(DBMAT 31)
ASSIGNMENT - 1 , DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
Part — II : Mathematics
Paper – III : RINGS AND LINEAR ALGEBRA
Maximum : 20 MARKS
Answer ALL questions.
1)
If the characteristic of a ring R is “2” and if
2
2
2
a, b ∈ R, commute. Show that
2
( a + b) = a + b = (a − b) .
R
ÐèþËÄæý$Ðèþ$$ Äñý$$MæüP Ìê„æü×ìýMæü ÑË$Ðèþ
“2”, R
ÌZ° Ðèþ$*ËMæüÐèþ$$Ë$ a,b Ë$ Ñ°Ðèþ$Äæý$Ðèþ$Æÿ$$¯èþ
( a + b) 2 = a 2 + b 2 = (a − b) 2 A° °Ææÿ*í³…ç³#Ðèþ$$.
2)
Define an Integral domain and give an example of a ring which is not an Integral Domain.
ç³NÆ>~…Mæü {糧óþÔèýÐèþ$$¯èþ$ °ÆæÿÓ_…_, ç³NÆ>~…Mæü {糧óþÔèýÐèþ$$M>° §é°Mìü E§éçßýÆæÿ×ìýÐèþ$$Ã.
3)
Prove that any set of n linearly independent vectors in an “n” dimensional vector space V(F) form
a basis of V.
V(F) JMæü “n” ç³ÇÐèþ*×ý çܨÔé…™èþÆ>âæýÐèþ$$. V ÌZ° {糆 “n” Ðèþ$*ËM>Ë$ º$$k ÝëÓ™èþ…{™èþ çÜÑ$† “V”
Äñý$$MæüP B«§éÆæÿ… AÐèþ#™èþ$…§æþ° ^èþ*ç³…yìþ.
4)
T : U → V be a linear transformation. Prove that the vectors. x1, x2 ,......, xn ∈U are linearly
independent, if T ( x1 ), T ( x2 ),....., T ( xn ) are linearly independent.
T : U → V JMæü º$$k ç³ÇÐèþÆæÿ¢¯èþÐèþ$$. T ( x1 ), T ( x2 ),....., T ( xn )
x1, x2 ,......, xn ∈ U Ë$ Mæü*yé º$$k ÝëÓ™èþ…{™éÅËÐèþ#™èþ$…§æþ° ^èþ*ç³#Ðèþ$$.
5)
a)
i)
Ë$ º$$k ÝëÓ™èþ…{™éÅËÆÿ$$™ôþ
Prove that the homomorphic image of a ring is a ring.
JMæü ÐèþËÄæý$… Äñý$$MæüP çÜÐèþ$Ææÿ*ç³™é {糆¼…ºÐèþ$$ Ðèþ$ÆæÿË ÐèþËÄæý$… AÐèþ#™èþ$…§æþ° °Ææÿ*í³…^èþ…yìþ.
ii)
Prove that an ideal Z is a maximal iff it is generated by a prime.
ç³NÆ>~…Mæü ÐèþËÄæý$Ððþ$O¯èþ Z ÌZ M A«¨Mæü™èþÐèþ$$ IyìþÄæý$ÌŒý M>Ðèþyé°Mìü BÐèþÔèýÅMæü ç³Æ>Åç³¢°Äæý$Ðèþ$…
çÜ…QÅ ^óþ f°™èþ… A° ^èþ*ç³…yìþ.
b)
i)
M
A¿êfÅ
a b
If R = ( M 2 , +, ⋅) is a ring over integers, then prove that M =
a, b ∈ z is a
0 0
right ideal but not a left ideal of R.
R = ( M 2 , +, ⋅) Ðèþ*{†M>
ÐèþËÄæý*°Mìü
a b
M =
a, b ∈ z
0 0
JMæü Mæü$yìþ IyìþÄæý$ÌŒý AÆÿ$$ GyæþÐèþ$
IyìþÄæý$ÌŒý M>§æþ° ^èþ*ç³…yìþ.
ii)
Prove that any integral domain can be embedded in a field.
{糆 ç³NÆ>~…Mæü {糧óþÔé°² JMæü „óü{™èþ…ÌZ CÐèþ$yæþaÐèþ^èþa° ^èþ*ç³…yìþ.
