Answers & Solutions - Aakash · PDF fileAnswers & Solutions for JEE ... CODE 1 Regd. Office :...

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1 Answers & Solutions for for for for for JEE (Advanced)-2017 Time : 3 hrs. Max. Marks: 183 CODE 1 Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.: 011-47623456 Fax : 011-47623472 PAPER - 2 (Code - 1) DATE : 21/05/2017 INSTRUCTIONS QUESTION PAPER FORMAT AND MARKING SCHEME : 1. The question paper has three parts : Physics, Chemistry and Mathematics. 2. Each part has three sections as detailed in the following table : Section Question Type Number of Questions Full Marks Category-wise Marks for Each Question Partial Marks Zero Marks Negative Marks Maximum Marks of the Section Single Correct Option 7 +3 If only the bubble corresponding to the correct option is darkened 0 If none of the bubbles is darkened –1 In all other cases 21 1 One or more correct option(s) 7 +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened +1 For darkening a bubble corresponding to each correct option, provided NO incorrect option is darkened 0 If none of the bubbles is darkened –2 In all other cases 28 2 Compre- hension 4 +3 If only the bubble corresponding to the correct answer is darkened 0 In all other cases 12 3 fgUnh ekè;e fgUnh ekè;e fgUnh ekè;e fgUnh ekè;e fgUnh ekè;e

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  • 1

    Answers & Solutions

    forforforforfor

    JEE (Advanced)-2017

    Time : 3 hrs. Max. Marks: 183

    CODE

    1

    Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005

    Ph.: 011-47623456 Fax : 011-47623472

    PAPER - 2 (Code - 1)

    DATE : 21/05/2017

    INSTRUCTIONS

    QUESTION PAPER FORMAT AND MARKING SCHEME :

    1. The question paper has three parts : Physics, Chemistry and Mathematics.

    2. Each part has three sections as detailed in the following table :

    Section QuestionType

    Number of Questions

    Full Marks

    Category-wise Marks for Each Question

    Partial Marks Zero Marks Negative Marks

    MaximumMarksof the

    Section

    SingleCorrectOption

    7 +3If only the bubble corresponding to the correct option

    is darkened

    0If none of the

    bubbles is darkened

    1In all other

    cases

    211

    One ormore

    correctoption(s)

    7 +4If only the bubble(s)

    corresponding toall the correct

    option(s) is(are)darkened

    +1For darkening a bubblecorresponding to each

    correct option, provided NO incorrect option is

    darkened

    0If none of the

    bubbles is darkened

    2In all other

    cases

    282

    Compre-hension

    4 +3If only the bubblecorresponding to

    the correct answeris darkened

    0In all other

    cases

    123

    fgUnh ek;efgUnh ek;efgUnh ek;efgUnh ek;efgUnh ek;e

  • 2

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    PHYSICS

    [kaM[kaM[kaM[kaM[kaM-1(vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 21)))))

    bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

    R;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

    izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mkj ds vuq:i cqycqys dks dkyk djsaA

    izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %

    iw.kZ vad : +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

    'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ugha fd;k gSA

    .k vad : 1 vU; lHkh ifjfLFkfr;ksa esaA

    1. ,d izlkjh xksys (expanding sphere) dh rkR{kf.kd (instantaneous) f=kT;k R ,oa nzO;eku M vpj jgrs gSA izlkj ds nkSjku

    bldk rkR{kf.kd ?kuRo iwjs vk;ru esa ,dleku jgrk gS ,oa vkaf'kd ?kuRo dh nj 1 d

    dt

    vpj (constant) gSA bl izlkjh

    xksys ds i"B ij ,d fcUnq dk osx v fuEu ds lekuqikrh gksxk

    (A) R (B) R3

    (C)1

    R(D) R2/3

    mkjmkjmkjmkjmkj (A)

    gygygygygy 34

    3M R=

    2 340 3

    3

    dR dR R

    dt dt

    = +

    ls foHkkftr djus ij

    2 3 10 3

    dR dR R

    dt dt

    = +

    2 33

    dRR R K

    dt=

    dRR

    dt

    2. fp=k }kjk n'kkZ;s lecgqHkqtksa dh Hkqtkvksa dh la[;k n = 3,4,5....... gSA lHkh cgqHkqtksa dk lagfr dsUnz (center of mass) vuqHkwfed

    ry ls h pkbZ ij gSA ;s fcuk fiQlys f{kfrt ry ij izfrxkeh 'kh"kZ (leading vertex) ds pkjksa vkSj ?kw.kZu dj vxzlfjr gks jgs

