mth301 solved finalterm papers solved mcqs

8/11/2019 MTH301 Solved Finalterm Papers Solved MCQs

1/81

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2/81

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

mailto:[email protected]:[email protected]


3/81

Q No. ! " # $ % & TotalMar(sQ No. ) * ! " # $ %

Mar(sQ No. & ) !* ! !! !" !#Mar(sQ No. !$ !% !& ! !) "* " "!Mar(sQ No. "" "# "$ "% "& " ")

Mar(s



4/81

Quest+on No, - Mar(s, / 0lease choose one

Interse*tion of two strai5(t lines is 77777777777777

S/rfa*e

#/r


5/81

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 = = =



6/81

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 =



7/81

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

= +


The follo1+n6 d+fferent+al +s e9act2( )dz x y y dx x dy= +



8/81

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


9/81

cos

tan

r a

where a is an arbitrary cons t

=


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



10/81

Initial line


11/81

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


Match the follo1+n6 4er+od+c funct+on 1+th +ts 6ra4h63 0 4

( )0 4 6

x f x

x

<


12/81

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



13/81

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

:


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

=



14/81

( )

( ) 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


15/81

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=



16/81

{ } s L t e=

{ } L t s=

Quest+on No, !" - Mar(s, / 0lease choose one

?(at is t(e


17/81

!

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



18/81

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+



19/81


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


20/81

An e


21/81

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,



22/81

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


34/81

,

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



35/81

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


36/81

at( of inte5ration is %i


37/81

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,




38/81

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


39/81

Quest+on No, " - Mar(s, !

Does t(e followin5 limit e;ist@ If 2es fin% its if no 5i


40/81

Use ?allis sine form/la to e


41/81

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


62/81

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= +



63/81

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



64/81

?(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


65/81

An eC+ an% ),>7,>3+ is

2 323 5

y z x

+ = =

3 525 2

y z x

+ ++ = =



66/81

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


67/81

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



68/81

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

=



69/81

21

2 xy x

+

21

2 y

x

+

21

2 xy x

21

2 y x


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


70/81

Quest+on No, & - Mar(s, / 0lease choose one ?(at are t(e arametri* e /ations t(at *orres on% to t(e

followin5


71/81


Is t(e followin5


72/81

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


?(i*( one of t(e followin5 is *orre*t ?allis Sine form/la w(enn

is e


73/81

-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



74/81

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

mth301 solved finalterm papers solved mcqs

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