Кўфн дан тестлар



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KO\'FN dan test


KO‘FN dan testlar
##1# f(z) – golomorf funksiya bo‘lsin. U holda = ? ni hisoblang.##

A) Imf(z)

B) Ref '(z)

+C) f '(z)

D) - Ref '(z)

E) Imf '(z)

##2## f(z) – golomorf funksiya bo‘lsin. U holda =? ni hisoblang.##

A) Imf '(z)

B) i·Ref '(z)

+C) - ·f '(z)

D) Ref '(z)

E) –i·Imf '(z)


##3# Ref(z) = x3 +6x2y – 3xy2 – 2y3, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) 2iz3

+B) (1 –2i)z3

C) 3(z –1)3

D) 2z3 – 3

E) z3 + 2z2


##4# Ref(z) = ex(x·cosy – y·siny), f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) e z ·sinz

+B) z·e z

C) z ·cosz· e z

D) z + e z

E) e z(z –1)


##5# Ref(z) = x·cosx·chy + y·sinx·shy, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

+A) z·cosz

B) z·sinz

C) z·chz

D) z·shz

E) chz·cosz


##6# Imf(z) = y·cosy·chx + x·siny·shx, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) i·z·shz

B) i·z·cosz

C) sinz·chz

D) cosz·shz

+E) z·chz


##7# z = (1+i )8·(1 - i ) – 6 uchun |z| va arg z mos ravishda…….. va …… ga teng.##

A)

B)

C)

+D)

E)


##8# Parallelogrammning uchta uchlari berilgan: z1 = 1+i, z2 = 2 +1,5·i, z3 = 3+3·i. z2 uchiga qarama-qarshi yotuvchi to‘rtinchi z4 uchini toping.##

+A) z4=2+2,5·i

B) z4=1,5+2·i

C) z4=1,5+2,5·i

D) z4=2+2·i

E) z4=2,5+ i


##9# cos(2+i ) sonining haqiqiy qismini toping.##

A) cos2· sin1,

+B) ch1·cos2,

C) sin2·sin1

D) sh1·cos2

E) sh1·sin2.

##10# ctg( - i·ln2) sonining mavhum qismini toping.##

A) 5/7


B) 0

C) –1


D) 12/15

+E)15/17


##11# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f( i ) = 0, arg f '( i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) i /2

+B) 1/3

C) i /4

D) 1/5

E) i /6
##12# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(2i ) = 0, arg f '( 2i ) = 0 shartlari bilan konform akslantirsin. U holda f( 3i )=? ni toping.##


+A) i /5

B) – i /4

C) 1 /3

D) – 2/3

E) 3i /4

##13# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(1+ i ) = 0, arg f '( 1+i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) (i+1)/3

B) (i-1)/(3+i)

C) i/(5-i)

D) –i/(5+i)

+E) (i-1)/(3i-1)
##14# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w-1| < 1 doiraga f( i ) = 1, arg f '( i ) = 0 shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) (i-3)/3

B) (3-i) /3

+C) (i+3)/3

D) –(i+3)/3

E) 3/2


##15# w = f(z) funksiya |z| < 2 doiraga Rew > 0 o‘ng yarim tekislikni f( 0 ) = 1, arg f '( 0 ) = shartlari bilan konform akslantirsin. U holda f(i )=? ni toping.##

+A) 1/3

B) 1/4

C) 1/5


D) 1/6

E) 1/2


##16# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) = 0 shartlari bilan konform akslantirsin. U holda f(0)=?

A) 1/2


B) i /2

C) –i /2

+D) –1/2

E) 1/3
##17# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) =/2 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##

A) –1/2

+B) 1/2

C) i /2

D) 1/4


E) –1/4.

##18# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 0 ) = 0, arg f ' (0) =-/2 shartlari bilan konform akslantirsin. U holda f (1/2)=? ni toping.##

+A) –i /2

B) i /2


C) 1/2

D) -1/3

E) i /3
##19# w = f(z) funksiya |z| < 1 doirani | w-1| < 1 birlik doiraga f(0) = 1/2, f (1 ) = 0 shartlari bilan konform akslantirsin. U holda f( 1/2 )=? ni toping.##

A) 1/3


B) 1/4

+C) 1/5

D) 1/6

E) 1/7
##20# w = f(z) funksiya |z-2| < 1 doirani |w-2i| < 2 birlik doiraga f( 2 ) = i , arg f ' (2 ) = 0 shartlari bilan konform akslantirsin. U holda f( 3/2) =? ni toping.##