    gSaA izR;sd cgqHkqt ds lagfr dsanz ds js[kkiFk (locus) dh pkbZ dh vfkdre o`f gSA rc dh h vkSj n ij fuHkZjrk

    fuEu esa ls nh tk,xh

    h h h

  • 3

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    (A)2

    sinhn

    =

    (B)1

    1

    cos

    h

    n

    =

    (C)2

    sinhn

    =

    (D)2

    tan2

    hn

    =

    mkjmkjmkjmkjmkj (B)

    gygygygygy lh

    /n

    2 n

    =

    sin cos

    n

    =

    sin

    hl =

    = l h

    = 1

    1sin

    h

    = 1

    1

    cos

    h

    n

    3. izdk'k fo|qr inkFkZ (photo electric material) ftldk dk;Z iQyu (work funtion) 0 gS] rjax&nS;Z

    0

    hc

  • 4

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    4. tSls dh fpf=kr fd;k x;k gS] ,d lfEer rkjs (symmetric star) ds vkdkj ds pkyd esa vifjofrZr kkjk I cg jgh gSA ;gk

    foijhr 'kh"kks (diametrically opposite vertices) ds chp nwjh 4a gSA pkyd ds dsUnz ij pqEcdh; {ks=k dk eku gksxk

    4a

    I

    (A)I

    a

    06 3 1

    4

    (B)I

    a

    06 3 1

    4

    +

    (C)I

    a

    03 3 1

    4

    (D)I

    a

    03 2 3

    4

    mkjmkjmkjmkjmkj (A)

    gygygygygy rkjs vkdkj ds pkyd ywi ds ,d Hkkx dks lefer ls ckgj ekuus ij

    T;kferh lsT;kferh lsT;kferh lsT;kferh lsT;kferh ls :

    30

    30

    30

    120

    2a

    I

    O

    a

    ( )ywi dk dsUnz

    lHkh 12 le:i Hkkxksa ds dkj.k ywi ds dsUnz ij pqEcdh; {ks=k izoQfr esa ;ksxkRed gSA

    BusV = [ ]0

    12 cos30 cos1204

    I

    a

    +

    = 0

    6 3 14

    I

    a

    5. rhu osDVj ,P Q

    ,oa R

    fp=k }kjk n'kkZ, x, gSaA osDVj R

    ij ,d fcUnq S n'kkZ;k x;k gSA fcUnq P o fcUnq S ds chp dh

    nwjh b R

    gSA,P Q

    ,oa S

    osDVjksa ds chp lEcUk gS

    SQ

    PbR| |

    R Q P=

    QS

    P

    O X

    Y

    (A) ( )21S b P bQ= +

    (B) ( )1S b P bQ= +

    (C) ( )1S b P bQ= +

    (D) ( ) 21S b P b Q= +

    mkjmkjmkjmkjmkj (A)

  • 5

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    gygygygygy S

    = | |P b R R+

    = | || |

    RP b R

    R+

    = P bR+

    = ( )P b Q P+

    = (1 )b P bQ+

    6. jkdsV Hkwry ds vfHkyacor lw;Z ,oa i`Foh dks tksM+us okyh js[kk esa lw;Z ls nwj dh rjiQ (radially outward from the direction

    of the sun) iz{ksfir fd;k x;k gSA lw;Z iFoh ls 3 105 xquk Hkkjh gS ,oa iFoh dh f=kT;k ls 2.5 104 xquh nwjh ij fLFkr gSA

    i`Foh ds xq:Rokd"kZ.k {ks=k ds fy, iyk;u xfr 11.2 kms1 gSA jkdsV dks lw;Z ,oa i`Foh fudk; ds xq:Rokd"kZ.k ls eqDr gksus

    ds fy, de ls de izkjafHkd osx (S) dk fudVre eku gS

    (iFoh dh ph; xfr vkSj ifjHkze.k rFkk fdlh vU; xzg dh mifLFkfr dh mis{kk djsa)

