TN 11th Question Paper 2022 Business Mathematics & Statistics

No. of Printed Pages : 15
6067
!6067IstYearBusinessMathematics! £vÄ Gs
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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.

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0 1 0
1. x 2 x = 0 GÛÀ x &ß ©v¨¦PÒ PõsP.
1 3 x

(A) −1, 1 (B) 0, −1 (C) −1, −1 (D) 0, 1
0 1 0
The values of x if x 2 x = 0 is :
1 3 x

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

2 −3 5
2. 6 0 4 &CÀ −7 &ß CønU Põµo :
1 5 −7

(A) −7 (B) −18 (C) 7 (D) 18
2 −3 5
The co-factor of −7 in the determinant 6 0 4 is :
1 5 −7

(a) −7 (b) −18 (c) 7 (d) 18

3. nP2=20 GÝ® ö£õÊx n &ß ©v¨¦ :
(A) 5 (B) 3 (C) 4 (D) 6
The value of n, when nP2=20 is :
(a) 5 (b) 3 (c) 4 (d) 6

4. ö£õ¸mPøÍ «sk® £¯ß£kzu»õ® GßÓ ÁøP°À, öÁÆ÷ÁÓõÚ n
ö£õ¸mPμ¸¢x r ö£õ¸mPøÍ J÷µ ÷|µzvÀ ÷uº¢öukzx Á›ø\¨£kzx®
ÁÈPÎß GsoUøP :
n! n!
(A) (n − r)! (B) r n (C) (n + r)! (D) nr
The number of permutation of n different things taken r at a time, when the
repetition is allowed is :
n! n!
(a) (n − r)! (b) rn (c) (n + r)! (d) nr

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5. 3x+2y−1=0 GßÓ ÷Põmiß x-öÁmkzxsk :

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

The x-intercept of the straight line 3x+2y−1=0 is :

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

6. x2+y2+ax+by−4=0 GßÓ Ámhzvß ø©¯® (1, −2) GÛÀ Auß Bµ® :

(A) 4 (B) 3 (C) 1 (D) 2
(1, −2) is the centre of the circle x2+y2+ax+by−4=0, then its radius :

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

π
7. &ß ÷Põn ©v¨¦ :
8

(A) 228609 (B) 208609 (C) 208309 (D) 228309

π
The degree measure of is :
8

(a) 228609 (b) 208609 (c) 208309 (d) 228309

8. 378309&ß ÷µi¯ß AÍÄ :

7π 5π 9π 3π
(A) (B) (C) (D)
24 24 24 24

The radian measure of 378309 is :

7π 5π 9π 3π
(a) (b) (c) (d)

24 24 24 24

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6067 4

x 2 − 4x , x 2
9. f (x ) =  GÛÀ, f (0) &ß ©v¨¦ :
 x + 2, x <2

(A) −1 (B) 2 (C) 0 (D) 5

x 2 − 4x if x 2
If f (x ) =  then, f (0) is :
x + 2 if x < 2

(a) −1 (b) 2 (c) 0 (d) 5

10. RÌPõq® \õº¦PÎÀ Gx JØøÓ \õº£õPÄ® ©ØÖ® Cµmøh \õº£õPÄ® C¸UPõx ?
(A) f (x)=x10 (B) f (x)=x3+5 (C) f (x)=x2 (D) f (x)=x5
Which of the following function is neither even nor odd ?

(a) f (x)=x10 (b) f (x)=x3+5 (c) f (x)=x2 (d) f (x)=x5

1 dy
11. y=x ©ØÖ® z = GÛÀ =
x dz

1
(A) −x2 (B) x2 (C) − 2 (D) 1
x

1 dy
If y=x and z = , then =
x dz

1
(a) −x2 (b) x2 (c) − (d) 1
x2

12. ÷uøÁa \õº¦ «Òußø© öPõshx GÛÀ :
(A) ?ηd? < 1 (B) ?ηd? > 1 (C) ?ηd?=0 (D) ?ηd?=1
If the demand function is said to be elastic, then :