6)
a)
i)
Prove that every non-empty subset of Linearly Independent set is Linearly
Independent and every superset of a linearly dependent set is linearly dependent.
º$$k çÜÓ™èþ…{™èþÅ çÜÑ$†ÌZ° {糆 Ôèý*¯óþÅ™èþÆæÿ Eç³çÜÑ$† º$$k çÜÓ™èþ…{™èþÅ çÜÑ$† A°, º$$k AçÜÓ™èþ…{™èþÅ
çÜÑ$† Äñý$$MæüP A«¨ çÜÑ$† (superset) º$$k AçÜÓ™èþ…{™èþÅ çÜÑ$† A° °Ææÿ*í³…^èþ$Ðèþ$$.
ii)
State and prove Rank-Nullity theorem.
Møsìý&Ôèý*¯èþÅ™èþ íܧ骅™èþÐèþ$$¯èþ$ {ç³Ðèþ_…_, °Ææÿ*í³…^èþ$Ðèþ$$.
b)
i)
W1 , W2 are
the
subspaces
of
V4
generated
by
{(1,1, 0, − 1) , (1, 2,3, 0 ) , ( 2,3,3, − 1)} and {(1, 2, 2, − 2 ) , ( 2, 3, 2, − 3) , (1, 3, 4, − 3)} respectivel
y Find (i) dim W1 ( ii) dim (W2+W2) (iii) dim(W1 ∩ W2 )
A…™èþÆæÿÐèþ$$ÌZ W1 , W2
Ë$
{(1,1, 0, − 1) , (1, 2,3, 0 ) , ( 2,3,3, − 1)} Ðèþ$ÇÄæý$$
{(1, 2, 2, − 2 ) , ( 2, 3, 2, − 3) , (1, 3, 4, − 3)} E´ë…™èþÆ>âæýÐèþ$$ËÆÿ$$¯èþ D {Mìü…¨ Ðésìý° Mæü¯èþ$Vö¯èþ$Ðèþ$$
V4
(i) dim W1 ( ii) dim (W2+W2) (iii) dim(W1 ∩ W2 )
ii)
T : U → V is a linear transformation, when U(F) and V(F) are vector spaces, prove that
null space N(T) is a sub space of U(F).
Ë$ Æðÿ…yæþ$ çܨÔé…™è Æ>âêË$ T : U → V JMæü º$$k ç³ÇÐèþÆæÿ¢¯èþÐèþ$Æÿ$$™ôþ
Ôèý*¯éÅ…™èþÆ>âæýÐèþ$$ N(T) E´ë…™èþÆ>âæýÐèþ$$ A° ^èþ*ç³…yìþ.
U(F) , V(F)
——————
U(F)
¯èþMæü$
(DBMAT 31)
ASSIGNMENT - 2 , DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
Part — II : Mathematics
Paper – III : RINGS AND LINEAR ALGEBRA
Maximum : 20 MARKS
Answer ALL questions.
1)
−2 1 3
Compute the inverse or the matrix A = 0 −1 1
1 2 0
2)
5 4
Find the eigen values and eigen vectors of the matrix of A =
1 2
Ðèþ*{†Mæü Äñý$$MæüP ÑÌZÐèþ$ Ðèþ*{†Mæü¯èþ$ Mæü¯èþ$MøP…yìþ.
Ðèþ*{†MæüMæü$ IV𠯌þ ÑË$Ðèþ˯èþ$
Ðèþ$ÇÄæý$$ IVðü¯Œþ çܨÔèý˯èþ$ Mæü¯èþ$MøP…yìþ.
3)
Let α = ( 2,1 + i, i ) , β = ( 2 − i, 2,1 + 2i ) be two vectors in V3 ( C ) , then compute α + β
and also
verify α + β < α + β
V3 ( C ) ç ò³O α = ( 2,1 + i, i ) , β = ( 2 − i, 2,1 + 2i )
Æðÿ…yæþ$ çܨÔè ÌñýO™ôþ
α +β
¯èþ$ Mæü¯èþ$Vö°
α +β < α + β
A° çÜÇ^èþ*yæþ…yìþ.
4)
In an inner product space V ( F ) , then prove that α , β ≤ α β for all α , β ∈ V
V ( F ) A¯óþ A…™èþÆæÿ ˻ꪅ™èþÆ>âæý…ÌZ α , β ∈ V Mæü$ α , β ≤ α β
5)
a)
A° ^èþ*ç³…yìþ.
