TN 10th Model Question Paper Maths

2345
2345
2345 No. of Printed Pages : 12
2345
2345
2345
2345
2345
2345
7973
2345

!7973Mathematics!
2345
2345
2345
2345
£vÄ Gs
2345
2345
2345 Register Number
2345
2345
2345

Part - III
Pou® / MATHEMATICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version)

÷|µ® : 2½ ©o ] [ ö©õzu ©v¨ö£sPÒ : 100
Time Allowed : 2½ Hours ] [Maximum Marks : 100

AÔÄøµ : (1) AøÚzx ÂÚõUPЮ \›¯õP Aa_¨ £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õP 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.

SÔ¨¦ : CÆÂÚõzuõÒ |õßS ¤›ÄPøÍU öPõshx.
Note : This question paper contains four sections.

¤›Ä & I/SECTION - I
(©v¨ö£sPÒ : 15)/(Marks : 15)

SÔ¨¦ : (i) C¨¤›ÂÀ EÒÍ 15 ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 15x1=15

(ii) öPõkUP¨£mkÒÍ |õßS ©õØÖ ÂøhPÎÀ ªPÄ® \›¯õÚ
Âøhø¯z ÷uº¢öukzx SÔ±mkhß Âøh°øÚ²® ÷\ºzx
GÊuÄ®.
Note : (i) Answer all the 15 questions.
(ii) Choose the correct answer from the given four alternatives and write the
option code and the corresponding answer.

[ v¸¨¦P / Turn over

7973 2

1. EÓÄ CÀ»õu \õº¦US Euõµn®, (©v¨£P® & R, xøn ©v¨£P® & R)
(A) y=x (B) y=x−1
(C) y=x 2 (D) C¸UP •i¯õx
An example for a function which is not a relation, (Domain - R, Codomain - R) is :
(a) y=x (b) y=x−1
(c) y=x 2 (d) not possible

a− b
2. a, b, c Gß£Ú J¸ ö£¸USz öuõhº Á›ø\°À EÒÍÚ GÛ-À, =
b− c
a a c b
(A) c (B) b (C) b (D)
a
a− b
If a, b, c are in G.P., then is equal to :
b− c
a a c b
(a) (b) (c) (d)
c b b a

3. öPõkUP¨£mh Á›ø\°ß Akzu EÖ¨¦ 3, 12 , 27 , . . .
(A) 39 (B) 32 (C) 54 (D) 48
The next term of the series 3, 12 , 27 , . . . is :
(a) 39 (b) 32 (c) 54 (d) 48

4. J¸ 4 £i £À¾Ö¨¦U ÷PõøÁø¯ J¸ D¸Ö¨¦ £À¾Ö¨¦U ÷PõøÁ¯õÀ
ÁSUS® ÷£õx QøhUS® «v°ß AvP£m\ £i :
(A) 2 (B) 0 (C) 4 (D) 1
What can be the degree of the remainder atmost, when a fourth degree polynomial is
divided by a quadratic polynomial ?
(a) 2 (b) 0 (c) 4 (d) 1

5. x3−a3 ©ØÖ® (x−a)2 BQ¯ÁØÔß «.ö£õ.©. :
(A) (x−a)2 (x2+ax+a2) (B) (x3−a3) (x+a)
(C) (x+a)2 (x2+ax+a2) (D) (x3−a3) (x−a)2
The L.C.M. of x3−a3 and (x−a)2 is :
(a) (x−a)2 (x2+ax+a2) (b) (x3−a3) (x+a)
(c) (x+a)2 (x2+ax+a2) (d) (x3−a3) (x−a)2

3 7973

α β
 ©ØÖ® A =I GÛÀ,
6. 2
A= 
 γ − α 

(A) 1−α2−βγ=0 (B) 1+α2+βγ=0
(C) 1+α2−βγ=0 (D) 1−α2+βγ=0
α β 2
If A = 
γ − α  is such that A =I, then :
 
(a) 1−α2−βγ=0 (b) 1+α2+βγ=0
(c) 1+α2−βγ=0 (d) 1−α2+βγ=0

7. (−2, 6), (4, 8) BQ¯ ¦ÒÎPøÍ CønUS® ÷|ºU÷PõmiØSa ö\[SzuõÚ
÷|ºU÷Põmiß \õ´Ä :
1 1
(A) −3 (B) 3 (C) −3 (D) 3
Slope of the straight line which is perpendicular to the straight line joining the points
(−2, 6) and (4, 8) is equal to :
1 1
(a) −3 (b) (c) − (d) 3
3 3

