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