8/16/2019 Questions - 01 Application of Derivatives

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Applied Mathematics – Chapter: 01 Application of Derivatives (24 Marks)1

A.Slope and Equation of Tangent & Normal Q 01(2 mks) Q 02

(mks) Q 0! (mks)

1. ind the !radient of the tan!ent of the c"rve  y=√  x3

 at  x=4 .

2mks #14

2. ind the point on the c"rve  y=3 x− x2

 at $hich slope is –%.

2mks #1&

&. At $hich point on the c"rve  y=3 x – x2

' the slope of tan!ent is –%.

2mks 1%

4. At $hat point on the c"rve'  y=e x

 the slope is 1 2mks

#1%

%. ind the point on the c"rve y=2 x2 – 6 x

 $here the tan!ent is parallel to the * +a*is. 2mks 14

,. ind the inclination of the tan!ent to the c"rve  y=e2 x

 at (1' +&).

2mks 141.

-. ind e"ation of tan!ent and normal to the c"rve  y= x (2− x )  at point (2,0) .

/2 1%

. ind the e"ation of the tan!ent and normal to the c"rve 4 x2+9 y 2=40  at (1,2 ) .

/2 14' #14

. ind the e"ation of tan!ent and normal to the c"rve 2 x2− xy+3 y

2=18  at (3,1) .

/2 #1%

10. ind the e"ation of the tan!ent and normal to the c"rve 13 x3+2 x2 y+ y3=1  at

(1,−2) #1&

11. ind the e"ation of the tan!ents to the c"rve  y= x2−2 x−3 ' $here it c"ts +

a*is. /, #1&

12. ho$ that the e"ation of tan!ent to the c"rve ( xa )m

+( yb )m

=2  at the point (a'3)

is x

a+ y

b=2

#14

1&. ind e"ation of tan!ent to the c"rve x=

1

t  ' y=1−

1

t   $hent =2.

/, 1%

8/16/2019 Questions - 01 Application of Derivatives

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Applied Mathematics – Chapter: 01 Application of Derivatives (24 Marks)2

14. he e"ation of the tan!ent at the point (2' &) on the c"rve  y=ax3+b  is

 y=4 x−5 . ind the val"es of a and 3.

/, #1%

2.". #ind $a%imum & $inimum Q. no. 02 ( marks) Q. no.

0! ( marks)1. Divide 0 into t$o parts s"ch that their prod"ct is ma*im"m.

2mks 1%

2. ind the ma*im"m and minim"m val"e of  x3−9 x2+24 x .

/2 #1%

&. ind the ma*im"m and minim"m val"e of  x3−18 x2+96 x .

/2 #1&4. ind the ma*im"m and minim"m val"e of  x

3=18 x2+96 x .

/2 14

%. ind ma*im"m and minim"m val"e of y= x

3−

15

2 x

2+18 x

.

/2 1%,. Divide 0 into t$o parts s"ch that their prod"ct is ma*im"m.

/, #14#1%-. A metal $ire of &,m lon! is 3ent to form a rectan!le. ind its dimensions $hen its

area is ma*im"m.&. /2' /,'/,

#14' 14'1%. A man"fact"rer can sell * items at price of 5s. (&&0 – *) each. he cost of

prod"cin! * items in 5s. is  x2+10 x+12 . 6o$ man7 items m"st 3e sold so that his

pro8t is ma*im"m /, #1&4.

'. adius of 'urature Q no. * 01(2 marks) Q. no.

02 ( marks)1. ind the radi"s of c"rvat"re of  y=e

 x

 at (0' 1).

2mks #1%

2. ind the radi"s of c"rvat"re of the c"rve

 x

sin ¿¿¿

 y= log¿

 at x=

π 

2 . 2mks

#1&

&. ind the radi"s of c"rvat"re of the c"rve  y2=4ax  at point (a ,2a) .

2mks #14

8/16/2019 Questions - 01 Application of Derivatives

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Applied Mathematics – Chapter: 01 Application of Derivatives (24 Marks)&

%.

4. ind the radi"s of c"rvat"re for the c"rve  y=2sin x−sin2 x  at  x=π 

2 /2

14

%. A 3eam is 3ent in the form of the c"rve  y=2sin x−sin2 x . ind the radi"s of

c"rvat"re of the 3eam at this point at x=

π 

2 .

/2 #1&' #14

,. ho$ that the radi"s of c"rvat"re at an7 point on the c"rve  y=a log ( secx /a )  

$here a is constant is asec ( x /a ) .

/2 #1%

-. ind radi"s of c"rvat"re of the c"rve  x=acos3θ , y=asin3θ  at θ=π /4 /2

1%