Series WX1YZ/2 SET~1

Q.P. Code 30/2/1

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 (_mZH$)
MATHEMATICS (STANDARD)
*
:3 : 80
Time allowed : 3 hours Maximum Marks : 80

ZmoQ> / NOTE :
(i) - 23
Please check that this question paper contains 23 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.

30/2/1 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. {ZåZ{b{IV _| go {H$g {ÛKmV g_rH$aU Ho$ _ybm| H$m `moJ\$b 4 h¡ ?

(a) 2x2 4x + 8 = 0 (b) x2 + 4x + 4 = 0

4
(c) 2 x2 x+1=0 (d) 4x2 4x + 4 = 0
2

2. {ÌÁ`m 14 cm dmbo EH$ d¥Îm Ho$ {ÌÁ`I§S>, {OgH$m Ho$ÝÐr` H$moU 90 h¡, H$s g§JV Mmn H$s
?

(a) 22 cm (b) 44 cm
(c) 88 cm (d) 11 cm
30/2/1 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. Which of the following quadratic equations has sum of its roots as 4 ?

(a) 2x2 4x + 8 = 0 (b) x2 + 4x + 4 = 0
4
(c) 2 x2 x+1=0 (d) 4x2 4x + 4 = 0
2

2. What is the length of the arc of the sector of a circle with radius 14 cm
and of central angle 90 ?
(a) 22 cm (b) 44 cm
(c) 88 cm (d) 11 cm
30/2/1 JJJJ Page 3 P.T.O.
3. `{X ABC PQR _|, A = 32 Am¡a R = 65 h¡, Vmo B H$s _mn h¡ :
(a) 32 (b) 65
(c) 83 (d) 97

4. `{X Am¡a àmH¥$V g§»`mE± h¢ Am¡a p g§»`m q H$m JwUO h¡, Vmo Am¡a q H$m HCF
?
(a) pq (b ) p
(c) q (d) p+q

5. EH$ Am`V ABCD {OgHo$ VrZ erf© B(0, 0), C(3, 0) Am¡a D(0, 4) h¢, CgHo$ erf© A Ho$
{ZX}em§H$ hm|Jo :
(a) (4, 0) (b) (0, 3)
(c) (3, 4) (d) (4, 3)

6. `{X g_rH$aU `w½_ 3x y+8=0 Am¡a 6x ry + 16 = 0 Ûmam {Zê${nV aoImE± g§nmVr

h¢, Vmo H$m _mZ hmoJm :
1 1
(a) (b)
2 2
(c) 2 (d) 2

7. EH$ W¡bo _| 100 nÎmo h¢ {OZ na 1 go 100 VH$ H$s g§»`mE± A§{H$V h¢ & Bg W¡bo _| go EH$
nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡ & Bg nÎmo na EH$ nyU© KZ g§»`m A§{H$V hmoZo H$s àm{`H$Vm
?
1 3
(a) (b)
20 50
1 7
(c) (d)
25 100

8. g_rH$aU `w½_ x = a Am¡a y = b Ûmam {Zê${nV aoImE± J«m\$s` ê$n _| :

(a) nañna g_m§Va hmoVr h¢
(b) {~ÝXþ (b, a) na à{VÀN>oXr hmoVr h¢
(c) g§nmVr hmoVr h¢
(d) {~ÝXþ (a, b) na à{VÀN>oXr hmoVr h¢
30/2/1 JJJJ Page 4
3. If ABC A = 32 and R = 65 , then the measure of
B is :
(a) 32 (b) 65
(c) 83 (d) 97

4.

(a) pq (b ) p
(c) q (d) p+q

5. The coordinates of the vertex A of a rectangle ABCD whose three vertices

are given as B(0, 0), C(3, 0) and D(0, 4) are :
(a) (4, 0) (b) (0, 3)
(c) (3, 4) (d) (4, 3)

6. If the pair of equations 3x y + 8 = 0 and 6x ry + 16 = 0 represent

coincident lines, then t
1 1
(a) (b)
2 2
(c) 2 (d) 2

7. A bag contains 100 cards numbered 1 to 100. A card is drawn at random

from the bag. What is the probability that the number on the card is a
perfect cube ?
1 3
(a) (b)
20 50
1 7
(c) (d)
25 100

8. The pair of equations x = a and y = b graphically represents lines which

are :
(a) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)

30/2/1 JJJJ Page 5 P.T.O.

