TN 12th Question Paper 2026 Business Mathematics and Statistics

FOR TN 12TH EXAM PREPARATION

TN 12th 2026
Question Paper ·
Business Mathematics
Statistics
EXAM YEAR TYPE SUBJECT

TN 12th 2026 Question Paper Business Mathematics Statistics

Notes · Sample Papers · Previous Year Papers · Mock Tests

m
m .co
m .co s e m
se g l a
a
No. of Printed Pages : 15
9067
!9067BusiMatheandStati! £vÄ Gs
Register Number

m
.co
PART - III
m
.co Pou® ©ØÖ® ¦Òΰ¯À
ÁoPU
s e m
s em l a
la
BUSINESS MATHEMATICS AND STATISTICS
g ag
a 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® m
EhÚi¯õPz öu›ÂUPÄ®.
m .co
s e
}»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®,
la
(2)

ö£ß]À £¯ß£kzuÄ®. ag
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS

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.

m
.co
£Sv & I / PART - I

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

s e g laªPÄ® Hئøh¯
g la (ii)
a
öPõkUP¨£mkÒÍ |õßS ©õØÖ ÂøhPÎÀ
a 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.

om .
[ v¸¨¦P / Turn over

.c e m
em l as
las ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 15

9067 2

 λ −1 0 
 
1. 0 λ −1 GßÓ Ao°ß uµ® GÛÀ, 2 λ &ß ©v¨¦ :
 
 
−1 0 λ
 

(A) 3 (B) 1

(C) ö©´ö¯s ©mk® (D) 2

 λ −1 0 
 
If the rank of the matrix 0 λ −1 is 2 then λ is :
 
 
−1 0 λ
 

(a) 3 (b) 1

(c) Only real number (d) 2

2. §ä⯠Ao°ß uµ® :
(A) (B)
∞ 0 (C) 1 (D) −1

Rank of a null matrix is :

(a) ∞ (b) 0 (c) 1 (d) −1

3. Γ(10) &ß ©v¨¦ :
(A) 9 (B) 10 (C) 9! (D) 10!

The value of Γ(10) is :

(a) 9 (b) 10 (c) 9! (d) 10!

π
2

4.
∫ cosx dx &ß ©v¨¦ :
π
−
2

(A) 1 (B) 0 (C) 4 (D) 2

π
2

The value of
∫ cosx dx is :

π
−
2

(a) 1 (b) 0 (c) 4 (d) 2

5. C»õ£a\õº¦ p(x) BÚx ö£¸©©øhÁx :
(A) MR=0 (B) (C)
MC−MR=0 MC+MR=0 (D) MC=0

The profit of a function p(x) is maximum when :

(a) MR=0 (b) MC−MR=0 (c) MC+MR=0 (d) MC=0

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 15

m
m .co
m .co s em
se g l a
3
a 9067

2
6. £µÁøͯ® y =4x BÚx Auß ö\ÆÁP»zxhß HØ£kzx® Aµ[Pzvß £µ¨¦ :
72 16
(A) 3
\. A»SPÒ (B) 3
\. A»SPÒ
1 8
(C) \. A»SPÒ (D) \. A»SPÒ
3 3
m
m .co
2
The area bounded by the parabola y =4x bounded by its latus rectum is :

(a)
72
sq.units

m .co (b)
16
sq.units
s e m
3

s e 3

l a
(c)
1

g l a
sq.units (d)
8
sq.units ag
3
a 3

2 2x
7. (D +4)y=e &Cß {µ¨¦a\õº¦ :
2x
(A) Acos2x+Bsin2x (B) (Ax+B)e

2x
(C) Ae
−2x
+Be (D) (Ax+B)e
−2x

2 2x
The complementary function of (D +4)y=e is :
2x
(a) Acos2x+Bsin2x (b) (Ax+B)e
−2x 2x −2x
(c) Ae +Be (d) (Ax+B)e