(a) ?ηd? < 1 (b) ?ηd? > 1 (c) ?ηd?=0 (d) ?ηd?=1

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13. MR, AR ©ØÖ® ηd &UPÐUS Cøh÷¯²ÒÍ öuõhº£õÚx :

AR
(A) MR=AR=ηd (B) ηd =
AR − MR

MR
(C) AR = η (D) ηd=AR−MR
d

Relationship among MR, AR and ηd is :

AR
(a) MR=AR=ηd (b) ηd =
AR − MR

MR
(c) AR = (d) ηd=AR−MR
ηd

1 1
14. ` 100 •P©v¨¦øh¯, J¸ £[S, 9 % PÈÄ Âø»US, % uµS ÃuzvÀ
2 2
QøhUS® GÛÀ, A¨£[Qß Áõ[Q¯ Âø» :

(A) ` 91 (B) ` 89 (C) ` 95 (D) ` 90

1
Purchasing price of one share of face value ` 100 available at a discount of 9 %
2
1
with brokerage % is :
2

(a) ` 91 (b) ` 89 (c) ` 95 (d) ` 90

15. Cøh{ø» = 45 ©ØÖ® Auß \µõ\› »UPöPÊ 0.25 GÛÀ, Cøh{ø»ø¯¨
ö£õÖzu \µõ\› »UP® :

(A) 0.0056 (B) 11.25 (C) 45 (D) 180
If median=45 and its co-efficient is 0.25, then the mean deviation about median
is :

(a) 0.0056 (b) 11.25 (c) 45 (d) 180

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16. C¸ £Pøh E¸mh¨£k® ÷£õx C¸ £Pøh°À JÆöÁõßÔ¾® Cµmøh £Põ
Gs ö£ÖÁuØPõÚ {PÌuPÄ :

1 1 1
(A) (B) (C) (D) 0
3 36 6

The probability of obtaining even prime number on each die, when a pair of dice is
rolled is :

1 1 1
(a) (b) (c) (d) 0
3 36 6

17. J¸ {PÌa]°ß öÁΨ£õk, ©Ø÷Óõº {PÌa]°ß {PÌøÁ £õvUPÂÀø» GÛÀ,
AƸ {PÌa]PÒ :

(A) JßøÓ JßÖ Â»UPõ {PÌa]PÒ

(B) JßøÓ JßÖ Â»US® {PÌa]PÒ

(C) JßøÓ JßÖ \õµõ {PÌa]PÒ

(D) JßøÓ JßÖ \õº¢u {PÌa]PÒ

If the outcome of one event does not influence another event then the two events
are :

(a) Not disjoint

(b) Mutually exclusive

(c) Independent

(d) Dependent

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18. C¸ ©õÔPÎß ©v¨¦PÒ Gvºzvø\°À |P¸® GÛÀ JmkÓÄ :
(A) •Êø©¯õÚ ÷|›øh (B) Gv›øh
(C) JmkÓÄ Cßø© (D) ÷|›øh
If the values of two variables move in opposite direction then the correlation is
said to be :

(a) Perfect positive (b) Negative

(c) No correlation (d) Positive

19. ¤ßÁ¸ÁÚÁØÔÀ GøÁ ÷|›øh JmkÓÄUPõÚ GkzxUPõmhõS® ?
(A) v¸¨¤a ö\¾zx® Põ»® ©ØÖ® _»£ ©õuz uÁøn
(B) Á¸Áõ´ ©ØÖ® ö\»Ä
(C) {øÓ ©ØÖ® Á¸Áõ´
(D) Âø» ©ØÖ® ÷uøÁ
Example for positive correlation is :

(a) Repayment period and EMI

(b) Income and expenditure

(c) Weight and Income

(d) Price and demand

20. (i, j) GßÓ ö\¯»õÚx wºÄUS EP¢u £õøu°À C¸¨£uØPõÚ {£¢uøÚPÎÀ
JßÖ :
(A) Ej−Ei=Li−Lj=tij (B) Ej−Ei=Lj−Li=tij
(C) Ej−Ei=Lj−Li ≠ tij (D) Ei−Ej=Lj−Li=tij
One of the conditions for the activity (i, j) to lie on the critical path is :

(a) Ej−Ei=Li−Lj=tij (b) Ej−Ei=Lj−Li=tij

(c) Ej−Ei=Lj−Li ≠ tij (d) Ei−Ej=Lj−Li=tij

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£Sv – II / PART - II

SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 30 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 7x2=14

Note : Answer any seven questions. Question No. 30 is compulsory.

