Pre University Board 2008 P.U.C Physics, Chemistry, Maths & Biology " Mathematics " code 75 For Englisg versuion see page no 9 - Question Paper
Code No. 75
[ Total No. of Printed Pages : 16
Total No. of Questions : 40 ]
June, 2008
( Kannada and English Versions )
Time : 3 Hours 15 Minutes ]
[ Max. Marks : 100
( Kannada Version )
: i) A, B, C, D 0od E 00 o 03
ZJ J CO 7 7 7 _D * CO
0%.
* c _0
ii) - a n 10 odn>, - b n 20 odn>, -c n 40 odn> Ood ran - d n 20 odn>, ran - e 10 rt
_> t 7 4
_D
iii) ,oZ6rt>o 0,4 0o>Q%do0o doO.
10 x 1 = 10
co y d. d. -0
4. a : b = 2 : 4 b : c = 3 : 5 wd, a : c (oo XodroSO.
_D 7 c
5. 24 aFrt> ,03,0 odn>o 48. aoro oXrt> ,eO3rt ,-3,O 482 wrtoJ . w , a3,arD oXrtrio XooSoO.
_0 * c
6. 9 ort> d&. 415 oS<oo ,3/ eX3 15 doJ ,eS /S,
<=i co7
eSoo XooSoO.
ot
7. oo 4)Jo Xeo, ( 4, - 5 ) wd , w 4)Jo ,aoeXdraoct XooSoO.
8. o. Xoo&SoO : Lt 3 2 + 4 + 2 .
9. S = 2t 3 - 3t 2 - 36t + 90 , ertrfo, XooSoO.
CO7 c
10. oo Xoo&SoO : J V3x + 7 dx.
>ri - B
X>Ad)rt> /di3d JO : 10 X 2 = 20
11. 53O : ( p q ) V ( p r ).
12. 5 uoo{3X)o, 0oj Xrarrt ?
13. 15 ort> 5 aoort>o orfe ,d>deZ<od, w oort> 0o,
CO CO CO 7 CO 0
,d>deZrt>oct ( Straight lines ) 0>(ou ?
2 - 1 4
1
2
dJD. B =
14. A =
3
2
0
iodDaDO.
15. 0ddD yzrD X<, d/dDd X<,n3dd ,d3,O i d. 53. yzr A (d
CO CO
250 X,n3dd ,d3,0 i d&. 50. yZ3r B 200 X<,ndd ,d3,0
i<DD iodDaDO.
16. 40 kmph dertd dD.dDd dco, 25 kmph dertd Ho ,&o< ertD.dDd dDd 48 sec y >dDertDJ.d. d <o 0Dj ? d dDJD d, ,d/3o Jdd3Ad.
eo _o _o
17. 15 iDrrt> d d&. 750 wdd, de ddd 120 iDrrt> d 0dD, ?
ro 24 0
18. dd oJ aodbrt>D ( 1, 3 ) dDJD. ( - 2, - 4 ) wdd, dJd ,DeidradD iODaDO.
19. y 2 = 8kx d d d <D , o3$<dD d 4 wdd, k dd<dDy iodDaDO.
7 CO 7 dt
f ( x ) d < d x = 4 d
X 4 - 256 x-4 . x* 4
20. f ( x ) = .
, x = 4 yA
a
.dAd d , a dd<dDo iodDaDO.
ejJ c co 7
21. x = e 2t dDJD. y = log ( 2t + 1 ) wd, iodoaDO.
dx
- C
I. X> Ad)n> /)3d odo dn JO : 3x5=15
23. [ ( p - q ) A ( q > r ) ] > ( p > r ) <ato JJ >Odo
24. 4 oa, 7 Xd do Jo 5 ofu d),oXn>oCR oo ,3y 0dli an>Y
X,do de,uo ? - 0do, an>
y CO 0 * CO
i) Xd d),Xrt> j dojo ?
ii) oa d,Xn> J dojo do Jo Xd d),Xrt> j doJd ?
iii) 0ddo 'oe d),Xrt> J droddo ?
x 2_2
25. o- d o adJ $a35rt>3A dOdr.
x 2 + x - 12 01 *
W d , A . adj A = | A | I 0odo dd/eXO.
|
' 1 |
2 |
3 ' | |
|
26. A = |
1 |
3 |
4 |
|
- 1 |
4 |
3 - |
II. X> Ad)rt> <d/d3>dd 0do JO : 2 x 5 = 10
27. 2 rtod,do doJo 4 ort,do odo Xo,do 33 art> d/doJ3>d. 3
0 <=i CO 0
rtod,do doJo 5 ort,do Xo,do 24 art> d/doJ3> d. 3n3d, 5
_D <=i CO 0 1
n od,do doJo 2 ort,do 0do, an> w Xo,do dooft,oJ3> d ?
