TN 11th Question Paper 2025 Business Maths

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8467
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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 |õßS ©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

8467 2

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

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

e x−1
2. lim =
x→0 x

(A) 1 (B) e (C) 0 (D) nxn−1
e x−1
lim =
x→0 x
(a) 1 (b) e (c) 0 (d) nx n−1

3. J¸ {ÖÁÚzvß ÷uøÁ ©ØÖ® Auß ö\»Äa \õº¦ •øÓ÷¯ p=2−x ©ØÖ®
c=−2x2+2x+7 GÛÀ, Cuß C»õ£a \õº£õÚx :

(A) −x2+7 (B) x2+7 (C) −x2−7 (D) x2−7
If demand and the cost function of a firm are p=2−x and c=−2x2+2x+7, then its profit
function is :
(a) −x 2 +7 (b) x 2 +7 (c) −x 2 −7 (d) x 2 −7

4. A = 5 GÛÀ A−1 &ß ©v¨¦.

(A) 1 (B) 5
1
(C) Põn C¯»õx (D) 5

−1
If A = 5 , then the value of A is _________.

(a) 1 (b) 5

1
(c) does not exist (d)
5

3 8467

5. J¸ öuõhº¦¨ ÷£õUSU öPÊ SøÓ¯õP C¸US® {ø»°À ©ØöÓõßÖ :
(A) ªøP (B) §a]¯®
(C) SøÓ (D) CÁØÔÀ HxªÀø»
When one regression coefficient is negative, the other would be :

(a) Positive (b) Zero

(c) Negative (d) None of them

6. 2x+5y አ 10, x/0, y/0 GßÓU 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 x/0,
y/0 and 2x+5y አ 10 is :

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

7. öuõhº¦¨ ÷£õUøP AÔ•P¨£kzv¯Áº :
(A) PõºÀ ¤¯º\ß (B) R.A. ¤åº
(C) QµõUìhß ©ØÖ® öPÍhß (D) \º L¤µõß]ì PõÀhß
The term regression was introduced by :

(a) Karl Pearson (b) R.A. Fisher

(c) Croxton and Cowden (d) Sir Francis Galton

8. A.M., G.M., ©ØÖ® H.M., &PÐUS Cøh÷¯¯õÚ ö£õ¸zu©õÚz öuõhº¦ :

(A) H.M / G.M / A.M (B) A.M < G.M < H.M
(C) A.M / G.M / H.M (D) G.M / A.M / H.M
The correct relationship among A.M., G.M., and H.M., is :

(a) H.M / G.M / A.M (b) A.M < G.M < H.M

(c) A.M / G.M / H.M (d) G.M / A.M / H.M

[ v¸¨¦P / Turn over

8467 4

9. •P ©v¨¦ ` 100 Eøh¯ 8% \µUS •u¼ß 200 £[SPøÍ ` 50 &US ÂØ£uß
‰»® QøhUS® öuõøP :
(A) ` 7,000 (B) ` 16,000 (C) ` 9,000 (D) ` 10,000
What is the amount realised on selling 8% Stock of 200 shares of Face Value ` 100 at ` 50 ?
(a) ` 7,000 (b) ` 16,000 (c) ` 9,000 (d) ` 10,000

10. Q1=30 ©ØÖ® Q3=50, GÛÀ PõÀ©õÚ Â»UPU öPÊ :

(A) 10 (B) 20 (C) 0.25 (D) 40
If Q1=30 and Q3=50, the coefficient of Quartile deviation is :
(a) 10 (b) 20 (c) 0.25 (d) 40

11. uØPõ¼P uÁøn £[Rmkz öuõøPUPõÚ GkzxUPõmk :
(A) ©õnÁºPÐUS Eu öuõøP AÎUS® |ßöPõøh {v
(B) Á[Q°ß uÛ |£º Phß
(C) J¸ Ãmk©øÚUPõÚ ö\¾zu¨£k® uÁønz öuõøP
(D) ÷©ØPsh AøÚzx®
Example of contingent annuity is :
(a) An endowment fund to give scholarships to students
(b) Personal loan from a bank
(c) Installments of payment for a plot of land
(d) All the above

2 ∂u
12. u=e x GÛÀ ∂ x &ß ©v¨¦ :

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

2 ∂u
If u=e x , then is equal to :
∂x
2 2 2
(a) 2e x (b) 2 x ex (c) 0 (d) ex

5 8467

1− x
13. f(x)= , x > 1 GÛÀ f (−x)=
1+ x

1 1
(A) − f(x) (B) −f(x) (C) f(x) (D) f(x)

1− x
If f(x)= , x > 1 then f (−x) is equal to :
1+ x

1 1
(a) −
f(x) (b) −f(x) (c) f(x) (d) f(x)

14. sin−1x &ß Ãa\P® __________.

