TN 11th Question Paper 2023 Business Mathematics And Statistics

Tamil Nadu
State Board

2023
QUESTION
PAPER

No. of Printed Pages : 16
6767
!6767IstYearBusinessMathematics! £vÄ Gs
Register Number

PART - III
ÁoPU Pou® ©ØÖ® ¦Òΰ¯À
BUSINESS MATHEMATICS AND STATISTICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version)

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 90
Time Allowed : 3.00 Hours ] [Maximum Marks : 90

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õPz öu›ÂUPÄ®.
(2) }»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ö£ß]À £¯ß£kzuÄ®.
Instructions : (1) Check the question paper for fairness of printing. If there is any
lack of fairness, inform the Hall Supervisor immediately.

(2) Use Blue or Black ink to write and underline and pencil to draw
diagrams.

£Sv – I / PART - I

SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 20x1=20

(ii) öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯ Âøhø¯z
÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx GÊuÄ®.
Note : (i) Answer all the questions.

(ii) Choose the most appropriate answer from the given four alternatives
and write the option code and the corresponding answer.

[ v¸¨¦P / Turn over

6767 2

1. EÒÏk&öÁαk £S¨£õ´Ä ö\¯À£k® Áõ´¨¤ØPõÚ íõUQßì&ø\©ß
{£¢uøÚPÎß GsoUøP :
(A) 4 (B) 1 (C) 2 (D) 3
The number of Hawkin’s-Simon conditions for the viability of an input-output
analysis is :
(a) 4 (b) 1 (c) 2 (d) 3

2. Kº AoU ÷PõøÁ°À ‰ßÖ {øµPÒ ({µÀPÒ) \ºÁ \©® GÛÀ, AÆÁoU
÷PõøÁ°ß ©v¨¦ :
(A) 1 (B) 0 (C) 3 (D) 2
If any three rows (columns) of a determinant are identical then the value of the
determinant is :
(a) 1 (b) 0 (c) 3 (d) 2

3. 5 Âøͯõmk õºPμ¸¢x |õßS ÷£øµ GzuøÚ ÁÈPÎÀ ÷uº¢öukUP»õ® ?

(A) 25 (B) 4! (C) 5 (D) 20
The number of ways in selecting 4 players out of 5 is :
(a) 25 (b) 4! (c) 5 (d) 20

4. D¸Ö¨¦ öPÊUPÎß TkuÀ :
(A) 2n (B) 2n (C) n+17 (D) n2
Sum of the binomial coefficients is :
(a) 2n (b) 2n (c) n+17 (d) n2

5. y2=−x GßÓ £µÁøͯzvß C¯USÁøµ°ß \©ß£õk :

(A) x−4=0 (B) 4x+1=0 (C) x+4=0 (D) 4x−1=0
The equation of directrix of the parabola y2=−x is :

(a) x−4=0 (b) 4x+1=0 (c) x+4=0 (d) 4x−1=0

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6. x2−7xy+4y2=0 GßÓ Cµmøh ÷|º÷PõkPÐUS Cøh¨£mh ÷Põn® :

 33  1 −1  5  1
(A) tan−1   (B) tan−1  3  (C) tan   (D) tan−1  
 5     33  2

The angle between the pair of straight lines x2−7xy+4y2=0 is :

 33  1  5  1
(a) tan−1   (b) tan−1   (c) tan−1   (d) tan−1  
 5  3  33  2

7. sin158 cos158 &ß ©v¨¦ :

3 1 1
(A) (B) 1 (C) (D)
2 4 2

The value of sin158 cos158 is :

3 1 1
(a) (b) 1 (c) (d)
2 4 2

8. p sec 508=tan 508 GÛÀ, p &ß ©v¨¦ :

(A) tan 508 (B) cos 508 (C) sec 508 (D) sin 508
If p sec 508=tan 508, then the value of p is :

(a) tan 508 (b) cos 508 (c) sec 508 (d) sin 508

9. y=2x2 GßÓ Áøµ£h® __________ GßÓ ¦ÒÎ ÁȯõP ö\À¾®.