1 2 3
i) Verify cayley-Hamilton theorem of a given matrix A = 2 −1 4 and hence, find A-1
3 1 −1
1 2 3
A = 2 −1 4
3 1 −1
ii)
Ðèþ*{†MæüMæü$ MóüÎ&àÑ$ÌŒýr¯Œþ íܧ骅™èþÐèþ$$¯èþ$ ç³ÇÖÍ…_ ™èþ§éÓÆ>A-1 Mæü¯èþ$MøP…yìþ.
3 4
Show that the matrix A =
is a diagonalizable matrix and find the diagonal
4 3
matrix.
3 4
A=
4 3
A¯èþ$ Ðèþ*{†Mæü¯èþ$ ÑMæüÈ~Äæý$ Ðèþ*{†Mæü A° ^èþ*í³, ÑMæüÆæÿ~Ðèþ*{†Mæü¯èþ$ Mæü¯èþ$MøP…yìþ.
b)
i)
3 1 1
Find the eigen values and eigen vectors of the matrix A = 2 4 2
1 1 3
ò³O
A
Ðèþ*{†Mæü
ò³O
A
Ðèþ*{†Mæü
Äñý$$MæüP IVðü¯Œþ ÑË$Ðèþ˯èþ$ Ðèþ$ÇÄæý$$ Ðésìý IVðü¯Œþ çܨÔèý˯èþ$ Mæü¯èþ$MøP…yìþ.
ii)
−1 −3 3 −1
1 1 −1 0
by reducing normal form.
Find the rank of the A =
2 −5 2 −3
−1 1 0 1
Äñý$$MæüP Møsìý° AÀË…ºÆæÿ*ç³Ðèþ$$ÌZ°Mìü Ðèþ*Ça Mæü¯èþ$MøP…yìþ.
6)
a)
i)
State and prove “Triangle inequality”
{†¿æý$f AçÜÐèþ*¯èþ™èþ¯èþ$ {ç³Ðèþ_…_, °Ææÿ*í³…^èþ$Ðèþ$$.
ii)
If {α1 , α 2 ,........, α n } is an orthonormal set in an inner product space V(F) and β ∈ V ,
then prove that γ = β − β , α1 α1 − β , α 2 α 2 ............ β , α n α n is orthogonal to each of
α1 , α 2 ,.α 3 ,....α n .
A…™èþÆæÿ ˻ꪅ™èþÆ>âæýÐèþ$$ V(F) ÌZ {α1 , α 2 ,........, α n } JMæü Ë…¿êÀË…º çÜÑ$† AÆÿ$$™ôþ, β ∈V
¯èþMæü$, çܨÔèý γ = β − β , α1 α1 − β ,α 2 α 2 ............ β , α n α n , {糆 α1 , α 2 ,.α 3 ,....α n .
Ë…º…V> E…r$…§æþ° ^èþ*ç³…yìþ.
b)
i)
Show that the vectors x,y in an innerproduct space V are orthogonal iff
2
2
2
2
2
ax + by = a x + b y , a, b ∈ C
A…™èþÆæÿ ˺ª A…™èþÆ>âæýÐèþ$$ V ÌZ x,y Ë$ çܨÔèýË$, Ë…ºçܨÔèýË$ M>Ðèþsê°Mìü BÐèþÔèýÅMæü ç³Æ>Åç³¢ °Äæý$Ðèþ$Ðèþ$$
2
2
2
2
2
ax + by = a x + b y , a, b ∈ C A° °Ææÿ*í³…^èþ$Ðèþ$$.
ii)
State and prove Bessels inequality in an innerproduct space.
»ñýòÜÌŒýÞ AçÜÐèþ*¯èþ™èþ¯èþ$ {ç³Ðèþ_…_, °Ææÿ*í³…^èþ$Ðèþ$$.
——————
(DBMAT 32)
ASSIGNMENT - 1 , DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
Part — II : Mathematics
Paper – IV : NUMERICAL ANALYSIS
Maximum : 20 MARKS
Answer ALL questions.