A) i

B) (5i+1)/2



C) (-13+16 i )/15

+D) (-12+14 i )/17

E) 3i
##21# 1/(1-z)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1/2


B) –1/2

+C) 3


D) –3

E) 1/6
##22# 2/(1+z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

+A) 12

B) 6


C) 3

D) 1/3


E) 1/12
##23# z(z+2)/(2-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 2


B) –2

C) –1/2

+D) 1/2

E) 1/3
##24# 1/(z2 +9) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1/9

B) –1/25

C) 1/49

+D) -1/81

E) 1/121
##25# 1/(1+z2)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1


+B) –2

C) 3


D) –4

E) 5
##26# (z2+4z4+z6)/(1-z2)4 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 5

B) –4


C) 3

D) –2


+E) 1
##27# z/(1-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 0


B) 1/2

C) 1/3


+D) 3

E) 2
##28# 1/(z+1)(z-2) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## +A) –3/8

B) 3/4

C) 3/2


D) –3/2

E) 3/8
##29# (2z-5)/(z2-5z+6) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 25/127

B) 12/35

+C) –35/216

D) –13/41

E) 3/7
##30# 1/(z2-1)2(z2+4) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 6/17

+B) 7/16

C) 5/18

D) 9/14

E) 8/15
##31# 1/sinz funksiyaning z = 2 nuqtadagi qoldig‘ini toping.##

A) 

+B) 1/



C) 2

D) 1/2


E) -

##32# ctgz funksiyaning z = 3 nuqtadagi qoldig‘ini toping.##

+A) 1/

B) 


C) 3

D) 1/3


E) -
##33# thz funksiyaning z = i/2 nuqtadagi qoldig‘ini toping.##

A) 


B) -

C) 3


D) 2

+E) 1


##34# cth2z funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##

A) 


B) -

+C) 0


D) –1

E) 1
##35# cosz/(z-1)2 funksiyaning z = 1 nuqtadagi qoldig‘ini toping.##

A) cos1

B) –cos1

C) sin1

+D) –sin1

E) 0
##36# 1/(e z +1) funksiyaning z = i nuqtadagi qoldig‘ini toping.##

A) -


B) 

C) 0


D) 1

+E) –1
##37# sinz/(z-1)3 funksiyaning z =1 nuqtadagi qoldig‘ini toping.##

A) 2

B) 1


+C) 0

D) –1


E) -2
##38# 1/sinz2 funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##

+A) 0


B) 1/2

C) 1


D) –1

E) 1/3
##39# cos[(z+2)/2z] funksiyaning z =  nuqtadagi qoldig‘ini toping.##

+A) ,

B) -,


C) 0,

D) 1/,

E) –1/.
##40# z cos2(/z) funksiyaning z = nuqtadagi qoldig‘ini toping.##

A) 3

+B) 2

C) 


D) 1

E) 0
##41# Integralni hisoblang: .##

A) –2

B) –1


+C) 0

D) 1


E) 2

##42# Integralni hisoblang: .##

A) i

+B) 2i

C) 3i

D) -i


E) 0

##43# Integralni hisoblang: .##

A) i

B) -i/2

C)i/3

+D)-2i/3

E) 0

##44# Integralni hisoblang: .##



A) 2i cos1

B) 4i sin1

C) 2i(sin1+cos1)

D) 4i (sin1-cos1)

+E) 4i (cos1-sin1)

##45# Integralni hisoblang: .##

A) 2i sin1

+B) i (cos1+2sin1)

C) 4i (sin1 +2cos1)

D) 4i cos1

E) i (2sin1-cos1)

##46# Integralni hisoblang: .##

+A) -2i /9

B) 0


C) i /3

D) 1


E) i

##47# Integralni hisoblang: .##

A) i /3

B) -i /81

+C) -i /121

D) 0


E) 2i / 169

##48# Integralni hisoblang: .##

A) 0

B) i


C) –i

+D) i


E) -i

##49# Integralni hisoblang: .##

+A) 0

B) –i


C) 

D)-


E) 1

##50# Integralni hisoblang: .##

A) 2i

B) -2i

C)1

D)-1


+E) 0

##51# (z) – golomorf funksiya bo‘lsin. U holda =? ni toping.##

A) Imf(z)

B) Ref '(z)

+C) f '(z)

D) - Ref '(z)

E) Imf '(z).

