Кўфн дан тестлар

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) = e^x(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) = e^x(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