Sol.Paper-2

Embed Size (px)

Citation preview

  • 8/3/2019 Sol.Paper-2

    1/4

    WJ]O QHJSZIUQDZ QUNGD"L ZSNGD ! >

    WJ]OQHJS FJ] IUQD UDQU SNSD]"=

    >) s / s

    >2 x / | nie s

    s

    >2 x

    |

    (glvdi,

    Neelig mjuh wd gdu

    =s 2 =x s 2 x

    Ijw qtmu}naulig mjuh wd gdu

    s

    =2 =|

    s

    >2 | s 2

    |

    >

    Uhd}dfj}d x 2|

    >

    x| 2 >

    =) x 2 | {

    x / | / { 2 3

    =x / { 2 3

    { 2 =x

    ==

    ==

    |{

    x{

    2

    ==

    ==

    xx5

    xx5

    2

    4

    1

    1) x= >lq fnauj} jf f(x, 2 x5 / sx1 / =x= 1x / ~

    (x >, nie (x / >, n}d n`qj fnauj} f(x,

    M| fnauj} uhdj}db

    f(>, 2 3

    > / s / = 1 / ~ 2 3

    s / ~ 2 3 )))(l,

    f( >, 2 3

    > s / = / 1 / ~ 2 3

    s / ~ 2 6 )))(ll,

    Nee (l, nie (ll,

    =~ 2 6

    ~ 2

    1 s 2 1)

    5) 1

    =

    =

    >

    5

    1

    )))))))))) i

    >i

    2 i

    >

    4) 7 1x/> / (1x/5,2 4x/1 4x/=

    j} 1x/> _ 7 / 11R 2 4x/= _4>R

    j} 1x/> _=3R 2 4x/= _5R

    j} 1x/> _=3R 2 4x/> _=3R

    j}

    >x

    4

    1

    2 >

    j}

    >x

    4

    1

    2

    3

    4

    1

    x / > 2 3 x 2

    >

    6) (>3>,= 2 hnvd 1 iji"{d}j elgluq

    (>3>3>,= 2 hnvd 4 iji"{d}j elgluq

    Qj (>3>3>3>3>,= 2 hnvd < iji"{d}j elgluq

    7) Wd hnvd n / m / a 2 6 )))(l,

    (n / m / a,= 2 16

    _Ji q~tn}lig mjuh qledq jf (l,R

    n= / m= / a= / =(nm / ma / na, 2 16

    n= / m= / a= / = 8 2 16

    _ nm / ma / na 2 8R

    n= / m= / a= 2 (16 >6, 2 =3)

    Ijw wd hnvd

    n1 / m1 / a1 1nma 2 (n / m / a, (n= / m= / a=

    nm ma na,

    2 (n / m / a, _(n= / m= / a=, (nm / ma / na,R

    2 6 _(=3 8,R 2 (6 >=, 2 7=)

    ^tdq) > = 1 5 4 6 7 8 < >3 >> >= >1 >5 >4 >6 >7 >8 >< =3

    Niq) E A E A N A N A M M N M A M M A E E E N

    ^tdq) => == =1 =5 =4 =6 =7 =8 =< 13 1> 1= 11 15 14 16 17 18 1< 53

    Niq) N N N N N M M E N M E N M A N A A A E M^tdq) 5> 5= 51 55 54 56 57 58 5< 43 4> 4= 41 45 44 46 47 48 4< 63

    Niq) M M M N A M N E E M N M N N N M M N A A

    ^tdq) 6> 6= 61 65 64 66 67 68 6< 73 7> 7= 71 75 74 76 77 78 7< 83

    Niq) N N A M N A A A M E M E N A M M M A A E

    ^tdq) 8> 8= 81 85 84 86 87 88 8<

  • 8/3/2019 Sol.Paper-2

    2/4

    WJ]O QHJSZIUQDZ QUNGD"L ZSNGD ! =

    8) ==

    11

    mnmn

    mn

    2 n / m

    8)71 / 5)=7 2 >1)