1)
Find u x , Where ∆u x = x ( x − 1)
∆ux = x ( x − 1) AÆÿ$$™ôþ u x ÑË$Ðèþ¯èþ$ Mæü¯èþ$MøP…yìþ.
2)
Find the missing values in the following table.
x
45 50 55 60 65
y
3.0 2.0 -2.4
ò³O ç³sìýtMæüÌZ ÌZí³…_¯èþ ÑË$Ðèþ˯èþ$ Mæü¯èþ$Vö¯èþ$Ðèþ$$.
3)
Derive Laplace-Everett’s formula.
Ìê´ëÏ‹Ü& GÐèþÆðÿsŒýÞ çÜ*{™é°² Æ>ºr$tÐèþ$$.
4)
Use Bessel’s formula to find y25 , given that y20 = 2.4; y24 = 32; y28 = 35, y32 = 40
ò³O ÑË$Ðèþ˯èþ$ Eç³Äñý*W…_,
5)
a)
i)
y25
ÑË$Ðèþ¯èþ$ »ñýòÜÌŒýÞ çÜ*{™èþ… §éÓÆ> Mæü¯èþ$MøP…yìþ.
Derive Newton’s Forward Interpolation formula
¯èþ*År¯Œþ ç³#ÆøVæüÐèþ$¯èþ A…™èþÆóÿÓÔèý¯èþ çÜ*{™èþÐèþ$$¯èþ$ Æ>ºr$tÐèþ$$.
ii)
Obtain f ( x) , when x = 1.4 from the following table by using Newton’s Forward
Interpolation Formula.
x
1.1 1.3 1.5 1.7 1.9
f(x) 0.21 0.69 1.25 1.89 2.61
ò³O ç³sìýtMæü ¯èþ$…yìþ
b)
i)
x = 1.4
Ðèþ§æþª f ( x) ÑË$Ðèþ¯èþ$ ¯èþ*År¯Œþ & ç³#ÆøVæüÐèþ$¯èþ 糧æþª† §éÓÆ> Mæü¯èþ$MøP…yìþ.
Construct a forward difference table from the following data. Evaluate
∆ 3 y1 ; y x and y5
x
yx
0
1
1
1.5
2
2.2
3
4
3.1 4.6
ò³O ç³sìýtMæü¯èþ$ ç³#ÆøVæüÐèþ$¯èþ ¿ôý§æþ ç³sìýtMæü¯èþ$ Mæürt…yìþ Ðèþ$ÇÄæý$$
∆ 3 y1 , y x
Ðèþ$ÇÄæý
y5 ÑË$Ðèþ˯èþ$ Æ>ºr$tÐèþ$$.
ii)
Prove that (i) E∇ = ∆ = ∇E
(ii) (1 + ∆ )(1 − ∇ ) = 1 ˯èþ$ °Ææÿ*í³…^èþ…yìþ.
6)
a)
i)
Explain sterling’s formula.
íÜtÇÏ…VŠü Üç *{™é°² ÑÐèþÇ…ç³#Ðèþ$$.
ii)
Find y30 , use Gauss-Forward Formula from the following data
y21 = 18.4708; y25 = 17.8144; y29 = 17.1070; y33 = 16.3432; y37 = 15.5154
ò³O ÑË$Ðè Ë ¯èþ$…yìþ
b)
i)
y30 ÑË$Ðèþ¯èþ$ V>‹Ü ç³#ÆøVæüÐèþ$¯èþ çÜ*{™èþÐèþ$$ §éÓÆ> Mæü¯èþ$MøP…yìþ.
Explain Gauss-Forward Formula.
V>‹Ü&ç³#ÆøVæüÐèþ$¯èþ °Äæý$Ðèþ$Ðèþ$$¯èþ$ ÑÐèþÇ…ç³#Ðèþ$$.
ii)
State Everetts Formula, from this find log 23.75 from the following data
x
21
22
23
24
25
26
log
1.3222
1.3424
1.3617
1.3802
1.9190
1.4150
ò³O ç³sìýtMæü ¯èþ$…yìþ, GÐèþÆðÿsŒý çÜ*{™é°² {ç³Ðèþ_…_, §é°° Eç³Äñý*W…_ log 23.75 ÑË$Ðèþ¯èþ$ Mæü¯èþ$MøP…yìþ.