(A) (2, 0) (B) (0, 0) (C) (0, 2) (D) (2, 1)
The graph of y=2x2 is passing through the point :

(a) (2, 0) (b) (0, 0) (c) (0, 2) (d) (2, 1)

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10. f (x)=x2 −x+1 GÛÀ, f (x+1) BÚx :

(A) 1 (B) x2 (C) x2+x+1 (D) x
If f (x)=x2 −x+1, then f (x+1) is :
(a) 1 (b) x2 (c) x2+x+1 (d) x

2 ∂u
11. u = ex GÛÀ = __________.
∂x

(A) 2ex 2 (B) 2x ex 2 (C) 0 (D) ex
2

2 ∂u
If u = ex , then = __________.
∂x

2 2 2
(a) 2ex (b) 2x ex (c) 0 (d) ex

12. £[S Ãu® PnUQh Ai¨£øh¯õPU öPõÒͨ£kÁx :
(A) \¢øu ©v¨¦ (B) ‰»uÚ® (C) •P ©v¨¦ (D) CvÀ HxªÀø»
The calculation of dividend is based on :
(a) Market value (b) Capital (c) Face value (d) None of these

13. uØPõ¼P uÁøn £[Rmkz öuõøPUPõÚ GkzxUPõmk :
(A) ©õnÁºPÐUS EuÂz öuõøP AÎUS® |ßöPõøh {v
(B) Á[Q°ß uÛ|£º Phß
(C) J¸ Ãmk©øÚUPõP ö\¾zu¨£k® uÁønz öuõøP
(D) ÷©ØPsh AøÚzx®
Example of Contigent annuity is :
(a) An endowment fund to give scholarship to the students.
(b) Personal loan from a Bank.
(c) Instalment of payment for a plot of land.

(d) All the above.

5 6767

14. ¤ßÁ¸ÁÚÁØÖÒ Gx Cøh{ø»ø¯U SÔUS® ?
(A) Q3 (B) Q1 (C) D2 (D) Q2
Which of the following represents Median ?
(a) Q3 (b) Q1 (c) D2 (d) Q2

15. f (x)=sinx GßÓ \õº¤ß «¨ö£¸ ©v¨£õÚx :

1 −1 3
(A) 2
(B) 1 (C) 2
(D)
2

The maximum value of f (x)=sinx is :

1 −1 3
(a) (b) 1 (c) (d)
2 2 2

16. ^mkU Pmi¼¸¢x ì÷£k ^møhz ÷uº¢öuk¨£uØPõÚ {PÌuPÄ :

4 1 1 1
(A) (B) (C) (D)
13 52 4 13

The probability of drawing a spade from a pack of cards is :

4 1 1 1
(a) (b) (c) (d)
13 52 4 13

17. X ©ØÖ® Y Gß£Ú C¸ ©õÔPÒ GÛÀ AvP£m\©õP C¸¨£x :

(A) ‰ßÖ öuõhº¦¨ ÷£õUSU ÷PõkPÒ
(B) J¸ öuõhº¦¨ ÷£õUSU ÷Põk
(C) £» öuõhº¦¨ ÷£õUSU ÷PõkPÒ
(D) Cµsk öuõhº¦¨ ÷£õUSU ÷PõkPÒ
If X and Y are two variables then there can be atmost :
(a) Three regression lines
(b) One regression line

(c) More regression lines
(d) Two regression lines

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18. C¸ ©õÔPÎß ©v¨¦PÒ J÷µ vø\°À |P¸® GÛÀ, JmkÓÄ :

(A) •Êø©¯õÚ ÷|›øh (B) Gv›øh

(C) JmkÓÄ Cßø© (D) ÷|›øh
If the value of the two variables move in same direction, then the correlation is
said to be :

(a) Perfect positive (b) Negative

(c) No correlation (d) Positive

19. Áø»¯ø©¨¦¨ £S¨£õ´Âß SÔU÷PõÍõÚx :

(A) ö©õzu vmh Põ»zøu ]Ö©©õUSuÀ

(B) EØ£zvz uõ©u®, SÖURkPÒ, •µs£õkPÒ BQ¯ÁØøÓ ]Ö©©õUSuÀ

(C) ö©õzu vmh ö\»ÂøÚ ]Ö©©õUSuÀ

(D) ÷©ØPsh AøÚzx®
The objective of network analysis is to :

(a) Minimize the total project duration

(b) Minimize the production delays, interruption and conflicts

(c) Minimize the total project cost

(d) All the above

20. 2x+5y≤10, x/0, y/0, GßÓ Pmk¨£õkPÐUS Cn[P Z=3x+5y GßÓ
SÔU÷PõÒ \õº¤ß «¨ö£¸ ©v¨¦ :