 2 4
 GÛÀ A
21. A=  −1 PõsP.
− 3 2 

 2 4 −1
If A =   then, find A .
− 3 2 

22. “LOGARITHMS” GßÓ Áõºzøu°À EÒÍ GÊzxUPøͨ £¯ß£kzv,
(GÊzxUPÒ «sk® Ch®ö£ÓõuÁõÖ Aºzu® EÒÍ AÀ»x Aºzu©ØÓ)
4 GÊzx ÁõºzøuPÒ GzuøÚ Aø©UP»õ® ?

Find how many four letter words can be formed from the letters of the word
“LOGARITHMS”(letters not repeated and words are with or without meanings).

23. J¸ uÍzvß «xÒÍ J¸ ¦ÒÎ Bv°¼¸¢x EÒÍ öuõø»Ä A¨¦Òΰß
y &Aa]¼¸¢x Auß öuõø»øÁ¨ ÷£õÀ ‰ßÖ ©h[öPÛÀ A¨¦Òΰß
C¯[S Áøµø¯U PõsP.
A point in the plane moves so that its distance from the origin is thrice its distance
from the y-axis. Find its locus.

24. cot 758&ß ©v¨¦ PõsP.

Find the value of cot 758.

25. y=x 3 +19 GßÓ \õº¤ß CÖv {ø» ©v¨£õÚx 27 &US \©ö©ÛÀ, x &ß
©v¨¦PøÍU PõsP.
For the function y=x3+19, find the values of x when its marginal value is equal
to 27.

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26. ` 132 &À QøhUS® ` 100 \© ©v¨¦ÒÍ 62 £[SPÎß \¢øu ©v¨¤øÚU PõsP.

Find the market value of 62 shares available at ` 132 having the par value of
` 100.

3
27. P(A) = ©ØÖ® P(B) = 1 GßP. A, B Gß£Ú \õµõ {PÌÄPÒ GÛÀ P(A ∩ B) &I
5 5
PõsP.

3 1
Let P(A) = and P(B) = . Find P(A ∩ B) if A and B are independent events.
5 5

28. ¤ßÁ¸® ÂÁµ[Pμ¸¢x JmkÓÄUS öPÊÂøÚ PnUQkP.

ΣX=50, ΣY=−30, ΣX2=290, ΣY2=300, ΣXY=−115, N=10.

Calculate the co-efficient of correlation from the following data :

ΣX=50, ΣY=−30, ΣX2=290, ΣY2=300, ΣXY=−115, N=10.

29. ¤ßÁ¸® £µ[PÐUS uºUP Áø»¯ø©¨¦ ÁøµP.

ö\¯ÀPÒ C ©ØÖ® D BQ¯ Cµsk® A &øÁ¨ ¤ß öuõhºQÓx. ö\¯À
E BÚx C &I¨ ¤ß öuõhºQÓx. ö\¯À F BÚx ö\¯À D &I¨ ¤ß öuõhºQÓx.
ö\¯À E ©ØÖ® ö\¯À F BÚx B &°ß •¢øu¯ ö\¯ÀPÍõS®.
Draw the logic network for the following :

Activities C and D both follow A, activity E follows C, activity F follows D, activity E
and F precedes B.

1
30. x= ©ØÖ® y=cost GÛÀ dy PõsP.
t dx

1 dy
If x = , y=cost then find .
t dx

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6067 10

£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.

