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MATHEMATICS PAPER IIB.- MAY 2 0 1 1 .

COORDINATE GEOMETRY & CALCULUS.

TIME : 3 hrs Max .

Marks.75

Note : This ques t ion paper con sists of three s ec t ions A,B and C.

SECTION A

VERY SHORT ANSWER TYPE QUESTIONS. 1 0 X2 =2 0

Noe : Atte m pt all ques t ions . Each ques t ion carries 2 m arks.

1. If 2 2 2 2 12 0x y gx fy+ + + = repr esen ts circle with cent er (2,3) fin d g,f

and rad ius

2. Fin d the equ ation of th e sph ere th at pas ses th rough th e point (4,3,-

1) an d ha ving center at (3,8,1)

3.Find pole of th e lin e 2x+3y+4=0 with resp ect to y2=8 x

4.Find t h e equ at ion of h yperbola wh ose foci ar e at (5,0) th e tra n sverse

axis length 8

5. Findth

n derivative of Sin5x.Sin3x

6. Evaluate2 2

1 21 1

dxx x

+ +

7. Evaluate1

( 1)( 2)dx

x x

+ +

8 Evaluate2

01 x dx

9 .Calculate the approximate value of9

2

1x dx u sing Tra pezoidal ru le with 4

par t s

10 . Find order an d degree of

6

2 5

2differential equation 6d y dy ydx dx

+ =

SECTION B

SHORT ANSWER TYPE QUESTIONS. 5 X4 =20

Note : Ans wer any FIVE ques tion s. Each ques tion c arries 4 m arks.

11 . Fin d len gth of chord intercept ed by th e circle 2 2 3 22 0x y x y+ + =

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on th e lin e y=x-3

12. Find the equ at ion of the tan gent an d norma l to the para bola y2=8x at

(2,4)

13 .Fin d eccentr icity, foci, len gth of lat u sr ectu m an d equ at ion directrices of

th e Hyperb ola x2-4 y2=4

14 . Find th e con dit ion th at stra igh t line

cos sin may touch the circle r=2acosk

A Br

= +

15 2Evaluate 1 3 ,x x dx+

16 Solve2 2( )

dyx y xy

dx =

17 Solve3tan cos

dyy x x

dx+ =

SECTION C

LONG ANSWER TYPE QUESTIONS. 5 X7 =3 5

Note : Ans wer any Five of th e following. Each que stio n carries 7 m arks.

18 . If (1, 2) (3, -4) , (5, -6) a n d (c,8) ar e con cyclic find c

19 . If (3,5 ) is a lim itin g point of coa xial sys tem of circle of wh ich2 2x 2 2 24 0y x y+ + + = find other limiting point

20.Sh ow th at th e point s of inters ection of perpen dicu lar tan gents to an

ellipse lies on a circle

21 . Ifx

ey1

sin

= , then sh ow tha t ( ) 01 122

= yxyyx and hence deduce tha t

( ) ( ) ( ) .01121 2122

=++++ nnn

ynxynyx

22. Find redu ction formu la of cot ,n xdx hence find4cot ,xdx

23 . Find0 1 sin

xdx

x

+

24 . Find area enclosed between curves 2 2y 4 , 4(4 )x y x= =