o m
dy
c
GßÓ ÁøPUöPÊa \©ß£õmiß .ö£õxz wºÄ :
8. = cosx

e m
s
dx

©õÓzuUP ©õÔ¼ a
gl
(A) y=cosx+c, c

(B)
(C)
y=sinx+1

y=sinx+c, c
a
©õÓzuUP ©õÔ¼
(D) y=sinx−2

dy
The general solution of the differential equation = cosx is :
dx

(a) y=cosx+c, c is an arbitrary constant

(b) y=sinx+1

m
(c) y=sinx+c, c is an arbitrary constant

.co
(d) y=sinx−2

m
m (A)
9. .coh=1 GÛÀ, ∆(x )=
2

s e m
s e 2x + 1 (B) 2x (C) 1

g l a
(D) 2x −1

g la If h=1 then ∆(x )=
2
a
a (a) 2x + 1 (b) 2x (c) 1 (d) 2x −1

10. L f(a)=
(A) f(a)− f(a−h) (B) f(a)+ f(a−h) (C) f(a) (D) f(a)− f(a+h)

L f(a)=
(a) f(a)− f(a−h) (b) f(a)+ f(a−h) (c) f(a) (d) f(a)− f(a+h)

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 15

9067 4

11. E(6x) &Cß ©v¨¦ :
(A) 0 (B) 6 E(x) (C) 36 E(x) (D) E(x)

The value of E(6x) is :

(a) 0 (b) 6 E(x) (c) 36 E(x) (d) E(x)

12. J¸ \©Áõ´¨¦ ©õÔ°ß {PÌuPÄ \õº¦ ¤ßÁ¸©õÖ Áøµ¯ÖUP¨£mkÒÍx.
X = x −1 −2 0 1 2

P(x ) k 2k 3k 4k 5k

GÛÀ, &Cß ©v¨£õÚx :
k

1 1
(A) 15
(B) §ä¯® (C) JßÖ (D) 4

The probability function of a random variable is defined as :

X = x −1 −2 0 1 2

P(x ) k 2k 3k 4k 5k

Then value of k is :

1 1
(a) (b) Zero (c) One (d)
15 4

13. X~N(5, 25) GÛÀ, vmh C¯À{ø»¨ £µÁ¼ß ©õÔ Z Gߣx :
X−5 X−25 X−25 X−5
(A) Z= (B) Z= (C) Z= (D) Z=
5 5 25 25

If X~N(5, 25) then the standard normal variate Z will be :

X−5 X−25 X−25 X−5
(a) Z= (b) Z= (c) Z= (d) Z=
5 5 25 25

14. ¤ßÁ¸ÁÚÁØÖÒ GøÁ £õ´\õß £µÁø» E¸ÁõUPõx ?
(A) J¸ PÚAi ©soÀ Põn¨£k® £õUj›¯õUPÎß GsoUøP
(B) {ªh CøhöÁΰÀ ö£Ó¨£k® öuõø»÷£] AøǨ¦PÎß
10

GsoUøP
(C) J¸ £UPzvß Aa_¨¤øÇPÎß GsoUøP
(D) ö£m÷µõÀ {ø»¯zvØS Á¢x ÷\¸® ÁõiUøP¯õͺPÎß GsoUøP
Which of the following cannot generate a Poisson distribution ?

(a) The number of bacteria found in a cubic foot of soil

(b) The number of telephone calls received in a ten minute interval

(c) The number of misprints per page

(d) The number of customers arriving at a petrol station

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 15

m
m .co
m .co s e m
se g l a
5
a 9067

15. TÖPμ¸¢x PnUQh¨£mh G¢uöÁõ¸ ¦Òΰ¯À AÍøÁPЮ __________

GÚ¨£k®.
(A) •iÄÒÍ AÍøÁ (B) öuõSv £s£ÍøÁ
(C) GsnzuUPuØÓ AÍøÁ (D) TÖ £s£ÍøÁ
m
.co
Any statistical measure computed from sample data is known as __________.

m
.co m
(a) Finite measure (b) Parameter

s e
em
(c) Uncountable measure (d) Statistic

s l a
16.
g la vmh¨¤øǯõÚx :
TÖ\µõ\›°ß ag
a
σ σ σ 2
σ
(A) n
(B) 2n
(C) (D)
n n

The standard error of sample mean is :