(A) 25 (B) 6 (C) 31 (D) 15
The maximum value of the objective function Z=3x+5y subject to the constraints
2x+5y≤10, x/0, y/0 is :

(a) 25 (b) 6 (c) 31 (d) 15

7 6767

£Sv - II / PART - II
SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 30 &US
7x2=14
Pmhõ¯©õP Âøh¯ÎUPÄ®.
Note : Answer any seven questions. Question No. 30 is Compulsory.

x x +1
21.
x −1 x
&ß ©v¨¦ PõsP.

x x +1
Evaluate
x −1 x

22. _ÁØÔß «xÒÍ 5 BoPÎÀ 7 £h[PøÍ GzuøÚ ÁÈPÎÀ ö£õ¸zu»õ® ?
In how many ways 7 pictures can be hung from 5 picture nails on a wall ?

23. y2=20x GßÓ £µÁøͯzvß •øÚ ©ØÖ® S¯® BQ¯ÁØøÓU PõsP.

Find the focus and vertex of the parabola y2=20x.

2x + 5
24. ©v¨¤kP : xlim
→∞ 2
x + 3x + 9

2x + 5
Evaluate : lim 2
x →∞ x + 3x + 9

25. x A»SPÒ öPõsh J¸ ö£õ¸Îß EØ£zvUPõÚ ö©õzu ö\»Ä C (¹£õ°À).

C(x ) = 50 + 4x + 3 x GÛÀ, 9 A»SPÒ EØ£zvUPõÚ CÖv {ø»a ö\»Ä ¯õx ?

The total cost C in Rupees of making x units of a product is C(x ) = 50 + 4x + 3 x .

Find the marginal cost of the product at 9 units of output.

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26. ` 18 AvP Âø»°À EÒÍ ` 100 &I •P©v¨£õPU öPõsh 325 £[SPÎß
\¢øu ©v¨ø£U PõsP.
Find the Market value of 325 shares of Face value ` 100 at a premium of ` 18.

27. ©õÚ® J¸ \xµzvß |õßS £UP[PÎß ÁȯõP •øÓ÷¯ ©oUS 100 Q.«.,
200 Q.«., 300 Q.«. ©ØÖ® 400 Q.«. £ÓUQÓx. \xµ¨£UP[PÎß «x _ØÔ Á¸®
©õÚzvß \µõ\› ÷ÁPzøuU PõsP.
An aeroplane flies, along the four sides of a square at speeds of 100, 200, 300 and
400 kilometres per hour respectively. Find the average speed of the plane in its
flight around the square.

28. ¤ßÁ¸® ÂÁµ[Pμ¸¢x JmkÓÄU öPÊøÁU PnUQkP.
N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597.

Calculate the correlation co-efficient from the following data.

N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597.

29. ¤ßÁ¸® ÂÁµ[PøÍU öPõsk J¸ Áø»¯ø©¨ø£ E¸ÁõUSP.

ö\¯À A B C D E F G H

EhÚi •¢øu¯
- - A B C, D C, D E F
{PÌÄ
Develop a network based on the following information.

Activity A B C D E F G H

Immediate
- - A B C, D C, D E F
predecessor

30. tan 1508 &ß ©v¨¦U PõsP.

Find the value of tan 1508.

9 6767

£Sv - III / PART - III

SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 40 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 7x3=21

Note : Answer any seven questions. Question No. 40 is Compulsory.

 1 1 3
 
31.  2 λ 4  GßÓ AoUS ÷|º©õÖ CÀø» GÛÀ, λ &ß ©v¨¦ PõsP.
 9 7 11
 

 1 1 3
 
Find λ, if the matrix  2 λ 4  has no inverse.
 9 7 11
 

32. B[Q» APµõv°À EÒÍ ‘CHAT’ GßÓ Áõºzøu°ß uµ® PõsP.
Find the rank of the word ‘CHAT’ in dictionary.

33. a, b &PÎß G®©v¨¦PÐUS (a−2)x 2 +by 2 +(b−2)xy+4x+4y−1=0 GÝ®
\©ß£õk ÁmhzøuU SÔUS® ? C¢u Ámhzvß \©ß£õmøh²® GÊxP.
For what values of a and b does the equation (a−2)x2+by2+(b−2)xy+4x+4y−1=0
represents a circle ? Write down the resulting equation of the circle.