9. `{X ~hþnX 6x2 + 37x (k 2) H$m EH$ eyÝ`H$, Xÿgao eyÝ`H$ H$m ì`wËH«$_ hmo, Vmo k H$m
?

(a) 4 (b) 6

(c) 6 (d) 4

10. EH$ R>mog AY©-Jmobo, {OgH$m ì`mg h¡, H$m g§nyU© n¥ð>r` joÌ\ ?

2 2
(a) 3 d (b) 2 d

1 3
(c) d2 (d) d2
2 4

11. gmW CN>mbo OmVo h¢, Vmo A{YH$-go-A{YH$ EH$ nQ> àmßV hmoZo H$s
?

3 4
(a) (b)
8 8

5 7
(c) (d)
8 8

12. Xr JB© AmH¥${V _|, DE BC & `{X AD = 2 BH$mB©, DB = AE = 3 BH$mB© Am¡a

EC = x BH$mB© h¡, Vmo x H$m _mZ hmoJm :

(a) 2 (b) 3
9
(c) 5 (d)
2

30/2/1 JJJJ Page 6

9. If one zero of the polynomial 6x2 + 37x (k 2) is reciprocal of the other,
then what is the value of k ?

(a) 4 (b) 6

(c) 6 (d) 4

10.

2 2
(a) 3 d (b) 2 d

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

11. If three coins are tossed simultaneously, what is the probability of getting
at most one tail ?

3 4
(a) (b)
8 8

5 7
(c) (d)
8 8

12. In the given figure, DE BC. If AD = 2 units, DB = AE = 3 units and

EC = x units, then the value of x is :

(a) 2 (b) 3
9
(c) 5 (d)
2

30/2/1 JJJJ Page 7 P.T.O.

13. 6 cm b§~r h¡ & Bg gwB© Ûmam 7:20 a.m. Am¡a 7:55 a.m. Ho$
~rM Omo H$moU a{MV hmoJm, dh h¡ :

35 35
(a) (b)
4 2

(c) 35 (d) 70

14. ~hþnX p(x) = x2 + 4x + 3 Ho$ eyÝ`H$ h¢ :

(a) 1, 3 (b) 1, 3
(c) 1, 3 (d) 1, 3

15. Xr JB© AmH¥${V _|, EH$ d¥Îm Ho$ n[aJV EH$ MVw^w©O PQRS ~Zm h¡ & `hm± PA + CS ~am~a
h¡ :

(a) QR Ho$ (b) PR Ho$

(c) PS Ho$ (d) PQ Ho$
16. `{X Am¡a , {ÛKmV ~hþnX p(x) = x2 ax b Ho$ eyÝ`H$ h¢, Vmo 2 + 2 H$m _mZ
hmoJm :
(a) a2 2b (b) a2 + 2b
2 2
(c) b 2a (d) b + 2a
x y
17. aoIm + = 1 VWm {ZX}em§H$ Ajm| go ~Zo {Ì^wO H$m joÌ\$b h¡ :
a b
1
(a) ab (b) ab
2
1
(c) ab (d) 2ab
4

30/2/1 JJJJ Page 8

13. The hour-hand of a clock is 6 cm long. The angle swept by it between
7:20 a.m. and 7:55 a.m. is :
35 35
(a) (b)
4 2

(c) 35 (d) 70
14. The zeroes of the polynomial p(x) = x2 + 4x + 3 are given by :
(a) 1, 3 (b) 1, 3
(c) 1, 3 (d) 1, 3
15. In the given figure, the quadrilateral PQRS circumscribes a circle. Here
PA + CS is equal to :

