ANSWERS, HINTS & SOLUTIONS PART TEST I PAPER-2 ANSWERS KEY

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1 AITS-PT-I (Paper-)-PCM-JEE(Advaced)/8 FIITJEE JEE(Advaced)-8 ANSWERS, HINTS & SOLUTIONS PART TEST I PAPER- ANSWERS KEY Q. No. PHYSICS Q. No. CHEMISTRY Q. No. MATHEMATICS ALL INDIA TEST SERIES. D. B 7. B. A 5. C 8. A. B 6. C 9. A. A, D 7. B, C, D 5. A, B, D 5. C 8. A, C 5. A, B 6. A, C 9. A 5. B, C 7. B, C, D. A, D 5. D 8. B, D. B, C, D 5. B, D 9. B. A 55. A. B. D 56. A FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

2 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 Physics PART I SECTION A. D H g g(r). Momet of iertia of combied system about y-ais R m mr mr mr mr Coservatio of agular mometum alog y-ais R mv mr v R. f k o the block B = mg ˆi kˆ ˆi kˆ P ˆ f mg (v k k) mgv dq mgv mgv dt. For equilibrium Rg cosd Rg si d = At the positio of maimum tesio i the rope Rdgcos ( Rdgsi ) = 5 At ay, dt Rdgcos Rdgsi Tma dt Rg (cos si )d Rg Rg T Rg si cos ma T + dt d Rdg dn 5. Acceleratio of particle P ad Q alog the iclie is same. Acceleratio of particle P perpedicular to the iclie plae is cos 6 = 5 m/s So, v P 5() = v P = m/s FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

3 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 6. R = u = costat dr d R dt dt d dr dt R dt I time dt radius decreases by dr RdR = uddt dr ud dt R d ud dt R R u d R Iu d R Iu d F R 7. For pure rollig motio, static frictio would act i the forward directio o the sphere. Work doe by static frictio is chage i the kietic eergy of the sphere. Work doe by static frictio o the complete sphere + Plak system is zero. 8. F applied by eteral aget = Weight + thrust force = g + v Eergy lost i the complete lift = W F K.E. U = 9. For perfectly i elastic collisio both blocks have same velocity after collisio. v.. e R gr mgr m 5 kg SECTION C T. W = rp rdp = (.)( ) 5 = 9 J FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

4 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8. v v gy ad v si = v (as give i questio) v si v gy ta = dy d v gy v gy O y y bead v (gv) y g / a + b + c = 8 L. Time to cross, t = v cos ul ut = d L ta v cos ul v dcos L si ul vmi m/s d L L u B B u d D A v C 5. If they meet a height h after time T of the projectio of the secod. The, h = u(t) g(t) v(t t) g(t t) (i) 5t t T t For miimum T, dt dt 5t t 6 = t =.6 = 6 g 6. For car + trailer system P ma = (mg si + kmv )v For car oly P ma = (mg si + kmv )v (mg si + kmv )v = (mg si + kmv )v gsi k 5v For dow the iclie kmv t = mg si v t = 5v FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

5 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 7.

v v v v v Coservatio of agular mometum with respect to cetre of mass (COM) frame v m mv v v From coservatio

cosiderig torque of real ad pseudo force i the frame of P, R R mg m R R g R mg m R mgr R R R IP m m R mr C

g() v at t = sec = 8 k k. s + k = + = 7.

5 5 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 7. At the startig (with respect to COM frame) At the istat of maimum elogatio (with respect to the COM frame) v v v v v Coservatio of agular mometum with respect to cetre of mass (COM) frame v m mv v v From coservatio of eergy with respect to cetre of mass frame v v v m m = U 8 8 sprig U 7mv sprig mv = Joule v 8. cosiderig torque of real ad pseudo force i the frame of P, R R mg m R R g R mg m R mgr R R R IP m m R mr C mg N O mgr g 6 mr R rad/s P f s dv 9. sg at t = sec dt s. At t = sec velocities of plak ad block are equal. g() v at t = sec = 8 k k. s + k = + = 7. Sice, the upper block will move faster tha the middle block ad hece force of frictio o upper block is towards left f mg g aa leftward f f A B f FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

6 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 6 m f m g mg ab g (leftward) aa/b g (rightward) For slidig dow the block B, A has to move a distace L 8 relative to block B. L gt 8 L t sec. g SECTION D. mg T = ma mg T = ma So, a = a Relative acceleratio of bead with respect to ed = a displacemet of block = at = 6.5 m f = T a mg T mg a. A = Mg N cos For disc, N si = f + f cos Nsi Mgsi cos f cos ( cos ) R M = L ad L ta N A N Mg f f N f f N W f gr cos N 5. dv v k(l ), where k is a costat. d v / L vdv k (L )d v v v (L ) v KL So iitial retardatio = KL = v L m/s FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