2
σ σ σ σ
(a) (b) (c) (d)
n 2n n n

m
.co
17. ö£õxÁõP ö£¸®£õ¾® £¯ß£kzu¨£k® SÔ±mk Gs :
(A) Âø» SÔ±mk Gs (B) öPõÒÍÍÄ SÔ±mk Gs
e m
(C) Gί SÔ±mk Gs (D) ©v¨¦ SÔ±mk Gs
las
Most commonly used index number is :
ag
(a) Price index number (b) Volume index number

(c) Simple index number (d) Value index number

18. X Áøµ£hzvß ÷©À Pmk¨£õmk GÀø»ø¯ AÎUPUTi¯x :
(A) X+A
2
R (B) X+A 2 R (C) X+A
2
R (D) X+A
2
R

m
.co
The upper control limit for X chart is given by :

m
m .co(a) X+A
2
R (b) X+A
2
R (c) X+A
2
R

s em
(d) X+A
2
R

s e g la
g la 19. Áh÷©ØS ‰ø» GߣuøÚ SÔ¨£x . __________
a
a (A) RÌ Á»x ‰ø» (B) ÷©À Chx ‰ø»
(C) RÌ Chx ‰ø» (D) ÷©À Á»x ‰ø»
North-West corner refers to __________.

(a) bottom right corner (b) top left corner

(c) bottom left corner (d) top right corner

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 15

9067 6

20. ]øuÁØÓ wºÂÀ JxURmk AøÓPÎß GsoUøP BÚx :
(A) &US \©©ØÓx
m+n−1 (B) &US \©® m+n−1

(C) &US \©©ØÓx
m+n+1 (D) &US \©® m+n+1

In a non-degenerate solution number of allocations is :

(a) Not equal to m+n−1 (b) Equal to m+n−1

(c) Not equal to m+n+1 (d) Equal to m+n+1

£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 number 30 is Compulsory.

1 4 0 5
21.
 
GßÓ Ao°ß uµzvøÚU PõsP.
9 2 −1 4
 

1 4 0 5
Find the rank of the matrix
 
9 2 −1 4
 

dx
22. ©v¨¤kP ∫ 2
( 2x+3 )
dx
Evaluate
∫ 2
( 2x+3 )

2 2 2
23. x +y =a GßÓ ÁøÍÁøµ°ß ÁøPUöPÊa \©ß£õmøh PõsP.
2 2 2
Find the differential equation of the curve x +y =a

2
24. f(x)=x +3x ©ØÖ® h=1 GÛÀ, ∆ f(x)=2x+4 GÚ {ÖÄP.
2
If f(x)=x +3x and h=1 then show that ∆ f(x)=2x+4

25. uÛzu \©Áõ´¨¦ ©õÔ BÚx ¤ßÁ¸® {PÌuPÄa \õºø£¨ ö£ØÖÒÍx X

GÛÀ, GÚ Põs¤UPÄ®.
k=0.1

X 1 2 3 4

P(X =x ) k 2k 3k 4k

The discrete random variable X has the probability function

X 1 2 3 4

P(X =x ) k 2k 3k 4k

Show that k=0.1

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 15

m
m .co
m .co s e m
se g l a
7
a 9067

26. ¤øǯØÓ I¢x |õn¯[PÒ J÷µ \©¯zvÀ _sh¨£kQßÓÚ. AÁØÔÀ \›¯õP
3uø»PÒ ö£ÖÁuØPõÚ {PÌuPÄ PõsP.
Five fair coins are tossed simultaneously. Find the probability of getting exactly 3 heads.