8. J¸ Ámhzvß ø©¯® (−6, 4). J¸ Âmhzvß J¸ •øÚ (−12, 8) GÛÀ,
Auß ©Ö•øÚ :
(A) (−3, 2) (B) (−18, 12) (C) (0, 0) (D) (−9, 6)
The centre of a circle is (−6, 4). If one end of the diameter of the circle is at (−12, 8)
then the other end is at :
(a) (−3, 2) (b) (−18, 12) (c) (0, 0) (d) (−9, 6)

9. Cµsk ÁiöÁõzu •U÷Põn[PÎß £µ¨£ÍÄPÒ •øÓ÷¯ 16 ö\.«. 2,
36 ö\.«. 2 •uÀ •U÷Põnzvß Szx¯µ® 3 ö\.«. GÛÀ, ©ØöÓõ¸
•U÷PõnzvÀ AuøÚ Jzu Szx¯µ® :
(A) 4 ö\.«. (B) 6.5 ö\.«. (C) 4.5 ö\.«. (D) 6 ö\.«.
The areas of two similar triangles are 16 cm2 and 36 cm2 respectively. If the altitude of
the first triangle is 3 cm, then the corresponding altitude of the other triangle is :
(a) 4 cm (b) 6.5 cm (c) 4.5 cm (d) 6 cm

[ v¸¨¦P / Turn over

7973 4

10. 12 «. }Í•ÒÍ ÷|ºUSzuõÚ Sa], 8 «. }Í•ÒÍ {Çø»z uøµ°À
HØ£kzxQÓx. A÷u ÷|µzvÀ J¸ ÷Põ¦µ® 40 «. }Í•ÒÍ {Çø»z uøµ°À
HØ£kzxQÓx GÛÀ, ÷Põ¦µzvß E¯µ® :
(A) 75 «. (B) 40 «. (C) 60 «. (D) 50 «.
If a vertical stick 12 m long casts a shadow 8 m long on the ground and at the same
time a tower casts a shadow 40 m long on the ground, then the height of the tower is :
(a) 75 m (b) 40 m (c) 60 m (d) 50 m

11. (1+cot2θ) (1−cosθ) (1+cosθ)= __________
(A) sec2θ−tan2θ (B) tan2θ−sec2θ
(C) cos2θ−sin2θ (D) sin2θ−cos2θ
(1+cot2θ) (1−cosθ) (1+cosθ)= __________
(a) sec2θ−tan2θ (b) tan2θ−sec2θ
2 2
(c) cos θ−sin θ (d) sin2θ−cos2θ

12. ABC GßÓ ö\[÷Põn •U÷PõnzvÀ ∠B=908, ∠A J¸ SÖ[÷Põn® GÛÀ
sinA+cosA &ß ©v¨¦ :
(A) < 1 (B) 1
(C) 2 (D) > 1
If A is an acute angle of a ∆ABC, right angled at B, then the value of sinA+cosA is :
(a) less than one (b) equal to one
(c) equal to two (d) greater than one

13. J¸ ÷|ºÁmhU T®¦ ©ØÖ® ÷|ºÁmh E¸øÍ°ß Bµ•® E¯µ•® •øÓ÷¯
\©®. E¸øÍ°ß PÚAÍÄ 120 ö\.«.3 GÛÀ, T®¤ß PÚAÍÄ :
(A) 40 ö\.«.3 (B) 1200 ö\.«.3 (C) 90 ö\.«.3 (D) 360 ö\.«.3
Radius and height of a right circular cone and that of a right circular cylinder are
respectively, equal. If the volume of the cylinder is 120 cm3, then the volume of the
cone is equal to :
(a) 40 cm3 (b) 1200 cm3 (c) 90 cm3 (d) 360 cm3

14. ÂÁµ[PÎß öuõS¨¦ JßÔß vmh»UP® 2 2 . Av¾ÒÍ JÆöÁõ¸
©v¨¦® 3 &BÀ ö£¸UPU QøhUS® ¦v¯ ÂÁµz öuõS¨¤ß vmh»UP® :
(A) 6 2 (B) 12 (C) 9 2 (D) 4 2
Standard deviation of a collection of data is 2 2 . If each value is multiplied by 3, then
the standard deviation of the new data is :
(a) 6 2 (b) 12 (c) 9 2 (d) 4 2