——————
(DBMAT 32)
ASSIGNMENT - 2 , DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
Part — II : Mathematics
Paper – IV : NUMERICAL ANALYSIS
Maximum : 20 MARKS
Answer ALL questions.
1)
Derive Weddle’s rule
ÐðþyæþzÌŒýÞ °Äæý$Ðèþ*°² Æ>ºr$tÐèþ$$.
2
2)
Evaluate
2
−x
∫ e dx by using Simpson’s −
0
íÜ…ç³Þ¯ŒþÞ
3)
1
−
3
2
1
rule taking h = 0.25
3
2
°Äæý$Ðèþ$Ðèþ$$ §éÓÆ> ∫ e− x dx ÑË$Ðèþ¯èþ$ Æ>ºr$tÐèþ$$ C^èþar
h = 0.25 .
0
Solve the following system of equation by using Gauss-elimination method.
x + y + z = 6, 3 x + 3 y + 4 z = 20, 2 x + y + 3 z = 13
ò³O çÜÒ$MæüÆæÿ×ýÐèþ$$Ë ÐèþÅÐèþçܦ¯èþ$ V>‹Ü&™öËW…ç³# 糧æþª† §éÓÆ> Ý뫨…^èþ…yìþ.
4)
Find a real root of the equation
f ( x) = x3 − 2 x − 5 = 0
f ( x) = x3 − 2 x − 5 = 0 çÜÒ$MæüÆæÿ×ýÐèþ$$¯èþMæü$ ÐéçÜ¢Ðèþ Ðèþ$*ËÐèþ$$˯èþ$ Mæü¯èþ$MøP…yìþ.
5)
a)
i)
Derive Trapezoidal rule
{sñýí³gêÆÿ$$yæþÌŒý °Äæý$Ðèþ$Ðèþ$$¯èþ$ Æ>ºr$tÐèþ$$.
5.2
ii)
Find the value of
∫ log
e
x dx by weddle’s rule
4
5.2
ÐðþyæþÌŒýÞ °Äæý$Ðèþ$Ðèþ$$ §éÓÆ> ∫ log e x dx ÑË$Ðèþ¯èþ$ Mæü¯èþ$MøP…yìþ.
4
b)
i)
Explain Taylor’s series method.
sôýËÆŠÿ {Ôóý×ìý 糧æþª†° ÑÐèþÇ…ç³#Ðèþ$$
ii)
Solve
dy
= y with y (0) = 1 by Picard’s method and Compare it with exact solution.
dx
í³M>ÆŠÿz 糧æþª† §éÓÆ>
çÜÇ^èþ*yæþ…yìþ.
6)
a)
i)
dy
= y , y (0) = 1 ¯èþ$
dx
Ý뫨…^èþ…yìþ Ðèþ$ÇÄæý$$ D ÑË$Ðèþ¯èþ$ Mæü_e™èþ ÑË$Ðèþ™ø
Explain Regula-Falsi method
ÆðÿVæü$ÅÌê&¸ëÅÍÞ ç³§æþª†° ÑÐèþÇ…ç³#Ðèþ$$.
ii)
Find the root of the equation x 2 + 4 sin x = 0 by using Newton’s method correct to 4
decimal places.
x 2 + 4 sin x = 0 çÜÒ$MæüÆæÿ×ýÐèþ$$
Äñý$$MæüP Ðèþ$*Ìê°² 4 §æþÔé…ÔéË ÐèþÆæÿMæü$, ¯èþ*År¯ŒþÞ&糧æþª† §éÓÆ>
Mæü¯èþ$MøP…yìþ.
b)
i)
Solve the following system of equations by using Crammar’s rule
3x + 2 y − z + t = 1
x − y − 2 z + 4t = 3
2 x − 3 y + z − 2t = −2
5 x − 2 y + 3 z + 2t = 0
ò³O çÜÒ$MæüÆæÿ×ýÐèþ$$Ë ÐèþÅÐèþçܦ¯èþ$ {M>Ðèþ$ÆŠÿÞ ç³§æþª†ÌZ Ý뫨…ç³#Ðèþ$$.
ii)
Solve the following system of equations by using Gauss-Seidal method.
