Series WX1YZ/C SET~3

Q.P. Code 430/C/3

Roll No. narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$
_wI-n¥ð >na Adí` {bIo§ &
Candidates must write the Q.P. Code on
the title page of the answer-book.

J{UV (~w{Z`mXr)
MATHEMATICS (BASIC)
*
:3 : 80
Time allowed : 3 hours Maximum Marks : 80

NOTE :
(i) - 27
Please check that this question paper contains 27 printed pages.
(ii) - - -
-
Q.P. Code given on the right hand side of the question paper should be written on the title
page of the answer-book by the candidate.
(iii) - 38
Please check that this question paper contains 38 questions.
(iv) -

Please write down the serial number of the question in the answer-book before
attempting it.
(v) - 15 -
10.15 10.15 10.30 -
-
15 minute time has been allotted to read this question paper. The question paper will be
distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the
question paper only and will not write any answer on the answer-book during this period.

430/C/3 JJJJ ^ Page 1 P.T.O.

 :
:
(i) 38
(ii)
(iii) 1 18 (MCQ) 19 20

(iv) 21 25 (VSA)

(v) 26 31 (SA)
(vi) 32 35 (LA)
(vii) 36 38

(viii) 2 2
2 3

22
(ix) =
7

(x)

IÊS> H$

(MCQ) 1

1. Xmo KZm|, {OZ_| go àË`oH$ H$m {H$Zmam 5 cm h¡, Ho$ g§b½Z \

h¡ & Bggo àmßV KZm^ H$m n¥îR>r` joÌ\$b h¡ :
(a) 200 cm2
(b) 300 cm2
(c) 125 cm2
(d) 250 cm2

430/C/3 JJJJ Page 2

General Instructions :
Read the following instructions very carefully and strictly follow them :
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) This question paper is divided into five Sections A, B, C, D and E.
(iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and
questions number 19 and 20 are Assertion-Reason based questions of 1 mark
each.
(iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type
questions, carrying 2 marks each.
(v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions,
carrying 3 marks each.
(vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions
carrying 5 marks each.
(vii) In Section E, Questions no. 36 to 38 are case study based questions carrying
4 marks each. Internal choice is provided in 2 marks questions in each
case study.
(viii) There is no overall choice. However, an internal choice has been provided in
2 questions in Section B, 2 questions in Section C, 2 questions in Section D and
3 questions in Section E.
22
(ix) Draw neat diagrams wherever required. Take = wherever required, if not
7
stated.
(x) Use of calculators is not allowed.

SECTION A

This section comprises multiple choice questions (MCQs) of 1 mark each.

1. Two cubes each of 5 cm edge are joined end to end. The surface area of
the resulting cuboid is :

(a) 200 cm2

(b) 300 cm2

(c) 125 cm2

(d) 250 cm2

430/C/3 JJJJ Page 3 P.T.O.

2. q~XþAm| (c, 0) Am¡a (0, c) Ho$ ~rM H$s Xÿar h¡ :
(a) c 2 BH$mB©
(b) 2c BH$mB©

(c) 2 c BH$mB©
(d) c BH$mB©

3. {ÛKmV g_rH$aU x2 + px q = 0 Ho$ _yb ~am~a hm|Jo, `{X :

(a) p2 = 4q (b) p2 = 4q
(c) p2 = 2q (d) p2 = 2q

4. Xmo g§»`mAm| H$m HCF 27 VWm CZH$m LCM 162 h¡ & `{X BZ_| go EH$ g§»`m 54 h¡, Vmo
Xÿgar g§»`m h¡ :
(a) 36 (b) 45

(c) 9 (d) 81

5. {XZ Ho$ {H$gr g_`, EH$ ì`{º$ H$s D±$MmB© Am¡a CgH$s N>m`m H$s bå~mB© EH$g_mZ h¢ &
gy`© H$m CÞVm§e (altitude) h¡ :
(a) 30 (b) 45
(c) 60 (d) 90