5 7973

15. 20 ö£õ¸mPÎÀ, 6 ö£õ¸mPÒ SøÓ£õkøh¯øÁ. \©Áõ´¨¦ •øÓ°À J¸
ö£õ¸Ò ÷uº¢öukUS®÷£õx, Ax SøÓ¯ØÓuõPU Qøh¨£uØPõÚ
{PÌuPÄ :
3 7 2
(A) 10 (B) 10 (C) 3 (D) 0
There are 6 defective items in a sample of 20 items. One item is drawn at random. The
probability that it is a non-defective item is :
3 7 2
(a) (b) (c) (d) 0
10 10 3

¤›Ä & II/SECTION - II
(©v¨ö£sPÒ : 20) / (Marks : 20)
SÔ¨¦ : (i) £zx ÂÚõUPÐUS Âøh¯ÎUPÄ®. 10x2=20
(ii) ÂÚõ Gs 30 &US Psi¨£õP Âøh¯ÎUPÄ®. •uÀ
14 ÂÚõUPÎÀ C¸¢x H÷uÝ® 9 ÂÚõUPøÍz ÷uºÄ ö\´¯Ä®.
Note : (i) Answer 10 questions.
(ii) Question number 30 is compulsory. Select any 9 questions from the first
14 questions.

16. A={a, b, c}, B={1, {a, b, c}, 2} BQ¯ C¸ Pn[PÎÀ A ⊂ B Gߣøu \›£õºUP.
AÆÁõÖ CÀø»ö¯ÛÀ EÚx Âøhø¯ {¹¤UPÄ®.
Verify A ⊂ B for the sets A={a, b, c}, B={1, {a, b, c}, 2}. If not justify your answer.

17. A={−2, −1, 1, 2} ©ØÖ® f = { ( x, 1 x ) : x  A} GÛÀ, f &ß Ãa\PzøuU PõsP.
÷©¾® f Gߣx A &°¼¸¢x A &US J¸ \õº£õS©õ ?
If A={−2, −1, 1, 2} and f = { ( x, 1 x ) : x  A} , write down the range of f. Is f a
function from A to A ?

18. ‰ßÖ GsPÎß ÂQu® 2 : 5 : 7 GßP. •u»õ® Gs, Cµshõ® Gso¼¸¢x
7 &IU PÈzx¨ ö£Ó¨£k® Gs ©ØÖ® ‰ßÓõ® Gs BQ¯Ú J¸ Tmkz
öuõhº Á›ø\ø¯ HØ£kzvÚõÀ, AÆöÁsPøÍU PõsP.
Three numbers are in the ratio 2 : 5 : 7. If the first number, the resulting number on
subtraction of 7 from the second number and the third number form an arithmetic
sequence, then find the numbers.

[ v¸¨¦P / Turn over

7973 6

19. £À¾Ö¨¦U ÷PõøÁ°À ÁSzuÀ £i•øӰߣi ÁSzv (x+2); DÄ (x−1)
©ØÖ® «v 4 BPÄ® Aø©²©õÚõÀ AuØS›¯ ÁS£k® £À¾Ö¨¦U
÷PõøÁø¯ PõsP.
In the division algorithm of polynomials the divisor is (x+2), quotient is (x−1) and the
remainder is 4. Find the dividend.

20. 30 EÖ¨¦PÒ öPõsh AoUS GÆÁøP Á›ø\PÒ C¸UP C¯¾® ?
A matrix consists of 30 elements. What are the possible orders it can have ?

3 2
©ØÖ® B = 
3 0
21. A=    GÛÀ AB ©ØÖ® BA BQ¯ÁØøÓU PõsP.
4 0 3 2

3 2 3 0
If A =   and B =   then find AB and BA.
4 0 3 2

22. A(−3, 5) ©ØÖ® B(4, −9) BQ¯ ¦ÒÎPøÍ CønUS® ÷Põmkz xsøh
P(−2, 3) GßÓ ¦ÒÎ Em¦Ó©õP G¢u ÂQuzvÀ ¤›US® ?
In what ratio does the point P(−2, 3) divide the line segment joining the points
A(−3, 5) and B(4, −9) internally ?