##52# – golomorf funksiya bo‘lsin. U holda =? ni toping.##

A) Imf '(z)

B) i·Ref '(z)

+C) - ·f '(z)

D) Ref '(z)

E) –i·Imf '(z)

##53# Ref(z) = x3 +6x2y – 3xy2 – 2y3, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) 2iz3

+B) (1 –2i)z3

C) 3(z –1)3

D) 2z3 – 3

E) z3 + 2z2
##54# f(z) = ex(x·cosy – y·siny), f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) e z ·sinz

+B) z·e z

C) z ·cosz· e z

D) z + e z

E) e z(z –1)


##55# Ref(z) = x·cosx·chy + y·sinx·shy, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

+A) z·cosz

B) z·sinz

C) z·chz

D) z·shz

E) chz·cosz


##56# Imf(z) = y·cosy·chx + x·siny·shx, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##

A) i·z·shz,

B) i·z·cosz,

C) sinz·chz

D) cosz·shz,

+E) z·chz.


##57# z = (1+i )8·(1 - i ) – 6 uchun |z| va arg z mos ravishda.##

A)

B)

C)

+D)

E)


##58# Parallelogrammning uchta uchlari berilgan: z1 = 1+i, z2 = 2 +1,5·i, z3 = 3+3·i. z2 uchiga qarama-qarshi yotuvchi to‘rtinchi z4 uchini toping.##

+A) z4=2+2,5·i

B) z4=1,5+2·i

C) z4=1,5+2,5·i

D) z4=2+2·i

E) z4=2,5+ i

##59# cos(2+i ) sonining haqiqiy qismini toping.##

A) cos2· sin1

+B) ch1·cos2

C) sin2·sin1

D) sh1·cos2

E) sh1·sin2

##60# ctg( - i·ln2) sonining mavhum qismini toping.##

A) 5/7


B) 0

C) –1


D) 12/15

+E)15/17


##61# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f( i ) = 0, arg f '( i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) i /2

+B) 1/3

C) i /4

D) 1/5

E) i /6
##62# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(2i ) = 0, arg f '( 2i ) = 0 shartlari bilan konform akslantirsin. U holda f( 3i )=? ni toping.##

+A) i /5

B) – i /4

C) 1 /3

D) – 2/3

E) 3i /4

##63# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(1+ i ) = 0, arg f '( 1+i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) (i+1)/3

B) (i-1)/(3+i)

C) i/(5-i)

D) –i/(5+i)

+E) (i-1)/(3i-1)
##64# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w-1| < 1 doiraga f( i ) = 1, arg f '( i ) = 0 shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##

A) (i-3)/3

B) (3-i) /3

+C) (i+3)/3

D) –(i+3)/3

E) 3/2
##65# w = f(z) funksiya |z| < 2 doiraga Rew > 0 o‘ng yarim tekislikni f( 0 ) = 1, arg f '( 0 ) = shartlari bilan konform akslantirsin. U holda f(i )=? ni toping.##

+A) 1/3

B) 1/4


C) 1/5

D) 1/6


E) 1/2
##66# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) = 0 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##

A) 1/2


B) i /2

C) –i /2

+D) –1/2

E) 1/3


##67# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) =/2 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##

A) –1/2

+B) 1/2

C) i /2

D) 1/4

E) –1/4
##68# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 0 ) = 0, arg f ' (0) =-/2 shartlari bilan konform akslantirsin. U holda f (1/2)=? ni toping.##

+A) –i /2

B) i /2

C) 1/2

D) -1/3

E) i /3
##69# w = f(z) funksiya |z| < 1 doirani | w-1| < 1 birlik doiraga f(0) = 1/2, f (1 ) = 0 shartlari bilan konform akslantirsin. U holda f( 1/2 )=? ni toping.##

A) 1/3


B) 1/4

+C) 1/5

D) 1/6

E) 1/7


##70# w = f(z) funksiya |z-2| < 1 doirani |w-2i| < 2 birlik doiraga f( 2 ) = i , arg f ' (2 ) = 0 shartlari bilan konform akslantirsin. U holda f( 3/2) =? ni toping.##

A) i


B) (5i+1)/2

C) (-13+16 i )/15

+D) (-12+14 i )/17

E) 3i
##71# 1/(1-z)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1/2

B) –1/2

+C) 3

D) –3


E) 1/6
##72# 2/(1+z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

+A) 12


B) 6

C) 3


D) 1/3

E) 1/12


##73# z(z+2)/(2-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## A) 2

B) –2


C) –1/2

+D) 1/2

E) 1/3
##74# 1/(z2 +9) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1/9


B) –1/25

C) 1/49

+D) -1/81

E) 1/121
##75# 1/(1+z2)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 1

+B) –2


C) 3

D) –4


E) 5

##76# (z2+4z4+z6)/(1-z2)4 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 5