6. {Ì^wO ABC _|, DE || BC h¡ & `{X AD : DB = 2 : 3 hmo, Vmo DE : BC ~am~a h¡ :

(a) 2:3 (b) 3:5

(c) 2:5 (d) 3:2

430/C/3 JJJJ Page 4

2. The distance between the points (c, 0) and (0, c) is :

(a) c 2 units

(b) 2c units

(c) 2 c units

(d) c units

3. The roots of the quadratic equation x2 + px q = 0 are equal, if :

(a) p2 = 4q (b) p2 = 4q
(c) p2 = 2q (d) p2 = 2q

4. The HCF of two numbers is 27 and their LCM is 162. If one of the
numbers is 54, the other number is :

(a) 36 (b) 45

(c) 9 (d) 81

5. At some time of the day, the height and length of the shadow of a man
:
(a) 30 (b) 45
(c) 60 (d) 90

6. In ABC, DE || BC. If AD : DB = 2 : 3, then DE : BC is equal to :

(a) 2:3 (b) 3:5

(c) 2:5 (d) 3:2

430/C/3 JJJJ Page 5 P.T.O.

7. `{X EH$ A.P. H$m gmd© AÝVa 6 h¡, Vmo a20 a14 H$m _mZ h¡ :

(a) 36

(b) 6

(c) 36

(d) 6

8. Xr JB© AmH¥${V _|, H|$Ð O dmbo d¥Îm na PA Am¡a PB ñne©-aoImE± h¢ & `{X APB = 50
h¡, Vmo AOB ~am~a h¡ :

(a) 130 (b) 50

(c) 120 (d) 90

9. {ZåZ{b{IV ~§Q>Z Ho$ {bE

go H$_ A§H$ N>mÌm| H$s g§»`m
10 1
20 5
30 13
40 15
50 16

~hþbH$ dJ© h¡ :$
(a) 30 40 (b ) 40 50
(c) 20 30 (d) 10 20

430/C/3 JJJJ Page 6

7. If common difference of an A.P. is 6, then value of a20 a14 is :

(a) 36
(b) 6

(c) 36
(d) 6

8. In the given figure, PA and PB are tangents to a circle centred at O. If

APB = 50 , then AOB is equal to :

(a) 130 (b) 50

(c) 120 (d) 90

9. For the following distribution

Number of
Marks below
Students
10 1

20 5

30 13

40 15

50 16

the modal class is :

(a) 30 40 (b ) 40 50
(c) 20 30 (d) 10 20

430/C/3 JJJJ Page 7 P.T.O.

 7
10. `{X cosec A = h¡, Vmo tan A . cos A H$m _mZ hmoJm :
5

7 2 6
(a) (b)
5 5

24 5
(c) (d)
49 7

11. EH$ {ÛKmV ~hþnX {OgHo$ eyÝ`H$ 6 Am¡a 0 h¢, h¡ :

(a) x (x2 + 6) (b ) 6x (x + 6)

(c) 6x2 1 (d) 6 (x2 x)

12. {ÌÁ`m r dmbo Cg d¥ÎmI§S>, {OgH$m H|$Ðr` H$moU 90 h¡, H$m joÌ\$b h¡ :

r2 1 2
(a) r
2 2

2 r 1 2
(b) r
4 2

r2 1 2
(c) r
4 2

2 r
(d) r 2 sin 90
4

13. `{X x = a sin Am¡a y = b cos h¡, Vmo b2x2 + a2y2 ~am~a h¡ :

(a) 1 (b) a2b2

a2 b2
(c) (d) a2 + b2
2 2
a b

430/C/3 JJJJ Page 8

 7
10. If cosec A = , then value of tan A . cos A is :
5

7 2 6
(a) (b)
5 5

24 5
(c) (d)
49 7

11. A quadratic polynomial having zeroes 6 and 0 is :

(a) x (x2 + 6) (b ) 6x (x + 6)

(c) 6x2 1 (d) 6 (x2 x)

12. Area of a segment of a circle of radius r and central angle 90 is :

r2 1 2
(a) r
2 2

2 r 1 2
(b) r
4 2

r2 1 2
(c) r
4 2

2 r
(d) r 2 sin 90
4

13. If x = a sin and y = b cos , then b2x2 + a2y2 is equal to :

(a) 1 (b) a2b2

a2 b2
(c) (d) a2 + b2
2 2
a b

430/C/3 JJJJ Page 9 P.T.O.