27. •uÀÁøP ¤øÇ GßÓõÀ GßÚ ?
m
What is Type I error ?
m .co
.co
m ÁºzuP \®£¢u©õÚ C»õ£[PÐhß öuõhº¦øh¯ ¦ÒÎlas e m
28.
e
Gmk BskPÐUPõÚ
s
ÂÁµ[PÒ aRÌUPsh AmhÁøn°À öPõkUP¨£mkÒÍx. g
l a
ag
Bsk C»õ£® (` )

1986 15,420

1987 15,470

1988 15,520

1989 21,020

m
.co
1990 26,500

1991 31,950

e m
1992 35,600

las
1993 34,900
ag
‰ßÖ Bsk Põ»zøuU öPõsh |P¸® \µõ\› •øÓø¯¨ £¯ß£kzv ÷£õUS
©v¨¦PøÍU PnUQkP.
The following figures relate to the profits of a commercial concern for 8 years.

Year Profit (` )

1986 15,420

m
m .co
.co
1987 15,470

e m
e m
1988 15,520

l as
las 1989 21,020

ag
ag 1990 26,500

1991 31,950

1992 35,600

1993 34,900

Find the trend of profits by the method of three yearly moving averages.

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 15

9067 8

29. RÌUPsh AÎzuÀ (C»õ£®) Aoø¯ P¸xP.

`Ì{ø»
ö\¯Ø£õk
(S1) (S2) (S3) (S4)

A1 5 10 18 25

A2 8 7 8 23

A3 21 18 12 21

A4 30 22 19 15

`Ì{ø»¨£õmiß {PÌÄPÐUS «a]ÖÂß «¨ö£¸ Âv°ß£i ]Ó¢u
ö\¯À£õmøh PõsP.
Consider the following pay-off (Profit) matrix Action States.

States

Action

(S1) (S2) (S3) (S4)

A1 5 10 18 25

A2 8 7 8 23

A3 21 18 12 21

A4 30 22 19 15

Determine best action using maximin principle.

2
30. CÖv{ø» ö\»Äa \õº¦ MC=14−6x+4x ©ØÖ® ©õÓõa ö\»Ä 12 GÝ®÷£õx,
ö\»Äa \õºø£U PõsP.
2
The Marginal Cost function MC=14−6x+4x . Then find the cost function if fixed cost is 12.

£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 number 40 is Compulsory.

31. x−4y+7z=14, 3x+8y−2z=13, 7x−8y+26z=5

GßÓ \©ß£õkPÒ J¸[Pø©Ä AØÓøÁ GÚU PõmkP.
Show that the equations are inconsistent.

x−4y+7z=14, 3x+8y−2z=13, 7x−8y+26z=5

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 15

m
m .co
m .co s e m
se g l a
9
a 9067

2
x
32. ©v¨¤kP : ∫ 6
dx
x −4

2
x

∫
m
Evaluate dx

.co
6
x −4

o m m
. c s e
33. y=x
2

e m
GßÓ £µÁøͯzvØS® y=4 GßÓ ÷PõmiØS® Cøh¨£mh £µ¨ø£U
l a
PõsP.
l as ag
a g
Find the area bounded by the parabola y=x
2
and the line y=4.

4
34. y =2, y =−6, y =8, y =9
3 4 5 6
©ØÖ® y =17
7
GÛÀ, ∆ y
3
PnUQkP.
4
Given y =2, y =−6, y =8, y =9 and y =17, calculate ∆ y .
3 4 5 6 7 3

35. J¸ |õn¯® ‰ßÖ •øÓ _sh¨£kQÓx. Gߣx PnUQh¨£mh uø»PÎß X

GsoUøP GÛÀ, &Cß vµÒ £µÁÀ \õºø£U Psk¤iUPÄ®. X

m
.co
A coin is tossed thrice. Let X be the number of observed heads. Find the cumulative distribution

function of X.

s em
g la ¤ß£ØÔ Auß \µõ\›
36. X

»UP® GÛÀ, σ=4
a&IU PõsP.
GÝ® ©õÔ¯õÚx C¯À{ø» £µÁø»
P(30<X<35)
µ=30 ©ØÖ® vmh

Z 1.25 0

Area 0.3944 0

X is a normally distributed variable with mean µ=30 and standard deviation σ=4. Find

P(30<X<35).