B) –4


C) 3

D) –2


+E) 1
##77# z/(1-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 0


B) 1/2

C) 1/3


+D) 3

E) 2
##78# 1/(z+1)(z-2) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## +A) –3/8

B) 3/4

C) 3/2


D) –3/2

E) 3/8
##79# (2z-5)/(z2-5z+6) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 25/127

B) 12/35

+C) –35/216

D) –13/41

E) 3/7
##80# 1/(z2-1)2(z2+4) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##

A) 6/17

+B) 7/16

C) 5/18

D) 9/14

E) 8/15
##81# 1/sinz funksiyaning z = 2 nuqtadagi qoldig‘ini toping.##

A) 

+B) 1/



C) 2

D) 1/2


E) -
##82# ctgz funksiyaning z = 3 nuqtadagi qoldig‘ini toping.##

+A) 1/

B) 

C) 3


D) 1/3

E) -
##83# thz funksiyaning z = i/2 nuqtadagi qoldig‘ini toping.##

A) 

B) -


C) 3

D) 2


+E) 1
##84# th2z funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##

A) 


B) -

+C) 0


D) –1

E) 1
##85# cosz/(z-1)2 funksiyaning z = 1 nuqtadagi qoldig‘ini toping.##

A) cos1

B) –cos1

C) sin1

+D) –sin1

E) 0
##86# 1/(e z +1) funksiyaning z = i nuqtadagi qoldig‘ini toping.##

A) -


B) 

C) 0


D) 1

+E) –1
##87# sinz/(z-1)3 funksiyaning z =1 nuqtadagi qoldig‘ini toping.##

A) 2

B) 1


+C) 0

D) –1


E) -2
##88# 1/sinz2 funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##

+A) 0


B) 1/2

C) 1


D) –1

E) 1/3
##89# cos[(z+2)/2z] funksiyaning z =  nuqtadagi qoldig‘ini toping.##

+A) 

B) -


C) 0

D) 1/


E) –1/
##90# z cos2(/z) funksiyaning z = nuqtadagi qoldig‘ini toping.##

A) 3,

+B) 2,

C) ,


D) 1,

E) 0
##91# Integralni hisoblang: .##

A) –2

B) –1


+C) 0

D) 1


E) 2

##92# Integralni hisoblang: .##

A) i

+B) 2i

C) 3i

D) -i


E) 0

##93# Integralni hisoblang: .##

A) i

B) -i/2

C)i/3

+D)-2i/3

E) 0

##94# Integralni hisoblang: .##



A) 2i cos1

B) 4i sin1

C) 2i(sin1+cos1)

D) 4i (sin1-cos1)

+E) 4i (cos1-sin1)

##95# Integralni hisoblang: .##

A) 2i sin1

+B) i (cos1+2sin1)

C) 4i (sin1 +2cos1)

D) 4i cos1

E) i (2sin1-cos1)

##96# Integralni hisoblang: .##

+A) -2i /9

B) 0


C) i /3

D) 1


E) i

##97# Integralni hisoblang: .##

A) i /3

B) -i /81

+C) -i /121

D) 0


E) 2i / 169

##98# Integralni hisoblang: .##

A) 0

B) i


C) –i

+D) i


E) -i

##99# Integralni hisoblang: .##

+A) 0

B) –i


C) 

D)-


E) 1

##100# Integralni hisoblang: .##

A) 2i

B) -2i



C)1

D)-1


+E) 0


1 - C

21 - C

41 - C

61 - B

81 - B

2 - C

22 - A

42 - B

62 - A

82 - A

3 - B

23 - D

43 - D

63 - E

83 - E

4 - B

24 - D

44 - E

64 - C

84 - C

5 - A

25 - B

45 - B

65 - A

85 - D

6 - E

26 - E

46 - A

66 - D

86 - E

7 - D

27 - D

47 - C

67 - B

87 - C

8 - A

28 - A

48 - D

68 - A

88 - A

9 - B

29 - C

49 - A

69 - C

89 - A

10 - E

30 - B

50 - E

70 - D

90 - B

11 - B

31 - B

51 - C

71 - C

91 - C

12 - A

32 - A

52 - C

72 - A

92 - B

13 - E

33 - E

53 - B

73 - D

93 - D

14 - C

34 - C

54 - B

74 - D

94 - E

15 - A

35 - D

55 - A

75 - B

95 - B

16 - D

36 - E

56 - E

76 - E

96 - A

17 - B

37 - C

57 - D

77 - D

97 - C

18 - A

38 - A

58 - A

78 - A

98 - D

19 - C

39 - A

59 - B

79 - C

99 - A

20 - D

40 - B

60 - E

80 - B

100 - E

8
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