14. a¡{IH$ g_rH$aU `w½_ 5x + 4y = 20 Am¡a 10x + 8y = 16 :
(a) H$m H$moB© hb Zht h¡
(b) Ho$ An[a{_V ê$n go AZoH$ hb h¢
(c) H$m A{ÛVr` hb h¡
(d) Ho$ Xmo hb h¢

15. eyÝ` ~hþnX H$s KmV :

(a) 0 hmoVr h¡ (b) 1 hmoVr h¡

(c) H$moB© dmñV{dH$ g§»`m hmoVr h¡ (d) n[a^m{fV Zht h¡

16. {ÌÁ`mAm| r1 Am¡a r2 (r2 > r1) dmbo AY©JmobmH$ma H$Q>moao H$m Hw$b n¥îR>r` joÌ\$b (Am§V[aH$
VWm ~mø) h¡ :

2 2 2 2
(a) 2 (r 1 r 2) (b) (r 1 r 2)
2 2
(c) 3 r2 r1 (d) 3 r 21 r 22

17. 30 {XZ Ho$ _mh _| 5 a{ddmam| Ho$ hmoZo H$s àm{`H$Vm h¡ : $

1 2
(a) (b)
7 7
1 5
(c) (d)
15 30

18. `{X {H$gr ~§Q>Z Ho$ _mÜ` Am¡a ~hþbH$ H«$_e: 17 Am¡a 20 h¢, Vmo _ybmZwnmVr gyÌ H$m Cn`moJ
H$aHo$ Bg ~§Q>Z H$m _mÜ`H$ hmoJm :
31
(a) 20 (b)
3

(c) 18 (d) 17

430/C/3 JJJJ Page 10

14. The pair of linear equations 5x + 4y = 20 and 10x + 8y = 16 has :
(a) no solution
(b) infinite number of solutions
(c) a unique solution
(d) two solutions

15. Degree of a zero polynomial is :

(a) 0 (b) 1
(c) any real number (d) not defined

16. Total surface area (internal and external) of a hemispherical bowl having
radii r1 and r2 (r2 > r1) is :

(a) 2 (r 21 r 22 ) (b) (r 21 r 22 )

(c) 3 r 22 r 21 (d) 3 r 21 r 22

17. The probability that a month of 30 days has 5 Sundays, is

1 2
(a) (b)
7 7
1 5
(c) (d)
15 30

18. If the mean and the mode of a distribution are 17 and 20 respectively,
then the median of the distribution, using empirical formula, is :
31
(a) 20 (b)
3

(c) 18 (d) 17

430/C/3 JJJJ Page 11 P.T.O.

 19 20 1
(A) (R)
(a), (b), (c) (d)

(a) A{^H$WZ (A) Am¡a VH©$ (R) XmoZm| ghr h¢ Am¡a VH©$ (R), A{^H$WZ (A) H$s ghr
ì¶m»¶m H$aVm h¡ &
(b) A{^H$WZ (A) Am¡a VH©$ (R) XmoZm| ghr h¢, naÝVw VH©$ (R), A{^H$WZ (A) H$s ghr
ì¶m»¶m H$aVm h¡ &
(c) A{^H$WZ (A) ghr h¡, naÝVw VH©$ (R) µJbV h¡ &
(d) A{^H$WZ (A) µJbV h¡, naÝVw VH©$ (R) ghr h¡ &

