ALL INDIA TEST SERIES

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1 FIITJEE Students Frm Classrm / Integrated Schl Prgrams have secured t Znal, 6 State & 8 City Tpper Ranks. in Tp 00, 78 in Tp 00 and 05 in Tp 500 All India Ranks bagged by FIITJEE Students frm All Prgrams have qualified in JEE (Advanced), 05. FIITJEE ALL INDIA TEST SERIES FULL TEST I Time Alltted: urs Maximum Marks: 4 Pleas e r ead th e instructins carefully. Yu are alltted 5 m inutes specifically fr this purpse. Yu are nt allwed t leave the Exam inatin all befre the end f the test. INSTRUCTIONS A. General Instructins. Attempt ALL the questins. Answers have t be marked n the OMR sheets.. This questin paper cntains Three Parts.. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. 4. Each part has nly ne sectin: Sectin-A. 5. Rugh spaces are prvided fr rugh wrk inside the questin paper. N additinal sheets will be prvided fr rugh wrk. 6. Blank Papers, clip bards, lg tables, slide rule, calculatr, cellular phnes, pagers and electrnic devices, in any frm, are nt allwed. B. Filling f OMR Sheet. Ensure matching f OMR sheet with the Questin paper befre yu start marking yur answers n OMR sheet.. On the OMR sheet, darken the apprpriate bubble with black pen fr each character f yur Enrlment N. and write yur Name, Test Centre and ther details at the designated places.. OMR sheet cntains alphabets, numerals & special characters fr marking answers. C. Marking Scheme Fr All Three Parts. (i) Sectin-A (0 t 0 and 0 t ) cntains 6 multiple chice questins which have nly ne crrect answer. Each questin carries +8 marks fr crrect answer and mark fr wrng answer. Sectin-A (04 t 09 and t 0) cntains 4 multiple chice questins which have nly ne crrect answer. Each questin carries +4 marks fr crrect answer and mark fr wrng answer. Name f the Candidate Enrlment N. JEE (Main)-06 FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

2 AITS-FT-I-PCM-JEE(Main)/6 Useful Data PYSICS Acceleratin due t gravity g = 0 m/s Planck cnstant Charge f electrn Mass f electrn h = J-s e = C m e = 9. 0 kg Permittivity f free space 0 = C /N-m Density f water water = 0 kg/m Atmspheric pressure P a = 0 5 N/m Gas cnstant R = 8.4 J K ml CEMISTRY Gas Cnstant R = 8.4 J K ml = 0.08 Lit atm K ml =.987 Cal K ml Avgadr's Number N a = Planck s cnstant h = Js = ergs Faraday = culmb calrie = 4. jule amu = kg ev = J Atmic N: =, e =, Li=, Be=4, B=5, C=6, N=7, O=8, N=9, Na=, Mg=, Si=4, Al=, P=5, S=6, Cl=7, Ar=8, K =9, Ca=0, Cr=4, Mn=5, Fe=6, C=7, Ni=8, Cu = 9, Zn=0, As=, Br=5, Ag=47, Sn=50, I=5, Xe=54, Ba=56, Pb=8, U=9. Atmic masses: =, e=4, Li=7, Be=9, B=, C=, N=4, O=6, F=9, Na=, Mg=4, Al = 7, Si=8, P=, S=, Cl=5.5, K=9, Ca=40, Cr=5, Mn=55, Fe=56, C=59, Ni=58.7, Cu=6.5, Zn=65.4, As=75, Br=80, Ag=08, Sn=8.7, I=7, Xe=, Ba=7, Pb=07, U=8. FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

3 AITS-FT-I-PCM-JEE(Main)/6 Physics PART I SECTION A Single Crrect Chice Type This sectin cntains 0 multiple chice questins. Each questin has fur chices,, and ut f which ONLY ONE is crrect.. In an adiabatic prcess where in pressure is increased by % if decreases by abut. 4 % % 4% 9 % 9 4 Cp, then the vlume C v. A sphere f mass m and radius R is kept n a rugh wedge. The acceleratin f wedge fr the sphere t remain in equilibrium with respect t wedge shuld be. g g R m 0 0 a g g. A slid sphere f mass m and radius R is lying n a rugh hrizntal plane. A cnstant frce 4mg acts vertically at pint P such that OP makes an angle 60 0 with hrizntal. Find the minimum value f cefficient f frictin s that sphere starts pure rlling. O mg P FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