2
23. \õ´Ä 3
©ØÖ® (5, −4) GßÓ ¦ÒÎ ÁÈa ö\À¾® ÷|ºU÷Põmiß
\©ß£õmøhU PõsP.
2
Find the equation of the straight line whose slope is and passing through (5, −4).
3

24. ¤ßÁ¸® ÂÁµ[PÐUS uS¢u £h® ÁøµP.
J¸ ÷Põ¦µzvß Ea]°øÚ, J¸Áº ÷Põ¦µzv¼¸¢x 87.6 «. yµzvÀ uøµ°À
EÒÍ J¸ Psnõi°À £õºUQÓõº. Psnõi ÷©À ÷|õUQ¯ÁõÖ EÒÍx.
AÁº Psnõi°¼¸¢x 0.4 «. yµzv¾®, AÁ›ß Qøh{ø»¨ £õºøÁU
÷Põmiß ©mh®, uøµ°¼¸¢x 1.5 «. E¯µzv¾® EÒÍx. (©ÛuÛß Ai,
Psnõi ©ØÖ® ÷Põ¦µzvß Ai BQ¯øÁ J÷µ ÷|ºU÷PõmiÀ EÒÍÚ)
Draw the diagram for the given information.
A man sees the top of a tower in a mirror which is at a distance of 87.6 m. from the
tower. The mirror is on the ground, facing upward. The man is 0.4 m. away from the
mirror, and the distance of his eye level from the ground is 1.5 m. (The foot of man, the
mirror and the foot of the tower lie along a straight line.)

7 7973

25. 08 ≤ θ ≤ 908 GßÓ θ - - & ß GÀ»õ ©v¨¦PÐUS® cos 2θ+sin 2θ=1 Gߣøuz
u¸ÂUPÄ®.
Derive the identity cos2θ+sin2θ=1 for all θ such that 08 ≤ θ ≤ 908.

26. secθ(1−sinθ) (secθ+tanθ)=1 GßÓ •ØöÓõ¸ø©ø¯ {ÖÄP.
Prove the identity secθ(1−sinθ) (secθ+tanθ)=1.

27. 21 ö\.«. Bµ•ÒÍ J¸ Ámhzv¼¸¢x 1208 ø©¯U÷Põn® öPõsh J¸
ÁmhU÷Põn¨ £Svø¯ öÁmiö¯kzx, Auß Bµ[PøÍ JßÔønzx
J¸ T®£õUQÚõÀ, QøhUS® T®¤ß ÁøÍ£µ¨ø£U PõsP  π = 22  .
 7 
A sector containing an angle of 1208 is cut off from a circle of radius 21 cm and folded
 22 
into a cone. Find the curved surface area of the cone.  π = 
 7 

28. 20, 14, 16, 30, 21 ©ØÖ® 25 BQ¯ ¦ÒÎ ÂÁµ[PÐUS vmh»UP® Põn
÷uøÁ¯õÚ AmhÁønø¯ ©mk® Aø©UPÄ®.
Draw the necessary table to find the Standard Deviation for the data 20, 14, 16, 30, 21
and 25.

29. 1 •uÀ 100 Áøµ°»õÚ •Ê GsPμ¸¢x \©Áõ´¨¦ •øÓ°À
÷uº¢öukUP¨£k® J¸ Gs •Ê PÚ©õP CÀ»õ©À C¸UP {PÌuPÄ PõsP.
A number is selected at random from integers 1 to 100. Find the probability that it is
not a perfect cube.

30. (A) x 2 − ( 3 + 1) x + 3 = 0 GßÓ \©ß£õmøh ÁºUP¨ §ºzv •øÓ°À
wºUP.
AÀ»x
(B) J¸ EÒÏhØÓ AøµU÷PõÍzvß öÁÎ Bµ® ©ØÖ® EÒ Bµ®
•øÓ÷¯ 4.2 ö\.«. ©ØÖ® 2.1 ö\.«. GÛÀ Auß ö©õzu ¦Ó¨£µ¨ø£U
PõsP.
(a) Solve the equation x 2 − ( 3 + 1 ) x + 3 = 0 by completing the square method.
OR
(b) Find the total surface area of a hollow hemisphere whose outer and inner radii
are 4.2 cm and 2.1 cm respectively.