−4 11 −5 
 35 35 35 
1 3 7   
31.  
A =  4 2 3  ©ØÖ® B =  −1 −6 25 
GßÓ AoPÒ JßÖUöPõßÖ ÷|º©õÖ
 35 35 35 
1 2 1   
 6 1 −10 
 35 35 35 
GÚUPõmkP.
−4 11 −5 
 35 35 35 
1 3 7   
Show that the matrices A =  4 2 3 
−1 −6 25 
and B =  are inverses of
 35 35 35 
1 2 1   
 6 1 −10 
 35 35 35 
each other.

32. 7 B[Q» ö©´ö¯ÊzxPÒ ©ØÖ® 4 B[Q» E°öµÊzxPμ¸¢x,
3 ö©´ö¯ÊzxUPÒ ©ØÖ® Cµsk E°öµÊzxPøÍ ÷uº¢öukzx, GzuøÚ
ÁõºzøuPÒ E¸ÁõUP»õ® ?
Out of 7 consonants and 4 vowels, how many words of 3 consonants and
2 vowels can be formed ?

33. ÷Põn[PÒ A, B ©ØÖ® C Gß£Ú J¸ Tmkz öuõhº Á›ø\°À EÒÍÚ GÛÀ,
sinA − sinC
cotB = GÚ {ÖÄP.
cosC − cosA
If three angles A, B and C are in arithmetic progression, prove that
sinA − sinC
cotB = .
cosC − cosA

1− 3x
34. GßÓ \õºø£ x &I ö£õÖzx ÁøP°kP.
1+ 3x

1− 3x
Differentiate the function with respect to x.
1+ 3x

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35. y=x3+10x2−48x+8 GßÓ \õº¤ß CÖv {ø»¯õÚx x&I ÷£õÀ C¸©h[S GÛÀ
x&ß ©v¨¦PÒ ¯õx ?
Find the values of x, when the marginal function of y=x3+10x2−48x+8 is twice
the x.

36. J¸Áº 17% PÈÂÀ EÒÍ 12% \µUS •uÀPøÍ ` 54,000 &US Áõ[QÚõº.
AuØPõP AÁº ö\¾zv¯ uµS 1% GÛÀ, AÁ›ß Á¸©õÚzvß ÃuzøuU PõsP.
A person bought 12% stock for ` 54,000 at a discount of 17%. If he paid 1%
brokerage, find the percentage of his income.

37. I¢x SÊUPÎß Á¸©õÚ® R÷Ç öPõkUP¨£mkÒÍx. CÁØÔß \µõ\›ø¯¨
ö£õÖzx \µõ\› »UP® ©ØÖ® Auß Â»UPUöPÊ PõsP.
Á¸©õÚ® (`) 4,000 4,200 4,400 4,600 4,800
Calculate the mean deviation about mean and its coefficient of the income groups
of five, given below.
Income ( ` ) 4,000 4,200 4,400 4,600 4,800

38. J÷µ BsiÀ £izu 10 ©õnÁºPÒ A ©ØÖ® B £õh[PÎÀ ö£ØÓ uµ[PÒ R÷Ç
öPõkUP¨£mkÒÍÚ. uµ JmkÓÄU öPÊÂøÚ PnUQkP.
A &ß uµÁ›ø\ 1 2 3 4 5 6 7 8 9 10

B &ß uµÁ›ø\ 6 7 5 10 3 9 4 1 8 2
The rank of 10 students of same batch in two subjects A and B are given below.
Calculate the rank correlation coefficient.
Rank of A 1 2 3 4 5 6 7 8 9 10

Rank of B 6 7 5 10 3 9 4 1 8 2

39. C¸ öuõÈØ\õø»PÎß ö£õ¸Íõuõµ Aø©¨¤ß öuõÈÀ ~m£ Ao 0.6 0.9 

0.2 0.8 
GÛÀ íõUQßì&ø\©ß {£¢uøÚPÎߣi öuõÈØ\õø»PÎß ö\¯À£õk
\õzv¯©õÚuõ GÚ \›£õºUP.
The technology matrix of an economic system of two industries is 
0.6 0.9 
.
0.2 0.8 
Test whether the system is viable as per Hawkins-Simon conditions.