7 7 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 Chemistry PART II SECTION A NH OH H SO NH SO H O Iitial m mol. m mol.m mol. m mol NH., NHOH..8 / poh pk log b. / =.76 + log = = 5.6 ph = = 8.6 E E T a a T T 98 T = 596 K = o C o 8 C 6 BF 6NaH B H 6NaF 7. P F bod legth is less tha P Cl bod legth P F 59.6 pm P Cl.5 pm. 8. (i) Li has stroger reducig character tha Na i aqueous solutio. (ii) Li CO is thermally less stable tha Na CO. 9. Pyrosilicates have geeral formula Si 6 O 7.. (i) Formula of bora is Na [B O 5 (OH) ].8H O.... (ii) Aqueous solutio of bora is weakly alkalie. K P P P NH HS Additio of NH HS(s) at equilibrium does ot chage the cocetratio of NH (g). K spagco 5 Ag M CO KspAgCl.8 Cl Ag = 9-6 M. 5. r SECTION C FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

8 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/ Cr OH IO OH CrO I 5H O =, y =, z = y z 7 6. A g B g Cg a a a a 5 [A] = a = 5 = [B] = a = 5 = [C] = K C AB c = 8 7. CO g Cs COg = P atm, P atm CO P CO Kp PCO CO 8. t t P P / / 5 = = = 9. Boro Nitride, Boric acid, Beryllium hydride, Graphite.. (i) -8 M HCl (ii). M solutio of NH Cl (iii). M soluti of B(OH) CH COOH C.5. HCOOH C.5. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

9 9 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 H K C K C a a = - ph = - log - =. The followig molecules/io are plaar CO,NO, XeF,I,COCl,SO,I Cl (solid). 6 Al OH NaOH NaAlO H O Soluble Z OH NaOH Na ZO H O Soluble S OH NaOH Na SO H O Soluble SECTION D. For shortest wavelegth RH mi R H 9 mi 9 mi m RH = 5. m 5. S Cl g SCl g Iitial At equilibrium. 7.6 S Cl. SCl 7.6 K c SCl S Cl = poh at th equivalece poit = 9. =.7 At th equivalece poit Salt poh pkb log Base.7 pkb log.75.5 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

10 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8.7 pkb log pkb.7 log At th equivalece poit Salt poh pkb log Base.75 poh.7 log log.5 poh.7 log log poh.7 log poh.7.8 poh 5.66 ph = 5.66 = 8. Mathematics PART III 7. Put i I ad t i I t SECTION A We get d Let u the du u 8. dy yd y yd dy y d yd y y y y l c 9. lk k k So, f(k) = k + lk f f e e (, ) P, lk k FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

11 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 5. y y y 5 y 5 7 9, y for / 9 f d = 5 5/ y dy y y d Let y = v( ) 6v dv v d v dv d 6v y y ta l 6 l c = = 7 5. (A) C ( ) 5 (B) ( ) 5 (C) ( ) (D) ( ) = 9 5. Let g() = f() g() = g() = So; g(c ) = for at least oe C (, ) Similarly g(c ) = for at least oe C (, ) Usig LMVT o (C, C ) gc gc g(c) = C C f(c ) = 5. Let f As the decimal part icreases the i the epressio p, q becomes very large q So, q q q si q 5 Hece, lim f Thus, f() is cotiuous at each irratioal FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

12 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/ cos y cos y 7 7 ; So; g 7 ; So; g() mi = 7 So; f() = + cos / 55. A cos d / = si / / = 6( ) = y = f() y = f () 56. = itersect at poits SECTION C 57. : g : : 58. Q() is a icreasig fuctio So, 6 6 e e Q d d e e Q(e 6 ) N N So, l l So,... k... k So, limit = e 6. For least area = So; A mi = 56 d FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

13 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 6. ta t si, So; ta si si ta t, ta si ma Sice; i, : ta > ad the same is subtracted from N r ad D r both So; maimum value occurs at O + Therefore ta t ; t 6, 6. So; + 7 = k 7 k Also 7 k 7 k 7 k 7 6 k k 7, 7 (Rejected) 7 k 7 k, 6 y = k : k > So: k 7, Similarly: cosider case-ii if k < the Secod Method Clearly: m < k < k For slope of ON ( 7 + 6) = k Must have equal roots For slope of OM = k Must have equal roots k, 7 m M O N m 6. g(f()) = So; g(f()) f() = f g f f So; g ad g 5 6. f () = [] + {} / 9/ 9/ / So, d d = 7 / 65. Let 8 t f dt 8 t t f() =, f() = egative So; f() has oe root i [, ] FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

14 AITS-PT-I (Paper-)-PCM (Sol)-JEE(Advaced)/8 66. f is a odd fuctio So; f(7) = 7, f(5) = 5, f() =, f(), f() SECTION D 67. Let = t ad I t dt I t dt = t t dt (Usig itegratio by parts) I I I I So,... I 68. Roots of the f() = are (, ) ad the f(f()) = (where f() = t) f(t) = t =, So; total umber of distict real solutios = + = 69. f() = ( ) 5 ( + ) 6 ( ) f() = if =,,, Clearly: there are ifleio poits FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -6, Ph 66, 65699, Fa 659

Q. No. PHYSICS CHEMISTRY MATHEMATICS

Q. No. PHYSICS CHEMISTRY MATHEMATICS AITS-CRT-I (Paper-)-PCM(Sol)-JEE(Advaced)/5 FIITJEE Studets From All Programs have bagged 4 i Top 00, 66 i Top 00 ad 74 i Top 500 All Idia Raks. FIITJEE Performace i JEE (Advaced), 04: 5 FIITJEE Studets