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MARCH – 2020MATHEMATICS PAPER- 2B

Time :3 Hrs Total Marks : 75 M

SECTION-A

I. Answer ALL the questions. Each question carries ‘2’ marks. 10 x 2 = 20M

1) Find the pole of 0 0ax by c c with respect to 2 2 2x y r .

2) Find the value of k if the points 4, 2 and , 3k are conjugate points with

respect to the circle 2 2 5 8 6 0x y x y .

3) Show that the angle between the circles 2 2 2x y a , 2 2x y ax by is 3

4

.

4) If 1

, 22

is one extremite of a focal chord of a parabola 2 8y x . Find the co –

ordinate of the other extremity.

5) Show that the angle between the two asymptotes of a hyperbola 2 2

2 21

x y

a b is

12 tanb

a

(or) 12sec e .

6) Evaluate 8

181

xdx

x .

7) Evaluate 1 logx x x

e dxx

.

8) Find 2

6 4

0

sin cos x x dx

.

9) Find the area bounded between the curves 2 ,y x y x .

10)Form the differential equation from 21y C x where C is an arbitrary

constant.

Disclaimer: This Question paper is purely for preparation purpose only. Manabadi.com is no where claiming this to be the Main Examination Paper.

SECTION-B

II. Answer ANY FIVE questions. Each question carries ‘4’ marks. 5 x 4 = 20M

11)The line y mx c and the circle 2 2 2x y a intersect at A and B if 2AB

then show that 2 2 2 21C m a .

12)If the straight line 2 3 1x y intersect the circle 2 2 4x y at the points A and B then

find the equation of the circle having AB as a diameter.

13)Find the eccentricity, co ordinates of foci, length of latus rectum and equations

of directrices of the ellipse 2 29 16 36 32 92 0x y x y .

14)Find the equation of tangent and normal to the ellipse 2 29 16 144x y at the

end of the latus rectum in the 1st quadrant.

15)Tangents to the hyperbola 2 2

2 21

x y

a b makes angles 1 2,Q Q with transverse axis

of a hyperbola show that the point of intersection of these tangents lies on the

curve 2 22xy k x a when 1 2tan tan k .

16)Evaluate 2

0

sin cos

sin cos

a x b xdx

x x

.

17)Solve 2cos sin secdy

x y x xdx

.

SECTION-C

III. Answer ANY FIVE questions. Each question carries ‘7’ marks. 5 x 7 = 35M

18)Show that the points 1, 2 3, 4 5, 6 19,8 are concyclic and find the equation

of the circle on which they lie.

19)Find the direct common tangents of the circles 2 2 22 4 100 0x y x y and

2 2 22 4 100 0x y x y .

20)Show that the equation of a parabola in the standard form is 2 4y ax .

Disclaimer: This Question paper is purely for preparation purpose only. Manabadi.com is no where claiming this to be the Main Examination Paper.

21)Evaluate2sin 3cos 4

3sin 4cos 5

x xdx

x x

.

22)Obtain reduction formula for cosn xdx for 2n and deduce the value of

5cos xdx .

23)Evaluate 20

sin

1 cos

x xdx

x

.

24)Solve3

2 2 5

dy x y

dx x y

.