Mit Aoe MCQ Z Transform
-
Upload
rishabh-singhal -
Category
Documents
-
view
223 -
download
0
Transcript of Mit Aoe MCQ Z Transform
Question 1 Z-transform of the sequence {f(k)} is F(z)=Option A
∑k=−∞
∞
f (k ) zk
Option B∑k=−∞
∞
f (k ) z−k
Option C∑k=−∞
∞
[ f (k ) ]−1zk
Option D∑k=−∞
∞
[ f (k ) ]−1z−k
Option ECorrect Answer BExplanation No ExplanationDifficulties 1Sub Topic Z-transform
Question 2 Z-transform of f ( k )=cos αk ;k ≥0 is
Option A z( z−cosα )z2−2 zcos α+1
;|z|>1
Option Bzsinα
z2−2 zcos α+1;|z|>1
Option Czcos α
z2−2 zcos α+1;|z|>1
Option D z (z−sinα )z2−2 zcos α+1
;|z|>1
Option E
Correct Answer A
Explanation(Optional) No Explanation
Difficulties 1
Sub Topic Z-transform
Question 3 Z-transform of f ( k )=sinαk ;k ≥0 is
Option A z( z−cosα )z2−2 zcos α+1
;|z|>1
Option B zsinα
z2−2 zcos α+1;|z|>1
Option C zcos α
z2−2 zcos α+1;|z|>1
Option D z (z−sinα )z2−2 zcos α+1
;|z|>1
Option E
Correct Answer B
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 4 Z-transform of f ( k )=cosh αk ; k≥0 is
Option A zsinhα
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option B zcosh α
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option C z (z−cosh α)z2−2 zcosh α+1
;|z|>max {|ea|,|e−a|}Option D z (z−sinhα)
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option E
Correct Answer C
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 5 Z-transform of f ( k )=sinh αk ;k ≥0 is
Option A zsinhα
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option B zcosh α
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option C z (z−cosh α)z2−2 zcosh α+1
;|z|>max {|ea|,|e−a|}Option D z (z−sinhα)
z2−2 zcosh α+1;|z|>max {|ea|,|e−a|}
Option E
Correct Answer A
Explanation No Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 6The inverse Z-transform of
z sinhα
z2−2 z cosh α+1is
Option Acosh αk ; k≥0
Option Bα sinhαk ;k ≥0
Option Csinhαk ;k ≥0
Option Dαcoshαk ; k≥0
Option E
Correct Answer C
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 7The inverse Z-transform of
z sinα
z2−2 z cosα+1is
Option A cos αk ;k ≥0
Option B k sinαk ;k ≥0
Option C kcos αk ; k≥0
Option D sinαk ;k ≥0
Option E
Correct Answer D
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 8The inverse Z-transform of
z( z−cosα )z2−2 zcos α+1
;|z|>1 is
Option A α sin k ;k ≥0
Option B cos αk ;k ≥0
Option C kcos α ;k ≥0
Option D αcos k ;k ≥0
Option E
Correct Answer B
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 9The inverse Z-transform of
z (z−cosh α)z2−2 zcosh α+1
;|z|>1 is
Option A coshα k ;k ≥0
Option B α sinhα ;k ≥0
Option C k cos α ;k ≥0
Option D α coshk ; k≥0
Option E
Correct Answer A
Explanation No Explanation
Difficulties
Sub Topic
Question 10 The Z-transform of unit impulse function is
Option A Z
Option B 1
Option C δ (k )
Option D 0
Option E
Correct Answer B
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 11The Z-transform unit impulse function is δ (k ) = f ( k )={1 ,∧K=0
0 ,∧K≠0is
Option A k
Option B z
Option C 1
Option D 0
Option E
Correct Answer C
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 12 The Z-transform of f ( k ) = cos3 k ; k ≥0 is
Option A z sin3
z2−2 zcos 3+1;|z|>1
Option B zcos 3
z2−2 zcos 3+1;|z|>1
Option C z ¿¿Option D z ¿¿Option E
Correct Answer D
Explanation No Explanation
Difficulties
Sub Topic Z-transform
Question 13 The Z-transform of f ( k ) = cosh 5k ; k ≥0 is
Option A zsinh 5
z2−2 zcosh 5+1;|z|>max {|e5|;|e−5|}
Option B z ¿¿Option C z cosh 5
z2−2 zcosh 5+1;|z|>max {|e5|;|e−5|}
Option D z ¿¿Option E
Correct Answer B
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 14 The Z-transform of f ( k ) = sin 5k ; k ≥0 is
Option A zcos 5
z2−2 zcos 5+1;|z|>1
Option B z sin5
z2−2 zcos 5+1;|z|>1
Option C z ¿¿Option D
z (z−sin 3)z2−2 zcos 5+1
;|z|>1
Option E
Correct Answer B
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 15 The Z-transform of f ( k ) = ak ; k ≥0 is
Option A zz−a
;|z|>|a|
Option B aa−z
;|z|>a
Option C azz−a
;|a|>|z|
Option D azz−a
;|z|>|a|
Option E
Correct Answer A
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 16 The Z-transform of U (k )={0 ,∧k<0
1 ,∧k ≥0 is
Option A 11−z
;|z|<1
Option B z1−z
;|z|<1
Option C 1z−1
;|z|>1
Option D zz−1
;|z|>1
Option E
Correct Answer D
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 17 The Z-transform of f ( k ) = ak ; k<0 is
Option A zz−a
;|z|>|a|
Option B 1z−a
;|z|>a
Option C za−z
;|z|<|a|
Option D 1a−z
;|z|<|a|
Option E
Correct Answer C
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 18 The Z-transform of f ( k ) = 2k ; k ≥0 is