4 AITS-FT-I-PCM-JEE(Main)/ The fig belw shws the plts f PV versus P fr nt xygen gas at tw different temperature Read the fllwing statements cncerning the abve curve. (i) the dtted line crrespnds t the ideal gas behavir (ii) T > T (iii) the value f PV at the pint where the curves nt meet n the y-axis is the same (iv) which f the fllwing statement is true. (i) nly (i) and (ii) All f these Nne f these 5. A unifrm rd f mass M and length L is kept n a hrizntal surface. The rd receives an impulse J at its lwest pint, nrmal t its length as shwn, then chse the crrect statement. The velcity f pint P just after impact is J M J P L/6 L/ The velcity f pint P just after impact is J M Kinetic energy after impact is Kinetic energy after impact is J M J M FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

5 5 AITS-FT-I-PCM-JEE(Main)/6 6. Which ne f the figure gives the temperature dependence f density f water crrectly Density Density Temperature Temperature Density Density Temperature Temperature 7. In the given ptentimeter circuit length f the wire AB is m and resistance is R = 4.5. The length AC fr n deflectin in galvanmeter is : m.8 m dependent n r Nne f these 8. A plane sinusidal undiminished sund wave is travelling in +x directin in a gaseus medium. Excess pressure amplitude fr any lcatin is p 0. Wave speed in the medium is 60 ms -. At sme mment, instantaneus values f excess pressure at psitins (0,0,0) & (+, +, 0) are +p and +p 0 /. The frequency f wave is: 60Z 0Z 60 Z 0 Z. FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

6 AITS-FT-I-PCM-JEE(Main)/ A pint charge q 50 C is lcated in the x y plane at the pint f psitin vectr r ˆ i j. What is the electric field at the pint f psitin vectr r 8i ˆ 5j v 00 m 4 0 m v v 900 m v 4500 m 0. A listener is at rest with respect t the surce f sund. A wind starts blwing alng the lime jining the surce and the bserver. Which f the fllwing quantities d nt change? Wavelength Frequency Time perid Velcity f sund. A pint charge Q is lcated just abve the centre f the flat face f hemisphere as shwn in figure. The electric flux thrugh the flat face and curved face f hemisphere are respectively Q Q Q Q A),, Q Q,. Find min between disc and flr fr equilibrium Q Q, Q P 4 4 Disc (m, R). In a carnival ride called the rtr, peple stand n a ledge inside a large cylinder that rtates abut a vertical axis. When it reaches a high enugh rtatinal speed, the ledge drps away. If radius be m and the perid f rtatin be sec, then the minimum cefficient f frictin fr the peple nt t slide dwn is Ledge FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

7 7 AITS-FT-I-PCM-JEE(Main)/6 4. The binding energy f 7 Cl 5 nucleus is 98 MeV. Find its atmic mass. The mass f hydrgen atm ( ) is.0084 amu and that f a neutrn is amu. Given amu = 9 MeV A frame made f thin hmgeneus wire, is shwn in figure. Assume that the number f successively embedded equilateral triangle with sides decreasing by half tends t infinity. The side AB has a resistance R. The equivalent resistance between A and B is x. 7 x is infinite x is zer x = R 0 x R 6. Cnsider the fllwing reactin; 6C 7N 0n The atmic masses f the nuclei are M.00785u, M n u, M C.006 u, M N u and amu = 9 MeV. The kinetic energy f prtn required t initiate the reactin is.99 MeV.99 MeV.99 MeV 4.99 MeV 7. The YDSE is made in a liquid. The 0 th bright fringe in the liquid lies where the 6 th dark fringe lies in vacuum. The refractive index f the liquid is apprximately The time cnstant f charging f the circuit shwn in the figure RC RC RC RC/ R C R FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