m
.co
Z 1.25 0

m
.co
Area 0.3944 0

e m
em ö©õzu ÁoP® ö\´²® J¸Áº, uõß ÂØ£øÚ ö\´u ö©õzu
l s
a B¨¤ÒPÎÀ,
las 37.
g
a •øÓ°À öu›Ä
ag B¨¤ÒPÒ SøÓ£õkÒÍøÁ GÚU TÖQÓõº. \©Áõ´¨¦
4%

ö\´¯¨£mh B¨¤ÒPÎÀ, B¨¤ÒPÒ SøÓ£õkÒÍøÁ GÛÀ, |À»
600 36

B¨¤ÒPÒ SÔzu vmh¨¤øÇø¯U PõsP.
A wholesaler in apples claims that only 4% of the apples supplied by him are defective.

A random sample of 600 apples contained 36 defective apples. Calculate the standard error

concerning good apples.

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 15

9067 10

38. öPõkUP¨£mkÒÍ ¦ÒÎ ÂÁµ[PÐUS ÁõÌUøPz uµU SÔ±mk Gsøn
PnUQkP.
AÍÄ Âø»
ö£õ¸ÒPÒ
2 0 05 2005 2 0 10

A 10 7 9

B 12 6 8

C 17 10 15

D 19 14 16

E 15 12 17

Calculate the cost of living index number for the following data.

Quantity Price
Commodities
2005 2005 2010

A 10 7 9

B 12 6 8

C 17 10 15

D 19 14 16

E 15 12 17

39. R÷Ç öPõkUP¨£mkÒÍ JxURk PnUQß ö\»Ä AoUPõÚ EP¢u wºøÁ PõsP.

Ch®
ÂØ£øÚ¯õͺ

1 2 3 4

P 11 17 8 16

Q 9 7 12 6

R 13 16 15 12

S 14 10 12 11

Find the optimal solution for the assignment problem with following cost matrix.

Area

1 2 3 4

P 11 17 8 16
Salesmen

Q 9 7 12 6

R 13 16 15 12

S 14 10 12 11

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 15

m
m .co
m .co s e m
se g l a
11
a 9067

40. wºUP :
y y
(e +1)cosx dx+e sinx dy=0

y y
Solve (e +1)cosx dx+e sinx dy=0

m
m .co
.co £Sv &
s e m
em
IV / PART - IV

s l a
g la ÂÚõUPÐUS® Âøh¯ÎUPÄ®. ag
a
SÔ¨¦ : AøÚzx 7x5=35

Note : Answer all the questions.

41. (A) A©ØÖ® GßÓ C¸ ÂØ£øÚ¨ ö£õ¸ÒPÎß uØ÷£õøu¯ \¢øu ÂØ£øÚ
B

50%©ØÖ® BP EÒÍx. ~Pº÷Áõ›ß ¸¨£[PÒ JÆöÁõ¸ Áõµ•®
50%

©õÖQßÓÚ. ö\ßÓ Áõµ® &I Áõ[Q¯ÁºPÎÀ ÷£º «sk® &I
om
A 60% A

Áõ[SQßÓÚº. ÷£º &US ©õÔÂkQÓõºPÒ. ö\ßÓ Áõµ®
40% B

. c B

Áõ[Q¯ÁºPÎÀ ÷£º Aøu «sk® Áõ[SQÓõºPÒ.
80% ÷£º &US
e m 20% A

©õÔ ÂkQÓõºPÒ. C¸ Áõµ[PÐUS¨ ¤ÓS AÁºPÎß \¢øu¨
las
£[RkPøÍU PõsP. C¢u ÷£õUS öuõh¸©õÚõÀ G¨÷£õx \©{ø»
ag
Gmh¨£k® ?

