldzone (allignedperpendicular to the directionofvelocity). Thesheet on whichtheyare striking is pierced at certain points(marked as H1, H2 etc.) as showninthe diagram.It is known that H+ comes back to zone-I from H2 when projected from H1. Mark out the correct options. (A) Out ofallremaining ions when projected fromH1, only 3 N willcome back to zone-I. (B) When allthe remaining ions were projected fromH2, onlyO2+ willcome back in zone-I. (C) When allthe remaining ions were projected fromH3, none ofthe themwillcome back to zone-I. (D) When allthe remaining ions wereprojected fromH4, none ofthe themwillcome back to zone-I. Q12. In the following six electronic configuration (remaining inner orbitals are completelyfilled). Mark the correct option(s). C–I C–II C–III C–IV C–V C–VI (A) Stability order : C–II > C–I & C–IV > C–III (B) Order of spin multiplicity : C–IV > C–III = C–I > C–II (C) C–V violates all the three rules of electronic configuration (D) IfC–VI representsAthenA2+ whenkept near a magnet faces weak repulsions (actsas dimagnetic).
- ROUGH WORK Q13. Following represents the Maxwell distribution curve for an ideal gas at two temperatures T1 & T2. Whichofthefollowing option(s) are true? (A) Total area under the two curves is independent of moles of gas (B) If dU1= f Umps1 & dU2 = f Umps2 then A1 = A2 (C) T1 > T2 and hence higher the temperature, sharper the curve. (D) The fraction of molecules having speed = Umps decreases as temperature increases. Q14. Whichofthefollowing statement(s) is(are) correct: (A) The correct order ofreactivitytowards nitration is C6H6 = C6D6 = C6T6 (B) The correct order of C–O bond length in CO, CO2 and CO3 2– is CO < CO2 < CO3 2– (C) The correct order of acidic strength is H3PO4 < H3PO3 < H3PO2 (D) noneofthese Q15. An equilibrium mixture contains 4 moles of PCl5, 2 moles PCl3 and 2 moles of Cl2 at a particular temperature. 4 moles of N2 is added in the equilibrium mixture. Which of the following are correct regarding theabove equilibrium. (A) The value ofKp does not change on additionoffurther 4 moles ofN2 at constant pressure (B) The equilibriumshift to forward directionwhentemperature is raised. (C) There isno effect ofaddition offurther 8 moles ofN2 at equilibriumat constant volume. (D) Whenthe pressure ofthe equilibriummixture is doubled, the degree ofdissociationis also doubled.
- ROUGH WORK Q16. Whichofthe following are incorrect statements (A) KHF2 exist as K+ , H+ and F– in aqueous solution. (B) The correct order ofsolubilityofLithiumhalides is LiF> LiCl> LiBr > LiI (C) The equivalent mass ofFe2 (S3 )3 , when it is converted to Fe2 O3 and SO4 2– is 60 M (where M is molar mass of Fe2 (S3 )3 ) (D) noneofthese Q17. Select the correct alternative(s). The power of a convex lens (R.I. = 1.5) (A) will decrease on immersing in water (B) will increase on immersing in water (C) is less for violet rays compared to red rays (D) is +10 D if it forms the image ofan object placed at 12 cm, at a distance of 60 cmon the other side. Q18. The line PQ in the ray diagram represents a thin lens &AB is a principal axis. Then lens is (A) converging (B) diverging (C) bi-concave (D) concavo-convex Q19. A particle of mass 3 kg is moving under the action ofa centralforce whose potential energyis given by U(r) = 10r3 Joule here r is in meter. If radius of orbit of particle r = 10 m then (A) the energy of particle is 2.5 × 104 Joule (B) The energy of particle is 0.5 × 104 Joule (C)Angular momentum of particle about the centre is 3000 kg–m2 /s (D)Angular momentum of particle about the centre is 1000 kg–m2 /s
- ROUGH WORK Q20. A bobbin of mass m and moment of inertia I relative to its own axis is being pulled along a horizontalsurface bythe light string tightlywrapped as shown in figure. There is no slipping on the surface throughout the motion (A) The angular velocity of bobbin when string is pulled horizontally with velocity V is= r V 3 (B) The angular velocity of bobbin when string is pulled horizontally with velocity V is= r V (C) If string is pulled by horizontal acceleration a. Then tension in string is T = 9 a 2 4 r I m (D) If string is pulled by horizontal acceleration a. Then tension in string is T = 2 2 2 a m r I Q21. Ahollow uniformsphericalballis giveninitialpushup aninclined ofinclination angle . The balls rolls purely. The coefficient of static friction between the ball and incline is . During its upwards journey (A) friction acts up along the incline (B) friction acts down along the incline (C) > 5 2 tan (D) > 7 2 tan
- ROUGH WORK Q22. Uniformsquareplate is connected to two identicalverticalidealsprings (as shown infigure) &systemisin equalibrium. Suddenlytheright spring is removed, thenthenet accelerationofpointAimmediatelyafter removing right springis (A) 2 3 g (B) 2 g (C) 8 5 g (D) 4 3 g Q23. A smooth track in the form of a quarter circle of radius 6 m lies in the vertical plane. Aparticle moves from P1 to P2 under the action of forces 2 1 F , F and 3 F . Force 1 F is always toward P2 and is always 20 N in magnitude. Force 2 F always acts horizontally and is always 30 N in magnitude.Force 3 F alwaysactstangentiallytothetrackandisofmagnitude 15 N. Select the correct alternative(s) (A) work done by 1 F is 120 J (B) work done by 2 F is 180 J (C) work done by 3 F is 45 (D) 1 F is conservative in nature Q.24 AuniformrodAB &lengthLis released fromrest inthe positionshown. It swings down to verticalpositionand strikes a secondand identicalrod CD is resting on frictionless surface. Ifimpact isprefectlyelastic then velocityofrod CD immediatelyafter impact is (A) 4 1 2gL (B) 3gL 2 1 (C) 4gL 3 1 (D) 2gL

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