BE-102BE (Ist Semester)Exam – Jan -2015

Mathematics

Max Time: 3 Hrs. Max Marks: 80

Note: - 1. Attempt All Questions of Section A, B andC

2. In Section A each question carry 2 mark3. In Section B each question carry 5 marks4. In Section C each question carry 7 marks

Qus.1- Choose the correct answer:-

(1) If then is

(a) (b)

(c) (d) None of these

¼1½ ;fn rc gSaA

¼v½ ¼c½

¼l½ ¼n½ buesa ls dksbZ ugha

(2) The function is minimum at the

point (a) (b)

(c) (d) (-3,3)

¼2½ og fcUnq ftl ij Qyu fuEu gSaA

¼v½ ¼c½

¼l½ ¼n½ (-3,3)

(3) Let then value of is

(a) (b)

(c) (d) None of these.

¼3½ ;fn rc dk eku gSaA

¼v½ ¼c½

¼l½ ¼n½ buesa ls dksbZ ugha

(4) is equal to-

(a) (b)

(c) (d)

(5) If then is

(a) (b)

(c) (d)

¼5½ ;fn rc gksxk

¼v½ ¼c½

¼l½ ¼n½

(6) Eigen values of the matrix are

(a) (b)

(c) 1 (d) 6,-1

¼6½ esfVªDl dh vMxu eku gSa

¼v½ ¼c½

¼l½ ¼n½ 6,-1

(7) A tree with 6 vertices has:- (a) 4 Edges (b) 5 Edges(c) 6 Edges (d) 7 Edges

¼7½ 6 ‘’kh"kZ okys o`{k esa Hkqtk,s gksxhA¼v½ Hkqtk, ¼c½ Hkqtk,

¼l½ Hkqtk, ¼n½ 7 Hkqtk,

(8) Let he is intelligent and he is

Hardworking the symbolic form of following statement is (a) (b)

(c) (d)

¼8½ ;fn og cqf)eku gSa vkSj og esgurh gSa

mijksDr dFkuks dk lkadsfrd :Ik gSa& ¼v½

¼c½

¼l½ ¼n½

(9) The equation has the solution

(a) (b)

(c) (d)

¼9½ lehdj.k dk gy gSa

¼v½ ¼c½

¼l½ ¼n½

(10) is equal to

(a) (b)

(c) (d)

Section-B

Qus.2- Reduce the matrix A to its NORMAL form and find Rank of A

OR

Determine the value of and , if following

equations have (i) no solution ( unique solv

(iii)Infinite many solution.

vFkokIkz’u-2& ;fn fuEu lehdj.kksa ds (i) dksbZ gy ugha (ii)

dksb gy (iii) vusd gy gSa rks ⋋ vkSj dk eku Kkr

djs&

Qus.3- Draw simplified network of

ORState and Prove D Morgan law.

Ikz’u-3& dk ljyhd`r ifjiFk

cuk;sAvFkok

Mh eksxZu dk fu;e fyf[k;s o fl) dfj;sA

Qus.4- Expand as for as term containing

ORDiscuss the maxima and minima of

Ikz’u-4& dk rd izlkj dfj;sA

vFkok dk mfPp"B o fuEu,B dh foospuk djsA

Qus.5- Evaluate the series.

ORProve that

Ikz’u-5& Js.kh dk eku

Kkr djsaAvFkok

fl) dfj;s

Qus.6- Solve

OR

Solve

Ikz’u-6& gy dfj;s

vFkok

gy fdj;s

Section-C

Qus.7- Find Eigen value & Eigen victory of the matrix

ORVerify clayey Hamilton for the matrix A and find

its inverse.

esfVªDl dk vkbxu eku vkSj vkbxeu

lfn’k Kkr djsaAvFkok

esfVªDl ds fy;s dSyh gSfeYVu

izes; dh tkWp djsaA vkSj esfVªDl dk izfrykse Kkr djsaA

Qus.8- Define the following terms:

(i) Tree (ii) Euler’s graph(iii) Subgraph (iv) circuit

ORConvert into disjunctive

normal form Ikz’u-8& fuEu dks ifjHkkf"kr djks

¼1½ Vªh ¼2½ vk;yj xzkQ¼3½ mixzkQ ¼4½ ifjiFk

vFkok dks distinctive normal :Ik

esa ifjofrZr djsA

Qus.9- if then show that

(i)

(ii)OR

If where then prove

That

Ikz’u-9& ;fn rc fl) dfj;s fd

(i)

(ii)vFkok

;fn tgka rc fl) dfj;s

fd

Qus.10- Prove the duplication formula,

OR

Evaluate

Ikz’u-10& MqIyhds’ku QkeZwyk fl) dfj;A

vFkok

gy dfj;s

Qus.11- Solve

ORSolve the simultaneous

Ikz’u-11& gy dfj;s

vFkok;qxir lehdj.k gy djsa&

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