AÀ»x

2 2
dy 3x 1+x
(B) wºUP : dx
+
3
y =
3
1+x 1+x

m
.co
(a) Two products A and B currently share the market with shares 50% and 50% each

m
.co
respectively. Each week some brand switching takes place. Of those who bought A

the previous week, 60% buy it again whereas 40% switch over to B.

s em Of those who

em la
bought B the previous week, 80% buy it again whereas 20% switch over to A. Find

las their shares after two weeks.
g
If the price war continues, when is the equilibrium reached ?

a
ag
OR

2 2
dy 3x 1+x
(b) Solve : + y =
3 3
dx 1+x 1+x

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 15

9067 12

5
x
42. (A) ©v¨¤kP : ∫ dx
x+ 7−x
2

AÀ»x
(B) Á¸h[PÐUS J¸•øÓ GkUP¨£k® J¸ |Pµzvß ©UPÒ öuõøP
10

PnUöPk¨¤ß ÂÁµ[PÒ R÷Ç öPõkUP¨£mkÒÍÚ. B® Á¸hzvß 1955

©UPÒ öuõøPø¯ ©v¨¤kP.

Á¸h® 1951 1961 1971 1981

©UPÒ öuõøP (C»m\zvÀ) 35 42 58 84

5
x

∫
(a) Evaluate : dx
x+ 7−x
2

OR

(b) The population of a city in a census taken once in 10 years is given below. Estimate the

population in the year 1955.

Year 1951 1961 1971 1981

Population in Lakhs 35 42 58 84

2
43. (A) J¸ ö£õ¸Îß ÷uøÁa \õº¦ ©ØÖ® AΨ¦a \õº¦ •øÓ÷¯ P
d
= 18−2x−x

P
s
\©{ø» Âø»°À ~Pº÷Áõº E£› ©ØÖ® EØ£zv¯õͺ E£›ø¯U
= 2x−3

PõsP.
AÀ»x
(B) J¸ \©Áõ´¨¦ ©õÔ &UPõÚ {PÌuPÄ Ahºzva \õº£õÚx X

 4x
3
 , 0 <x<1
f ( x )=



0, ©ØöÓ[Q¾® GÛÀ,
E(X) ©ØÖ® V(X) Psk¤iUPÄ®.
2
(a) The demand and supply function of a commodity are P = 18−2x−x and P = 2x−3.
d s

Find the consumer’s surplus and producer’s surplus at equilibrium price.

OR

(b) Consider a random variable X with probability density function


3
 4x , if 0 <x<1
f ( x )=



0, otherwise

Find E(X) and V(X).

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 15

m
m .co
m .co s e m
se g l a
13
a 9067

44. (A) Cøhaö\¸PÀ •øÓø¯¨ £¯ß£kzv 1986 B® Á¸hzvØPõÚ
öuõÈØ\õø»°ß EØ£zvø¯U PõsP.

Á¸h® 1974 1978 1982 1990

m
m .co
EØ£zv (B°µ® hßPÎÀ) 25 60 80 170

.co s e m
s em AÀ»x
l a
g l a ag
a Á¸® ÁõiUøP¯õͺPÎß GsoUøP \µõ\›¯õP J¸ {ªhzvØS
(B) Á[QUS
Cµsk BS®. J¸ {ªhzvÀ :

(i) ÁõiUøP¯õͺ GÁ¸® ÁµÂÀø»

(ii) 3 AÀ»x AuØS ÷©À ÁõiUøP¯õͺ Á¸ÁuØPõÚ
{PÌuPÂøÚU PshÔP. (e
−2
=0.1353)

m
(a)

m .co
Using interpolation method estimate the output of a factory in 1986 from the following

data.

s e
g la
Year
a
1974 1978 1982 1990

Output in 1000 tonnes 25 60 80 170

OR

(b) The average number of customers, who appear in a counter of a certain bank per

minute is two. Find the probability that during a given minute.

m
m (i) No customer appears
.co
m .co s e m
e a
−2

l
(ii) Three or more customers appear. (e =0.1353)

las ag
ag
45. (A) x+2y+z=7, 2x−y+2z=4, x+y−2z=−1 GßÓ \©ß£õkPøÍ Q÷µ©›ß
Âvø¯¨ £¯ß£kzv wºUP.

