Chhattisgarh Swami Vivekanand Technical University 2007-4th Sem B.E Electronics & Tele-Communication Engineering (Mathematics-4, -07) - Question Paper

(b) Solve is series the equation :    10

328411(14)    *TO

s

* I Or

A rod ot lagih / with tasnUtcd ado a initially it a &teVraw, Itt ends are wdiealycooled. to 0*C aod are kspt zt that teseaaorc. Fnd *e teapen&re taction (c, f).

a* y

(e) Sotvc * 7 * wbkfa awo the

(0./)(/./)*(x.0)0 md

t

M* ⁰⁰ ~

Or

A tnsszsxuMa fane IOCO bn loot a imcilty uoda ptady*aic coodtboctt wiih potmrrtl 1300 wots *l tfaessdaf csd(x-0)iad 1200 voi&ai the receiTi&g cad (z * 1000X The tenamil ead of the foe is suddenly grrwyvlmA but tf* pOttTltaJ ( the SOUTCe t$ kept It 1300 Tote- Airainntlhciaduittpccapdkaiaaccto be oegltpble, find (he poCrrtfa? E (r, /).

Uoil-JV

4. (*) Write sbout Initial value theorem for Z-tnnsform.

(b)    Z-tnnsform. solve (fae difference equation:

+*" ^mSr

I $ I Or

Ftod the tnvcne 2-traasforra of: 2x

(e) FtaJ tfae amc Z-tnaafom of: x*-Sr¹+tr-4

Or

Sbtc aad prove the Fifaal VUae tbeoraa fix x-transfana.

Unh-V

5. (a) The duly cooaarybon of tkctnc pcrtr ( sslboca of kW-hows) is a random vanabte having txobab&tydmsity fuactkn:

/(x)l'^{J W} 1 0. xSO*

If ibe total productoa is 12 million kW-bour*. 2    determine the probability that there is power cut

(shortage) oo any given day.

x>0

(b) A die is tossed thrice. A success is 'getting 1 or 6* oo a toss. Find (be mean and tbc variance of tbc oumbcr of accniti.

Fiod ihe mean and variaiKc of Binomial Dntribulkxv

(c) Fit Poisson distribution lo ihe following dau:

x,    : 0 I 2 3 4

Observed

frequcacie'

f_t    : 30 62 46 10 2

Or

Show (hat the area under the normal curve is unity.

J28411(14)

U. E. (Fourth Semester) Examination, Nov.-Dcc., 2007

(AEl, El, Et St T Kub'b. Ilraucli)

MATHEMATICS-1 V

Time Allowed : Three hours

Maximum Marks : 80

Minimum Pass Marks : 28

Note : Attempt all questions. Each question carries equal nuirks. There is internal choice in each question.

Umt-I 1. (a) Find J₀(x) and J, (je) .    2 (b) Solve is series the equation :    10

328411(14)    *TO

s

* I Or

A rod ot lagih / with tasuUtcd ado a initially it a &teperaw, Ics cads arc tuddeoly cookd. to 0*C aod are kspt zt that teseaaorc. Fnd *e teapen&re taction (c, f).

a* y

(c) Sotvc 0 fakb awo the

(<*./)(/./)*(*.0)0 md

t **

M* ⁰⁰ ~

Or

A tnsszsxuMa fane IOCO bn loot a imcilty uoda Uody*saic coodtboctt wilh potmrrtl 1300 wots al tfaesodaf csd(x-0)aad 1200 nobs anberccefri&g cad (z * 1000X The tcnninal end of ihe line is suddenly grrwyvimA but the poeen&a] at the source is kept at 1300ToAiraTmtihciaduittDceaodkkatnccto be oegltpble, find (he poCrttfa? E (r, /).

Uoil-JV

4. (a) Write about Initial value theorem for Z-transform.

(b) U"! Z-tnnsform. solve the difference equation: +*" ^mSr

I $ I Or

Ftod the tnvene 2-traasforra of: 2x

(e) FtaJ tfae amc Z-tnaafom of: x*-Sr*+tr-4

Or

Sbtc aad prove the Fifaal VUae tbeoraa fix x-transfana.

Unh-V

5. (a) Tbc duly cooaarybon of tkctnc pcrtr ( sslboca of kW-feows) is a random vanabte having probability demity fuactkn:

/(x)l'^{J W} 1 0. xSO*

If the total productoa is 12 million kW-bour*.

2    determine the probability that there is power cut

(shortage) oo any given day.

x>0

(b) A die is tossed thrice. A success is 'getting 1 or 6* oo a toss. Find tbc mean and tbe variance of tbc oumbcr of accniti.

Fiod the mean and variance of Binomial Distribution.

(c) Fit Poisson distribution to the following (bu:

x,    : 0 I 2 3 4

Observed

frequcacie'

f_t    : 30 62 46 10 2

Or

Show (hat the area under the norma) curve is unity.