27 x + 6 y − z = 85
6 x + 15 y + 2 z = 72
x + y + 54 z = 110
ò³O çÜÒ$MæüÆæÿ×ýÐèþ$$Ë ÐèþÅÐèþçܦ¯èþ$ V>‹Ü&ïÜyæþÌŒý 糧æþª† §éÓÆ> Ý뫨…^èþ$Ðèþ$$
——————
(DBSTT 31)
ASSIGNMENT - 1, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
STATISTICS
Paper - III : APPLIED STATISTICS
Maximum : 20 MARKS
Answer ALL questions.
1)
a)
Explain the advantages of sampling over census.
b)
Explain SRSWOR & SRSWR. Show that sample mean is an unbased
estimate of population mean i.e. F( ) =
2)
a) Explain ANOVA along with its assumptions and uses. Explain one-way
classification.
b) Explain the principles of experimental designs.
3)
a) Describe the layout of RBD along with its advantages and disadvantages.
b) Explain the ANOVA of Latin square design.
4)
a) Explain S.Q.C, give its uses.
b) Explain the construction of
5)
and R chart variables.
a) What are vital statistics give its sourced and uses?
b) Explain the death vates and birth nater along with merits and demerits.
——————
(DBSTT 31)
ASSIGNMENT - 2, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
STATISTICS
Paper - III : APPLIED STATISTICS
Maximum : 20 MARKS
Answer ALL questions.
1)
a)
Explain the construction of life table and give its uses.
b) Explain the functions of CSO.
2)
3)
a)
Explain time series? Explain the components of time series.
b)
Explain the principle of least square method to find trendvalues.
a)
Define index number? Explain the construction of weighted index number.
b) Show that Fisher Index number is an ideal index number.
4)
a)
Sampling error
b)
Proportional allocation
c)
CRD Layout
d)
3 σ control limits
e)
Fertility and Fecundity
f)
A bridged life table
g)
Moving Averages
h)
Uses of Index numbers
i)
Simple index numbers
j)
Base shifting
——————
(DBSTT 32)
ASSIGNMENT - 1, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
STATISTICS
Paper-IV : OPERATIONS RESEARCH, COMPUTER PROGRAMMING AND
NUMERICAL ANALYSIS
Maximum : 20 MARKS
Answer ALL questions.
1)
a)
Define OR, give its scope and limitations and uses of OR.
b)
Define transportation problem and also give its mathematical formulation.
Solve the following problem by using North-West corner rule to get DBFS.
Stores
1
2
3
Supply
1
12
17
14
5
2
13
13
11
8
3
15
14
17
7
4
11
16
12
14
Demand
7
9
18
Factory
2)
a)
Explain simplex algorith for LPP.
b)
Using simplex method solve the following LPP.
Max
Z = 6x + 4y
Subject to 3x + 2y ≤ 18
x≤4
y≤6
x, y ≥ 0
3)
a)
Explain game theory? Define the following
i)
Maximum and Minimum.
ii)
Pure and Mixed strategies.
iii) Graphical method of solving.
b)
Solve the following problem graphically
Player B
Player A
4)
a) Explain concepts purchasing reading paper-type of purchasing make
sense.
b) Explain constants, strings, variables and expressions and also branch, looping,
GOTO, if then functions.
5)
a) Define interpolation along with its assumptions and uses of interpolation.
Also estimate x = 3.5 from the followings Data
x : 1
2
3
4
5
6
7
8
9
y = f(n) : 3
7
14
23
38
49
56
87
108
b) Estimate the value of y, when x = 65 by using Legranges method.
x:
59
60
61
62
y = f(n)
1317
1482
1826
1736
——————
(DBSTT 32)
ASSIGNMENT - 2, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
STATISTICS
Paper-IV : OPERATIONS RESEARCH, COMPUTER PROGRAMMING AND
NUMERICAL ANALYSIS
Maximum : 20 MARKS
Answer ALL questions.
1)
2)
a)
Explain inverse interpolation and numerical differentiation.
b)
Explain:
a)
and
rules.
i)
Simpson
ii)
Weddle’s and Trapezoidal rule.
Using Newton’s Raphson method find the root of the equation
x4 – x – 10 = 0.
b)
Using Gauss elimination method solve
2x 1 + 3x2 + 4 x 3 = 5
3x 1 + 4x2 + 5 x 3 = 6
4x 1 + 5x2 + 6 x 3 = 7
3)
a) How do you handle data in MS Excel? Explain various editing and techniques
in Excel.
b)
Explain how do you find the mean and variance of set of n observations using
MS Excel.
