TN 11th Question Paper 2024 Business Mathematics and Statistics

TN PUBLIC EXAM

QUESTION
PAPER
2024

No. of Printed Pages : 16
7667
!7667IstYearBusinessMathematics! £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 |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

7667 2

1. EÒÏk&öÁαk £S¨£õ´øÁ AÔ•P¨£kzv¯Áº :
(A) ÷£µõ]›¯º ÷Áì¼ W. ¼÷¯õßi¨
(B) \º. ¤µõß]ì PõÀhß
(C) Bºuº ÷P´¼
(D) ¤åº
The inventor of input-output analysis is :
(a) Prof. Wassily W. Leontief
(b) Sir Francis Galton
(c) Arthur Caylay
(d) Fisher

2. 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) rn (C) (n + r)! (D) n r

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

d2 y
3. y=e2x GÛÀ, x=0 CÀ Cß ©v¨¦ :
dx 2

(A) 2 (B) 4 (C) 0 (D) 9

d2 y
If y=e2x, then at x=0 is :
dx 2

(a) 2 (b) 4 (c) 0 (d) 9

3 7667

4. JmkÓÄU öPÊÁõÚx :

(A) r=bxy × byx (B) r = ± b xy × b yx

1 1
(C) r = ± (D) r=
b xy × b yx bxy × b yx

The correlation coefficient :

(a) r=bxy × byx (b) r = ± b xy × b yx

1 1
(c) r= ± (d) r=
b xy × b yx bxy × b yx

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

PõsP.
3 3 4 4
(A) 16 (B) 25 (C) 25 (D) 10

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

3 3 4 4
(a) (b) (c) (d)
16 25 25 10

1 1
6. tanA = ©ØÖ® tanB = 3 GÛÀ, tan (2A+B) &ß ©v¨¦ :
2

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

1 1
If tanA = and tanB = then tan (2A+B) is equal to :
2 3

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

[ v¸¨¦P / Turn over

7667 4

7. y=x 3 +19 GßÓ \õº¤ß CÖv {ø» ©v¨£õÚx 27 &US \©ö©ÛÀ, x &ß
©v¨¦PøÍU PõsP.
(A) ±3 (B) ±1 (C) ±4 (D) ±2
For the function y=x3+19, find the values of x when its marginal value is equal to 27.
(a) ±3 (b) ±1 (c) ±4 (d) ±2

8. ‘a’ Gߣx Bsk uÁønz öuõøP, ‘n’ Gߣx uÁønU Põ»[PÎß GsoUøP,
‘i’ Gߣx ` 1 &UPõÚ TmkÁmi GÛÀ, \õuõµn uÁøn £[Rmkz öuõøP°ß
GvºPõ» öuõøP :
a a
(A) P = i (B) A = i ( 1 + i ) ( 1 + i )n−1

a a
(C) P = i ( 1 + i ) 1 − ( 1 + i )−n  (D) A=
i
( 1 + i ) −1
n

If ‘a’ is the annual payment ‘n’ is the number of periods and ‘i’ is compound interest for
` 1 then future amount of the ordinary annuity is :

a a
(a) P= (b) A= ( 1 + i ) ( 1 + i ) n−1
i i

a a
(c) P= ( 1 + i ) 1 − ( 1 + i )−n  (d) A= ( 1 + i ) −1
n
i i

x 2
9. = 0 GÛÀ x &ß ©v¨¦ :
8 5

−16 −5 16 5
(A) 5
(B) 6
(C) 5
(D) 6

x 2
If = 0 then the value of x is :
8 5

−16 −5 16 5
(a) (b) (c) (d)
5 6 5 6

5 7667

dy
10. y=4ae4x GÛÀ &I PõsP.
dx

(A) 16aex (B) ae4x (C) 16ae4x (D) 4ae4x

dy
If y=4ae4x, then find :
dx

(a) 16ae x (b) ae4x (c) 16ae 4x (d) 4ae4x

11. sin(−4208) &ß ©v¨¦ :

1 3 −1 − 3
(A) 2 (B) (C) 2
(D)
2 2

The value of sin(−4208) is :

1 3 −1 − 3
(a) (b) (c) (d)
2 2 2 2

12. ax 2 +2hxy+by 2 =0, GßÓ Cµmøh ÷|ºU÷PõkPÎß \õ´ÄPÒ m 1 , m 2 GÛÀ
m1+m2 &ß ©v¨¦ :