40. 6x2+6y2+4x−8y−16=0 GßÓ Ámhzvß ø©¯® ©ØÖ® Bµ® PõsP.
Find the centre and radius of the circle 6x2+6y2+4x−8y−16=0.

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£Sv – IV / PART - IV

SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 7x5=35

Note : Answer all the questions.

1 2 0 −1
41. (A) A =   , B=   GÛÀ, (AB) =B A
−1 −1 −1 GÚU PõmkP.
1 1  1 2 

AÀ»x

sin(180
+ A) cos(90
− A) tan(270
− A)
(B) {ÖÄP : =−sinA cos2A
sec(540
− A) cos(360
+ A) cosec(270
+ A)

1 2 0 −1 −1 −1 −1
(a) If A =   , B=   then, show that (AB) =B A .
1 1  1 2 

OR

sin(180
+ A) cos(90
− A) tan(270
− A)
(b) Prove that : =−sinA cos2A
sec(540
− A) cos(360
+ A) cosec(270
+ A)

42. (A) 4 £¢x Ãa\õͺPÒ, 2 C»US {ø» Põ¨£õͺPÒ (Wicket Keeper) EÒÍhUQ¯
16 Q›UöPm Âøͯõmk õºPÒ Sʼ¸¢x SøÓ¢ux 11 ÷£º Ah[Q¯
Q›UöPm Ao E¸ÁõUP¨£kQÓx. SøÓ¢ux 3 £¢x Ãa\õͺPÒ ©ØÖ®
SøÓ¢ux J¸ C»US {ø» Põ¨£õͺ öPõsh 11 ÷£º Ah[Q¯ Q›UöPm
SÊøÁ GzuøÚ ÁÈPÎÀ Aø©UP»õ® ?
AÀ»x
(B) X GߣÁº 5 &À 4 •øÓ Esø©¨ ÷£_£Áº, J¸ £Pøh E¸mh¨£kQÓx.
Qøhzu Gs 6 GßÖ v¸. X TÖQÓõº. Esø©¯õP÷Á BÖ
ÂÊ¢xÒÍuØPõÚ {PÌuPÄ ¯õx ?
(a) A cricket team of 11 players is to be formed from 16 players including
4 bowlers and 2 wicket-keepers. In how many different ways can a team be
formed so that the team contains atleast 3 bowlers and atleast one wicket-
keeper ?
OR
(b) X speaks truth 4 out of 5 times. A die is thrown. He reports that there is a
six. What is the chance that actually there was a six ?

13 6067

43. (A) J¸ |P¸® ¦ÒÎ, (2, 1) ©ØÖ® (1, 2) GßÓ ¦ÒÎPμ¸¢x EÒÍ öuõø»ÄPÒ
2 : 1 GßÓ ÂQuzvÀ C¸US©õÖ |P¸QÓöuÛÀ, A¨¦Òΰß
C¯USÁøµø¯U PõsP.
AÀ»x
(B) Pmk©õÚz vmhzvß ö\¯ÀPÒ ©ØÖ® Axz öuõhº£õÚz uPÁÀPÒ
RÌUPõq® AmhÁøn°À uµ¨£mkÒÍx. CuØPõÚ Áø»¯ø©¨ø£
ÁøµP.

ö\¯À 0-1 1-2 1-3 2-4 2-5 3-4 3-6 4-7 5-7 6-7

Põ-»® (Áõ-µ[-P-ÎÀ) 3 8 12 6 3 3 8 5 3 8

÷©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.
(a) If the distance of a point from the points (2, 1) and (1, 2) are in the ratio
2 : 1, then find the locus of the point.
OR
(b) Construct the network for the project whose activities are given below.

Activity 0-1 1-2 1-3 2-4 2-5 3-4 3-6 4-7 5-7 6-7

Duration (in week) 3 8 12 6 3 3 8 5 3 8

Calculate the Earliest Start Time (EST), Earliest Finish Time (EFT), Latest
Start Time (LST) and Latest Finish Time (LFT) of each activity. Determine
the critical path and the project completion time.