4)
a)
Assignment problem.
b)
Sequencing problem.
c)
Graphical Method.
d)
2 x 2 game.
e)
Flow chart and decision force.
f)
Magnetic tape and floppy disk.
g)
M.S. Excel sheet.
h)
Finite differences.
i)
Numerical Integration.
j)
Gauss – Forward formula and Backward formula.
——————
(DBC 40)
ASSIGNMENT - 1, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
COMPUTER APPLICATIONS - III
Paper V – REPORT GENERATOR
Maximum : 20 MARKS
Answer ALL questions.
1)
Bring out macro creation, delection and Editing in Excel?
Excel
2)
Describe the parts of functions in Excel with Examples.
Excel
3)
Ä] macro ßÔ’Ñw šÔÈ ¼! #u È" (¿¼! # J| v †Y‹ ç" ( ”! Ã(ß«'È" #B
Ä]¨ Éɤ Þ ¾Þ+PARÄ/ §"
È" # ¼/ #PÞ S ·:YAÃ( ”! Ã(ß«'È" #2
How are charts created in Excel?
Excel
5)
Ä] a1¾Þ+(wÃ( JÄ: ”7 ¼! .¾Þ+( a Õ>›¾Þ+(B
Explain importing of data in Excel?
Excel data
6)
( H 1ß× ¾Þ+Ï Ã”4 ÉÈ" ¿†ß«'È" #2
State the components of Excel sheet?
Excel ß«~”7
4)
functions §"
¡YÞ (È" (‡¨ YÞ (¿†b ÉÈ" ¿†a7 (È" #B
Features of Print preview.
~—†vD ~«È" Q½ ¼/ #PÞ S D†ÌAÃ(2
7)
Bring out inserting rows and columns of work sheet?
ßÈ" ¾Þ+(S ß«~”7 È" #Ä] D|Þ (} È" ¾Þ+(ßÔÃ( ¨Ã(È" È" ¾Þ+(ßÔÃ( ”! Ã(ß«'È" #B
8)
Scenario Manager
Ô§1¿¼/ . ¨¾AËß× PÞ (|Þ (
9)
Footers
ß—Qu¾‹+Ö
10)
Work Books
È" ¾‹+S ß«~”7 È" #
——————
(DBC 40)
ASSIGNMENT - 2, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
COMPUTER APPLICATIONS - III
Paper V – REPORT GENERATOR
Maximum : 20 MARKS
Answer ALL questions.
1)
What are the features of MS – Excel?
MS – Excel
2)
Explain entering data and editing the data.
Excel
3)
Ä] | v: §" ( JÄ: J†u¾‹+ a Õ>›¾Þ+( È" (¿¼! # J| v †Y‹ JÄ: a Õ>›¾Þ+(B
Explain Mathematical and Statistical functions in Excel?
Excel
4)
¼/ #PÞ S Ã…Þ Ï: Ã( KÉ(B
Ä]¨ YÞ Ï ”7 È" (¿¼! # YÞ Ï: †PÞ ~ß«È (¼! .ç" ( ÉÈ" ¿†a7 †| B
Bring out inserting rows and columns of work sheet?
ßÈ" ¾Þ+(S ß«~”7 È" #Ä] D|Þ (} È" ¾Þ+(ßÔÃ( ¨Ã(È" È" ¾Þ+(ßÔÃ( ”! Ã(ß«'È" #B
5)
What are headers in Excel?
Excel Ä] N× |Þ
6)
¾‹+Ö KÉ(B
State cell data sorting?
NÔÄD | v: Õ>¿w†Y‹
7)
Error checking in Excel.
Excel Ä]¨ Error a!
8)
P †Y‹ §" ( YÞ .¿d ~È1¼! #È" #B
Rows & Columns
¾4 È" (¿¼! # PAÃÈD (
9)
File Menu options
RN—ÄD
10)
Menu options
Filtering
—Ãw¿†Y‹
11)
Spell check
NÔ−ÄD a! P‹
——————
(DBC 41)
ASSIGNMENT - 1, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
COMPUTER APPLICATIONS - III
Paper-IV : DATA BASE APPLICATIONS
Maximum : 20 MARKS
Answer ALL questions.