2h 2h 2h 2h
(A) (B) (C) − (D) −
a b a b

If m1 and m2 are the slopes of the pair of lines given by ax2+2hxy+by2=0, then the value of
m1+m2 is :

2h 2h 2h 2h
(a) (b) (c) − (d) −
a b a b

[ v¸¨¦P / Turn over

7667 6

13. (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

∂q
14. q=1000+8p1−p2 GÛÀ, ∂p Cß ©v¨¦ :
1

(A) 1000 (B) −1 (C) 1000−P2 (D) 8
∂q
If q=1000+8p1−p2 , then ∂p is :
1

(a) 1000 (b) −1 (c) 1000−P 2 (d) 8

15. ` 100 •P©v¨¦ Eøh¯ 8% \µUS •u¼ß 200 £[SPμ¸¢x QøhUS® DÄz
öuõøP :
(A) ` 1500 (B) ` 1600 (C) ` 800 (D) ` 1000
The dividend received on 200 shares of Face Value ` 100 at 8% stock is :
(a) ` 1500 (b) ` 1600 (c) ` 800 (d) ` 1000

16. Ámh Á›ø\ ©õØÓ[PÒ Á»a_ØÖ, Cha_ØÖ ÷ÁÖ£õißÔ (J÷µ ©õv›¯õP)
C¸¨¤ß, n öÁÆ÷ÁÖ ö£õ¸mPÎÀ AøÚzx ö£õ¸mPøͲ® J÷µ ÷|µzvÀ
GkzxU öPõshõÀ, Aø©UP¨£k® Ámh Á›ø\ ©õØÓ[PÎß GsoUøP :
n! (n + 1)! (2n + 1)! (n − 1)!
(A) 2 (B) (C) (D)
2 2 2
If clockwise and anticlockwise circular permutations are considered to be same, the number
of circular permutation of n objects taken all at a time is :

n! (n + 1)! (2n + 1)! (n − 1)!
(a) (b) (c) (d)
2 2 2 2

7 7667

17. A, B GßÓ C¸ {PÌÄPÒ JßøÓ JßÖ \õº¢u {PÌÄPÒ GÛÀ, {£¢uøÚ
{PÌuPÄ P(B/A) Gߣx :

P(A∩B) P(A∩B)
(A) P(A) (B) P(A) P(B/A) (C) P(A) P(A/B) (D) P(B)

If two events A and B are dependent, then the conditional probability of P(B/A) is :

P(A∩B) P(A∩B)
(a) P(A) (b) P(A) P(B/A) (c) P(A) P(A/B) (d) P(B)

18. JmkÓÄU öPÊ Aø©Áx :
(A) −1 •uÀ 0 Áøµ (B) 0 •uÀ ∞ Áøµ
(C) −1 •uÀ ∞ Áøµ (D) −1 •uÀ +1 Áøµ
Correlation co-efficient lies between :
(a) −1 to 0 (b) 0 to ∞
(c) −1 to ∞ (d) −1 to +1

19. ø©¯® (4, 5) ©ØÖ® Bµ® 3 A»SPÒ Eøh¯ Ámhzvß \©ß£õk PõsP.
(A) x2+y 2−8x−10y+32=0 (B) x 2+y2−6x+2y−6=0
(C) x2+y2−8x−6y=0 (D) x 2+y2+8x−10y=0
Find the equation of the circle with centre at (4, 5) and radius 3 units.
(a) x 2+y 2−8x−10y+32=0 (b) x 2+y 2−6x+2y−6=0
(c) x 2+y 2 −8x−6y=0 (d) x 2+y 2+8x−10y=0

100C
20. 99 &ß ©v¨¦ PõsP :

(A) 1 (B) 100 (C) 0 (D) 99
Find the value of 100C99 :
(a) 1 (b) 100 (c) 0 (d) 99

[ v¸¨¦P / Turn over

7667 8

£Sv - II / PART - II
SÔ¨¦ : GøÁ÷¯Ý® HÊ ÂÚõU- P - Ð US Âøh- ¯ - Î U- P - Ä ®. ÂÚõ Gs 30 &US
Pm-hõ-¯-©õP Âøh-¯-ÎU-P-Ä®. 7x2=14

