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