1  2 3
34. tan−1   + tan−1   = tan−1   GÚ {ÖÄP.
2  11  4

1  2 3
Show that tan−1   + tan−1   = tan−1   .

 
2  11  4

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x +7
35. x A»SPÐUPõÚ ö©õzu ö\»Äa \õº¦ y = 3x   + 5 &À EØ£zv AÍÄ (x)
x +5

BÚx AvP›US® ö£õÊx, CÖv {ø»a ö\»ÁõÚx [MC] öuõhºa]¯õPU
SøÓQÓx GÚU PõmkP.

x +7
The total cost function y for x units is given by y = 3x   + 5 . Show that the
x +5

Marginal Cost [MC] decreases continuously as the output (x) increases.

36. ` 140 &À EÒÍ 20% \µUS •uÀ AÀ»x ` 70 &À EÒÍ 10% \µUS •uÀ, CÁØÖÒ
Gx ]Ó¢u •u½k ?

Which is better investment, 20% stock at ` 140 or 10% stock at ` 70 ?

37. öPõkUP¨£mh ÂÁµ[PÐUS Q1, D2 ©ØÖ® P90 BQ¯ÁØøÓU PõsP.

©v¨ö£s 10 20 30 40 50 60

©õnÁºPÎß
4 7 15 8 7 2
GsoUøP

Compute Q1, D2 and P90 from the following data.

Marks 10 20 30 40 50 60
4 7 15 8 7 2

No. of Students

11 6767

38. £zx ©õnÁºPÒ ÁoP¯À ©ØÖ® PnUS¨ £v¯À £õhzvÀ ö£ØÓ uµ[PÒ
¤ßÁ¸©õÖ :

ÁoP¯À 6 4 3 1 2 7 9 8 10 5
PnUS¨ £v¯À 4 1 6 7 5 8 10 9 3 2

uµ JmkÓÄU öPÊøÁU PõsP.
The following are ranks obtained by 10 students in Commerce and Accountancy.

Commerce 6 4 3 1 2 7 9 8 10 5
Accountancy 4 1 6 7 5 8 10 9 3 2

Find the Rank Correlation Co-efficient.

39. J¸ ©µ ¯õ£õ› ÷©ø\, |õØPõ¼ BQ¯ C¸ ö£õ¸ÒPøÍ ©mk÷© ¯õ£õµ®
ö\´QÓõº. AÁ›h® •u½k ` 10,000 EÒÍx. ÷©¾® 60 GsoUøP°»õÚ
ö£õ¸ÒPøÍ ©mk÷© øÁ¨£uØPõÚ ChÁ\v²® EÒÍx. J¸ ÷©ø\°ß Âø»
` 500 ©ØÖ® J¸ |õØPõ¼°ß Âø» ` 200 BS®. AÁº Áõ[SQßÓ GÀ»õ¨
ö£õ¸ÒPøͲ® ÂØÖÂkÁõº. J¸ ÷©ø\°¼¸¢x ` 50 C»õ£•® J¸
|õØPõ¼°¼¸¢x ` 15 C»õ£•® ö£ÖQÓõº GÛÀ, AÁº «¨ö£¸ C»õ£®
ö£ÖÁuØPõÚ ÷|›¯À vmhªhÀ PnUQøÚ ÁiÁõUSP.
A furniture dealer deals only in two items viz., tables and chairs. He has to
invest ` 10,000 and a space to store atmost 60 pieces. The cost of a table is ` 500
and the cost of a chair is ` 200. He can sell all the items that he buys. He is
getting a profit of ` 50 per table and ` 15 per chair. Formulate this problem as an
LPP, so as to maximize the profit.

dy
40. x=a sec3θ, y=b tan3θ GÛÀ PõsP.
dx

dy

Find , if x=a sec3θ, y=b tan3θ.
dx

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6767 12

£Sv - IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 7x5=35
Note : Answer all the questions.