−π π   −π π 
(A) [0, π] (B)  2 , 2  (C) R (D)  , 
 2 2

Range of sin−1x is __________.

−π π   −π π 
(a) [0, π] (b)  2 , 2  (c) R (d)  , 
 2 2

15. BvÁÈa ö\ÀÁx®, x &Aa]ß «x ø©¯zøu öPõshx©õÚ Ámhzvß
\©ß£õk :
(A) x2+y2=a2 (B) x 2−2ax+y2=0
(C) x2−2ay+y2=0 (D) y 2−2ay+x2=0
The equation of the circle with centre on the x-axis and passing through the origin is :
(a) x2+y2 =a 2 (b) x 2−2ax+y 2=0
(c) x 2−2ay+y 2 =0 (d) y 2−2ay+x 2=0

sin 2 θ
16. lim = __________ .
θ →0 2 θ

(A) 1 (B) ∞ (C) 2 (D) 0
sin 2 θ
lim = __________.
θ →0 2 θ

(a) 1 (b) ∞ (c) 2 (d) 0

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17. 13 ¸¢vÚºPÒ Kº CµÄ ¸¢vÀ P»¢x öPõÒQÓõºPÒ, AƸ¢vÀ
|øhö£Ö® øPU S¾USu¼ß GsoUøP :

(A) 286 (B) 715 (C) 13 (D) 78

Thirteen guests have participated in a dinner. The number of handshakes that happened in
the dinner is :

(a) 286 (b) 715 (c) 13 (d) 78

18. 4 cos3 408−3 cos 408 &ß ©v¨¦ :

1 3 1 1
(A) 2 (B) (C) 2
(D) − 2
2

The value of 4 cos3 408−3 cos 408 is :

1 3 1 1
(a) (b) (c) (d) −
2 2 2 2

19. J÷µ ©õv›¯õÚ 8 ©»ºPøÍ J¸ ÁøͯzvÀ Á›ø\¨£kzx® ÁøPPÎß
GsoUøP _________.

7 7! 8!
(A) 2 (B) 8 ! (C) 2
(D) 2

The number of ways 8 identical flowers can be arranged in a ring is _________.

7 7! 8!
(a) (b) 8! (c) (d)
2 2 2

7 8467

 4 −5 
 5 12  GßÓ Ao°ß ÷|º©õÖ :
20.  
 −2 1 
 
 5 2 

1 5  1 5 
30  2 12  7 2 12 
(A)   (B) 30  2 
4 
7 2 4  
   
5 5  5 5 

 1 −5   1 −5 
30  2 12  7  2 12 
(C)   (D)  
7  −2 4  30  −2 1 
   
 5 5   5 5 

 4 −5 
 12  is :
The inverse matrix of  5 
 −2 1 
 
 5 2 

1 5  1 5 
30  2 12  7 2 12 
(a)   (b)  
7 2 4  30  2 4 
   
5 5  5 5 

 1 −5   1 −5 
30  2 12  7  2 12 
(c)   (d)  
7  −2 4  30  −2 1 
   
 5 5   5 5 

£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.
21. f(x)=2x2−1 ©ØÖ® g(x)=1−3x GßÓ \õº¦PÒ \©® GÛÀ Auß \õº£PzøuU PõsP.
Find the domain for which the functions f(x)=2x2−1 and g(x)=1−3x are equal.