(a) QR (b) PR
(c) PS (d) PQ
16. If and are the zeroes of the quadratic polynomial p(x) = x2 ax b,
then the value of 2 + 2 is :
(a) a2 2b (b) a2 + 2b
2 2
(c) b 2a (d)
b + 2a
x y
17. The area of the triangle formed by the line = 1 with the coordinate
a b
axes is :
1
(a) ab (b) ab
2
1
(c) ab (d) 2ab
4
30/2/1 JJJJ Page 9 P.T.O.
18. Xr JB© AmH¥${V _|, AB PQ & `{X AB = 6 cm, PQ = 2 cm Am¡a OB = 3 cm h¡, Vmo
OP H$s bå~mB© hmoJr :

(a) 9 cm (b) 3 cm
(c) 4 cm (d) 1 cm

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) : d¥Îm Ho$ {H$gr q~Xþ na ñne©-aoIm ñne© q~Xþ go OmZo dmbr {ÌÁ`m na bå~
hmoVr h¡ &
(R) : ~mø q~Xþ go d¥Îm na ItMr JB© ñne©-aoImAm| H$s bå~mB`m± ~am~a hmoVr h¢ &
20. (A) : ~hþnX p(x) = x2 + 3x + 3 Ho$ Xmo dmñV{dH$ eyÝ`H$ h¢ &
(R) : EH$ {ÛKmV ~hþnX Ho$ A{YH$-go-A{YH$ Xmo dmñV{dH$ eyÝ`H$ hmo gH$Vo h¢ &
30/2/1 JJJJ Page 10
18. In the given figure, AB PQ. If AB = 6 cm, PQ = 2 cm and OB = 3 cm,
then the length of OP is :

(a) 9 cm (b) 3 cm

(c) 4 cm (d) 1 cm
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) : A tangent to a circle is perpendicular to the radius
through the point of contact.
Reason (R) : The lengths of tangents drawn from an external point to a
circle are equal.

20. Assertion (A) : The polynomial p(x) = x2 + 3x + 3 has two real zeroes.
Reason (R): A quadratic polynomial can have at most two real zeroes.

30/2/1 JJJJ Page 11 P.T.O.

 IÊS> I
(VSA) 2

21. {gÕ H$s{OE {H$ 2 + 3 EH$ An[a_o` g§»`m h¡, {X`m J`m h¡ {H$ 3 EH$ An[a_o`
g§»`m h¡ &

3
22. (H$) `{X 4 cot2 45 sec2 60 + sin2 60 + p = h¡, Vmo p H$m _mZ kmV H$s{OE &
4

AWdm
(I) `{X cos A + cos2 A = 1 h¡, Vmo sin2 A + sin4 A H$m _mZ kmV H$s{OE &

23. Xem©BE {H$ q~Xþ ( 2, 3), (8, 3) Am¡a (6, 7) EH$ g_H$moU {Ì^wO Ho$ erf© h¢ &

24. (H$) EH$ g_Vb O_rZ H$s 3 JwZr b§~r

h¡ & gy`© H$m CÞVm§e kmV H$s{OE &
AWdm
(I) ^y{_ Ho$ EH$ q~Xþ go, Omo _rZma Ho$ nmX-q~Xþ go 30 m H$s Xÿar na h¡, _rZma Ho$
{eIa H$m CÞ`Z H$moU 30 h¡ & _rZma H$s D±$MmB© kmV H$s{OE &

25. Xr JB© AmH¥${V _|, d¥Îm H$m H|$Ð O h¡ & q~Xþ A go Bg d¥Îm na AB Am¡a AC ñne©-aoImE±
ItMr JB© h¢ & `{X BAC = 65 h¡, Vmo BOC H$s _mn kmV H$s{OE &

30/2/1 JJJJ Page 12

 SECTION B

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

21. Prove that 2 + 3 is an irrational number, given that 3 is an irrational

number.

3
22. (a) If 4 cot245 sec2 60 + sin2 60 + p = , then find the value of p.
4
OR
(b) If cos A + cos2 A = 1, then find the value of sin2 A + sin4 A.