0 0 CO <=i 0
28. dood6 d&. 5,000, 4 % ,3jXor d&. 144 doJ d/O, d d rad odo d. 90 d, 3% ,3 5 doJo odo rnn3o d&. 108
j _0 Qi
d, 4% ,3>,5 dSdd, >d w3<do d&. 25 doJ adoJ . 3n3dd do
7 0 CO 7 0
0ddo ,3j5y Sd dra 0do, ?
29. aoD Xoa<D aro>FX Y = 1400 X - 03 -j XSXiD
d<dDDJ3. d 50 ,d,dj. Xoan
_o oS >
100 S $>&Xrt>D J</0,co deX aoarf. 100 dXrt>D JdzO,co
ti * ot * ot
deyrtod XS rtolrt>D 0>,rtDJ ? rtolrt -s>. 20 ddd 100 DdO
0-0 ti CO ti
4&Xrt> dX ddD XodD&SDO.
30. dezX.dDD ddeftbXodD X>Xod ,d>dez>J.,X
oOk c S'
ydDFdD , dD, ( LPP ) :
<4X0b ( Minimize ) : Z = 1-5x + 2-5y
x + 3y > 3 x + y > 2
x > 0, y > 0 n >0 aao rt> d oJ .
III. X>A4)n> <dz4)dd) oxdo Job : 3x5=15
31. X.deZ y = 4, a<doJ deZdD ,DeXdra x = 5, <oaa deZdD 12 wrort , w d d ddDd , DeXd rad XodDSDO.
d 2 y = 6a 2 dx 2 = ( x - 2y ) 3
32. x 2 - xy + y 2 = a 2 wd, 2 = ----3- 0oD
33. f ( x ) = x 5 - 5x 4 + 5x 3 - 1 wd, - Xad d dDJ rtOd drt>D
1 Q _D Q c
XodDSDO.
2
34. J e x 2 . x 3 dx d <dDD XodDSDO.
0 ot
- D
35. a) odo eod 8 Xoty odort> do Jo 5 TO odort$d. 3 odort oXdod3A 2 ,< Jrtdo, do w ed doJ e >3d, dd<do
y 7 o[ CO _D CO7
JrtJd 3 TO odort> doJ 0dd<do JrtJd 3 Xod) odort> dod
CO _D CO
,od>eoJ 0do ? 5
b) Lt - = nan - 1 d d n0d3 ,d/X ddrtTOAa 5
' v* _ n co co *
x a *
36. a) 17 s dd odo aoo, rao3d rtedrt dA,>Arf doJ ao
CO ct -0
X> Joado ,doJ|jd <d doed d. ao X>Ja<oo 9 ft/min ddd {>dodd, de ,do<dd ao doeoa<oo 0do s {doJ.d ? ao
5
15
2
b) 2 3x - 4 a, d } oY x ood ,JoJd>d dddo ( Term
x
independent of x ) XodDroSO.
5
|
3x - 8 3 3 3 3x - 8 3 37. a) 3 3 3x - 8 |
= 0 0od edd3ft a, 0,d, 5 _o 7 |
b) 2x + y + 2 = 0 deZ <oo x 2 + y 2 + 6x + 2y + 5 = 0 d JX@ ;,SfX aodo Jeo doJ SFTOdodo Xodbsoo. 5
_0 >J c
38. a) dddCo y 2 = x x + y = 2 deZCo do Xd
XodoSoO.