Option A 2 z2−z
;|z|<2
Option B 12−z
;|z|<2
Option C zz−2
;|z|>2
Option D 1z−2
;|z|>2
Option E
Correct Answer C
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 19 The Z-transform of f ( k ) = 2k +1 ; k ≥0 is
Option A 2 z2−z
;|z|<2
Option B zz−2
;|z|>2
Option C 2 z2−z
;|z|>2
Option D z2−z
;|z|<2
Option E
Correct Answer C
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 20The Z-transform of f ( k )=(2
3)k
; k≥0
Option A 2 z2 z−3
;|z|> 23
Option B z3 z−2
;|z|> 23
Option C 3 z3 z−2
;|z|> 23
Option D zz−3
;|z|>3
Option E
Correct Answer C
Explanation No Explanation
Difficulties
Sub Topic
Question 21 The Z-transform of f ( k )=1 ; k≥0
Option A z1−z
;|z|<1
Option B 1z−1
;|z|>1
Option C zz−1
;|z|>1
Option D 11−z
;|z|<1
Option E
Correct Answer C
Explanation No Explanation
Difficulties 1
Sub Topic Z-transform
Question 22 The Z-transform of f ( k )=e−ak ; k≥0
Option A z
z−e−a;|z|>|e−a|
Option B e−a z1−z
;|z|>|e−a|Option C ea
z−e−a;|z|>|ea|
Option D z
e−a−z;|z|>|e−a|
Option E
Correct Answer A
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 23 The Z-transform of f ( k )=sin (3k+2) ; k≥0
Option A zsin 1
z2+2 zcos3+1Option B z sin (3k+2 )
z2−2 zcos(3k+2)+1Option C z(sin 1+z sin 2)
z2−2 zcos 3+1Option D z (sin 3+sin 2)
z2−2 zcos 3+1Option E
Correct Answer C
Explanation No Explanation
Difficulties 2
Sub Topic Z-transform
Question 24If Z (1 )= z
z−1;|z|>1 then Z-transform of f ( k )=k 2 ; k≥0 is
Option A z( z+1)(z−1)3
Option B z( z+1)(z−1)2
Option C z
(z−1)2
Option D z
(z−1)3
Option ECorrect Answer AExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 25If Z (2¿¿k )= z
z−2;|z|>2¿ then Z-transform of f ( k )=k 2k ; k≥0 is
Option A z
(2−z)2
Option B z2
(z−2)Option C z2
(2−z)2
Option D 2 z
(2−z)2
Option ECorrect Answer DExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 26If Z (5¿¿k )= z
z−5;|z|>5¿ then Z-transform of f ( k )=k 25k ; k≥0 is
Option A (z+5)(z−5)3
Option B 5 z (z+5)(z−5)3
Option C z
(z−5)4
Option D 5 z
(z−5)4
Option ECorrect Answer BExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 27If Z (2¿¿k )= z
z−2;|z|>2¿ then Z-transform of f ( k )=2k
k; k≥1 is
Option Alog( z−2
z );|z|<2
Option Blog( z2 );|z|<2
Option Ctan−1( z2 );|z|<2
Option Dlog( z
z−2 );|z|>2
Option ECorrect Answer DExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 28If Z (sin k )= z sin1
z2−2 zcos 1+1; then Z-transform of f ( k )= sin k
k; k≥0 is
Option Acot−1( sin 1
z−cos1 )Option B
cot−1( z−cos1sin 1 )
Option Ctan−1( z−cos1
sin1 )Option D
log( z−cos1sin 1 )
Option ECorrect Answer BExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 29If Z [cos (3k+2 )]= z [ zcos 2−cos1]
z2−2 zcos3+1; then Z-transform of
[2kcos (3k+2)] isOption A z [zcos 2−2 cos1]
z2−4 zcos 3+4Option B z [cos 2−2cos1]
z2−4 z+1Option C z [zcos 2−cos1]
z2−4 zcos 3+4Option D z [zcos 2−cos1]
z2−4 z cos3+1Option ECorrect Answer AExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 30If Z (k )= z
(z−1)2; then Z-transform of f ( k )=k e−ak; k≥0 is
Option A e−a z
( z−e−a )2
Option B z
( z−e−a )2
Option C e−a z
(e−a z−1 )2
Option D e−a z
( z+e−a )2
Option ECorrect Answer AExplanation No ExplanationDifficulties 2Sub Topic Z-transform
Question 31Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 32Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 33Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 34Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 35Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 36Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 37Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 38
Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 39Option AOption BOption C
Option DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 40Option AOption BOption COption DOption ECorrect Answer
Question 41Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 42Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 43Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 44Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 45Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 46Option AOption B
Option COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic
Question 47Option AOption BOption COption DOption E
Correct AnswerExplanation No ExplanationDifficultiesSub Topic
Question 48Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficulties
Sub Topic
Question 49Option AOption BOption COption DOption ECorrect AnswerExplanation No ExplanationDifficultiesSub Topic