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ASSALAM O ALAIKUMAll Dearz fellows
ALL IN ONE MTH301 Final term A E!S " M#$z#reate% &' Far(an " Ali
&S )*s+ ,n% semHa*-ers .ro/
From Man%i &a(a/%%in!emem er /s in 2o/r ra2ers
Min%(a*-er1, 45mail6*omHeart(a*-er1, 45mail6*om
FINALTERM EXAMINATIONS rin5 ,010
MTH3017 #al*/l/s IITime8 90 min
Mar-s8 :0Student InfoSt/%ent ID8
#enter8
E;am Date8
For Teacher's Use Only
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Q No. ! " # $ % & TotalMar(sQ No. ) * ! " # $ %
Mar(sQ No. & ) !* ! !! !" !#Mar(sQ No. !$ !% !& ! !) "* " "!Mar(sQ No. "" "# "$ "% "& " ")
Mar(s
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Quest+on No, - Mar(s, / 0lease choose one
Interse*tion of two strai5(t lines is 77777777777777
S/rfa*e
#/r
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Quest+on No, " - Mar(s, / 0lease choose one
Let w = f);> 2> z+ an% ; = 5)r> s+> 2 = ()r> s+> z = t)r> s+ t(en 2
*(ain r/lewr
=
w x w y w z x r y r z r
+ +
w x w y w z r r r r r r
+ +
w x x w y y w z z x r s y r s z r s
+ +
w r w r w r r x r y r z
+ +
Quest+on No, # - Mar(s, / 0lease choose one
3hat are the 4ara2etr+c e5uat+ons that corres4ond to the
follo1+n6 7ector e5uat+on8^ ^
2( ) sin (1 cos 2 )r t t i t j
= +
2sin , 1 cos 2 , 0 x t y t z = = =
2sin , 1 cos 2 , 0 y t x t z = = =
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2sin , 1 cos 2 , 1 x t y t z = = =
2sin , cos 2 , 1 x t y t z = = =
Quest+on No, $ - Mar(s, / 0lease choose one
3hat are the 4ara2etr+c e5uat+ons that corres4ond to the
follo1+n6 7ector e5uat+on8
( )^ ^ ^
( ) 2 1 3 sin 3r t t i t j t k = +
2 1 , 3 , sin 3 z t x t y t = = =
2 1 , 3 , sin 3 y t x t z t = = =
2 1 , 3 , sin 3 x t z t y t = = =
2 1 , 3 , sin 3 x t y t z t = = =
Quest+on No, % - Mar(s, / 0lease choose one
3hat +s the der+7at+7e of follo1+n6 7ector/7alued funct+on8( ) (cos5 , tan , 6sin )r t t t t
=
sin5
( ) , sec , 6cos5
t r t t t =
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sin5
( ) ( , sec , 6cos )5
t r t t t =
2( ) ( 5sin 5 , sec , 6 cos )r t t t t
=
2( ) (sin 5 , sec , 6cos )r t t t t =
Quest+on No, & - Mar(s, / 0lease choose one
3hat +s the der+7at+7e of follo1+n6 7ector/7alued funct+on84
2
3( ) , 1 ,r t t t
t
= +
3 31 6
( ) 4 , ,1
r t t t t
= +
3
3
1 6( ) 4 , ,2 1r t t t t
= +
4 31 6
( ) 4 , ,2 1
r t t t t
= +
3 31 6
( ) 4 , ,2 1
r t t t t
= +
Quest+on No, - Mar(s, / 0lease choose one
The follo1+n6 d+fferent+al +s e9act2( )dz x y y dx x dy= +
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Tr/e
False
Quest+on No, ) - Mar(s, / 0lease choose one
?(i*( one of t(e followin5 is *orre*t ?allis Sine form/la w(en n
is e
8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs
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cos
tan
r a
where a is an arbitrary cons t
=
Quest+on No, - Mar(s, / 0lease choose one
If the e5uat+on of a cur7e: +n 4olar co/ord+nates: re2a+nsunchan6ed after re4lac+n6 ( , )r ;y ( , )r then the cur7e +ssa+d to ;e sy22etr+c a;out 1h+ch of the follo1+n68
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Initial line
8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs
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13
Does not e;ist
Quest+on No, # - Mar(s, / 0lease choose one
3hat +s the 4er+od of a 4er+od+c funct+on def+ned ;y( ) 4cos3 f x x= 8
4
3
23
Quest+on No, $ - Mar(s, / 0lease choose one
Match the follo1+n6 4er+od+c funct+on 1+th +ts 6ra4h63 0 4
( )0 4 6
x f x
x
<
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0a6e = )
Quest+on No, % - Mar(s, / 0lease choose one
3hat +s the 4er+od of 4er+od+c funct+on 1hose 6ra4h +s as;elo18
,
C
%
B
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Quest+on No, & - Mar(s, / 0lease choose one
?(at is t(e erio% of erio%i* f/n*tion w(ose 5ra ( is as elow@
0
:
Quest+on No, - Mar(s, / 0lease choose one
Let L denotes the La4lace Transfor2.