    (A) vs = 22 km s1 (B) v

    s = 42 km s1

    (C) vs = 62 km s1 (D) v

    s = 72 km s1

    mkjmkjmkjmkjmkj (B)

    gygygygygy Evs

    m

    M M1 =

    S

    r R = 2.5 10 4

    M M2 = 3 10

    5

    KE esa gkfu = PE esa ykHk

    2 1 212

    s

    GM m GM mmv

    R r= +

    5

    2

    4

    1 3 10

    2 2.5 10s

    GM G Mv

    R R= +

    2 13sGM

    vR

    =

    = 11.2 13 40.4 km/s=

    42 km/s

    7. ,d O;fDr ,d iRFkj dks dq,as esa fxjkrs le; vkSj dq,as dh ryh esa la?kV ls mRiUUk ofu ds le; varjky dk ekiu djds

    dq,as dh xgjkbZ dk irk yxkrk gSA og le;karjky ds ekiu esa =kqfV T = 0.01 lsdsaM ,oa dq,sa dh xgjkbZ L = 20 m ekirk gSA

    xq:Rokd"kZ.k Roj.k g = 10 m s1 ,oa ofu xfr 300 ms1 nh xbZ gSA L/L ds ekiu esa fudVre vkaf'kd =kqfV (fractional

    error) gS

    (A) 0.2%

    (B) 1%

    (C) 3%

    (D) 5%

    mkjmkjmkjmkjmkj (B)

  • 6

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    gygygygygy t1 =

    2L

    g

    t1

    t2L

    t2 =

    L

    V

    T = t1 + t

    2

    T = 2L L

    g V+

    T = 2 1 1

    2L L

    g VL +

    0.01 = 1 1 1

    3005 2 20L

    +

    0.01 = 1 1

    20 300L

    +

    0.01 = (15 1)

    300L

    +

    L = 0.01 300

    16

    100L

    L

    = 3

    10016 20

    = 1%

    [kaM[kaM[kaM[kaM[kaM-2 (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 28)))))

    bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

    R;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d fodYi lgh gSaA

    izR;sd iz'u ds fy, vks-vkj-,l- ij lkjs lgh mkj (mkjksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk djsaA

    izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %

    iw.kZ vad : +4 ;fn fliQZ lkjs lgh fodYi (fodYiksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk fd;k gSA

    vkaf'kd vad : +1 izR;sd lgh fodYilgh fodYilgh fodYilgh fodYilgh fodYi ds vuq:i cqycqys dks dkyk djus ij] ;fn dksbZ xyr fodYi dkyk

    ugha fd;k gSA

    'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ughaughaughaughaugha fd;k gSA

    .k vad : 2 vU; lHkh ifjfLFkfr;ksa esaA

    mnkgj.k % ;fn ,d iz'u ds lkjs lgh mkj fodYi (A), (C) vkSj (D) gSa] rc bu rhuksa ds vuq:i cqycqyksa dks dkyk djus ij

    +4 vad feysaxs_ fliQZ (A), (D) ds vuq:i cqycqyksa dks dkyk djus ij +2 vad feysaxsa_ rFkk (A) vkSj (B) ds vuq:i cqycqyksa

    dks dkyk djus ij 2 vad feysaxs D;ksafd ,d xyr fodYi ds vuq:i cqycqys dks Hkh dkyk fd;k x;k gSA

  • 7

    JEE (ADVANCED)-2017 (PAPER-2) CODE-1

    8. ,dleku pqEcdh; {ks=k (uniform magnetic field) B dkxt ds ry ds vfHkyEc fn'kk esa x = 0 ,oa 3

    2

    Rx = ds chp ds

    {ks=k (fp=k esa region 2) esa loZ=k (tSls fd fp=k esa fn[kk;k gS) mifLFkr gSA ,d d.k ftldk vkos'k +Q ,oa laosx p gS] og

    x-v{k ds vuqfn'k {ks=k 2 esa fcUnq P1(y = R) ij os'k djrk gSA fuEu esa ls dkSu lk(ls) dFku lgh [email protected]\

    3 /2R

    ( = )y R

    +Q P1

    OP

    2

    B

    x

    yRegion 1 Region 2 Region 3

    (A)2

    3

    pB

    QR> ds fy, d.k {ks=k 1 (region 1) esa iqu% os'k djsxk

    (B)8

    13

    pB

    QR= ds fy, d.k {ks=k 3 (region 3) esa x-v{k ij fcUnq P

    2 ls os'k djsxk

    (C) tc d.k lcls yEcs lEHkoiFk ls {ks=k 2 (region 2) ls {ks=k 1 (region 1) esa iqu% os'k djrk gS] rc fcUnq P1 vkSj y-v{k

    ls lcls nwj fcUnq ds fy, jsf[kd laosx ds ifjek.k esa cnyko / 2p gS

    (D) ,d fu;r B ds fy, ,eleku vkos'k Q ,oa ,d leku osx v okys d.kksa ds fy, fcUnq P1 ,oa {ks=k 1 (region 1) esa iqu%

    os'k fcUnq dh nwjh dk varj d.kksa ds O;eku ds O;qrekuqikrh gS

    mkjmkjmkjmkjmkj (A, B)

    gygygygygy d.k pqEcd