Calculus-March 2023

z Zz w

X

¹

 w Z Î

(i)

Z

~ y Ð ð Ã

7

^{(d) (c) (b) (a)}

ì

parallel asymptote

Æ

^x-axis

Æ

^(curve)

È

⁽ⁱⁱ⁾

(d) (c) (b) (a)

ì A

$ ¤ / Z

⁽ⁱⁱⁱ⁾

(d) (c) (b) (a)

(iv)

(b) (a)

(d) (c)

1/3

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* ] :

/

X

ì

ò i Ñ

bŠ

[ Z Ž » V ß Z Î Ð V

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x

Ó

X

ìè

S g 

á

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Š

Z

®

Å V

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Æ [ Z Ž

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X x Î

z

Ô zx

Šz

Ô w

z

Zz :

ìŒ

6

,

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] Ñ Z Î

0

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,t

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ì

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X

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] Ñ Z Î á zZ [ Z Ž

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**™

%æFN

(

à { & ] Ñ Z Î è z

cž

Ž



] Ñ Z Î ò i Ñ

¹⁰~

w Zz

z ^.1

(10 x 1 = 10 Marks)

X

ì–

C Ù

Z Î Æ w

a

X

ìŒ

6

,

V

/

(

²⁰⁰

) Î z

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[ Z Ž » w Z Î

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[ Z Ž Æ V ß Z Î

⁵ð

à Ã

D¨(

¤ Ð

~

k XZ



] Ñ Z Î

⁸~

zx

Šz ^.2

(5 x 6 = 30 Marks)

X

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] Z

⁶

C Ù

Î Z Æ w

a

X

ì Œ

6

,

V

/

(

⁵⁰⁰

) Î õ 0

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[ Ž Æ V ß Z Î

³ ð

à Ã

D¨(

¤ Ð

~

k XZ



] Ñ Z Î

⁵~

x Î

z ³

(3 x 10 = 30 Marks)

X

–

] Z

¹⁰

Maulana Azad National Urdu University

Bachelor of Science

I Semester Examination - March 2023 BSMM101CCT : Calculus

3 Hrs

: ‰ Ü z

^{: Time} Maximum. Marks 70 :

] * * ¶ K ]

Š Æ x g y X X X X X

ì X g Zz

^(length)

ð M Å

^arc

Æ

^(curve)

È

^(v)

(b) (a)

(d) (c)

X X X X X X X X

ì X

^perimeter

»

^(curve)

È

^(vi)

(d) (c) (b) (a)

(

ß

^/

9

⁾

X ì

solid of revolution

q - Z

^{Cuboid (vii)}

A

$ ¤ / Z

^(viii)

X A $ ¤ / Z

^(ix)

X A $ ¤ / Z

^(x)

z

Š zx

¥

™ x z

X

^asymptotes

Æ

^(curve)

È

⁽²⁾

X ž z ™ " $ U *  ƒ ¤ / Z

⁽³⁾

X ž z ™ " $ U *  ƒ ¤ / Z

⁽⁴⁾

™ z

X

^(evaluate)

~ . Z Ã

⁽⁵⁾

Æ

^(curves)

g Zz 6 ,

^x-axis

Ž z ™ x ¥

^(volume)

w »

^(solid)

k ^ k Z

⁽⁶⁾

˜ Æ t á Ð C ì

X

bounded region

X ž Z # , ™ x ¥

^(length)

ð M Å

⁽⁷⁾

ì A Ô

$ U

*

"

$

™

z

^constant

q - Z ˜ ¤ / Z

⁽⁸⁾

(ii) (i)

horizontal

B ‚ Æ

launch angle

g Zz

(initial speed)

g ë g ð Z ’ Z Å

840 m/s projectile

¤ / Z

⁽⁹⁾

¥

™ x z

X

^range

g Zz ‰ Ü z »

flight ,(maximum height)

„ ™ Zz + F , x n Z  ƒ Š H H

^fire

Ð

^origin

Æ } i

1/2

z x Î

™ z

X

^(trace)

® F , Ã

^(curve)

È

⁽¹⁰⁾

™ z

X

^(trace)

® F , Ã

^(curve)

È

⁽¹¹⁾

™ z

X

^(evaluate)

~ . Z Ã

^{(i) (12)}

™ z

X

^(evaluate)

~ . Z Ã

⁽ⁱⁱ⁾

(revolution)

l Š ¤ / Å

^(curve)

È 6 ,

^y=0

Ž z ™ x ¥

^(surface)

R Å

^(solid)

k ^ k Z

⁽¹³⁾

k Ð

Ž

ƒ X

Ò

Ã

y Zz U g

*

"

™$

z

X

(Kepler's Second law)

/õG ®Í }

u

z

Š

Æ k æ G F 5Î ´4

⁽¹⁴⁾

/ / /