19. (A) : EH$ KQ>Zm hmoZo H$s ~hþV g§^mdZm h¡ `{X BgHo$ KQ>Zo H$s àm{`H$Vm
0·9999 h¡ &

(R) : Cg KQ>Zm, {OgH$m K{Q>V hmoZm {ZpíMV h¡, H$s àm{`H$Vm gX¡d 1 hmoVr
h¡ &

20. (A) : H|$Ð O dmbo d¥Îm na PA Am¡a PB ñne©-aoImE± h¢ Am¡a OPA = 30

h¡ & V~, PAB EH$ g_~mhþ {Ì^wO h¡ &

(R) : ~mø q~Xþ go d¥Îm na ItMr JB© ñne©-aoImAm| H$s bå~mB`m± ~am~a hmoVr
h¢ &

430/C/3 JJJJ Page 12

Questions number 19 and 20 are Assertion and Reason based questions carrying
1 mark each. Two statements are given, one labelled as Assertion (A) and the
other is labelled as Reason (R). Select the correct answer to these questions from
the codes (a), (b), (c) and (d) as given below.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the
correct explanation of the Assertion (A).

(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not
the correct explanation of the Assertion (A).

(c) Assertion (A) is true, but Reason (R) is false.

(d) Assertion (A) is false, but Reason (R) is true.

19. Assertion (A) : An event is very likely to happen if its probability is

0·9999.

Reason (R) : Probability of a sure event is always 1.

20. Assertion (A) : PA and PB are tangents to the circle centred at O and
OPA = 30 . Then, PAB is an equilateral triangle.

Reason (R) : Lengths of tangents from an external point to a circle are

equal in length.

430/C/3 JJJJ Page 13 P.T.O.

 IÊS> I
(VSA) 2

21.

(i) g^r g§^d n[aUm_m| H$mo {b{IE &

(ii) A{YH$-go-A{YH$ 2 {MV àmßV H$aZo H$s àm{`H$Vm kmV H$s{OE &

22. EH$ d¥Îm H$m H|$Ð Am¡a {ÌÁ`m kmV H$s{OE {OgHo$ ì`mg Ho$ A§Ë` q~Xþ (3, 10) Am¡a
(1, 4) h¢ &

23. q~XþAm| ( 1, 1) Am¡a (5, 4) y-Aj {Og AZwnmV _| {d^m{OV

H$aVm h¡, Cg AZwnmV H$mo kmV H$s{OE &
n
24. (H$) Xem©BE {H$ {H$gr ^r àmH¥$V g§»`m Ho$ {bE, g§»`m 12 , A§H$ 0 na H$^r ^r
g_mßV Zht hmo gH$Vr h¡ &
AWdm
(I) Xmo An[a_o` g§»`mAm| H$m EH$-EH$ CXmhaU Xr{OE {OZH$m
(i) `moJ\$b n[a_o` g§»`m hmo &
(ii) JwUZ\$b An[a_o` g§»`m hmo &

25. (H$) A = 30 Am¡a B = 60 Ho$ {bE, {ZåZ{b{IV H$mo gË`m{nV H$s{OE :

tan B tan A
tan (B A) =
1 tan A tan B

AWdm
(I) _mZ kmV H$s{OE :

1
sin2 60 2 cos2 45 + cosec2 30
2

430/C/3 JJJJ Page 14

 SECTION B

This section comprises very short answer (VSA) type questions of 2 marks each.

21. Three coins are tossed together.

(i) Write all possible outcomes.

(ii) Find the probability of having at most 2 heads.

22. Find the centre and radius of a circle having end points of its diameter as
(3, 10) and (1, 4).

23. Find the ratio in which a line segment joining the points ( 1, 1) and (5, 4)
is divided by the y-axis.

n
24. (a) Show that 12
number.

OR

(b) Give example of two irrational numbers whose

(i) sum is a rational number.

(ii) product is an irrational number.