23. Show that the points ( 2, 3), (8, 3) and (6, 7) are the vertices of a
right-angled triangle.

24. (a) The length of the shadow of a tower on the plane ground is 3
times the height of the tower. Find the angle of elevation of the
sun.
OR
(b) The angle of elevation of the top of a tower from a point on the
ground which is 30 m away from the foot of the tower, is 30 . Find
the height of the tower.

25. In the given figure, O is the centre of the circle. AB and AC are tangents
drawn to the circle from point A. If BAC = 65 , then find the measure of
BOC.

30/2/1 JJJJ Page 13 P.T.O.

 IÊS> J

(SA) 3

26. (H$) g§»`mAm| 18180 Am¡a 7575 H$m A^mÁ` JwUZI§S>Z {d{Y Ûmam LCM kmV
H$s{OE & BZ Xmo g§»`mAm| H$m HCF ^r kmV H$s{OE &
AWdm
(I) VrZ K§{Q>`m± 6, 12 Am¡a 18 {_ZQ>m| Ho$ A§Vamb na ~OVt h¢ & `{X `o VrZm| K§{Q>`m±
EH$ gmW 6 a.m. na ~Ot hm|, Vmo CgHo$ níMmV² do VrZm| EH$ gmW H$~ ~O|Jr ?

27. {gÕ H$s{OE :

1 1 1
cos sin =
cos sin tan cot

28. `{X q~Xþ Q(0, 1), q~XþAm| P(5, 3) Am¡a R(x, 6) go EH$g_mZ Xÿar na hmo, Vmo x Ho$ _mZ
kmV H$s{OE &

29. EH$ H$ma Ho$ Xmo dmBna (wipers) h¢, Omo nañna H$^r AmÀN>m{XH$ Zht hmoVo h¢ & àË`oH$
dmBna H$s nÎmr H$s b§~mB© 21 cm h¡ Am¡a 120 Ho$ H$moU VH$ Ky_ H$a g\$mB© H$a gH$Vm
h¡ & XmoZm| n{Îm`m| H$s àË`oH$ ~whma Ho$ gmW {OVZm joÌ\$b gm\$ hmo OmVm h¡, dh kmV
H$s{OE &

30. (H$) `{X a¡{IH$ g_rH$aU {ZH$m`

2x + 3y = 7 VWm 2ax + (a + b)y = 28

Ho$ An[a{_V ê$n go AZoH$ hb hm|, Vmo Am¡a Ho$ _mZ kmV H$s{OE &
AWdm
(I) `{X 217x + 131y = 913 Am¡a 131x + 217y = 827 hm|, Vmo x Am¡a y Ho$ _mZ
kmV H$aZo Ho$ {bE g_rH$aU hb H$s{OE &
30/2/1 JJJJ Page 14
 SECTION C

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

26. (a) Find by prime factorisation the LCM of the numbers 18180 and
7575. Also, find the HCF of the two numbers.

OR

(b) Three bells ring at intervals of 6, 12 and 18 minutes. If all the

three bells rang at 6 a.m., when will they ring together again ?

27. Prove that :

1 1 1
cos sin = .
cos sin tan cot

28. If Q(0, 1) is equidistant from P(5, 3) and R(x, 6), find the values of x.

29. A car has two wipers which do not overlap. Each wiper has a blade of
length 21 cm sweeping through an angle of 120 . Find the total area
cleaned at each sweep of the two blades.

30. (a) If the system of linear equations

2x + 3y = 7 and 2ax + (a + b)y = 28

OR

(b) If 217x + 131y = 913 and

131x + 217y = 827,

then solve the equations for the values of x and y.

30/2/1 JJJJ Page 15 P.T.O.