    R

    >3)n|mx

    ,R|mxm=xn(n|,|m|n=xn(mx_ ============

    2,n|mx(

    ,n|mx(nmx|=

    ,n|mx(

    ,n|mx(|m

    ,n|mx(

    ,n|mx(xn ====

    2 n= x= / m=|= / =nmx|2 (nx / m|,=

    >>) Glvdi 1=7>6>6 2

    15 1 x

    1

    55812

    1

    51 x

    1 558 2 1 x65

    M| ajbsnl}lqlji 65x 2 558 x 2 7

    >=) =6 2 45

    >6)=< / =6)3 / 33=6)3

    / 3333=6)3

    2 4)5 / )45 / )345 / )3345 2 4) _>/ 5 / 5= / 51 / 55R56> _> / 5 / >6 / 65 / =46R56> 15> 15> lq elvlqlm`d m| >>

    >5) I 2 1=1~ / >=4

    >=4~1=1

    Qliad 1=1~ lq elvlqlm`d m| >=4 m| >< wd gdu >> nq }d"bnlied}

    >4) i= 2 x(i / >,= 2 x / |i= / > / =i 2 x / |=i 2 x / | i= >2 x / | x > 2 | >(x / =,= 2 i= / 5 / 5i

    2 x / 5 / = =i

    2 x / 5 / =(|

    >,2 x / 5 / =| =2 x / =| / =

    >6) [d}jdq li uhd s}jetau jf > = 1 5 )))))))))))))

    5< 43

    2 >= (= 4 >3 >= >4 =3 == =4 13

    1= 14 53 5= 54 43,

    >7) x 2 ==

    x=

    2 = / =

    x5 2 5 / = / 5 = 2 6 / 5 =

    5x

    >2

    =56

    >

    =56

    =56

    2

    5

    =56

    5x

    52 6 5 =

    x5 / 5x

    52 6 / 5 = / 6 5 = 2 >=)

    >8) _1(>=1 / i,R= Qj lu lq n itbmd} whlah lq nbt`uls`d jf 54>47 / i n`qj nq bt`uls`djf 54>47 lq =1) i 2 5 Qj uhnu lu lq elvlqlm`d m| =>8{>15|>6< whdi elvlede m| 484 glvdq}dbnlied} 2 485)

    =3) (16=15, (114>=, (45==1,

    2 ))))))))) 6 )))))))) > ())))))) 5, ())))))) 4,2 ))))))))) 6 )))))))))) 3qj tilu elglu 2 6 Niq)

    7>) (M, >= / > (=,= /> (1,= />))))))))))

    2 = 4 >3 >7)))) (4,= / > 2 =6

    7=) (4 =, > (< =, = (>6 =, 1

    (=< =,

    5 (45 =,

    4 >31 (E,

    ij) lq bt`uls`lde m| = nie uhdi qtmu}naudef}jb

    > = 1 5 4))))))) }dqsdulvd`|

    75) Fl}qu duud} jf dvd}| ud}b lq bjvde uh}dd qudsq

    mnaown}e li dnah idxu ud}b) Qdajie itbmd}

    jf dvd}| ud}b lq bjvde uwj qudsq mnaown}e

    nie uhl}e `duud} lq bjvde uwj qudsq fj}wn}e)

    Hdiad uhd idxu ahjlad wjt`e md U>>D)

  • 8/3/2019 Sol.Paper-2

    3/4

    WJ]O QHJSZIUQDZ QUNGD"L ZSNGD ! 1

    74) (M, Li flgt}d (N, (4 165, 2 44>)Li flgt}d (M, (78,2 6==)

    76) (M, A`dn}`|

    Li flgt}d N R 6 1 5 = 2 >8 8 2 >3

    Li flgt}d MR

    < 4

    4 1 2 54

    >4 2 13 Li flgt}d A R 6 4 = 4 2 13 >3 2 =3

    77) (M, Uhd snuud}i jf uhd qd}ldq lq aaa mmm

    nnn*aaa mmm nnn*a)

    78) (A, bij * ijs~ * js~}q * s~}qu

    El}dauljiq ;(7

  • 8/3/2019 Sol.Paper-2

    4/4

    WJ]O QHJSZIUQDZ QUNGD"L ZSNGD ! 5

    >, 2 =3

    Qj Qtil` lq =>qu f}jb uhd mjuujb)