SR. INTER MATHEMATICS-IIB

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SR. INTER MATHEMATICS-IIB
SECTION - I
Answer the following questions:-
10 x 2 = 20M
1)
If the length of the tangent from (2,5) to the circle x 2
2)
Obtain the parametric equation of the circle x 3
3)
Show that the angle between the circles x 2
4)
If
1
x log x log log x
7)
Evaluate e x
8)
Find
2
0
1 x dx
cos7 x sin 2 x dx
9)
0
3
4
8 x , find the coordinates of the other
dy
dx
3
6
5
6y
ak
SECTION - II
Answer any five of the following questions:5 x 4 = 20M
2
2
If the abscissa of points A,B are the roots of the equation x 2ax b 0 and ordinates of A,B are
the roots of y 2 2 py q 2 0 , then find the equation of a circle for which AB is a diameter .
Show that the circles x 2 y 2 8 x 2 y 8 0 and x 2 y 2 2 x 6 y 6 0 touch each other and
find the point of contact
Find the length of major axis, minor axis, latus rectum, eccentricity, coordinates of center, foci and
the equation of directorix of the ellipse 4 x 2 y 2 8 x 2 y 1 0
If P is a point of the ellipse
w
14)
37 , then find k.
8 .
ax ay is
.
0 is
2
.s
13)
dx on 1,
d2y
Find order and degree of
dx 2
w
12)
y2
1 x log x
dx
x
2
II)
11)
a2 , x2
1
, 2 is one extremity of a focal chord of the parabola y 2
2
extremity.
Define rectangular hyperbola and find its eccentricity
6)
10)
y 4
2
sh
ie
du
ca
t
5)
y2
2
y 2 5x 4 y k
io
n.
co
m
I)
x
a2
y2
b2
1, whose foci S and S ' then show that SP S ' P
2a
w
(constant)
15)
16)
17)
Find the equations of the tangents to the hyperbola 3x 2 4 y 2 12 which are
Perpendicular to the line y=x-7
Find the area enclosed between the curves y 2
dy
Solve
y sec x tan x
dx
4 x and x 2
4y
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20)
21)
SECTION – III
Answer any five of the following questions:
5 x 7 = 35 M
Find the value of ‘C’ if the points (2,0), (0,1), (4,5) and (0,C) are concylic
Find the equation of a circle which passes through the points (4,1), (6,5) and having centre on
4 x 3 y 24 0
Derive the equation of parabola y 2 4ax in standard form
2sin x 3cos x 4
Evaluate
dx
3sin x 4cos x 5
22)
Obtain reduction formula for I n
23)
Show that
x
dx
log
sin x cos x
2 2
Solve 2 x y 3 dx 2 y x 1 dy
0
2 , and also evaluate
2 1
w
w
w
.s
ak
sh
ie
du
ca
t
24)
2
sin n x.dx n
io
n.
co
m
III)
18)
19)
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sin 6 x.dx