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

1 3 4
21. 102 18 36 &ß ©v¨¦ PõsP.
17 3 6

1 3 4
Evaluate 102 18 36
17 3 6

22. nC =nC GÛÀ 12C &ß ©v¨¦ PõsP.
4 6 n

If nC4=nC6, find 12Cn.

f ( x ) = x 3 − 3 , x ≠ 0 GÛÀ f ( x ) + f   = 0 GÚU PõmkP.
1 1
23.
x x

1
If f ( x ) = x 3 − 3 , x ≠ 0, then show that f ( x ) + f   = 0.
1
x x

24. 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8 GßÓ öuõh›ß D2 ©ØÖ® D6 PõsP.

Find D2 and D6 for the following series 22, 4, 2, 12, 16, 6, 10, 18, 14, 20, 8.

25. ` 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.

9 7667

26. J¸ u¯õ›¨¦ {ÖÁÚ®, ^µõÚ Âø»°À Kº BsiØS 4000 A»SPÒ EØ£zv°øÚ
ÁÇ[SÁuØS JzxU öPõskÒÍx. C¸¨¦a ö\»Ä A»S JßÔØS J¸
BsiØS ` 50 ©ØÖ® \µUS C¸¨¦a ö\»Ä J¸ Kmh EØ£zvØS ` 160 GÚ
wº©õÛUP¨£mkÒÍx. EØ£zv¯õÚx EhÚi¯õP öuõh[SÁuØS JzxU
öPõÒͨ£mkÒÍx ©ØÖ® £ØÓõUSøÓ AÝ©vUP¨£kÁvÀø» GÛÀ, Kmh®
JßÖUS ö©õzu \µUS {ø»a ö\»Ä, ]Ö©® AøhÁuØS GzuøÚ A»SPÒ
EØ£zv ö\´¯ ÷Ásk® GÚU PnUQkP.

A manufacturing company has a contract to supply 4000 units of an item per year at uniform
rate. The storage cost per unit per year amounts to ` 50 and the set-up cost per production
run is ` 160. If the production run can be started instantaneously and shortages are not
permitted, determine the number of units which should be produced per run to minimize
the total inventory cost.

27. x 2+y 2+2x−6y+1=0 GßÓ Ámhzvß ø©¯® ax+2y+2=0 GßÓ ÷Põmiß «x
Aø©²ö©ÛÀ ‘a’ &ß ©v¨¦ PõsP.

If the centre of the circle x2+y2+2x−6y+1=0 lies on a straight line ax+2y+2=0, then
find the value of ‘a’.

28. (x−2y)13 Gߣuß Â›ÂÀ 5 &Áx EÖ¨ø£U PõsP.

Find the 5th term in the expansion of (x−2y)13.

29. f (x)=2x GÛÀ f (x)⋅f (y)=f (x+y) GÚ {ÖÄP.

If f (x)=2x, then show that f (x)⋅f (y)=f (x+y)

30. B[Q» APµõv°À EÒÍ “TABLE” GßÓ Áõºzøu°ß uµ® PõsP.

Find the rank of the word “TABLE” in English dictionary.

[ v¸¨¦P / Turn over

7667 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.

31. (a−1)x2+by 2+(b−8)xy+4x+4y−1=0 GßÓ \©ß£õk J¸ ÁmhzøuU SÔUS®
GÛÀ a, b &°ß ©v¨¦ PõsP.

Find the values of a and b if the equation (a−1)x2+by2+(b−8)xy+4x+4y−1=0 represents
a circle.

1+ x − 1− x
32. ©v¨¤kP : lim
x→0 x

1+ x − 1− x
Evaluate : lim
x→0 x

33. RÌUPsh {PÌÄPøÍU öPõsh vmhzvß Áø»¯ø©¨ø£ ÁøµP.

{PÌÄPÒ 1 2 3 4 5 6 7

EhÚi •¢øu¯
- 1 1 2, 3 3 4, 5 5, 6
{PÌÄ

Draw the event oriented network for the following data.