If { ( )} ( ) L F t f s= 1here s +s a constant.and 0( )
limt
F t t
e9+sts then
1h+ch of the follo1+n6 e5uat+on holds8
( )
( ) F t
L f s at
= +
( )
( ) F t
L f s at
=
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( )
( ) s
F t L f s ds
t
=
( ) { ( )} F t d L f st ds
=
Quest+on No, ) - Mar(s, / 0lease choose one
?(i*( of t(e followin5 is La la*e in
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M+d4o+nt of the l+ne >o+n+n6 these t1o 4o+nts
!atio etween t(ese two oints
Quest+on No, ! - Mar(s, / 0lease choose one
Let the funct+ons ( , ) P x y and ( , )Q x y are f+n+te and cont+nuous
+ns+de and at the ;oundary of a closed cur7e ? +n the 9y/
4lane. If( ) P dx Q dy+
+s an e9act d+fferent+al then ( )
C
P dx Q dy+ =
@ero
One
Infinite
Quest+on No, !! - Mar(s, / 0lease choose one
?(at is La la*e transform of t(e f/n*tion ( ) F t if ( ) F t t = @
{ } 1 L t
s=
{ } 2
1 L t
s=
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{ } s L t e=
{ } L t s=
Quest+on No, !" - Mar(s, / 0lease choose one
?(at is t(e
8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs
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!
7,
Quest+on No, !$ - Mar(s, / 0lease choose one
E7aluate the l+ne +nte6ral2(2 ) ( )
C
x y dx x y dy+ + 1here ? +s thel+ne se62ent fro2 -*: * to -!: * .
*
7
Do not e;ist
Quest+on No, !% - Mar(s, / 0lease choose one
?(i*( of t(e followin5 are %ire*tion ratios for t(e line oinin5
t(e oints (1, 3, 5) an% (2, 1, 4) @
3> , an% 9
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1> 7 an% 71
!: /" and !*
06C> 73 an% C
Quest+on No, !& - Mar(s, / 0lease choose one
2 3
{( , ) / 0 2 1 4},
(6 4 ) R
If R x y x and y then
x xy dA
= + =
4 2 2 3
1 0
(6 4 ) x xy dydx+
2 4
2 3
0 1
(6 4 ) x xy dxdy+
4 2
2 3
1 0
(6 4 ) x xy dxdy+
4 1
2 3
2 0
(6 4 ) x xy dxdy+
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Quest+on No, ! - Mar(s, / 0lease choose one
3h+ch of the follo1+n6 +s true for a 4er+od+c funct+on 1hose6ra4h +s as ;elo18
E7en funct+on 4a6e!*)
O%% f/n*tion
Neit(er e
8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs
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An e
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3 3 4 2
3 2
3 2
4 3
12
12
dz x y dx x y dy
p x y
y
Q x y
X p Q y X
yes
= + = = =
Quest+on No, "! - Mar(s, !
E7aluate
sin nx dx
1here n +s an +nte6er other than Bero.
Solut+on,
sin
cos
cos cos
1( cos cos )
0
nx dx
nxn
n nn n
n nn
= = +
= +
=
Quest+on No, "" - Mar(s, !
Fin% La l*e transform of t(e f/n*tion ( ) F t if 3( ) t F t e=
Solut+on,
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3 3
0
( 3)
0
( 3)
( 3)
( )
.