8 AITS-FT-I-PCM-JEE(Main)/ A fly F is sitting n a glass slab A, 45 cm thick and f refractive index /. The slab cvers the tp f a cntainer B 4 cntaining water upt a height f 0 cm. The bttm f cntainer is clsed by a cncave mirrr C f radius f curvature 40 cm. The psitin f final image frmed by all refractins and reflectin, assuming paraxial rays is at the bttm f glass slab in the middle f cntainer B in the middle f glass slab nne f these C A B F 4 0 cm 45 cm 0. Find the magnetic field at P due t the arrangement shwn. i i d d i d d d P. A cnducting lp f radius R is present in a unifrm magnetic field B perpendicular t the plane f the ring. If radius R varies as a functin f time t as R = R 0 + t. The e.m.f induced in the lp is R t B R0 t B clckwise R t B anticlck wise Zer. X X X X B X X X X X X X R X X X X X. In the arrangement shwn in given figure current frm A t B is increasing in magnitude induced current in the lp will have clckwise directin have anticlckwise directin be zer scillate between clckwise and anticlckwise A B FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

9 9 AITS-FT-I-PCM-JEE(Main)/6. Find the time-perid f SM f mass m. m K 9m 8K 8 K 4 K m K m K m 4. There is a unifrm magnetic field B nrmal t the xy plane. A cnductr ABC has length AB, parallel t the x-axis and length BC parallel t y-axis. ABC mves in the xy plane with velcity V ˆ ˆ x i Vy j. The ptential difference between A and C is prprtinal t. Vx Vy Vx Vy Vx v y Vx Vy 5. A particle f mass m was transferred frm the centre f the base f a unifrm hemisphere f mass M and radius R t infinity. The wrk perfrmed by external agent in this prcess n the particle is GmM R GmM R GmM R GmM R 6. A small cil f radius r is placed at the centre f a large cil f radius R, where R>>r. The cil are cplanar. The c-efficient f mutual inductance between the cils is r r r r R R R R FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

10 AITS-FT-I-PCM-JEE(Main)/ A cube f wd supprting 00 gm mass just flats in water ( = g/cc). When the mass is remved, the cube rises by cm. The vlume f cube is 000 cc 800 cc 500 cc nne f these 8. A charged particle ges undeflected in a regin cntaining electric and magnetite fields. It is pssible that: E B, V E E is parallel t B V B but E is nt parallel t B E B but V is nt parallel t E 9. A particle f charge per unit mass is released frm rigin with a velcity v vi magnetic field B B K. If the particle passes thrugh (, y, ) then y is equal t. v 0 0 B ˆ v B v B v B in a unifrm 0. Spherical particles f pllen are shaken up in water and allwed t settle. The depth f water is cm. What is the diameter f largest particles remaining in suspensin ne hur later? [The density f pllen =.8 0 kg m -, viscsity f water = 0 - pise, = 0 kg/m & g = 0 ms -. Take apprpriate assumptins] m m m m FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

11 AITS-FT-I-PCM-JEE(Main)/6 Chemistry PART II SECTION A Single Crrect Chice Type This sectin cntains 0 multiple chice questins. Each questin has fur chices,, and ut f which ONLY ONE is crrect.. n-factr fr Cl in reactin K CrO7 Cl KCl CrCl Cl C Br /h Mnbrmderivatives The number f pssible mnbrm prducts is excluding stere ismers The curve drawn belw shws the variatins f P as a functin f V fr a fixed mass and temp. f an ideal gas. It fllws frm the curve that T T T T T T T T T Nthing can be predicted abut temp. P V T T T 4. Fr adiabatic expansin f a perfect gas dp P is dv dv V V eq 0 G 0, k eq dv V 0 G 0, k eq dv V 0 5. If E cell fr a given reactin is negative which gives the crrect relatinship fr the value f and k eq? 0 0 G 0, k G 0, k eq 0 G FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