Events 1 2 3 4 5 6 7

Immediate
- 1 1 2, 3 3 4, 5 5, 6
Predecessors

11 7667

34. RÌUPõq® ÷|›¯À vmhªhÀ PnUQøÚ Áøµ£h® ‰»® wºUP.
3x 1 +x 2 £ 9; x 1 +2x 2 £ 8 ©ØÖ® x 1 , x 2 / 0 GßÓ Pmk¨£õkPÐUQn[P
z=40x1+50x2 &ß ö£¸© ©v¨ø£U PõsP.

Solve the following linear programming problems by graphical method.
Maximize z=40x1+50x2 subject to constraints 3x1+x2 £ 9; x1+2x2 £ 8 and x1, x2 / 0.

35. f (x)=x2−4x+6 GßÓ \õº¦ G¢öu¢u CøhöÁÎPÎÀ vmh©õPU Tk® AÀ»x
vmh©õPU SøÓ²® GÚU PõsP.
Find the interval in which the function f (x)=x2−4x+6 is strictly increasing and strictly
decreasing.

36. tan 758 &ß ©v¨¦ PõsP.

Find the value of tan 758.

37. ¹£õ´ JßÖUS J¸Áº |õßS öÁÆ÷ÁÖ Ch[PÎÀ 1 Q.Q, 2 Q.Q, 3 Q.Q ©ØÖ®
4 Q.Q AÍÂÀ uUPõÎø¯ Áõ[SQÓõº GÛÀ, \µõ\›¯õP, J¸ ¹£õ´US GzuøÚ
Q÷»õ Qµõ® uUPõÎ AÁµõÀ Áõ[P¨£mhx ?
A person purchases tomatoes from each of the 4 places at the rate of 1 kg., 2 kg., 3 kg. and
4 kg. per rupee respectively. On the average, how many kilograms has he purchased per
rupee ?

38. C¸ öuõÈØ\õø»PøͲøh¯ ö£õ¸Íõuõµ Aø©¨¤ß öuõÈÀ ~m£ Ao

 0.8 0.2 
0.9 0.7  GÛÀ íõUQßì&ø\©ß {£¢uøÚPÎߣi Ax ö\¯À£k® ÁøP°À
 

EÒÍuõ GßÖ Psk¤iUPÄ®.

 0.8 0.2 
The technology matrix of an economic system of two industries is 0.9 0.7  .
 

Test whether the system is viable as per Hawkins - Simon conditions.

[ v¸¨¦P / Turn over

7667 12

39. 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]
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]

{ÖÄP : tan−1 
2  −1  7  −1  1 
40.  + tan   = tan  
 11   24  2

 2   7  1
Prove that tan−1   + tan−1   = tan−1  
 11   24  2

£Sv - IV / PART - IV
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 7x5=35
Note : Answer all the questions.
41. (A) J¸ ö£õ¸Íõuõµ Pmhø©¨¤À {»UP› ©ØÖ® C¸®¦ EØ£zv
ö\´¯¨£kQßÓÚ. Cµsk ö£õ¸mPЮ JÆöÁõßÔß EØ£zv°À Cøh
EÒÏhõP £¯ß£kQÓx. J¸ hß C¸®¦ EØ£zvUS 0.4 hß C¸®¦ ©ØÖ®
0.7 hß {»UP› ÷uøÁ¨£kQÓx. CÆÁõ÷Ó J¸ hß {»UP› EØ£zvUS
0.1 hß C¸®¦ ©ØÖ® 0.6 hß {»UP› ÷uøÁ¨£kQÓx. G¢u J¸ EÒÏk
‰»uÚ•® ÷uøÁ¨£hÂÀø». C¢u Aø©¨¦ ö\¯À£k® {ø»°À
EÒÍuõP }[PÒ P¸xQÕºPÍõ ? J¸ hß C¸®¦ ©ØÖ® J¸ hß {»UP›
EØ£zv ö\´¯z ÷uøÁ¨£k® ÷Áø» |õmPÒ •øÓ÷¯ 5 ©ØÖ®
2. ö£õ¸Íõuõµ Pmhø©¨¤À 100 hß {»UP›²® 50 hß C¸®¦® EØ£zv
ö\´¯ ÷Ásk® GÛÀ, Cµsk ö£õ¸mPÎß ö©õzu EØ£zvø¯²®,
AuøÚ ö\´¯z ÷uøÁ¨£k® öuõÈ»õͺ |õmPÎß GsoUøPø¯²®
PnUQkP.
AÀ»x
(B) u=x3+y3+3xy2 GßÓ \õº¤ØS B´»›ß ÷uØÓzøua \›£õºUPÄ®.
(a) An economy produces only coal and steel. These two commodities serve as intermediate
inputs in each other’s production. 0.4 tonne of steel and 0.7 tonne of coal are needed to
produce a tonne of steel. Similarly 0.1 tonne of steel and 0.6 tonne of coal are required
to produce a tonne of coal. No capital inputs are needed. Do you think that the system
is viable ? 2 and 5 labour days are required to produce a tonnes of coal and steel
respectively. If economy needs 100 tonnes of coal and 50 tonnes of steel, calculate the
gross output of the two commodities and the total labour days required.
OR
(b) Verify Euler’s theorem for the function u=x3+y3+3xy2.

