MOCK TEST I (JEE MAIN)

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1 MCK TEST I (JEE MAIN) ANSWE KEYS, HINTS & SLUTINS PHYSICS. B A B is a vecto pependicula to both A and B A B ˆ i ˆ j + k ˆ i ˆ + ˆ j k ˆ Now, Now, ˆn i ˆ + 5j ˆ + 7kˆ A B A B i ˆ + 5j ˆ + 7kˆ i ˆ + 5j ˆ + 7kˆ 8. B Hoizontal velocity emains same o o o cos6 v cos5 v 5 m/s. A v 9 t dv a 9 dt ma 9 N F N F N + net N mg N. C p afte st impact ep ( p) p( + e) Similaly p afte nd impact ep( + e) pnet p + e + e + e +... p( + e) e So, 5. B Foce of eplosion is intenal and system is initially at est Let the velocities of the fist two fagments ae vi ˆ & vj ˆ and that of the fagment m be v ˆ i + v ˆ ˆ j + vk, p + p + p So, ( ) mvi ˆ + mvj ˆ + m v ˆi + v ˆj + v kˆ v v v, v and v FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

2 FMT-JEE-8-MAIN-PCM - P v ˆ v p ˆ m i + j mv Enegy eleased in eplosion E K K So, Kf mv + mv + ( m)( v + v + v ) f i mv mv 6. D Angula momentum about point of contact will be conseved L L i v v M Mv M Mv v v 7 f 7. C mg T ma and mgl ml a Iα l g a mg So, T T mg α a 8. C K dv I d V d dv K V V Kln + V 9. D By consevation of angula momentum, mv mv v v.(i) GMm GMm By consevation of enegy, + mv + mv V GM ( + ) V GM Now, mv m + V. D By equation of continuity Av av' FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

3 FMT-JEE-8-MAIN-PCM - P A π v' v v a π v' cm/sec.. D Fo cylinde A ; Q nc T p Fo cylinde B, Q ncv T Hence, ncp T ncv T C + C T v v Fo diatomic gas, 5 Cv T K. B dt dθ θ ( θ θ ) dt dt dt K θdt In fist case, o o dt 6 59 C ; θ C, dt min. Fo second case, dt o o C; θ C dt K θ dt 6 dt dt 6 min. K θ 6. C y a sinω t + cosωt a sinω t + cosωt π a sin ω t + The motion is SHM with amplitude a. B at ω T π T T π Constt. T 5. A 6. B elative velocity is ( v + v ) ( v + v ) pponent fequency is λ The no. of positive cests stiking pe sec. is same as fequency. v + v In sec. λ FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

4 FMT-JEE-8-MAIN-PCM - P Fom symmety, E due to a unifom linea chaged can only be adially diected. As a Gaussian suface, we can choose a cicula cylinde of adius and length. L, closed at each end by plane caps nomal to the ais. ε o E. ds qin E ε o E.ds + E.ds q in Cylindical Plane Suface o εoe( π l) + E.ds cos9 λl l λl λ E ε πl πε o The diection of E is adially outwads fo a line of positive chage. 7. B V E ( + 5y) + V Ey 5 5 y E 5j ˆ V/m. 8. A Wok done change in potential enegy U U U / E C ( EC) E C ε ( / ) E Cε U C' C Wok done / E C. ( ε ) 9. D The esistance of the paallel combination of Ω and Ω esistos is given by 5 +.Ω 6 This esistance is in seies with.8ω giving a total effective esistance. +.8Ω Ω. In the steady state, chage on the capacito C has stablised and hence no cuent passes though Ω esisto which is in seies with the capacito. Thus the cuent though the cicuit 6/.5 A, V.5..8V, I though Ω esisto.8/.9 A. AB. A.5 Ω, l 5cm, l cm. D l l l esistance.5 ( 5 ).5 5Ω l ( l l ) FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