25. (a) For A = 30 and B = 60 , verify that

tan B tan A
tan (B A) =
1 tan A tan B

OR

(b) Evaluate :

1
sin2 60 2 cos2 45 + cosec2 30
2

430/C/3 JJJJ Page 15 P.T.O.

 IÊS> J
(SA) 3

26. Xmo dJm] Ho$ joÌ\$bm| H$m `moJ\$b 468 m2 h¡ & `{X BZ dJm] H$s ^wOmAm| H$s bå~mB`m| H$m
AÝVa 6 m hmo, Vmo XmoZm| dJm] H$s ^wOmAm| H$s bå~mB`m± kmV H$s{OE &
27. (H$) {gÕ H$s{OE {H$ 2 + 3 3 EH$ An[a_o` g§»`m h¡ & `h {X`m J`m h¡ {H$ 3
EH$ An[a_o` g§»`m h¡ &
AWdm
(I) {gÕ H$s{OE {H$ 5 EH$ An[a_o` g§»`m h¡ &
BC BE
28. (H$) Xr JB© AmH¥${V _|, = Am¡a ABD = ACD h¡ & Xem©BE {H$
BD AC
ABD EBC.

AWdm
(I) Xr JB© AmH¥${V _|, ABC Am¡a AED Xmo g_H$moU {Ì^wO h¢, {OZHo$ H$moU B Am¡a E
H«$_e: g_H$moU h¢ & {gÕ H$s{OE {H$ :

(i) ABC AED

(ii) AB AD = AC AE

430/C/3 JJJJ Page 16

 SECTION C

This section comprises short answer (SA) type questions of 3 marks each.

26. Sum of the areas of two squares is 468 m2. If the difference between their
sides is 6 m, then find the sides of the two squares.

27. (a) Prove that 2 + 3 3 is an irrational number. It is given that 3 is

an irrational number.
OR

(b) Prove that 5 an irrational number.

BC BE
28. (a) In the given figure, = and ABD = ACD. Show that
BD AC
ABD EBC.

OR
(b) In the given figure, ABC and AED are two right triangles, right
angled at B and E respectively. Prove that :

(i) ABC AED

(ii) AB AD = AC AE

430/C/3 JJJJ Page 17 P.T.O.

29. Xr JB© AmH¥${V _|, H|$Ð O dmbo Xmo g§Ho$Ðr` d¥Îm Xem©E JE h¢ & BZ d¥Îmm| H$s {ÌÁ`mE±
OA = 3 cm Am¡a OB = 6 cm h¢ &

N>m`m§{H$V ^mJ H$m n[a_mn kmV H$s{OE ( = 3·14 H$m à`moJ H$s{OE)
30. {gÕ H$s{OE :
cot 2 (sec 1) (1 sin )
= sec2
1 sin (sec 1)
31. {ÛKmV ~hþnX 8x2 + 3x 5 Ho$ eyÝ`H$ kmV H$s{OE Am¡a eyÝ`H$m| VWm JwUm§H$m| Ho$ ~rM Ho$
g§~§Y H$s gË`Vm H$s Om±M H$s{OE &
IÊS> K
(LA) 5
32. (H$) {ZåZ{b{IV gmaUr {H$gr Jm±d Ho$ 100 \ (ha) Johÿ± H$m
CËnmXZ Xem©Vr h¡ :
CËnmXZ
\$m_m] H$s g§»`m
(kg/ha _|)
50 55 2
55 60 8
60 65 12
65 70 24
70 75 38
75 80 16
BZ Am±
AWdm
430/C/3 JJJJ Page 18
29. In the given figure, two concentric circles are shown, centred at O. The
radii of the circles are OA = 3 cm and OB = 6 cm.

Find perimeter of the shaded region. (Use = 3·14)

30. Prove that :
cot 2 (sec 1) 2 (1 sin )
= sec
1 sin (sec 1)
31. Find the zeroes of the quadratic polynomial 8x2 + 3x 5 and verify the
relationship between the zeroes and the coefficients.