5
b) 3 ort> d>od dod d&. 2,920 doon dOCo oSCoo ood 11 dodo oddd do eX 16 ,0C/ osCo dddS d&. 2,87520
_o oa co
eaeXOdd , w oSCoo eaeXOd asoXdo XodoSO. 5
>ri - E
X>A C/>d)de o d O : 1 x 10 = 10
39. a) 2 > oSrt> F 1 do F 2 d. dd dodo OeCo &o V 1 , V 2
do V 3 d. a, Xad &o*rt> ,ed Co dd/ra eAd . V , Ood 1
-c 3 6 -> 1
mg, V 2 Ood 50 mg do V 3 Ood 10 mg. F 1 1 mg V 1 d. 100 mg V 2 d do 10 mg V 3 d. F 2 1 mg V 1 d, 10 mg V 2 d do 100 mg V 3 d. F 1 d odo &Xdo C/O,oo d&. 1 d doo F 2 d od d&Xdd C/O,co d&. 15 d d>rto d. d> deX,
Xad d/dS X,o deyd Xad d ddwdd XodoSCooo
V co 6 t3 ~ 6
,d>dez>4X yCorX,do ,d,,Cod ,,ddd0 d.XdS. 4
& J 6 ct J co 6 _o
b) odo ,>d ,d>,O d/, edodd, doon>dd, tooddd doo oXjddd a rt> 58C wAd do ,eddd, dort>dd, rtododd do
J CO _0 7 D
Xxddd a rt>Y ,d,O dgd/ 62C wAd. ooddd do rtododdd d/d dd's 15 : 19 wdd, oodd"sd doo rtododdd d/ 0do
rs 7 _o rs eo
? 4
c) ( 0-98 ) 3 d Coo d,eo<Co<0 ddeCodo dCeA 5 dd/odddrt XodoSoO. 2
40. a) %eo d = 4 + 0-08x Oo %eo Wddo = 12 wdd, &o, Wddo,
li -e eJ
&o, d , doo &o, >ddo XodoSoO. aard, d d&. 120. 4
eJ a -o eJ d. d> ii
b) 3 ort> rood dod d&. 2,72525 doon d dod odo dooSdo
03. 06. 2007 dodo ddd, 15. 06. 2007 dod ,30<d/ StXdt 16 dddS ,eSed0%dd, dooSdo ,eSed0%d dddod XodSoO. OT.odd
cn 7 d. 6
<>ddd XodSoO. 4
oL
c) P ( A ) = 0-5, P ( B ) = 0-6 dD2b_o
P ( A U B ) = 0-8 Wd d , P ( A/B ) dod dodoSoO. 2
Instructions : i) The question paper consists offive Parts - A, B, C, D and E. Answer all the Parts.
ii) Part - A carries 10 marks, Part - B carries 20 marks, Part - C carries 40 marks, Part - D carries 20 marks and Part - E carries 10 marks.
iii) Write the question numbers properly as indicated in the question paper.
Answer all the ten questions : 10 x 1 = 10
1. Write the inverse of, If principal declares a holiday then we are happy.
2. Find the number of words formed using the letters of the word
MATHEMATICS.
x 3
3. Find x if
= 0.
12 x
4. If a : b = 2 : 4 and b : c = 3 : 5 then find a : c.
5. The average marks of 24 students is 48. If one more students marks is added to this, the average becomes 48-2. Find the marks of the new student.
6. What is the true discount on a bill of Rs. 415 due 9 months hence at 15% p.a.
7. Find the equation of the point circle with centre at ( 4, - 5 ).
3n 2 + 4n + 2
8. Evaluate : Lt
2n 2 + 5n + 6
9. If S = 2t 3 - 3t 2 - 36t + 90, find velocity.
10. Evaluate J yj3x + 7 dx.
PART - B
Answer any ten questions : 10 x 2 = 20
11. Negate the proposition : ( p q ) V ( p r ).
12. Find the number of diagonals of a polygon of 5 sides.
13. There are 15 points in a plane of which 5 are collinear. Find the number of straight lines which can be formed from these points.
1 2 1 - 1 2 4
6 2 4 3 2 0
, find 2A 1 - 3B.
14. If A =
and B =
15. If the average of daily wages of workers of two factories is Rs. 53 and average wage of factory A with 250 employees is Rs. 50, find the average wage of factory B with 200 employees.
16. A train running at the rate of 40 kmph passes a man riding a scooter on the road parallel to the railway line at 25 kmph in 48 seconds. Find the length of the train. The railway track and road are parallel to each other.
17. If 15 chairs cost Rs. 750, what will be the cost of 120 chairs at the same
price ?
18. Find the equation of the circle which is described on the diameter whose end points are ( 1, 3 ) and ( - 2, - 4 ).
19. If the length of the latus rectum of the parabola y 2 = 8kx is 4, find k.
' x4 - 256
, for x * 4 x - 4
20. If f ( x ) = .
a , for x = 4
find a given that f ( x ) is continuous at x = 4.
21. If x = e 2t and y = log ( 2t + 1 ), find dy .
22. Evaluate : J , *, dx.
1
yjx + 3 - yjx + 2
I. Answer any three questions : 3 x 5 = 15
23. Show that [ ( p -> q ) A (q->r)]->(p->r) is a tautology.
24. In how many ways 4 Hindi, 7 Kannada and 5 English books can be arranged in a row ? In how many ways
i) Kannada books are together
ii) Hindi books are together and Kannada books are together
iii) No two English books are together ?
