Download OU (Osmania-University) Intermediate 2018 Core Subjects 0293 Mathematics Previous Question Papers
Fetal No.4 of Printed?.PageS?4 RengNo. 1 ' X 9 0 IL. I
Part III ~
MATHEMATICS Paper IIIB)
1 (English Versien) '5 I
I?imIe: 3Hours] _ v I "' A ' . ' , _ ' . ; [Mam Marks; 75.
Note :-- This question paperI consists of THREE sections A, B and C.
. _ SECTION A _ _ , 10x2: 20
Very, short answer type questions : I I 7 '
I(i)_ ? Attempt ALL questions. I
'(ii) Each question carries TWO m2rks.
Find the equation of the circle whose centre is (?-1, 2) 2nd vIvhich passes
through_(5,6).1 ' I: I .l 1?: I 2
?If the length of the tangent. fro1n 2, 5) to the circle x? + y2I ? 5x I+ 4y
?_+k=Ois'\/_,then?r1dIk.? .f. '
? If the angle between the circle'sI x2 + _y2 - 12x ?? 6y + 41 O and
"x22+y+kx+6y?5I'9: Ois45? ?ndk? .
l-Find the equation of the paIrab012 whose vertex _is (3, ~2)I IandI focus
1s (3,1) . ' . , f I "' "
I v If 3xV?44y + k :6 is. 2 tangent to 6x2 ? 4y2 ==?5,I ?nd the value of k
Evaluate :
0293-0 _, ' _I . . . , - . .I , I , I , _ PTO I
10.
. 11.
11.
' 123.,
13/
24-?
0293~C
._ , j'-__[ ?2 ] .,
' Etaluate :
I cos.3 x?sin'x dx.? _
?Ev?luate : "
? 2 I ?. .
, 1? x dx. '
f F '? ,/
.Eval?ate :
7t/2 ~ '1 I I
I xsinxdx. / '
0 _ j 3 '
t 1 d .
' Find the general solutiqn of _y =? ex ?+ y. 3
dx. _ ,
SECTIONB ? ? "g '5x4?=_20 '
Short answer type questiOns : ? I
(i) I _Attempt ANY FIVE ? questions. I
(ii) Each: question carries FOUR -marks.
Find the area of the triangle formed by the normal at (3, +4) to the circle
3x2 + y2 ~22x ? 4y + 25': 0 With. the coordinate axes.
Find the equation '_and length of the common chord of the two circles :
1:2 ??"y2 .+_?3x + 5y 44 4 = 0 and 5 - E
.. x2 + y2_+v 5x + By + '4 ?0.
Find the equation of the ellipse?referred to its?major and minor axes as
' they coofdinate axes X, Y?respectively With. latusv rectum of length 4, ?and 7
distance between foci 4J? ?
Find the eccentriCity, length of latus rectum, foci and the equations of
directrice's of the ellipse :
9x_ + 16y2 _. 36x "+ 32y +192 :? '0. '
[ 3 ]
A2 .- ' , ,_ " ?2.12 '
. 5 , Show that angle between the two Yasymptotes; of a ?hype1'bola fa?Z?f ~3- .== 1
1S 2tan?1(b/a) (5r) 2sec.?1(e). I _ ,
16.1 Find the areaibhunded betWeen the, curves y 2 x62, y 7- J35":
17. V Solve. :. V ' I r 1 F
E; + 1 : ex?+ y.
SECTIONC I ? I , 1 5:67:35
' III. , Long answer type" ??uesti?onisf I 7 .
I F(i)? ? Att?thpt ANY FIVE q11estions.
"'(ii) ' Each question ? c?rri?s SEVEN marks;
? / Find the equation of a circle Which passes through (4, 1), (6, 5) and having .
. the centre on .:
?4x ,+ 3y ?-?? 24 =0.
1' Show that the circles :
.x2- + y2 ? 6x? 9y + 61,3 =0,
2
x-'+y2.?l?2xV'-?16y=0_'v
. touch {each other. 'Find the. point, of cqntact and the' eqlgation. of common
tangent at their point of contact
X Derive the equatlon of parabola in the standard form, that is y2-164ax.
_ 21. V Evaluate :
b ? I -
j? (x a)(b? x)dx.
0293-(3' ' '. - .. Pm.
I
10.
4 11.
1?1. ,
12 1 ' 5
Evaluate :
I 0033 xsin'x dx,?
?Evaluate :
I '2 . "
_ l?x fix.
I I '. . ,/ A
0. v} L '
.Evaluate : ,
71/2 , ? .I I
f xsinxdx.- /
0
. d , ,
' Find the general solution of *1 =_ ex 75+ 3?.
dx. 7. V ?
SECTIONB " ? , 5x4gzo'
? Short answer type questions :
(i) ? Attempt ANY FIVE questions.
(ii) Each question carries FOUR marks _ .
Find the area of the triangle formed by the normal at (3, .??4) to the circle . V '
I vx2 + y2 - 22x ?- 4y + 25= 0 with the coordinate axes
"121,.
?24?
Find the equatioh 'and length of the common} chord of the two cireles :_- t
I x+y+3x+5y+4 O'and ?
52+y2 +5x+3y+4= 0.
Fi?d the equationx of the ellipsereferred to its major and minor aXes as
the coordinate axes X,Y-respective1y With latus rectum of length 4, land ,
distance between foci 4%?
hFind the eccentricity, length of latus rectum, foci and the equations of . . '
directrices of the ellipse :
'9x_2 + 163/2 ?. 36x + 32y 5192' = '0, ?
? 0293-C
This post was last modified on 16 April 2020