{ }lim 0( 3)
1 1( )
31
(0 1)3
1......Ans
3
t t st
s t
s t
s t
L e e e
e dt
e s
s e
s
s
=
=
= = =
=
Quest+on No, "# - Mar(s, "
eter2+ne the Four+er co/eff+c+ent 0a of the 4er+od+c funct+ondef+ned ;elo1 8
( ) 2 1 0 2 f x x x= + < : then the e5uat+on: +n 4olar co/ord+nates: of thefor2 2 2 cos2r a = re4resent 1h+ch of the follo1+n6 fa2+ly ofcur7es8
Le2+nscate 4a6e "* #ar%io%s !ose */r
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,
C % B Quest+on No, & - Mar(s, / 0lease choose one 3hat +s the 4er+od of 4er+od+c funct+on 1hose 6ra4h +s as
;elo18
* ,6,C
3 : Quest+on No, - Mar(s, / 0lease choose one Let L denotes the La4lace Transfor2.If { ( )} ( ) L F t f s= 1here s +s a constant: then 1h+ch of thefollo1+n6 e5uat+on holds8 { ( )} { ( )}
d L t F t f s
ds=
{ ( )} ( ) L t F t f s t = + { ( )} ( ) L t F t f s=
{ ( )} ( ) s
L t F t f s ds
= Quest+on No, ) - Mar(s, / 0lease choose one
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The 6ra4h of an odd funct+on +s sy22etr+cal a;out////////////////
;7a;is 27a;is or+6+n
Quest+on No, !* - Mar(s, / 0lease choose one #ons+der the funct+on 2 2 2( , , ) 1 f x y z x y z = . 3hat +s the 7alue
of1 1
0, ,2 2
f
J
1 1 1
0, ,2 2 2
f =
1 1
0, , 22 2
f =
1 1 1
0, ,2 2 2
f =
1 1
0, , 02 2
f =
Quest+on No, ! - Mar(s, / 0lease choose one The 4ath of +nte6rat+on of a l+ne +nte6ral 2ust ;e/////////////
strai5(t an% sin5le7
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at( of inte5ration is %i
8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs
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1
{sin 3 }3
L t s
=
43!
{sin 3 } L t s
=
Quest+on No, !% - Mar(s, / 0lease choose one If L %enotes la la*e transform t(en
5{ }t L te =
5
2
1{ }
5t L te
s=
5
2
1{ }
5t L te
s= +
( )5
2
1{ }
5t L te
s=
+
( )5
2
1{ }
5t L te
s=
Quest+on No, !& - Mar(s, / 0lease choose one
E7aluate the l+ne +nte6ral (3 2 ) (2 )C
x y dx x y dy+ + 1here ? +sthe l+ne se62ent fro2 -*: * to -*: ! .
1 0 ! 7,
Quest+on No, ! - Mar(s, / 0lease choose one
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E7aluate the l+ne +nte6ral2(2 ) ( )
C
x y dx x y dy+ + 1here ? +s thel+ne se62ent fro2 -*: * to -*: ! .
7 /! 0 , Quest+on No, !) - Mar(s, / 0lease choose one
+7er6ence of a 7ector funct+on +s al1ays a ////////////
S*alar ector
Quest+on No, "* - Mar(s, / 0lease choose one
?(i*( of t(e followin5 is tr/e for a f/n*tion w(ose 5ra ( is 5i
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Quest+on No, " - Mar(s, !
Does t(e followin5 limit e;ist@ If 2es fin% its if no 5i
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Use ?allis sine form/la to e
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Quest+on No, " - Mar(s, $ Determine t(e fo/rier *o7effi*ient nb of t(e followin5 f/n*tion6
2( ) 0 2 f x x x = < ,+6
7
7,
0
,
Quest+on No, "$ - Mar(s, / 0lease choose one
lane is an e;am le of 777777777777777777777
#/r
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2
{( , ) / 0 2 1 1},
( 2 ) R
If R x y x and y then
x y dA
= + =
1 2
2
1 0
( 2 ) x y dydx
+
2 1
2
0 1
( 2 ) x y dxdy
+
1 2
2
1 0
( 2 ) x y dxdy
+
2 0
2
1 1
( 2 ) x y dxdy
+
Quest+on No, "& - Mar(s, / 0lease choose one
To e t(e inte5ran% is e; resse% in termsof ;> 2> z wit(
dr dx i dy j= +
dr dx i dy j dy k = + +
dr dx dy dz = + +
dr dx dy= +
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Quest+on No, " - Mar(s, / 0lease choose one
Mat*( t(e followin5 e /ation in olar *o7or%inates wit( its 5ra (6
e!e is an a!&it!a! constant.