 4 −2 −1 
 2 2 1  5 5 5
  
B = −1 3 −1 
41. (A) A =  1 3 1 ©ØÖ® GßÓ AoPÒ JßÖUöPõßÖ
 5 5 5
 1 2 2 −1 −2
  4 
 5 5 5
÷|º©õÖ GÚU PõmkP.
AÀ»x
1 1 π
(B) tanα = ©ØÖ® tanβ = GÛÀ, (2α+β)= GÚ {ÖÄP.
3 7 4

 4 −2 −1 
 5 5 5
 2 2 1 −1 3 −1 
 
(a) Show that the matrices A =  1 3 1 and B=  5 5 5  are inverse
 1 2 2 
−1 −2 4 
   5 5 5
of each other.
OR
1 1 π
(b) If tanα = and tanβ = then prove that (2α+β)= ⋅
3 7 4

12
 2 1
42. (A)  2x +  &ß Â›ÂÀ x &Ia \õµõu EÖ¨¤øÚU PõsP.
 x
AÀ»x
Eq Eq
(B) x GßÓ ö£õ¸Îß ÷uøÁ q = 5 − 2p1 + p2 −p12p2 GÛÀ, Ep ©ØÖ® Ep
1 2
GßÓ £Sv ö|QÌa]PøÍ p1=3 ©ØÖ® p2=7 GÝ®ö£õÊx PõsP.
12
 2 1
(a) Find the term independent of x in the expansion of  2x +  .
 x
OR
(b) If the demand for a commodity x is q = 5 − 2p1 + p2 −p12p2 , find the partial

Eq Eq

elasticities Ep and Ep when p1=3 and p2=7.
1 2

13 6767

43. (A) Pouz öuõSzuÔu¼ß£i

n2 (n + 1)2
13 + 23 + 33 + ........ + n3 = (AøÚzx neN) GÚ {ÖÄP.
4

AÀ»x

(B) f (x ) = 
2−x x <2
GßÖ Áøµ¯ÖUP¨£mh \õº¦ f &Cß öuõhºa]z
2 + x x2

ußø©ø¯ x=2 &À Bµõ´P.
(a) By mathematical Induction, prove that

n2 (n + 1)2
13 + 23 + 33 + ........ + n3 = for all neN.
4

OR
(b) Verify the continuity of the defined function f (x) given by

2 − x , x < 2
f (x ) =  at x=2.
2 + x , x  2

44. (A) J¸ vmhzvß Põ» AmhÁøn ¤ßÁ¸©õÖ :

ö\¯À 1-2 1-6 2-3 2-4 3-5 4-5 6-7 5-8 7-8
Põ» AÍÄ
7 6 14 5 11 7 11 4 18
(|õmPÎÀ)

CuØPõÚ Áø»¯ø©¨ø£ ÁøµP. ÷©¾® GÀ»õ vmh ö\¯¾US® •¢øu¯
öuõhUP Põ»® (EST), •¢øu¯ •iÄ Põ»® (EFT), \«£zv¯ öuõhUP Põ»®
(LST) ©ØÖ® \«£zv¯ •iÄ Põ»® (LFT) PõsP. wºÄUS EP¢u £õøuø¯²®,
vmh® •iÁøh¯ BS® Põ»zøu²® PõsP.
AÀ»x

(x − 1) (x − 2)

(B) (x − 3) (x 2 + x +1)
GßÓ \õºø£ x &I¨ ö£õÖzx ÁøP°kP.

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6767 14

(a) A project has the following time schedule.

Activity 1-2 1-6 2-3 2-4 3-5 4-5 6-7 5-8 7-8
Duration (in days) 7 6 14 5 11 7 11 4 18

Construct the network and calculate earliest start time (EST), earliest finish
time (EFT), latest start time (LST) and latest finish time (LFT) of each activity,
and determine the critical path of the project and duration to complete the
project.

OR

(x − 1) (x − 2)
(b) Differentiate the function with respect to x.
(x − 3) (x 2 + x +1)

45. (A) PnÁºPÒ ©ØÖ® AÁºu® ©øÚ¯ºPÎß Á¯vØQøh÷¯¯õÚ JmkÓÄU
öPÊøÁ PõsP.

PnÁºPÎß Á¯x 23 27 28 29 30 31 33 35 36 39
©øÚÂPÎß Á¯x 18 22 23 24 25 26 28 29 30 32

AÀ»x

(B) ö£õ¸Ò A &Cß Á¸hõ¢vµz ÷uøÁ 800 A»SPÒ ©ØÖ® Kµ»S Âø»
` 0.02. ÷Põ¸uÀ ö\»Ä J¸ ÷Põ¸u¾US ` 5 ©ØÖ® Bsk C¸¨¦a ö\»Ä
A»S JßÔØS 10% BS®. GÛÀ,

(i) ªS Buõ¯U ÷Põ¸uÀ AÍÂøÚ A»S ©v¨¤À PõsP.