5 FMT-JEE-8-MAIN-PCM - P5 ρl ρl ρl ρl ρdl A A l V m / d m l o m l l l 5 9 : : : : : : 5 : 5 : m m m 5. A The magnetic field at P due to the flat coil of n tuns, adius, caying cuent i is µ ni µ ni µ n π i µ µ B.. / ( d >> )... d + d π d π d n i i d P. C B µ Ni l whee N Total numbe of tuns, l length of the solenoid. 7 π N.8 N π Since N tuns ae made fom the winding wie so length of the wie L π N π length of each tuns [ ] L π. m π. D E l 6A E L + l dl dt t/t E l l ( e ) l 6A L t. l t/. 6 e E L bt Potential dop acoss L E - l 6 e e S 5t 5. D It is mentioned in the poblem that on filling the vessel with the liquid, point B is obseved fo the same setting; this means that the image of point B, is obseved at A, because of efaction of the ay at C. Fo efaction at C, sin sin i Now, µ.5 a l AD sin AC + h Whee h is the height of vessel. A Liquid µ.5 B 5 cm N C i D h T FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

6 FMT-JEE-8-MAIN-PCM - P6 BD 5 sin i BC 5 + h 5 h 9 7h h..5 + h h 6 + 6h h h 8.5 cm 6. C In this case L M M ( ) L ( µ ) M L M L L M ( µ ) ( µ ) f and F so PL f and P f and hence powe of system PP + P + P P + P µ µ P + F P µ i.e. the lens will be equivalent to a conveging mio of focal length ( / µ ) 7. A Fo eyepiece, v E 5 cm, f E +5 cm u.7 cm. cm E L v + u. cm hee v 8 cm E f + cm u. cm 8. B Wavelength associated with a paticle is given by h λ me h 5 A o fo electon M 9. kg o λ mev V 5 λ. A Fo minima dsinθ n λ Fo fist minima n.55 sin θ.. sinθ.8.55 FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

7 FMT-JEE-8-MAIN-PCM - P7 9. D hv hv + E E hv hv c But v λ λ λ E hc hc λ λ λ λ. D The esistivity of pue Si is given by ρ σ e n µ + n µ en µ + µ e e h h e h o n eρ µ + µ i 9 e h 6.6 m When 9 atoms of phosphoous (dono atoms of valence five) ae added pe m, the semiconducto becomes n type semiconducto. 9 6 n n n N n.6 e h e d h e sitivity ρ 5. Ωm 9 9 neµ ee.6. CHEMISTY. A HF has high melting point than HCl due to intemolecula hydogen bonding while HCl < HB < HI (melting point) due to incease in molecula weight.. C The oom enegy /T deives fom kinetic (moment) enegy of a gas o mateial.. A. A 5. B ν ν a z ( b ) Now, tan 5 a ab ν 9 8 ν s - 6. A Tb T c z θ FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

8 FMT-JEE-8-MAIN-PCM - P8 7. C 8 Volume a 5 cm.5 cm d g cm - Mass of unit cell 5 - g 7g Mass of one molecule 6. mole.95 - g 5 No. of Fe molecules pe unit cell.95 + The Fe + 8. D The decease is S chaacte between bond angle and 9.5 is 8.% Fo.5 o decease the decease in S chaacte Thus S-chaacte 5.98.% 9. D m + m Aveage mola mass g mol A Mola volume at STP (V m ).8 L 8.8 Density.6 gl.8. A. D The highest ise would be ecoded. If neutalization pocess is complete NaH + HS NaS + H Let meq of NaH, H S y, then y fo complete neutalization N V N V. C. B HS NaH HS VNaH then 5, 5 ml each V t ( Ao) n o n const Ao t o n t Ao const o n t Ao const n t Ao const o but fom question n, n. C Because elimination of H is easie that of D and this type of elimination takes place in tans manne. 5. A FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