SECTION D
This section comprises long answer (LA) type questions of 5 marks each.
32. (a) The following table gives production yield per hectare of wheat of
100 farms of a village :
Production yield Number of
(in kg/ha) farms
50 55 2
55 60 8
60 65 12
65 70 24
70 75 38
75 80 16
Find the mean and median of the data.
OR
430/C/3 JJJJ Page 19 P.T.O.
 (I) ZrMo {XE JE &
^ma
N>mÌm| H$s g§»`m
(kg _|)
40 45 5
45 50 11
50 55 20
55 60 24
60 65 28
65 70 12

33. (H$) a¡{IH$ g_rH$aU `w½_ 4x + y + 7 = 0 VWm 2x 3y + 7 = 0 H$mo J«m\$s` {d{Y

go hb H$s{OE &
AWdm
(I) EH$ H$jm Ho$ {bE 7 Hw${g©`m| Am¡a 4 _oOm| H$m Hw$b _yë` < 7,000 h¡; O~{H$
5 Hw${g©`m| Am¡a 3 _oOm| H$m Hw$b _yë` < 5,080 h¡ & àË`oH$ Hw$gu Am¡a àË`oH$ _oO
H$m _yë` kmV H$s{OE &

34. {gÕ H$s{OE {H$ EH$ ~mø q~Xþ go d¥Îm na ItMr JB© ñne©-aoImAm| H$s bå~mB`m± ~am~a
hmoVr h¢ &

35. Xr JB© AmH¥${V _|, ACB = 90 Am¡a CD AB & {gÕ H$s{OE {H$
2
CD = BD AD.

430/C/3 JJJJ Page 20

 (b) Find the mean and the mode of the data given below :
Weight Number of
(in kg) students
40 45 5
45 50 11
50 55 20
55 60 24
60 65 28
65 70 12

33. (a) Solve the pair of linear equations 4x + y + 7 = 0 and 2x 3y + 7 = 0

graphically.

OR

(b) 7 chairs and 4 tables for a classroom together cost < 7,000; while
5 chairs and 3 tables together cost < 5,080. Find the cost of each
chair and each table.

34. Prove that the lengths of the tangents drawn from an external point to a
circle are equal.

35. In the given figure, ACB = 90 and CD AB. Prove that CD2 = BD AD.

430/C/3 JJJJ Page 21 P.T.O.

 IÊS> L>
3 4

àH$aU AÜ``Z 1

36. EH$ µ\¡$eZ {S>µOmBZa \¡${~«H$ n¡Q>Z© {S>µOmBZ H$a ahm h¡ & àË`oH$ n§{º$ _| Hw$N> N>m`m§{H$V dJ©
Am¡a N>m`ma{hV {Ì^wO| h¢ &

Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :

(i) àË`oH$ n§{º$ _| dJm] H$s g§»`m Ho$ {bE A.P. kmV H$s{OE & 1

(ii) àË`oH$ n§{º$ _| {Ì^wOm| H$s g§»`m Ho$ {bE A.P. kmV H$s{OE & 1

(iii) (H$) `{X àË`oH$ N>m`m§{H$V dJ© H$s ^wOm 2 cm h¡, Vmo N>m`m§{H$V joÌ\$b kmV
H$s{OE, O~ 15 n§{º$`m| H$mo {S>µOmBZ {H$`m J`m hmo & 2

AWdm

(iii) (I) n§{º$`m| H$s g§»`m _| {Ì^wOm| H$s Hw$b g§»`m kmV H$aZo H$m gyÌ
{b{IE & AV: S10 kmV H$s{OE & 2

430/C/3 JJJJ Page 22

 SECTION E

This section comprises 3 case study based questions of 4 marks each.

