Download OU (Osmania-University) Intermediate 2018 Core Subjects 0193 Mathematics Previous Question Papers
'TotaIN?ohoaf Questions?24 Regd. 1
Total No. of Printed Pages?4 'No. ' { 8 g 0 i Q 3' L? S Q
- . _ . .Part-Illl. .
, MATHEMATICS,Paper-I(B)' . '
? (English Version) ?
Timez3HourS| V - _ ? _ ~ I ' I . -'|Max.M?rks:75
Note : - This questibn paper cohsists of three sediohsA, B and C.
SECTION - A ' ? .- '10 x' 2 =21) ?
I. . Very short answer type questions :'
?(i) Attempt all questions.
(ii) Each question carries two marks;
'1. Find the Value dfx, if the slope of the line pas?Sing through (2, 5) and (x, 3) is 2.
l0
Transfmm the equation x + y + 1 = 0 into nmmal form. w
3. Find ?the ratio in which the xz?plane divides the line joining A? (?2, 3,4) and
B (1, 2, 3). ' ' ' '
4.? > F ind, thgj'ntextgepts of the plane 4x. + 3y * 22 +_ 2 == 0 on the'co-ordinate axes.
,& f I ' . sin ax -
. ' Isy/?f- ? COlnpute xllglo( Sin b\?j? 13$ 0, a i b
20.1L19i3/T5may-7) T" ' 2|10f4 1 _ ? ? ..'P.T;o.,
. ? 11111 C031".
. ?6. _. Compute x __) 11/2 (x~ ?/2
' ' 1 3?1 d
7., It y?=a+A.(A???a),?nda?
8. _ 1fy=(cot-' 1312,1111dgi/7
?9. . If the inelease in the side of a square is 2%. then 11nd the approxi111ate .-
? 15;;
peicentage oi merease 111 its a1ea. 1 1%?: 11130
4424?! i a [6L ? . 11,-:
, ' IV iii; 14914"
i _ 10,-4 Finci the value of C in Lagiange 5 mean value theoremt?or the functioh
f(;1-=) .1-? 1 on [2, 3]. ' '
151,. 2,10%!" "'
2 1?)?
12"?) >035
SECTION 3? B.
' Short answer type questions;
? (i) ? Attempt any five questions? .
(ii) Each question carries fo11r1narks. 1.
1 1?. ?Find the locus of the third vertex of a right angled triangle the ends (1f whose
hypotenuse are (4 O) and (0 4).
12. When the axes are rotated through an anglelt? 6? ?nd the transformed equation of
12+2 31y? y2= 2a2.'
13. Find the value of k, if the lines 21 ? 3y + k? " 0, 3x ? .4y ? 13 = O and
81 ? 1 1y- 33= 0 are concuITent.
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14. Find the real cbnstants a,.b, so that theifunction f given by
Si11A,if\:<0'
-* f(x)=12+a110
is continuous on R. . 1' mi?
15. Find the derivative ofx' sin x from the ?rst principle. .
, M \2; 1
16. Show that at any point (x, y) 011 the curve y = 'b e?, the length of , the ?3
sub-tangent is a constant and the length of the subnormal is '2?.
17. A particle IS moving along a line according to S ?- f(t)= 4t3 4 3t2 + 5t ? 1 Where .
.S is measured in metres and t is measured in seconds.Fi11d the velocity a11d
acceleration at timet At what time the aceeleration 1s zero. ?7 _ . .' . 1,. V 1
SECTION?C? _ ' ' 1' . " 5x7=3s
Long answer type questions. :
(i) Attempt any ?ve questions.
(ii?) Each questiori carries seven marks.
18. F ind the?circumcenter of the triangle whose vertices? are..(1, 3), (?3, S) and (5, ?1).
I ,
19. It the equation 2112+ 211w + by2=_ 0 represents a pair of straight 1i11es,the11
B:
Show that the angle 6 between the lines 1s give11 by
cos 6=??J??L??a+b . f
A \?(a ? b)2 + 4h2
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2.0.
Show that the lines Joining the origin to the points of intersection of? the curve.
? ~ .12 -?- \y + y2 + 3x + 3y? 2? ? 0 and the straight line 1 ? _?y x]: = O are muttially
0/,?
?x
C.) . -
1 / V ,1!"
' 11.33
h ?3?)? Ix/
perpendicular.?
Find the angle between two diagonals ofa cube.
. 1 Show. that the equation of thetangent to the curve ('2) + (a ?? 2 (21 ? 0, b at 0)_ , ,
' . ' i" L '
at the pomt (at b) Is 11+ b ? 2.
From a "rectangular sheet of dimensions 30 _cm X 80 cm fom equal squares oi
side x cm we removed at the comers and the sides me then turned up so as to ?-
, form ah open rectangular box Find the value of x, so that the volume of the
box 13 the gieatest. IV? 7
96>
ri? ?e
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This post was last modified on 16 April 2020