9 FMT-JEE-8-MAIN-PCM - P9 N N N Eplosion C + N + H + C CH 6. D 7. C Ag being salt is alloyed with coppe. The composition of a silve alloy in epessed as its fineness. The amount of Ag in, pats of the alloy hence. 8.5% Ag and 7.5% Cu 8. C As S + NaH NaAs + NaAsS + H soluble 9. A K C K K. C Follow stuctue of one dimensional silicates. B H NH HN H N N CH fliplicy possible HN H H NH H N N. C ing bond between C and C as well as the Hydogen atom can migate independently to fom cyclopentane caboaldehycle and cycloheananone espectively. CHCl N Indole C H 5 Na N H Cl Cl -HCl N ouinolive. C. C 5. A FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

10 FMT-JEE-8-MAIN-PCM - P 6. B 7. A Uotopine (CH ) 6 N heamethyl diamine NH (CH ) 6 NH (i) K Pt Cl 6 thee ions (ii) Pt ( NH ) (iii) Pt ( NH ) Cl Cl - Two ions (iv) Pt ( NH ) and conductivity no. of ions 8. A At isoelectic point migation of α - amino acid not obseved Cl 5 - one molecule Cl Cl - fou ions 9. A CH H CH+ HB + ( A) B NH C A NaH CHI ( should be CH when it shows halofom) I. B Accoding to bent ule. MATHEMATICS. C Let n m m n m n is a thee digit numbe & m n is an intege whee numeato is thee digit & denominato m is fou digit. m n 5 n + ( + ) + is a two digit no B a a a...a n+ n+ it follows that a n+ an+ a n+ a a a a a n+ n+ n+ n+ n+ + + n an+ n an+ an+ + a. C FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

11 FMT-JEE-8-MAIN-PCM - P a. c b. c cosθ Taking dot poduct with a, cosθ α Taking dot poduct with b, cosθ β Taking dot poduct with c αcosθ + βcosθ + γ a b c cosθ a b c cosθ cos θ cosθ cosθ So, cos cos θ + γ θ So, γ cos θ α + β + γ. B Let t t t 6 t t t 6 t t + t, 9 5. A a b,.5 A sina sina c E D b 7 c a b B a C BD AB + AD AB bc AD ( AC) AB + AC a + c bc AE a + b 7 7 AD, AE 7 ( + ) 7 BD, CE B FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

12 FMT-JEE-8-MAIN-PCM - P st tem of A.P. & G.P. a Let common atio be & common diffeence be d. a + d a () & a + d a +.5 () Fom () & (), a a + a.5 a a a.5 a a < < a a a a.5 > & a a a + a.5 > a (, ), 7. C Let the subsets be n wods fom the alphabet {, }. Let a n be the no. of binay wods with no two successive ones. The wods can stat eithe with and may continue in an ways o they stat with & may continue in an ways an an + an a, a a 5 a 8 a a a a 55, a A f ( ) 5 I d 7 d 6 Let z dz I z 5 6 logz [ ] 8/79 5/6 log 7 α, β 7 9. D FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

13 FMT-JEE-8-MAIN-PCM - P. B + cos C cos B sin A cos B A cos B A cosc. cos π A + B cos π C cos B A { } cosc cos A + B cosccos B A cosc cos A + B + cos B A cosc o sinb sin A Not possible o C 9 P sina sin 9 A + + sina < P e < (if ) + > e e e < < < if e + e + < tan. A Diffeentiating with espect to f ( ) + f '( ) f ( ) f '( ) +. C g( ) d d + a + a + a + a 56 a a a a a + a + a + a A.M. G.M. ( a a a a ) But A.M. G.M. A.M. G.M. a a a a. B π cos6cos7cos8cos9 I d sin + e π π b b ( a a ) I cos 6 cos7 cos8 cos9 d f d f a + b d I 5 cos6cos7 cos6 + cos d π 5 cos6cos7cos d + FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