22. BsiØS 8% GßÓ ÁmiÂQuzvÀ 16 Á¸h[PÐUS ö\¾zu¨£k® Põzv¸¨¦
uÁønz öuõøP ` 1,500 &ß uØ÷£õøu¯ ©v¨ø£U PõsP.
[(1.08) −16 =0.2919]
What is the present value of an annuity due of ` 1,500 for 16 years at 8% per annum ?
[(1.08) −16 =0.2919]

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8467 8

23. ¤ßÁ¸® ÂÁµ[Pμ¸¢x JmkÓÄU öPÊøÁU PnUQkP.
N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597
Calculate the correlation coefficient from the following data.
N=9, ΣX=45, ΣY=108, ΣX2=285, ΣY2=1356, ΣXY=597

24. ©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\› ÷ÁPzøu PõsP.
An aeroplane flies along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres
per hour respectively. What is the average speed of the plane in its flight around the square ?

25. p=40−x GßÓ ÷uøÁa \õº¤À ηd=1 GÛÀ EØ£zv AÍøÁU PõsP.
For the given demand function p=40−x, find the output when ηd=1.

7 4 11
26. wºUP : −3 5 x =0
−x 3 1

7 4 11
Solve : −3 5 x = 0
−x 3 1

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

2tanA
28. A=308 GÛÀ sin2A = GÚ {ÖÄP.
1+ tan 2 A

2tanA
If A=308 then prove that sin2A =
1+ tan 2 A

29. 0 •uÀ 9 Áøµ EÒÍ C»UP[Pøͨ £¯ß£kzv 67 GßÓ GsoÀ öuõh[S©õÖ
G¢u C»UP•® J¸ uhøÁUS ÷©À v¸®£ ÷uõßÓõ©À, GzuøÚ 5 C»UP
öuõø»÷£] GsPøÍ E¸ÁõUP •i²® ?
How many five digit telephone numbers can be constructed using the digits 0 to 9 if each
number starts with 67 with no digit appearing more than once ?

30. x2 +y 2−2x+6y−15=0 GßÓ Ámhzvß Âmhzvß J¸ •øÚ (−2, −7) GÛÀ
©ØöÓõ¸ •øÚ PõsP.
If (−2, −7) is one extremity of a diameter of the circle x2+y2−2x+6y−15=0, find the
other extremity.

9 8467

£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.

2 x−1
31.
x2 − 5 x+6
& I £Sv ¤ßÚ[PÍõP ©õØÖP.

Resolve into partial fractions.

2 x−1
x 2 − 5 x +6

32. J÷µ BsiÀ £izu 10 ©õnÁºPÒ A ©ØÖ® B £õh[PÎÀ ö£ØÓ uµ[PÒ R÷ÇU
öPõkUP¨£mkÒÍÚ. uµ JmkÓÄU öPÊÂøÚU 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

∂u ∂u 2
33. u=x2(y−x)+y2(x−y), GÛÀ + =− 2 ( x − y ) GÚU PõmkP.
∂x ∂y

∂u ∂u 2
If u=x2(y−x)+y2(x−y), then show that + =− 2 ( x − y ) .
∂x ∂y

34. ÷|º©õÖ Ao•øÓ°À wºUP.
2x+3y−5=0; x−2y+1=0
Solve by matrix inversion method.
2x+3y−5=0; x−2y+1=0.

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8467 10

35. x2=8y GßÓ £µÁøͯzvß S¯®, •øÚ ©ØÖ® C¯USÁøµ°ß \©ß£õk
BQ¯ÁØøÓU PõsP.
Find the co-ordinates of the focus, vertex, equation of the directrix of the parabola x2=8y

36. RÌUPsh ö\¯ÀPøÍU öPõsh vmhzvß Áø»¯ø©¨ø£ ÁøµP. ö\¯ÀPÒ
A, B, C J÷µ ÷|µzvÀ Bµ®¤UP¨£k® A < F, E ; B < D, C ; E, D < G

Construct the network for the projects consisting of various activities and their precedence
relationships are as given below :

A, B, C can start simultaneously A < F, E ; B < D, C ; E, D < G

37. y=500e7x+600e−7x GÛÀ y2−49y=0 GÚU PõmkP.

If y=500e7x+600e−7x, then show that y2−49y=0.

sin ( B−C ) sin ( C−A ) sin ( A−B )
38. + + = 0 GÚ {ÖÄP.
cos B cos C cos C cos A cos A cos B

sin ( B−C ) sin ( C−A ) sin ( A−B )
Prove that + + =0
cos B cos C cos C cos A cos A cos B

39. 3x+4y−k=0 GßÓ ÷PõhõÚx x2+y2−64=0 GßÓ ÁmhzvØS J¸ öuõk÷Põk
GÛÀ k &ß ©v¨¦ PõsP.
Find the value of k so that the line 3x+4y−k=0 is a tangent to the circle x2+y2−64=0.