12 AITS-FT-I-PCM-JEE(Main)/6 6. The slubility f AgBr in water and in 0.0M CaBr, 0.0M KBr, and 0.05M AgNO be S, S, S and S 4 respectively, give the relatin f slubilities. S S S S4 S S S S4 S S S S4 S4 S S S 7. Which f the fllwing traids have apprximately equal size? Na, Mg, Al iselectrnic F, Ne, O iselectrnic Fe,C,Ni Mn, Fe,Cr iselectrnic 8. Which f the fllwing is zer verlapping which leads t nn-bnding? z + + z - - p x + - p y All z - + p x p x 9. The resultant diple mment f tw cmpund NOF and NO F is.8 D and 0.47D respectively. Which diple mment d yu predict?.8 D fr NO F and 0.47D fr NOF 0.47 D fr NO F and.8 D fr NOF Fr bth NO Fand NOF, diple mment () is 0.8D. Fr bth NO F and NOF. Diple mment () is 0.47D. 0. A Zn B aq g A C P aq A N Cl D aq 4 g Find cmpund A which imparts glden yellw clur t the Bunsen flame. NaO LiO KO RbO FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

13 AITS-FT-I-PCM-JEE(Main)/6. Relative rate f reactin f fllwing amine with methyl idide is N N N N A > B > C A > C > B B > C > A B > A > C. The tw cmpunds shwn belw are O O and (i) (ii) Diasteremer Enantimer Epimer Nne. Which f the fllwing wuld nt rearrage t a mre stable frm? Cmpare relative stability f fllwing resnating structure O O - O (i) (ii) + (iii) C C N N N- I > II > III II > I > III I > III > II II > III > I C FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

14 AITS-FT-I-PCM-JEE(Main)/ A (mle)/pt Duble bnd equivalent (degree f unsaturatin) f is 4 6. Br/CCl 4 Br Br Br Br 7. Is-electric pint f alanine is (p = 6). At which p, maximum cncentratin f zwitter in f alanine will be present? p > 6 p < 6 p = 6 p = 7 8. What is the structure f L - glucse? CO CO O O O O O O O O C -O C -O CO Nne O O O O C -O FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

15 5 AITS-FT-I-PCM-JEE(Main)/6 9. Which reactins are used fr the preparatin f the halgen acid? KBr SO cnc. K SO Br CaF SO cnc Ca SO F 4 4 NaCl SO cnc NaSO Cl KI SO cnc K SO I Which f the fllwing rders regarding thermal stability f hydrides M f grup 5 is crrect? N P As N P As N P As N P As. The frmula f Azurite is CuCO Cu O CuCO CuO CuCO CuO CuSO CuO. In this sequence X, Y, Z are respectively X 4 Cr + green slutin yellw slutin Z Blue slutin Y Acidified O, Alkaline O, Acidified O Alkaline O, Acidified O, Zn/Cl Acidified O, eat, alkaline O Alkaline O, Acidified O, n standing. What will be the clur f the slutin when Mn(O) is treated with cnc. NO and sdium bismuthate (r red lead r lead dixide)? yellw Purple Green Blue 4. In NaCl the centres f tw nearest like charged ins are present at a distance f a a a a FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

16 AITS-FT-I-PCM-JEE(Main)/ Cmplexes given belw shws Ph P Cl PPh Pt Pt Cl C Cl Optical ismer Gemetrical ismerism Ph P Cl Pt Cl Cl Pt PPh Cl C-rdinate ismerism Bridge ismerism 6. The C.FS.E f CN Cl 6 is In the extractin f cpper, metal is frmed in the Bessemer cnverter due t reactin. Cus CuO 6Cu SO CuS Cu S Fe CuO Cu FeO CuO 4Cu O 8. Which f the fllwing curve represents the enry s law? lg P lg P lg x lg x lg P lg P lg x lg x FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

17 7 AITS-FT-I-PCM-JEE(Main)/6 9. When tw half-cells f electrde ptential f E and E are cmbined t frm a cell f electrde E, then (where n, n and n are number f electrns exchanged in first, secnd and cmbined half cells): E E E E n E E n E n n E n E n E E E 0. Fr a first rder hmgeneus gaseus reactin A B C then initial pressure was P i while ttal pressure after time t was P t. Then expressin fr rate cnstants K in terms P i, P t and t is..0 p i.0 P i K lg K lg t Pi Pt t Pt Pi.0 P i K lg t Pi Pt Nne f these FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