AÀ»x

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 15

9067 14

(B) R÷Ç öPõkUP¨£mkÒÍ ÷£õUSÁµzx PnUQß Bµ®£ Ai¨£øh
Hئøh¯ wºÂøÚ ÷ÁõP¼ß ÷uõµõ¯ •øÓ°À PõsP.
÷\¸ªh® AΨ¦
D1 D2 D3

S1 9 8 5 25

ÁÍ[PÒ S2 6 8 4 35

S3 7 6 9 40

÷uøÁ 30 25 45

(a) Solve the equations x+2y+z=7, 2x−y+2z=4, x+y−2z=−1 by using Cramer’s

rule.

OR

(b) Determine an initial basic feasible solution to the following transportation problem by

using Vogel’s Approximation Method(VAM).

Destination Supply

D1 D2 D3

S1 9 8 5 25

Source S2 6 8 4 35

S3 7 6 9 40

Requirement 30 25 45

46. (A) J¸ u¯õ›¨£õͺ ÁÇ[Q¯ P®¤ Áhzvß \µõ\› •Ô²® Á¼ø© 1,800

BPÄ® vmh »UP® BPÄ® EÒÍx. P®¤ Áhzvß •ÔÄ Á¼ø©
100

¦v¯ öuõÈÀ~m£® ‰»® AvP›zxÒÍx GÚ E›ø©¯õͺ TÖQÓõº. AÁº
TØøÓa ÷\õvUP, P®¤ Áh® ©õv›¯õP GkUP¨£mk Auß \µõ\› •Ô²®
50

Á¼ø© GßÖ PshÔ¯¨£kQÓx. u¯õ›¨£õÍ›ß TØøÓ
1,850 GßÓ 0.01

ªøPPõs {ø» ÷\õuøÚ°À Bu›UP»õ©õ ?
AÀ»x
(B) Gί \µõ\› •øÓ°ß ‰»® RÌPsh ¦ÒÎ ÂÁµ[PÐUS £¸ÁPõ»
SÔ±kPøÍU PõsP.
Á¸h® I Põ»õsk II Põ»õsk III Põ»õsk IV Põ»õsk
2008 72 68 62 76

2009 78 74 78 72

2010 74 70 72 76

2011 76 74 74 72

2012 72 72 76 68

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 14 of 15

m
m .co
m .co s e m
se g l a
15
a 9067

(a) The mean breaking strength of cables supplied by a manufacturer is 1,800 with a

Standard Deviation 100. By a new technique in the manufacturing process, it is claimed

that the breaking strength of the cables has increased. In order to test this claim a

sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can

you support the claim at 0.01 level of significance ?

OR
m
m .co
(b) Calculate the seasonal indices from the following data using Simple Average method.

Year
.co
I Quarter II Quarter III Quarter IV Quarter

m s e m
2008

s e 72 68 62 76

l a
g l a
2009 78 74 78 72
ag
a 2010

2011
74

76
70

74
72

74
76

72

2012 72 72 76 68

2 5x
47. (A) wºUP : (D −10D+25)y=4e +5.

AÀ»x
(B) »õ줯º, £õ] ©ØÖ® L¤åº Âø»USÔ±mk GsPøÍU RÌUPsh
uµÄPÐUS Psk¤izx ©ØÖ® AÁØÔØPõÚ P¸zx ÂÍUP® u¸P.
m
Âø» c. o AÍÄ
ö£õ¸ÒPÒ
e m
2000

las
2010 2000 2010

A›] 38

12
ag 35

18
6

7
7

10
÷Põxø©
ÁõhøP 10 15 10 15

G›ö£õ¸Ò 25 30 12 16

Cuµ ö\»ÄPÒ 30 33 8 10

2 5x
(a) Solve : (D −10D+25)y=4e +5.

m
OR

.co
(b) Calculate the Laspeyre’s, Paasche’s and Fisher’s price index numbers for the following

m
.co m
data. Interpret on the data.

m s e
s e Commodities
Price Quantity

g l a
la a
2000 2010 2000 2010

ag Rice 38 35 6 7

Wheat 12 18 7 10

Rent 10 15 10 15

Fuel 25 30 12 16

Miscellaneous 30 33 8 10

- o O o -

[ v¸¨¦P / Turn over

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 15