25. Resolve into partial fractions 2
|
verify A . adj A = | A |J |
II. Answer any two questions : 2 x 5 = 10
x 2 + x - 12
27. If 2 men and 4 women can do a work in 33 days and 3 men and
5 women can do the same work in 24 days, how long shall 5 men and 2 women take to do the same work ?
28. A man sells Rs. 5,000, 4 1 % stock at Rs. 144 and invests the proceeds partly in 3% stock at Rs. 90 and partly in 4% stock at Rs. 108. He thereby increases his income by Rs. 25. How much of the proceeds were invested in each stock ?
29. The production manager of a company obtained the following equation for the learning effect :
Y = 1400 X - 03 .
This function is based on the companys experience for assembling the first 50 units of the product. The company was asked to bid a new order of 100 additional units. Find the labour hours required to assemble additional 100 units. Find the labour cost for producing additional 100 units at the rate of Rs. 20 per hour.
30. Solve graphically the following LPP :
Minimize Z = 1-5x + 2-5y subjected to the constraints x + 3y > 3 x + y > 2 x > 0, y > 0.
III. Answer any three questions : 3 x 5 = 15
31. Find the equation of the parabola with directrix x = 5, axis y = 4 and length of latus rectum = 12.
d 2 y 6a
32. If x 2 - xy + y 2 = a 2 , show that 2 = a
2
dx 2 ( x - 2y ) 3
33. Determine the maximum and minimum values of the function
f ( x ) = x 5 - 5x 4 + 5x 3 - 1.
2
34. Evaluate : J e x . x 3 dx.
0
Answer any two questions. 2 x 10 = 20
35. a.) A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 white balls and second drawing will give 3 red balls. 5
x n - a n
b) Prove that Lt - = na n - 1 for all integral values of n. 5
x a x - a
36. a) A ladder 17 feet long leans against a smooth wall. If the lower end which is on a smooth horizontal floor is moving at the rate of
9 ft/min, find the rate at which the upper end is moving when the
lower end is 8 feet from the wall.
5
15
2
b) Find the term independent of x in the expansion of [ 3x -
5
3x - 8 3 3
3 3x - 8 3
37. a.) Solve
= 0
3 3 3x - 8
without direct expansion.
5
b) Show that the line 2x + y + 2 = 0 is a tangent to the circle
x 2 + y 2 + 6x + 2y + 5 = 0. Also find the point of contact.
5
38. a.) Find the area enclosed between the parabola y 2 = x and the line
5
x + y = 2.
b) A bill for Rs. 2,920 was drawn on September 11th for 3 months after
date and was discounted at 16% p.a. for Rs. 2,875-20. On what date
Answer any one question. 1 x 10 = 10
39. a.) Consider two different types of foodstuffs F 1 and F 2 . Assume that these foodstuffs contain vitamins V 1 , V 2 and V 3 respectively. Minimum daily requirement of these vitamins are 1 mg of V 1 , 50 mg of V 2 and 10 mg of V 3 . Suppose that the foodstuff F 1 contains 1 mg of V 1 , 100 mg of V 2 and 10 mg of V 3 , whereas foodstuff F 2 contains 1 mg of V 1 , 10 mg of V 2 and 100 mg of V 3 . Cost of one unit foodstuff F 1 is Re. 1 and that of F 2 is Rs. 1-5. Formulate
L.P.P. to find the minimum cost diet that would supply the body at least the minimum requirement of each vitamin. 4
b) Average temperature of a place on Monday, Tuesday, Wednesday and Friday was found to be 58C and the average temperature on Monday, Tuesday, Thursday and Friday was 62C. If the ratio of temperatures on Wednesday and Thursday is 15 : 19, find the temperatures on Wednesday and Thursday. 4
c) Find the value of ( 0-98 ) 3 using binomial theorem upto 5 places of decimals. 2
40. a) The marginal cost = 4 + 0-08x and the marginal revenue = 12. Find the total revenue, total cost and total profit. Assume the fixed cost is Rs. 120. 4
b) A bill for Rs. 2,725-25 was drawn on 03. 06. 2007 and made payable 3 months after due date. It was discounted on 15. 06. 2007 at 16% p.a. What is the discounted value of the bill and how much has the banker gained in this transaction ? 4
c) If P ( A ) = 0-5, P ( B ) = 0-6 and P ( A U B ) = 0-8,
find P ( A/B ). 2
MATHEMATICS 0 X,drt>o 0<eA%Xo0o 0Oo, rt>S d,0o
<A <* eJ co ZJ
(e,oo ?
x 3
= 0 d , x XoOoSoO.
ot
|
Attachment: |
| Earning: Approval pending. |