18 AITS-FT-I-PCM-JEE(Main)/6 Mathematics 8 PART III SECTION A Single Crrect Chice Type This sectin cntains 0 multiple chice questins. Each questin has fur chices,, and ut f which ONLY ONE is crrect. x. If [x] dentes the integral part f x and m x, n = least integral value f m n m > n m + n = 0 n m = 0 sinx then. If cs x x a has n slutin, then cmplete set f values f a is,. Let i i i i P P P P,4, and P N, then 4, fp e.e.e...e where i lim f n is n i i 4. sin z where z is nn real and i i can be then angle f a triangle if Rez lmz Rez lmz 0 nne f these 5. Let S then S S 088 Re z, lm z 056 S S If a, a, a a 0 are A.Ms between and 67 then the maximum value f a a a.a 0 is (0) 0 (40) 0 (60) 0 (80) 0 FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

19 9 AITS-FT-I-PCM-JEE(Main)/6 7. If A cscs x sincs x, then least and greatest value f A are 0 and and and 0 and 8. If x sin sin y cs cs, where then x y = x + y = x + y = y x = n 9. Let n be a psitive integer such that sin cs then n n n = 6 n = n = n =, 4, 5 0. Cmplete set f values f x in (0, ) satisfying lg sin x lg sinx 0 is, 4, 0,,,. Let A = {x, x, x, x 4, x 5 }; B = {y, y, y, y 4, y 5 } then the number f ne-ne mapping frm A t B such that f x y, i =,, 5 is i i Cefficient f x 5 in ( + x + x + x 4 ) n is 5 n C5r 5 n Cr n n C C 5 n n C5r Cr r0 r0 r0 r0 r 5r. If tw events A and B are such that PA, PB and PA B equal t 0 5 then B P A B is 4 FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

20 AITS-FT-I-PCM-JEE(Main)/ If 4 and ax bx a a x a x... a x when a, b, a 0, a a 8 R such that a 0 + a + a 0 a a a a a a 0 then a a a 5 5 a, b a, b a =, b nne f these If A aij where 0 0 i j i j aij then A - is i j i j Equatin f the circle having centre at (, -) and cutting the intercept f length 6 unit n the line x 5y + 8 = 0 is x + y 6x + y 8 = 0 x + y 6x + y 8 = 0 x + y 6x + y 8 = 0 nne f these 7. Minimum distance between the curve y = 4x and x + y x + = 0 is equal t Lcus f the mid pint f the chrds f the hyperbla x y = a, that tuch the parabla y = 4ax is x x a y y x a x x x a y 9. If the tangents frm the pint (, ) t the ellipse y x a x x y are at right angles then is 9 4 nne f these FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

21 AITS-FT-I-PCM-JEE(Main)/6 0. a b x sin x lim x0 sin x c, a, b, c R {0} exists and has nn-zer values then a, b, c are in AP a, b, c are in GP a, b, c are in P nne f these. Suppse f : R R is a differentiable functin and f() = 4 then the value f 8f() 4f() f() f() f x lim tdt x x 4. If f x x tan x and f is inverse f g then g(x) is equal t g x x g x x g x x g x x. If the functin f x cs x ax b increases alng the centre number scale, the range f value f a is given by a b b a a a 4. The value f lgx dx is x x x x x sec x c tan x c lg x x nne f these 5. K K K n K n K n lim K is equal t K K K K nne f these 6. 4 x I e dx equals t e e e e FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594

22 AITS-FT-I-PCM-JEE(Main)/6 7. Area bunded by the curve sq unit y sin x, y-axis and y cs x is equal t sq unit sq unit dy tan y is equal t dx x x 8. The slutin f the differential equatin e sec y.x x x sin y e x x c x x x sin y e x e c x x x sin y e x e c x x sin y e x x c sq unit 9. Value f a b a c d a.d abc is always equal t a.c a.b.c a.b a.b.c nne f these 0. The equatin f the plane passing thrugh the pints (, -, 0), (, -4, 5) and parallel t the line x = y = 4z is 5x 90y 79z 40 x y 6z 85 7x 6y z 85 9x 7y z 85 FIITJEE Ltd., FIITJEE use, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fax 6594