44. (A) y=a cosmx+b sinmx GÛÀ y2+m2y=0 GÚU PõmkP.
AÀ»x
(B) Pouz öuõSzuÔuÀ Âv¨£i n2+n J¸ ""Cµmøh¨£øh Gs'' (AøÚzx
n∈N) GÚ {ÖÄP.
(a) If y=a cosmx+b sinmx, then show that y2+m2y=0.
OR
(b) By the principle of mathematical induction prove that n2+n is an even number,
for all n∈N.

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45. (A) f (x)=2x3+9x2+12x+1 GßÓ \õº¤ß ÷uUP {ø»¨ ¦ÒÎ ©ØÖ® ÷uUP{ø»
©v¨¤øÚU PõsP.
AÀ»x
(B) EØ£zv ö£õ¸mPÎß GsoUøP 500 &¼¸¢x 1000 &BP E¯¸®÷£õx
EØ£zv ö\»Ä ` 6,000 &¼¸¢x ` 9,000 &BP E¯¸QÓx. x,y &US Cøh¨£mh
öuõhº¦ Kº J¸£ia \õºö£ÛÀ ö\»Ä (y) ©ØÖ® u¯õ›UP¨£k®
ö£õ¸mPÎß GsoUøP (x) CÁØÖUQøh¨£mh öuõhº¤øÚ PõsP.
(a) Find the stationary points and stationary values for the function :
f (x)=2x3+9x2+12x+1.
OR
(b) As the number of units produced increases from 500 to 1000 and the total
cost of production increases from ` 6,000 to ` 9,000. Find the relationship
between the cost (y) and the number of units produced (x) if the relationship
is linear.

46. (A) ö\»Äa \õº¦ C = 2x  x + 5  + 7 &À EØ£zv AÍÄ x BÚx öuõhºa]¯õP
 x+2
AvP›US® ö£õÊx CÖv {ø»a ö\»ÁõÚx (MC) öuõhºa]¯õPU
SøÓQÓx GÚ {ÖÄP.
AÀ»x
(B) ` 80 &US QøhUS® ` 100 •P ©v¨¦ÒÍ £[SPÎÀ J¸ |£º ` 96,000
•u½k ö\´QÓõº. £[S {ÖÁÚ® ÁÇ[S® £[S Ãu® 18% GÛÀ
¤ßÁ¸ÁÚÁØøÓU PõsP.
(i) AÁº Áõ[Q¯ £[SPÎß GsoUøP
(ii) ö©õzu DÄz öuõøP
(iii) •u½mkUPõÚ Á¸©õÚ Ãu®

x+5
(a) For the cost function C = 2x   + 7 , prove that Marginal Cost (MC) falls
 x+2
continuously as the output x increases.
OR
(b) A man invest ` 96,000 on ` 100 shares at ` 80. If the company pays him 18%
as dividend, find
(i) the number of shares he bought
(ii) the dividend
(iii) percentage of return

15 6067

47. (A) ¤ßÁ¸® ÂÁµ[PÐUS PõÀ©õÚ Â»UPzøuU PõsP.
C.I 10-20 20-30 30-40 40-50 50-60 60-70 70-80

f 12 19 5 10 9 6 6

AÀ»x
(B) ¤ßÁ¸ÁÚÁØÖUS JmkÓÄU öPÊÂøÚU PõsP. ÷©¾® Auß
Emö£õ¸øÍ öÁΨ£kzx.
u¢øu°ß E¯µ®
(A[S»[PÎÀ) 65 66 67 67 68 69 71 73

©PÛß E¯µ®
(A[S»[PÎÀ) 67 68 64 68 72 70 69 70

(a) Compute Quartile deviation from the following data.

C.I 10-20 20-30 30-40 40-50 50-60 60-70 70-80

f 12 19 5 10 9 6 6

OR
(b) Find out the coefficient of correlation and interpret.

Height of father
65 66 67 67 68 69 71 73
(in inches)

Height of son
67 68 64 68 72 70 69 70
(in inches)

-o0o-

[ v¸¨¦P / Turn over