[ v¸¨¦P / Turn over

7973 8

¤›Ä - III/SECTION - III
(©v¨ö£sPÒ : 45) / (Marks : 45)

SÔ¨¦ : (i) ¤ßÁ¸£øÁPÎÀ G÷uÝ® 9 ÂÚõUPÐUS Âøh¯ÎUPÄ®. 9x5=45
(ii) ÂÚõ Gs 45 &US Psi¨£õP Âøh¯ÎUPÄ®. •uÀ
14 ÂÚõUPμ¸¢x 8 ÂÚõUPøÍz ÷uºÄ ö\´¯Ä®.

Note : (i) Answer 9 questions.

(ii) Question number 45 is compulsory. Select any 8 questions from the first
14 questions.

31. J¸ ÁõöÚõ¼ {ø»¯® 190 ©õnÁºPÎh® AÁºPÒ Â¸®¦® Cø\°ß
ÁøPPøÍz wº©õÛUP J¸ PnUöPk¨¦ |hzv¯x. 114 ÷£º ÷©ØPzv¯
Cø\ø¯²®, 50 ÷£º Qµõª¯ Cø\ø¯²®, 41 ÷£º Pº|õhP Cø\ø¯²®,
14 ÷£º ÷©ØPzv¯ Cø\ø¯²® Qµõª¯ Cø\ø¯²®, 15 ÷£º ÷©ØPzv¯
Cø\ø¯²® Pº|õhP Cø\ø¯²®, 11 ÷£º Pº|õhP Cø\ø¯²® Qµõª¯
Cø\ø¯²® ©ØÖ® 5 ÷£º C®‰ßÖ Cø\ø¯²® ¸®¦QßÓÚº GÚU
PnUöPk¨¤À öÁΨ£mhx. CzuPÁÀPμ¸¢x ¤ßÁ¸ÁÚÁØøÓU
PõsP.
(A) ‰ßÖ ÁøP Cø\ø¯²® ¸®£õu ©õnÁºPÎß GsoUøP.
(B) C¸ ÁøP Cø\ø¯ ©mk® ¸®¦® ©õnÁºPÎß GsoUøP.
(C) Qµõª¯ Cø\ø¯ ¸®¤ ÷©ØPzv¯ Cø\ø¯ ¸®£õu
©õnÁºPÎß GsoUøP
A radio station surveyed 190 students to determine the types of music they liked. The
survey revealed that 114 liked rock music, 50 liked folk music and 41 liked classical
music, 14 liked rock music and folk music, 15 liked rock music and classical music,
11 liked classical music and folk music, 5 liked all the three types of music.

Find :

(a) how many did not like any of the 3 types ?

(b) how many liked any two types only ?

(c) how many liked folk music but not rock music ?

9 7973

32. \õº¦ f : [−7, 6) → R RÌUPshÁõÖ Áøµ¯ÖUP¨£mk EÒÍx.
x 2 + 2 x + 1 ; − 7 ≤ x < − 5

f ( x) = x + 5 ; −5≤x ≤ 2
x − 1 ; 2<x<6


¤ßÁ¸ÁÚÁØøÓU PõsP.
4 f (−3) + 2f (4)
(A) f(−7)−f(−3) (B) f (−6) − 3f (1)
A function f : [−7, 6) → R is defined as follows

x 2 + 2 x + 1 ; − 7 ≤ x < − 5

f ( x) = x + 5 ; −5≤x ≤ 2
x − 1 ; 2<x<6


4 f (−3) + 2f (4)
find : (a) f(−7)−f(−3) (b)
f (−6) − 3f (1)

33. J¸ Tmkzöuõhº Á›ø\°À Akzukzu ‰ßÖ EÖ¨¦PÎß TkuÀ 18
©ØÖ® AÆÄÖ¨¦PÎß ÁºUP[PÎß TkuÀ 140 GÛÀ, A®‰ßÖ
GsPøÍU PõsP.
Find the three consecutive terms in an A.P. whose sum is 18 and the sum of their
squares is 140.

34. }UPÀ •øÓ°À wº : 3(2x+y)=7xy; 3(x+3y)=11xy
Solve 3(2x+y)=7xy; 3(x+3y)=11xy using elimination method.

35. ÁSzuÀ •øÓ‰»® ÁºUP ‰»® PõsP.
4+25x 2−12x−24x 3+16x 4
Find the square root of the polynomial 4+25x2−12x−24x3+16x4 by division method.