Case Study 1

36. A fashion designer is designing a fabric pattern. In each row, there are
some shaded squares and unshaded triangles.

Based on the above, answer the following questions :

(i) Identify A.P. for the number of squares in each row. 1

(ii) Identify A.P. for the number of triangles in each row. 1

(iii) (a) If each shaded square is of side 2 cm, then find the shaded
area when 15 rows have been designed. 2

OR

(iii) (b) Write a formula for finding total numbe

number of rows. Hence, find S10. 2

430/C/3 JJJJ Page 23 P.T.O.

 àH$aU AÜ``Z 2
37. « :
{dH$mg Ho$ dm{f©H$ N>ëbm| H$s JUZm H$aZm h¡ & Eogm hr EH$ Q´>§H$ `hm± {XIm`m J`m h¡ &

ACBA ({MÌ XoI|) {M{ÌV {H$`m h¡ &

`{X Ordm AB H|$Ð na 90 H$m H$moU ~ZmVr h¡ Am¡a Q´>§H$ H$s {ÌÁ`m 21 cm h¡, Vmo kmV
H$s{OE :

(i) Ordm AB H$s bå~mB© & 1

(ii) OAB H$m joÌ\$b & 1

(iii) (H$) d¥ÎmI§S> ACBA H$m joÌ\$b & > 2

AWdm

(iii) (I) {ÌÁ`I§S> OACBO H$m n[a_mn & 2

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 Case Study 2
37. Age of a tree : The most accurate way to determine the age of a tree is to
count the annual rings of wood growth. One such trunk has been shown
here.

To make an identification mark, the forest department has painted

segment ACBA. (See diagram) If chord AB makes an angle 90 at the
centre and radius of the trunk is 21 cm, then find the :

(i) length of chord AB. 1

(ii) area of OAB. 1

(iii) (a) area of segment ACBA. 2

OR

(iii) (b) perimeter of sector OACBO. 2

430/C/3 JJJJ Page 25 P.T.O.
 àH$aU AÜ``Z 3

38. I§^m| (nmobm|) H$mo àVrH$m| `m AmH¥${V`m| Ho$ gmW

CHo$am J`m h¡ Am¡a Á`mXmVa npíM_r H$ZmS>m Am¡a CÎma-npíM_ g§`wº$ amÁ` A_o[aH$m _| nmE
OmVo h¢ &
{XE JE {MÌ _|, g_mZ D±$MmB© Ho$ Xmo I§^o 28 m & BZ XmoZm| Ho$ ~rM EH$
hr aoIm Ho$ EH$ q~Xþ go, XmoZm| I§^m| Ho$ erf© Ho$ CÞ`Z H$moU H«$_e: 60 Am¡a 30 h¢ &

Cn`w©º$ Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :

(i) EH$ gm\$ Zm_m§{H$V {MÌ ~ZmBE & 1

(ii) (H$) I§^mo§ H$s D±$MmB© kmV H$s{OE & 2

AWdm

(ii) (I) `{X àojUm| Ho$ q~Xþ go I§^m| Ho$ erf© H$s Xÿ[a`m| H$mo p VWm q Ho$ ê$n _|
{b`m OmVm h¡, Vmo p Am¡a q Ho$ ~rM g§~§Y kmV H$s{OE & 2

(iii) àojU q~Xþ H$m ñWmZ kmV H$s{OE & 1

430/C/3 JJJJ Page 26

 Case Study 3

38. Totem poles are made from large trees. These poles are carved with
symbols or figures and mostly found in western Canada and
northwestern United States.

In the given picture, two such poles of equal heights are standing 28 m
apart. From a point somewhere between them in the same line, the
angles of elevation of the top of the two poles are 60 and 30
respectively.

Based on the above, answer the following questions :

(i) Draw a neat labelled diagram. 1

(ii) (a) Find the height of the poles. 2

OR

(ii) (b) If the distances of the top of the poles from the point of
observation are taken as p and q, then find a relation
between p and q. 2

(iii) Find the location of the point of observation. 1

430/C/3 JJJJ Page 27 P.T.O.