(ii) ]Ö© \µUS {ø»a ö\»ÂøÚU PõsP.

(iii) ªS Buõ¯U ÷Põ¸uÀ AÍøÁ ¹£õ°À PõsP.

(iv) ªS Buõ¯U ÷Põ¸uÀ AÍøÁ Á¸h ÁÇ[PÀ Ai¨£øh°À PõsP.

(v) J¸ Á¸hzvØPõÚ ÷Põ¸uÀPÎß GsoUøPø¯U PõsP.

15 6767

(a) Calculate the coefficient of correlation for the ages of husbands and their
respective wives.

Age of husbands 23 27 28 29 30 31 33 35 36 39
Age of wives 18 22 23 24 25 26 28 29 30 32

OR
(b) The annual demand for an item A is 800 units and unit price is ` 0.02. If
ordering cost is ` 5 per order and annual holding cost is 10% of unit price,
then determine the following :
(i) EOQ in units.
(ii) Minimum inventory cost.
(iii) EOQ in Rupees.
(iv) EOQ in years of supply.
(v) Number of orders per year.

46. (A) •øÓ÷¯ 25%, 30% ©ØÖ® 50% ö£õ¸mPøÍ EØ£zv ö\´¯UTi¯ A, B, C
GßÓ C¯¢vµ[PøÍ J¸ {ÖÁÚ® öPõskÒÍx. AÁØÔß SøÓ£õk
\uÃu[PÒ •øÓ÷¯ 5, 4 ©ØÖ® 2 BS®. C¢u EØ£zv ö\´¯¨£mh
ö£õ¸mPμ¸¢x JßÖ ÷uº¢öukUP¨£mk¨ £›÷\õvUP¨£kQÓx. Ax
SøÓ£õkÒÍx GÛÀ, Ax C¯¢vµ® B &°ÚõÀ EØ£zv ö\´¯¨&
£mhuØPõÚ {PÌuPÄ ¯õx ?
AÀ»x
(B) (1, 0), (0, 1) GßÓ ¦ÒÎPÎß ÁȯõPÄ®, x+y=1 GßÓ ÷Põmiß ÷©À
ø©¯zøu²® Eøh¯ Ámhzvß \©ß£õk PõsP.
(a) A company has three machines A, B, C which produces 25%, 30% and 50%
of the product respectively. Their respective defective percentages are 5, 4
and 2. From these products one is chosen and inspected. If it is defective,
what is the probability that it has been made by the machine B.
OR

(b) Find the equation of the circle on the line joining the points (1, 0), (0, 1) and
having its centre on the line x+y=1.

[ v¸¨¦P / Turn over

6767 16

47. (A) JÆöÁõ¸ Põ»õsk CÖv°¾® 8% Bsk Ámi°À ` 2,000 GÚ 10
BskPÐUS ö\¾zu¨£k® uÁøn £[Rmkz öuõøP°ß •vºÄz
öuõøP°øÚU PõsP. [(1.02)40=2.2080]
AÀ»x
(B) 4 Q÷»õ öÁ[Põ¯®, 3 Q÷»õ ÷Põxø© ©ØÖ® 2 Q÷»õ A›]°ß ö©õzu
Âø» ` 320. 2 Q÷»õ öÁ[Põ¯®, 4 Q÷»õ ÷Põxø©, 6 Q÷»õ A›]°ß
ö©õzu Âø» ` 560. 6 Q÷»õ öÁ[Põ¯®, 2 Q÷»õ ÷Põxø© ©ØÖ® 3 Q÷»õ
A›]°ß ö©õzu Âø» ` 380 GÛÀ, ÷|º©õÖ Ao •øÓ°À J¸
Q÷»õÂØPõÚ ö£õ¸ÒPÎß Âø»ø¯ PõsP.
(a) If the payment of ` 2,000 is made at the end of every quarter for 10 years at
the rate of 8% per year, then find the amount of annuity.
[(1.02)40=2.2080]
OR
(b) The total cost of 4 kg onion, 3 kg wheat and 2 kg rice is ` 320. The total cost
of 2 kg onion, 4 kg wheat and 6 kg rice is ` 560. The total cost of 6 kg onion,
2 kg wheat and 3kg rice is ` 380. Find the cost of each item per kg by Matrix
Inversion method.

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