13 7667

42. (A) 2x 2+7xy+3y 2+5x+5y+2=0 Gߣx Cµmøh ÷|ºU÷PõkPøÍU SÔUS®
GÚU PõmkP. ÷©¾® CU÷PõkPÎß uÛzuÛa \©ß£õkPøͲ® PõsP.
AÀ»x

(B) wºUP : tan−1(x+1)+tan−1(x−1)= tan−1 
4

7

(a) Show that the equation 2x2+7xy+3y2+5x+5y+2=0 represent two straight lines
and find their separate equations.
OR
4
(b) Solve : tan−1(x+1)+tan−1(x−1)= tan−1  
7

43. (A) J¸ vmhzvØPõÚ £À÷ÁÖ ö\¯ÀPÒ ©ØÖ® AuØPõÚ ÷|µ® R÷Ç
uµ¨£mkÒÍx.
ö\¯À 1 - 2 1 - 3 2 - 4 3 - 4 3 - 5 4 - 9 5 - 6 5 - 7 6 - 8 7 - 8 8 - 10 9 - 10

÷|µ® 4 1 1 1 6 5 4 8 1 2 5 7

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
(B) ¤ßÁ¸® ÂÁµ[PÐUS PõÀ©õÚ Â»UPzøuU PõsP.
CI 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
f 12 19 5 10 9 6 6

(a) A project schedule has the following characteristics.

Activity 1 - 2 1 - 3 2 - 4 3 - 4 3 - 5 4 - 9 5 - 6 5 - 7 6 - 8 7 - 8 8 - 10 9 - 10
Time 4 1 1 1 6 5 4 8 1 2 5 7

Construct the network and calculate the earliest start time, earliest finish time, latest
start time and latest finish time of each activity and determine the Critical path of the
project and duration to complete the project.
OR
(b) Compute Quartile deviation from the following data.
CI 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
f 12 19 5 10 9 6 6

[ v¸¨¦P / Turn over

7667 14

n ( n + 1)( 2n + 1)
44. (A) Pouz öuõSzuÔu¼ß £i 12 + 2 2 + 32 + ..... + n 2 =
6

(AøÚzx neN) GÚ {ÖÄP.

AÀ»x

dy sin 2 (a + y )
(B) siny=xsin(a+y) GÛÀ, = GÚ {ÖÄP.
dx sin a

n ( n + 1 )( 2n + 1)
(a) By Mathematical Induction, prove that 12 + 2 2 + 32 + ..... + n 2= ,
6
for all neN.

OR

dy sin 2 (a + y )
(b) If siny=xsin(a+y), then prove that = .
dx sin a

45. (A) £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¨
4 1 6 7 5 8 10 9 3 2
£v¯À

C¸ £õh[PÎÀ ©õnÁºPÎß AÔÄ G¢u AÍÂØSz öuõhº¦øh¯x ?

AÀ»x

(B) •P©v¨¦ ` 10,000 EÒÍ 20% \µUS •uÀPøÍ J¸Áº 42% AvP Âø»°À
ÂØQÓõº. ÂØÖ Qøhzu £nzøuU öPõsk 22% PÈÂÀ EÒÍ 15% \µUS
•uÀPøÍ Áõ[SQÓõº. ÁÇ[P¨£mh uµS 2% GÛÀ, AÁµx Á¸©õÚzvÀ
HØ£k® ©õØÓzøuU PõsP.

15 7667

(a) The following are the ranks obtained by 10 students in Commerce and Accountancy
are given below :

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

To what extent is the knowledge of students in two subjects related ?