36. Cµsk ªøP GsPÎß ÁºUP[PÎß Âzv¯õ\® 45. ]Ô¯ Gsoß ÁºUP®
BÚx, ö£›¯ Gsoß |õßS ©h[QØSa \©® GÛÀ, A¢u GsPøÍU
PõsP.
The difference of the squares of two positive numbers is 45. The square of the smaller
number is four times the larger number. Find the numbers.

[ v¸¨¦P / Turn over

7973 10

5 2  2 −1 
37. A=   ©ØÖ® B =   GÛÀ, (AB) =B A Gߣøu \›£õºUPÄ®.
T T T
 7 3  − 1 1 

5 2  2 −1  T T T
If A =   and B =   verify that (AB) =B A .
7 3 −1 1 

38. (−3, 4), (−5, −6), (4, −1) ©ØÖ® (1, 2) BQ¯ÁØøÓ •øÚPÍõPU öPõsh
|õØPµzvß £µ¨£ÍøÁU PõsP.
Find the area of the quadrilateral whose vertices are (−3, 4), (−5, −6), (4, −1) and
(1, 2).

39. J¸ •U÷Põn® ABC &ß £UP[PÎß ø©¯¨¦ÒÎPÒ •øÓ÷¯ D(3, 4),
E(8, 9) ©ØÖ® F(6, 7) GÛÀ, •U÷Põnzvß •øÚPøÍU PõsP.
The mid points D, E, F of the sides of a triangle ABC are (3, 4), (8, 9) and (6, 7)
respectively. Find the vertices of the triangle.

40. J¸ uõ©øµ¨ §ÁõÚx uspº ©mhzvØS ÷©À 20 ö\.«. E¯µzvÀ EÒÍx.
usiß «v¨£Sv uspº ©mhzvØS R÷Ç EÒÍx. PõØÖ Ã_® ÷£õx usk
uÒͨ£mk, uõ©øµ¨ §ÁõÚx usiß Bµ®£ {ø»°¼¸¢x 40 ö\.«.
yµzvÀ uspøµz öuõkQÓx. Bµ®£ {ø»°À uspº ©mhzvØSU R÷Ç
EÒÍ usiß }Í® PõsP.
A lotus is 20 cm above the water surface in a pond and its stem is partly below the
water surface. As the wind blew, the stem is pushed aside so that the lotus touched the
water 40 cm away from the original position of the stem. How much of the stem was
below the water surface originally ?

41. J¸ ÷Põ¦µzvß Ai°¼¸¢x Gvº¦Ó•ÒÍ J¸ Pmihzvß Ea]US
HØ£kzx® HØÓU÷Põn® 308 . Pmihzvß Ai°¼¸¢x ÷Põ¦µzvß
Ea]US HØ£kzx® HØÓU÷Põn® 608⋅ ÷Põ¦µzvß E¯µ® 50 «. GÛÀ,
Pmihzvß E¯µ® GßÚ ?
The angle of elevation of the top of a building from the foot of the tower is 308 and the
angle of elevation of the top of the tower from the foot of the building is 608. If the
tower is 50 m high, find the height of the building.

11 7973

42. J¸ vs© E¸øÍ°ß Bµ® ©ØÖ® E¯µzvß TkuÀ 37 ö\.«. GßP. ÷©¾®,
Auß ö©õzu ¦Ó¨£µ¨¦ 1628 \.ö\.«. GÛÀ, AÆĸøÍ°ß PÚ AÍøÁU
PõsP.
The sum of the base radius and the height of a right circular solid cylinder is 37 cm. If
the total surface area of the cylinder is 1628 sq.cm, then find the volume of the cylinder.

43. J¸ ¦ÒÎ ÂÁµz öuõS¨¤À Σx=35, n=5, Σ(x−9)2=82 GÛÀ, Σx2 ©ØÖ®
Σ ( x − x )2 BQ¯ÁØøÓU PõsP.

For a collection of data if Σx=35, n=5, Σ(x−9)2=82, then find Σx2 and Σ ( x − x )2 .

44. C¸ £PøhPÒ J÷µ ÷|µzvÀ ÷\µ E¸mh¨£k® ÷£õx QøhUS® •P
GsPÎß TkuÀ 3 &BÀ ©ØÖ® 4 &BÀ ÁS£hõ©¼¸UP {PÌuPÄ PõsP.
Two dice are rolled simultaneously. Find the probability that the sum of the numbers
on the faces is neither divisible by 3 nor by 4.