40. ©v¨¤kP : lim
(
log 1+ x 4 )
x→0 tan 4 x

Evaluate : lim
(
log 1+ x 4 )
4
x→0 tan x

11 8467

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

41. (A) C¸ ö£õ¸Íõuõµ ¤›ÂØPõÚ £›ÁºzuøÚ Ao R÷Ç öPõkUP¨£mkÒÍx.

ÂØ£øÚ CÖvz ö©õzu
¤›Ä
1 2 ÷uøÁ EØ£zv
1 4 3 13 20
2 5 4 3 12

(i) öuõÈÀ~m£ Aoø¯ GÊxP.
(ii) ¤›Ä 1 &ß CÖvz ÷uøÁ¯õÚx 23 A»SPÒ AvP›US® ÷£õx
EØ£zvPøÍU PõsP.
AÀ»x
(B) A GßÓ ö£õ¸Îß ÷uøÁ q=13−2p1−3p22 GÛÀ p 1 =p 2 =2 GßÓ
Eq Eq
©v¨¦PÐUS ©ØÖ® GßÓ £Sv ö|QÌa]PøÍU PõsP.
Ep1 Ep2

(a) You are given the following transaction matrix for a two sector economy.

Sales Final Gross
Sector
demand output
1 2
1 4 3 13 20
2 5 4 3 12

(i) Write the technology matrix.
(ii) Determine the output when the final demand for the output sector 1 alone
increases to 23 units.
OR

(b) The demand for a quantity A is q=13−2p1−3p22 . Find the partial elasticities

Eq Eq
and when p1=p2=2
Ep1 Ep2

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8467 12

42. (A) B1, B2 ©ØÖ® B3 Gß£Ú SªÌ ÂÍUSPøÍ Eøh¯ ‰ßÖ ö£miPÒ GßP.
AÆÂÍUSPÎÀ, ]» ÂÍUSPÒ SøÓ²øh¯Ú. ö£miPÒ B1, B2 ©ØÖ®
B 3 &À EÒÍ SøÓ²øh¯ SªÌ ÂÍUSPÎß ÂQuõa\õµ[PÒ •øÓ÷¯
1 1 3
,
2 8
©ØÖ® 4 GßP. ‰ßÖ ö£miPÎÀ, H÷uÝ® J¸ ö£mi°¼¸¢x
÷uº¢öukUP¨£mh SªÌÂÍUS SøÓ²øh¯x GÚU PshÔ¯¨£mhõÀ,
A¢u ÂÍUS, ö£mi B1 &¼¸¢x ÷uº¢öukUP¨£kÁuØPõÚ {PÌuPøÁU
PõsP.
AÀ»x
n( n+1 )
(B) Pouz öuõSzuÔuÀ •øÓ°À 1+ 2 +3+...+ n = , (AøÚzx neN )
2
GÚ {ÖÄP.
(a) Three boxes B1, B2, B3 contain Lamp bulbs some of which are defective. The defective
1 1 3
proportions in box B1, box B2 and box B3 are respectively , and . A box is
2 8 4
selected at random and a bulb drawn from it. If the selected bulb is found to be defective,
what is the probability that the selected bulb is from the box B1 ?
OR
(b) Using Mathematical Induction Method, prove that
n( n+1 )
1+ 2 + 3+...+ n = , for all n ∈ N
2

43. (A) 4x 2 +12xy+9y 2 −6x−9y+2=0 GßÓ Cµmøh ÷|ºU÷PõkPÒ Cøn¯õÚ
Cµmøh ÷|ºU÷PõkPøÍU SÔUS® GÚU PõmkP. ÷©¾® CU÷PõkPÎß
uÛzuÛa \©ß£õkPøͲ® PõsP.
AÀ»x
(B) ©õÔPÒ X, Y &ß \µõ\›PøͲ® AÁØÔØQøh÷¯¯õÚ JmkÓÄU
öPÊøÁ²® R÷ÇU öPõkUP¨£mkÒÍ C¸ öuõhº¦¨ ÷£õUSa
\©ß£õkPμ¸¢x PõsP.
4X−5Y+33=0
20X−9Y−107=0
(a) Show that the pair of straight lines 4x2+12xy+9y2−6x−9y+2=0 represents two
parallel straight lines and also find the separate equations of the straight lines.
OR
(b) Find the means of X and Y variables and the coefficient of correlation between them
from the following two regression equations :
4X−5Y+33=0
20X−9Y−107=0