OR

(b) A person sells a 20% stocks of Face Value ` 10,000 at a premium of 42%. With the
money obtained he buys a 15% stock at a discount of 22%. What is the change in his
income if the brokerage paid is 2%.

46. (A) ‰ßÖ GsPÎß TkuÀ 20. •uÀ Gsøn 2 &BÀ ö£¸UQ, CµshõÁx
GsønU Tmi, ‰ßÓõÁx GsønU PÈUP, QøhUS® ©v¨¦ 23 BS®.
•uÀ Gsøn ‰ßÓõÀ ö£¸UQ Á¸® ©v¨¦hß Cµsk ©ØÖ® ‰ßÓõ®
GsPøÍU Tmh QøhUS® ©v¨¦ 46 GÛÀ, A¢u GsPøÍ ÷|º©õÖ Ao
•øÓ°À PõsP.

AÀ»x
(B) J¸ öuõÈØ\õø»°À EÒÍ A 1 , A 2, A 3 GßÓ 3 C¯¢vµ[PÒ •øÓ÷¯
1000, 2000, 3000 v¸SPÒ JÆöÁõ¸ |õЮ EØ£zv ö\´QßÓÚ. AÁØÔÀ
A1 Gߣx 1% &®, A2 Gߣx 1.5% &®, A3 Gߣx 2% &® SøÓ²ÒÍ v¸SPøÍ
EØ£zv ö\´QßÓÚ. J¸ |õÎß •iÂÀ, EØ£zv°¼¸¢x \©Áõ´¨¦
•øÓ°À J¸ v¸S ÷uº¢öukUP¨£mh÷£õx, Ax SøÓ²ÒÍuõP
Põn¨£mhx. Ax C¯¢vµ® A1 &ß EØ£zv°¼¸¢x Á¢ux GߣuØPõÚ
{PÌuPÄ GßÚ ?
(a) The sum of three numbers is 20. If we multiply the first by 2 and add the second
number and subtract the third, we get 23. If we multiply the first by 3 and add second
and third to it, we get 46. By using matrix inversion method find the numbers.

OR

(b) A factory has 3 machines A1, A 2, A3 producing 1000, 2000, 3000 screws per day
respectively. A1 produces 1% defectives, A2 produces 1.5% and A3 produces 2%
defectives. A screw is chosen at random at the end of a day and found defective. What
is the probability that it comes from machine A1 ?

[ v¸¨¦P / Turn over

7667 16

47. (A) (1, 0), (−1, 0) ©ØÖ® (0, 1) BQ¯ ¦ÒÎPÎß ÁȯõPa ö\À¾® Ámhzvß
\©ß£õmøhU PõsP.
AÀ»x
x− 2
(B) ( x + 2 )( x − 1)2 &I £Sv ¤ßÚ[PÍõP ©õØÖP.

(a) Find the equation of the circle passing through the points (1, 0), (−1, 0) and (0, 1).
OR
(b) Resolve into partial fraction.

x− 2
( x + 2 )( x − 1 )2

-o0o-

QUESTION PAPERS
GET PREVIOUS YEAR QUESTION PAPERS FOR ALL CLASSES FOR CBSE, ISCSE, ISC AND ALL ALL
STATE BOARDS HERE AT

Andhra Pradesh Board Question Papers
BOARD
WISE Assam Board Question Papers
Bihar Board Question Papers
Chhattisgarh Board Question Papers
Goa Board Question Papers
Gujarat Board Question Papers
Haryana Board Question Papers
Himachal Pradesh Board Question Papers
J&K State Board Question Papers
Jharkhand Board Question Papers
Karnataka Board Question Papers
Kerala Board Question Papers
Madhya Pradesh Board Question Papers
Maharashtra State Board Question Papers
Manipur Board Question Papers
Meghalaya Board Question Papers
Mizoram Board Question Papers
Nagaland Board Question Papers
Orissa Board Question Papers
Punjab Board Question Papers
Rajasthan Board Question Papers
Tamil Nadu Board Question Papers
Telangana State Board Question Papers
Tripura Board Question Papers
Uttarakhand Board Question Papers
Uttar Pradesh (UP) Board Question Papers
West Bengal (WB) Board Question Papers