45. ( A) J¸ ö£¸USz öuõh›ß •uÀ EÖ¨¦ 375 ©ØÖ® 4 &BÁx EÖ¨¦ 192
GÛÀ, Auß ö£õx ÂQuzøu²®, •uÀ 14 EÖ¨¦PÎß Tkuø»²®
PõsP.
AÀ»x
(B) 4 «. Âmh•®, 10 «. E¯µ•® EÒÍ E¸øÍ ÁiÁz öuõmi°¾ÒÍ
uspµõÚx 10 ö\.«. Âmh•ÒÍ J¸ E¸øÍ ÁiÁ SÇõ´ ÁÈ÷¯
©oUS 2.5 Q.«. ÷ÁPzvÀ öÁÎ÷¯ØÓ¨£kQÓx. öuõmi°À £õv¯ÍÄ
uspº öÁÎ÷¯ØÓ¨£h BS® ÷|µzøuU PõsP. (Bµ®£ {ø»°À
öuõmi •ÊÁx® uspº {µ¨£¨£mkÒÍx GÚU öPõÒP.)
(a) The first term of a geometric series is 375 and the fourth term is 192. Find the
common ratio and the sum of the first 14 terms.
OR
(b) Water in a cylindrical tank of diameter 4 m and height 10 m is released through
a cylindrical pipe of diameter 10 cm at the rate of 2.5 km/hr. How much time
will it take to empty the half of the tank ? (Assume that the tank is full of water
to begin with)

[ v¸¨¦P / Turn over

12345
12345
7973 12 12345
12345
12345
12345
12345
12345
12345
12345
¤›Ä - IV/SECTION - IV 12345
12345
12345
12345
12345
(©v¨ö£sPÒ : 20) / (Marks : 20) 12345
12345
12345
12345
12345
SÔ¨¦ : JÆöÁõ¸ ÂÚõ¾® EÒÍ Cµsk ©õØÖ ÂÚõUPμ¸¢x
J¸ ÂÚõøÁz ÷uº¢öukzx C¸ ÂÚõUPÐUS® Âøh¯ÎUPÄ®.
Note : Answer both the questions choosing either of the alternatives. 2x10=20

46. (A) 3 ö\.«. Bµ•ÒÍ Ámhzvß ø©¯zv¼¸¢x 9 ö\.«. öuõø»ÂÀ J¸
¦ÒÎø¯U SÔUP. A¨¦Òΰ¼¸¢x ÁmhzvØS C¸ öuõk÷PõkPÒ
Áøµ¢x, Auß }Í[PøÍU PnUQkP.
AÀ»x
(B) PQ=4 ö\.«., QR=6 ö\.«., PR = 7.5 ö\.«. ©ØÖ® QS=7 ö\.«. AÍÄPÒ
öPõsh Ámh |õØPµ® PQRS ÁøµP.
(a) Take a point which is 9 cm away from the centre of a circle of radius 3 cm, and
draw two tangents to the circle from that point and calculate their lengths.
OR
(b) Construct a cyclic quadrilateral PQRS with PQ=4 cm, QR=6 cm, PR=7.5 cm,
QS=7 cm.

47. (A) y=x 2+3x+2 &ß Áøµ£h® ÁøµP. Aøu¨ £¯ß£kzv x2+2x+4=0
GßÓ \©ß£õmøhz wºUPÄ®.
AÀ»x
(B) J¸ ¼mhº £õ¼ß Âø» ` 15 GßP. £õ¼ß AÍÄUS®, Âø»US®
EÒÍ öuõhº¤øÚU Põmk® Áøµ£h® ÁøµP. AuøÚ¨ £¯ß£kzv,
(i) ÂQu\© ©õÔ¼ø¯U PõsP.
(ii) 3 ¼mhº £õ¼ß Âø»ø¯U PõsP.
(a) Draw the graph of y=x2+3x+2 and use it to solve the equation x2+2x+4=0.
OR
(b) The cost of milk per litre is ` 15. Draw the graph for the relation between the
quantity and cost. Hence find :
(i) the proportionality constant.
(ii) the cost of 3 litres of milk.

-oOo-