1)
What is Tables? How to create a table, explain step by step?
vQ ²(ÄD D§" YA§ É(B vQ ²(ÄD ,ß«v wPÞ -§" ( JÌê ßÔ’Ñw†a1Ä] Éß«'ÆYA ~È1¼! (†| 2
2)
What is Report? Explain how to create a Report using Design view.
¿¬V¾Þ+(w D§" YA§ É(B | Rj/ §D È" Q½§" ( Hß«¼/ .Z†b ¿¬V¾Þ+(wç" ( JÌê ”7 ¼! .¾Þ+( a Õ>›¾4 ÉÈ" ¿†a7 †| 2
3)
Explain controls for graphics and change the layout of a pivot table list.
®YA—P‹ Ö ¨¼! (†~”7 Ï Ã( È" (¿¼! # È" #T½ ß«v wPÞ ÅßÔ(w ¼/ #PÞ S ÄQ DÈ" 'vD È" .¾Þ+(− ÉÌ! ¢PÞ ¿†a7 (È" #2
4)
What is Primary key & Foreign key.
^RN«È" (À P_ È" (¿¼! # °>¿§D P_ D§" YA§ É(B
5)
Write about types of operators use in Expressions.
Expressions Ä] Hß«¼/ .Z†a Eß«¾+u¾Þ+Ç YÞ (¿†b ~È1¼! (†| 2
6)
Discuss about modules in MS – Access.
MS – Access Ä]¨ È" .|Þ (½Ãǧ" ( YÞ (¿†b a7 ¿d†a7 †| 2
7)
Page numbers dialog box.
c«jD §" †²¾‹+Ö R|! ÌêY‹ »êP‹ Ö2
8)
Access Menus.
¼! .P! ÖŒÔ È! (§" .ŒÔ2
9)
List the control used in a form.
°>¾Þ+†Ä]¨ PÞ †~v]ÄD Ö§" ( ”! Ã(ß«'È" #2
10)
Record.
¿PA¾Þ+(}2
——————
(DBC 41)
ASSIGNMENT - 2, DEC - 2014.
B.A. DEGREE EXAMINATION.
(Examination at the end of Third Year)
COMPUTER APPLICATIONS - III
Paper-IV : DATA BASE APPLICATIONS
Maximum : 20 MARKS
Answer ALL questions.
1)
Explain about features of MS – Access.
MS – Access ¼/ #PÞ S È" #T½ Ã…Þ ×êç" ( ÉÈ" ¿†ß«'È" #2
2)
Explain about Action Queries.
¼! .…Þ §D P! ËÀç" ( YÞ (¿†b ÉÈ" ¿†a7 †| 2
3)
Explain about Expressions and Macros.
Expressions È" (¿¼! # Macros YÞ (¿†b ÉÈ" ¿†a7 †| 2
4)
5)
Explain:
a)
Inserting graphics from a file and
b)
Aligning graphics.
MPÞ RN—Ã( §" (†| ®YA—P‹ Ö ~ß«È Ì! N«u(wu È" (¿¼! #
®YA—P‹ Ö ß«†P › K¾Þ+−¾Þ+a7 (u§" ( ÉÌ! ¢PÞ ¿†a7 (È" #2
Explain the ways to edit data in table.
MPÞ ß«v wPÞ Ä]¨ Þ ”1›†Ì! È" #§" ( J| vD a ¼! #uà ߫ Þ ¦”7 (ç" ( ÉÌ! ¢PÞ ¿†a7 (È" #2
6)
Explain personalized menu features.
‘ß«¾Þ+Ö§" RÄ/ n|‹ È! (§" .’ D†Ì! È" # ÉÌ! ¢PÞ ¿†a7 (È" #2
7)
Explain Relationships in MS – Access.
MS – Access Ä] Relationships YÞ (¿†b ~È1¼! (†| 2
8)
Sections of Reports.
¿¬V¾Þ+(wÄ]¨ Éɤ Þ Section ç" ( YÞ (¿†b ~È1¼! (†| 2
9)
Define RDBMS.
RDBMS D§" YA§ É(B
10)
Referential Integrity.
¾!+ß—¾!+¨Ö¼! (ÄD F†v/ ®Zv 2
——————
© Copyright 2024 ExpyDoc
