M3 Miii Unit 2 Mcq 573948

l\

,/

'\-/

1.

Unit no-SrFourier Trasform and Z- Trasform

tn the f.ourier intggral

Il*r'^'l.Ji*f (u) e-i^u4r,r]di

f(x)=!-

whicr, of thq following is

foui'ier transform of f (u)

A

li*rr"> r-i,u4u b)

{2ro

r-iAu41

c) fi*f fr,> s-iAu41 d) None of these

2. lf f(u) is defined in the interval 0
,- )) Fs(2)= If f @)ti"7udu c) F(2)= e-i^"71u1auf \./

,-,

r ^6

[1.-

d) None ofthese

3.

lf

.f(x) satisfies Diri,qh.!et's conditions and absolutely integrable then inverse fourier

transform

\.il

is,

f(x)=1 Ii*n 61t'^',14

b)

f

(*\=

* fi

,

4,

r 1t1e-i7x

c) f(x)=* f*rQ)r-iLx41 d) None of these 4.

The

integralf(x)=1ir-tl* f (u)sinlu sinlxclu)dx

)^Fourier

\,/b) c)

integral

Fourier sine integral Fourier cosine integral

d) None of these 5.

The integral F.(I)=

[f f

tu)rorluduis

called

alrFourier transform \161 Forjrier cosinb transform

c) Fourier sine transform d) None ofthese 6.

The integra

I

f (x) = i

t:

F,(7)siil"xrll

a) Fourier transform b) lnverse Fourier transform ).2

-d)

lnv erse

si

ne tra n sform

lnverse cosine transform

represents

is called

7

.

The integrat

a) b)

6t'r d)

B.

C

j; J; f (u)coslu du represents

equivalent foEm of

Fourier transform Fourier sine transform ourier cosi n e tra nsfo rm None ofthese

/(x) = e-' (x>0)is 21 ,);; b)i'*l

Fourier sine transform of

, _^7

"9t,*, 'Fourier sine transfornr of,"-o' is tan -'[]) lf 9. x a) f (x) -- Ii

d\;i

,f,"n Fourier sine integral

IS

tan-'t!)tnt at

:iff

tan-1(l)stntxdx b) /(x) c) f (x) =? 1i tan-|t!)'nuat

d)

None of these

10. Fourier sine transform of

a) ;

b)

1

is

J;

-;

o

c) f (x) : fiti;ribxf d) None of these d'x

t3. tf fc\) rntegrai

for the function

/(x)

If ]at

a) 1

L4. Fourler

*then

the value of the iRtegral

dl

ft,l'l



lo,l,l>

-: r-^

d),2 t

[x,0<x<1

/(x)

[2-x,l sx<2 ,A,x2l

L

@..3)

then the value of

r

cll

b)-1-

sine transform of

B

u4,

.

b)e-*

:+

-:

then fourier integral

f (x) = e-'

ts

"\ :.

dl

41

12. lf Fourier sine transfor:m of l. .@ xslnmx , .

\ Jo r+r,

a

is

equalto

rn boo[. ,

2stn7(7-cos7\

a)

)2

2sinl(L-sinl>

b)

2sinl(sinl-1-)

c)

12

d)

None of these

Answers: 1=a 1

1-c

2-b

3-a

4-b

12-

13-c

14-a

\--l

5-b

Z-transform

...,f (1),f (2),...]

1.

The sequenc"

2.

a) Finite sequence b) Causal sequence c) Monotonic sequence d) None of these, lf z.= x * iy, then lzl )'3 represents points a) Outside the circle b) inside the circle c) on the circle d) None of thes'e

3.

The sequenc e f (k), (rn

4.

a) lnfinite sequence b) Finite sequence c) Causal sequence d) None ofthese lf z = x * iy,then lzl = 4,represents points a) outside the circle b) inside the circle c) on the circle d) None ofthese

5.

The z-transform of the sequence

f (k)

-

[0,0,0,

< k S n)

6-c

7-c

B-a

:

is called

is called

[/(lr)]defined or exists if \ff=, f (k)-k z is

a) Absolutelyconvergent b) Conditionallyconvergent

c) d) 6.

Divergent None of these

tf {/(/<)}is the sequence for

a) L?* f (k)-kz

k>

0 then which of the following is correct?

9-a

10-c

Itof

b)

c) 7.

rf

(k)-k z

E--Lf &)-kz

dj *""" "r ir-."tE

[/(lc)]is the sequence for -oo < k < a) Lff=of (k)-kz

oo

then which of the following is correct?

b) L?*f(k)kz

c) L!*f d)

8.

(k)-kz

Nbne of these

rf t/(k)1='l+,2,1,),]Jil,un ztf &)\is

a) 2z*t**,**.

bl

4z+t+i+)

*,** * d) 4zz + 2z * 1*** #

cl e.

rf

L

+.22

*

4z

z{f (k)} = F(z) then z{f,f"=--l(m)}

a) '

"b)

c)

is

7-z 'P

#

fQ)

d)'

z-7 f@) 1+z

10. The z-transform of unit impulse sequence sequence al,

f

d(k)'

Z_L

zb) 1_,

c)

0

..-.*f t 11. The z-trbnsfprm of disgrete unit step sequence

3) 1 -{*c)z '

d) 12. lf

7-z 0

f (k) = ak , (k > -al-,z ' z-a

o) then

zlakj

is

JI;.1

c) ;. z d)'

13. '{f

z+a

/(lr) = sin ak ot,

(l( > 0) then zfsinak]

is

z(z-Sins)