r a
a=
Quest+on No, ") - Mar(s, / 0lease choose one
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?(i*( of t(e followin5 is tr/e for a erio%i* f/n*tion w(ose5ra ( is as elow@
E7en funct+on
O%% f/n*tion
Neit(er e
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An eC+ an% ),>7,>3+ is
2 323 5
y z x
+ = =
3 525 2
y z x
+ ++ = =
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3 515 2
y z x
= =
3 515 5
y z x + + = =
$/estion No8 3 ) Mar-s8 1 + 7 lease *(oose one
T(e le
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Ref No, T+2e, )* 2+nMar(s, %*
Student Info StudentI ,?enter, O0 ST
E9a2 ate, *& Au6 !* *
For Teacher's Use Only QNo.
! " # $ % & Total
Mar(sQ No. ) * ! " # $ %Mar(sQ No. & ) !* ! !! !" !#Mar(sQ No. !$ !% !& ! !) "* " "!Mar(sQ No. "" "# "$ "% "& " ")Mar(s
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Quest+on No, - Mar(s, / 0lease choose one There +s one/to/one corres4ondence ;et1een the set of 4o+ntson co/ord+nate l+ne and ////////////
Set of real nu2;ers
Set of inte5ers
Set of nat/ral n/m ers
Set of rational n/m ers
Quest+on No, ! - Mar(s, / 0lease choose one Strai5(t line is a s e*ial -in% of 7777777777777777 S/rfa*e
?ur7e
lane
ara ola Quest+on No, " - Mar(s, / 0lease choose one 2
2 2( , ) (0, 0)lim
x y
xy x y
=+ 0 1 06C Quest+on No, # - Mar(s, / 0lease choose one If 2 3( , ) ln f x y x y y x= +
t(en2
2
f x
=
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21
2 xy x
+
21
2 y
x
+
21
2 xy x
21
2 y x
Quest+on No, $ - Mar(s, / 0lease choose one
S/ ose 2( , ) 2 3 1 2 f x y xy y where x t and y t = = + = 6 ?(i*( one of t(e
followin5 is tr/e@
4 2df
t dt
= +
16df
t t dt
=
1 2df
t dt
= +
210 1
df t t
dt = + + Quest+on No, % - Mar(s, / 0lease choose one
Mat*( t(e followin5
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Quest+on No, & - Mar(s, / 0lease choose one ?(at are t(e arametri* e /ations t(at *orres on% to t(e
followin5
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Quest+on No, - Mar(s, / 0lease choose one
Is t(e followin5
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Tr/e False
Quest+on No, - Mar(s, / 0lease choose one T(e followin5 %ifferential is e;a*t
2( )dz x y y dx x dy= +
Tr/e False
Quest+on No, ! - Mar(s, / 0lease choose one
?(i*( one of t(e followin5 is *orre*t ?allis Sine form/la w(enn
is e
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-2 -1 1 2
1
2
3
4
-4 -3 -2 -1
-2
-1
1
2
-2 -1 1 2
-4
-3
-2
-1
Quest+on No, # - Mar(s, / 0lease choose one Mat*( t(e followin5 e /ation in olar *o7or%inates wit( its 5ra (6
4sinr =
1 2 3 4
-2
-1
1
2
-2 -1 1 2
1
2
3
4
-4 -3 -2 -1
-2
-1
1
2
-2 -1 1 2
-4
-3
-2
-1
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Quest+on No, $ - Mar(s, / 0lease choose one Mat*( t(e followin5 erio%i* f/n*tion wit( its 5ra (6
3 0 4( ) 0 4 6
x f x x