13 8467

44. (A) RÌUPsh ÷|›¯z vmhªhÀ PnUøP (LPP) wºUP.
x1+4x2 £ 24, 3x1+x2 £ 21, x1+x2 £ 9 ©ØÖ® x1, x2 / 0 GßÓ Pmk¨£õkPÐUS
Cn[P Z=2x1+5x2 &ß «¨ö£¸ ©v¨ø£U PõsP.
AÀ»x

 1  2n
&ß Â›ÂÀ x &Ia \õµõu EÖ¨¦ 1 ⋅ 3 ⋅ 5 . . . ( 2n − 1) 2
n
(B)  x + x  GÚ {ÖÄP.
  n!
(a) Solve the following LPP
Maximize Z=2x1+5x2 subject to the conditions x1+4x2 £ 24, 3x1+x2 £ 21, x1+x2 £ 9
and x1, x2 / 0.
OR
2n
 1
(b) Prove that the term independent of x in the expansion of  x +  is
 x

1 ⋅ 3 ⋅ 5 . . . ( 2n − 1) 2n
n!

45. (A) (cosα+cosβ)2+(sinα+sinβ)2= 4cos2  α−β  GÚ {ÖÄP.
 2 

AÀ»x
(B) Á¸hõ¢vµ ÷uøÁ ©ØÖ® ö£õ¸Ò A Âß Kµ»S Âø» R÷Ç
öPõkUP¨£mkÒÍx.

ö£õ¸Ò Á¸hz ÷uøÁ A»S Âø»
(A»SPÎÀ) (¹£õ°À)
A 800 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\»Ä.
(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.

[ v¸¨¦P / Turn over

8467 14

(a)
 α−β  ⋅
Prove that (cosα+cosβ)2+(sinα+sinβ)2= 4cos 2  
 2 

OR

(b) The following table gives the annual demand and unit price of item A.

Item Annual Unit
demand Price
A 800 0.02

Ordering cost is ` 5 per order and annual holding cost is 10% of unit price.
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) xm.yn=(x+y)m+n GÛÀ d y = y GÚU PõmkP.
dx x

AÀ»x
(B) ` 4,500 &US ` 10 ©v¨¦U öPõsh 12% £[S Ãu® öPõsh £[SPøÍ \©
Âø»°À v¸. _¢uº GߣÁº Áõ[SQÓõº. £[Qß Âø» ` 23 BP
AvP›US® ö£õÊx £[SPøÍ ÂØÖ Auß ‰»® QøhUS® öuõøPø¯
` 25 ©v¨¦ÒÍ 10% £[SPÎÀ ` 18 &US •u½k ö\´QÓõº GÛÀ, AÁµx
Á¸©õÚzvÀ HØ£k® ©õØÓzøuU PõsP.

dy y
(a) If xm.yn=(x+y)m+n, then show that =
dx x

OR

(b) Sundar bought ` 4,500, 12% of ` 10 shares at par. He sold them when the price rose to
` 23 and invested the proceeds in ` 25 shares paying 10% per annum at ` 18. Find the
change in his income.

15 8467

 1 2  1 3
47. (A) A =   ©ØÖ® B=   GÛÀ, (AB) =B A
−1 −1 −1 Gߣøu Põs¤UP.
−1 1  −1 2 
AÀ»x
(B) ¤ßÁ¸® ÂÁµ[PÐUSU PõÀ©õÚ Â»UPU öPÊøÁU PõsP.

©v¨ö£sPÒ 10 20 30 40 50 60

©õnÁºPÎß
5 8 10 8 7 2
GsoUøP

 1 2  1 3 −1 −1 −1
(a) If A = 
1 1  , B= 
1 2  then, show that (AB) =B A .
−  − 
OR
(b) Compute the coefficient of quartile deviation from the following data.

Marks 10 20 30 40 50 60
No. of students 5 8 10 8 7 2

-oOo-

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