7-2zcosa+7

4

[U(k)]

is

is

\.{

--:---_ 22

Ul

,

-zzsind+l zsind

tl^\

22-2zcosd.+7

d) 14. tf

zsind

Non'e of these.

f (k) =

cos

ak

(k > 0) then z{cosak}

is

zcosa

al ol z2-zzcosa+7

"_dl;ffi 799:!.\ Lt z2-2zsina+L

d) None of these. 15. The Z-transform of the sequence a) b) c) d)

[/(k)] = al'coshak (k > 0)is

z(z-cosha) z2-2azcoshq.+a2

z-coshq

.

z'?-zazcr.sfu+a'z

z-sinha z2-2azcoshq+az None of these.

t6. z{(k + t)ak)

Jr -

to

is equal

t.

z-

@'a1z

b)

z2 -;--z'-o'

z

c).

d)

C:eY

z ':-._v-a)'

lti'. The'z-lransform of {k exists if

a) k>0 b) k<0

1-8.

t

c)

lc2

d)

for all values of /r.

lf z[sin?k] = ,#r^then

zt#]

(z-cos?\

a) b)

tan-1 J-l t s,nz

c)

cot-1 J-! I sin2

d)

None of these.

sin-.l

J

(z-cos2)

t r",, i (

z,- cosZ\ J

1s. rfr(k) = ztkt {fo, all k) then ztf (t)}is 1 . 'a) _T22 _______:t 7-Zz-t 7-22 z,z b) z-? 2-z c)

), ;-zz-r

d)

None of these

\

=

is equal

to

20.

rtf(ri) --_! {te}n)r thenZ[f(*)]is

a) Iog(1 - z) b} log (1 - z-')' tt -log (1 - z-1) d) None ofthese 21.. tf

f (k) = s-4k (k > 0) then Z[/(k)]

is

>q) ;v t,

,-4

;-;=a -A

-e ^l

z-e4

d) None ofthese. 22. tl Z{u(k)} *then Zdk{u(k)} is equal to zt a)' ta z-o b)z ' z-a ,.2

c)

@-"r ?z

d) ;* 23. tt f (k): .", 1t;;

,

(k > 0) then Zff(k)) is

.1 a) z4a

b) * c) ;_-2 d) ;2a. fi lzl ) lal , then z-1{*},tequalto

A

2s. tf

ak,7*>

o1

b) c)

-ak,1t< <

d)

None ofthese.

o1

a-k,1k>07

lzl > lal , then

e-1{;},t

equal to

a) -ak,1x > o1 b) ak*1,1k < o; \4' ak-7'(k > 1) d) -ak-7,(k < 1) 26: tf F(z) : *.,(lzl >' 2) then z-1{r(z)}isequalto .

a) -zi,(t . b)

o)

'{-Dk,(/c <

o)

\

c) (zlr.-t,(k > 1) d) 2k,,1k > t1

I

27. tf F(z)

=

>

fii,lzl

1) then z-1{r(z)}iisequatto

a) 2k-3,(K>1) b) 3k-2,(r(>1) c) k-2,(1(>o) d) 2k-L,(I(>1) 28. lt

F(z) =

G*4)then

residue of F(z)zK-t at Z=3

&ith'en

residue of

is

a) 3rc b) -3k c) 2k+r d) 3k-r 29' lt F(.2) =

a) b) ti dl

r(z)zK-t

at Z=2 is

2t(

-Zk-7 2k-L 2k+t

30. lf

F(z) =

a),2

*then

(-i)k

residue of F(Z)zK-lat z=l

is

(i)k b) _ 2

c) + d) 0 .3L.|t F(z)

=

at,23 b)

ffithen f

is equalto

e,-Gr 32 GT_GT

.13 .l L'/

d) 32. tf

Q-:) (,-) None ofthese.

F(z)

:;r\-

Z-J----,then z-1[F(Z)] is equalto

\,_) l,_;) a) O--,(;)--'' o)' (i)-

-

,u

(;)*-'

c) (i)- *, Od) (;)--,O33.'rf

/(/c) = 5k + (|)u ,tl,"n z{f (k)}k

.z52

al

-+-

7

z +sz b)' 5-z 7-52 .zz ' z-S

cl

d) 3a. fi

5-z

None ofthese.

lzl > lal , then z-1

a) ak,1t , o1 b) -ak,1t < o1

c)

o-k,1t <

d)

None ofthese.

l*\*equalto

o;

35. lf lzl > 5, then z-1

f'l

tcJ

IS

a) $,{t>o) b) -$, {r > o) ,

c)

sk,1t > o;

d) -5k, (t > o)

Answers:4-c

5-a

10-d

3-b 11-b

12-c

18-c

19-a

20-c

25-c

26-c

27-b

28-d

33-a

34-b

35-c

1-b 9-b

2-a

t7-c

\,/ L.

,/

8-d

7-c

13-c

6-b 14-b

15-a

16-a

2t-b

22-b

29-b

30-c

23-c 31-b

24-a 32-b

uNtr No 4 vEcroR

DIFFERENTIATIoN

lf the two vectors A and B are inclined at an angle 0 then the dot product or scalar

product

is

d

7.8 =17118 lsin o b) 7.8 =2 E coss __

n

c) A.B=A B nsin9 d) 2.

None of these

The cross product of the vectors

7

and E inclined at an angle 0 and

perpendicular to the plane at V ana E is

a)

AxE=ABcos0 o2

n

is

\

the vector