14 FMT-JEE-8-MAIN-PCM - P π I cos6cos7cos d. D A Let cot, B C cot y, cot z s ( a + b + c) s + y + z y z y z + 6y + 5z 7 y + yz + z y + y 9z + 8z y z y z 9 5. B t t λ 6. C z + + z z + 7. A z + z z + + z z, ω, ω 7 f z z + z + ( ) ( ω ) ( ω ) f but f f ω and ω ae two common oots. Put y f diff. w..t. keeping y constant + y + y f ' + y f ' + e + + y e e e + y eplace y by & by, then f ' + e + e + e + e + f ( ) f ( ) f f ( ) f ' e d e e e 8. B BD BC + + B A E o 6o C FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

15 FMT-JEE-8-MAIN-PCM - P5 9. B n simplifying f ( ) g( ) + g( g( ) ) when g( ) α, β, γ Whee α, β, γ ae oots of g( ) α has solution g( ) β has solution g( ) γ has solution g α y β γ. A Let any point of y be t, t Let cicumcente of CPQ by (h, k) which is midpoint of C t + h & k t t h k t hk y y P C Q. A P a a a a + a a a a ( )( 5 )( 7 ) ( )( )( 6 )( 8 ) P( a ) + ve P( a ) ve P( a ) ve P( a ) + ve P( a5 ) + ve P( a6 ) ve P( a7 ) ve P( a8 ) + ve Hence, P( ) has all positive eal oots.. D Let + t in st integal t t t e t e t e e e e e e e dt + tlnt. e dt dt + lnte dt e t t t. C G, 9 5, B A (, k) H(, 5) (6, 7) E y D C (6, ) FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

16 FMT-JEE-8-MAIN-PCM - P y 6 point A(, k) satisfies this 7 k ( ) k 7 + Equation of AD y ( 6) Cicumadius Aea of cicumcicle 5π. B T AA I A ± ( n ) adj adj A A ± 5. C lim n f ( ) e cos n n e e lim n sin n n n e lim n g( ) e e n g ln f ln ; < ( ) Domain of h is (, ) g f ln ln fo < < 6. A cos cos + cos cos A, cosb & cosc ae nonnegative 7. C + cos A + cos B + cos C + cos A cosbcosc + + cos A + cos B + cos C + cos A cosbcosc C C C! 8 (! ) 8. D FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

17 FMT-JEE-8-MAIN-PCM - P7 S is not symmetic & T is efleive, symmetic & tansitive. 9. B Let i ˆ + yj ˆ + zkˆ whee, y, z ae positive integes + y + z The no. of values of is no. of positive integal solutions of n 9 n + y + z C C. D f ( ) & between &. By gaph f By gaph f ( ) has min. oots so f ae of opposite sign so one oot lies in has min. oots oots by olle s theoem. ' g f. f has min. oots Let g' ( ) has min. oots f ' has f ( ) f ( ) FIITJEE Ltd., FIITJEE Kathauta Chauaha, Vinama Khand, Gomti Naga, Lucknow 6. Ph: 5-678, FIITJEE Ltd., Nea M.G. Convent School, Secto - G, LDA Colony, Kanpu oad, Aashiana, Lucknow - 6. Ph: 5-6, 65. FIITJEE Ltd., Fou Season House, A-/, Secto - C, Aliganj, Lucknow - 6. Ph:

q r 1 4πε Review: Two ways to find V at any point in space: Integrate E dl: Sum or Integrate over charges: q 1 r 1 q 2 r 2 r 3 q 3

q r 1 4πε Review: Two ways to find V at any point in space: Integrate E dl: Sum or Integrate over charges: q 1 r 1 q 2 r 2 r 3 q 3 Review: Lectue : Consevation of negy and Potential Gadient Two ways to find V at any point in space: Integate dl: Sum o Integate ove chages: q q 3 P V = i 4πε q i i dq q 3 P V = 4πε dq ample of integating