31. Xr JB© AmH¥${V _|, d¥Îm H$m H|$Ð O VWm QPR d¥Îm Ho$ q~Xþ P na ñne©-aoIm h¡ & {gÕ
H$s{OE {H$ QAP + APR = 90 .

IÊS> K
(LA) 5

32. 45, 39, 33, ....... Ho$ {H$VZo nXm| H$m `moJ\$b 180 hmoJm ? Xmohao CÎma H$s
ì`m»`m H$s{OE &
33. (H$) g_wÐ-Vb go 75 m D±$Mr bmBQ>-hmD$g Ho$ {eIa go XoIZo na Xmo g_wÐr OhmOm| Ho$
AdZ_Z H$moU 30 Am¡a 60 h¢ & `{X bmBQ>-hmD$g Ho$ EH$ hr Amoa EH$
OhmO Xÿgao OhmO Ho$ R>rH$ nrN>o hmo, Vmo Xmo OhmOm| Ho$ ~rM H$s Xÿar kmV H$s{OE &
( 3 = 1·73 H$m à`moJ H$s{OE)
AWdm
(I) ^y{_ Ho$ EH$ q~Xþ go EH$ 30 m D±$Mo ^dZ Ho$ {eIa na bJr EH$ g§Mma _rZma Ho$
Vb Am¡a {eIa Ho$ CÞ`Z H$moU H«$_e: 30 Am¡a 60 h¢ & g§Mma _rZma H$s D±$MmB©
kmV H$s{OE & ( 3 = 1·73 H$m à`moJ H$s{OE)

34.
3 {_ZQ> H$s 100 Ad{Y`m| _| {H$VZr h¢ Am¡a Bgo ZrMo Xr JB© Vm{bH$m _| gmam§{eV {H$`m
J`m h¡
H$mam| H$s
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80
g§»`m
~ma§~maVm
7 14 13 12 20 11 15 8
(Ad{Y`m±)

30/2/1 JJJJ Page 16

31. In the given figure, O is the centre of the circle and QPR is a tangent to it
at P. Prove that QAP + APR = 90 .

SECTION D

This section comprises long answer (LA) type questions of 5 marks each.

32. How many terms of the arithmetic progression 45, 39, 33, ........ must be
taken so that their sum is 180 ? Explain the double answer.

33. (a) As observed from the top of a 75 m high lighthouse from the
sea-level, the angles of depression of two ships are 30 and 60 . If
one ship is exactly behind the other on the same side of the
lighthouse, find the distance between the two ships.
(Use 3 = 1·73)

OR
(b) From a point on the ground, the angle of elevation of the bottom
and top of a transmission tower fixed at the top of 30 m high
building are 30 and 60 , respectively. Find the height of the
transmission tower. (Use 3 = 1·73)
34. A student noted the number of cars passing through a spot on a road for
100 periods each of 3 minutes and summarised it in the table given
below. Find the mean and median of the following data.
Number of
0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80
cars
Frequency
7 14 13 12 20 11 15 8
(periods)

30/2/1 JJJJ Page 17 P.T.O.

35. (H$) EH$ {Ì^wO H$s ^wOmE± AB Am¡a BC VWm _mpÜ`H$m AD EH$ AÝ` {Ì^wO
ABC
PQR ^wOmAm| PQ Am¡a QR VWm _mpÜ`H$m PM Ho$ g_mZwnmVr h¢ &
Xem©BE {H$ ABC PQR h¡ &
AWdm
(I) g_m§Va MVw^w©O ABCD H$s ^wOm CD Ho$ _Ü`-q~Xþ M go EH$ aoIm BM ItMr JB©
Omo {dH$U© AC H$mo q~Xþ L AD H$mo q~Xþ E na H$mQ>Vr h¡ &
{gÕ H$s{OE {H$ EL = 2BL.
IÊS> L>
3 4
àH$aU AÜ``Z 1
36. EH$ {dÚmb` Ho$ dm{f©H$ {Xdg na à~§YH$m| Zo AnZo g~go hmoZhma {dÚm{W©`m| H$mo ZH$X
nwañH$ma Ho$ gmW-gmW ñ_¥{V-
O¡gm ~Zdm`m J`m VWm BgH$m AmYma ABCD gm_Zo H$s Amoa go {XIVm Wm & {gëda
ßboqQ>J H$m IM© < 20 à{V dJ© go_r h¡ &

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

(i) MVwWmªe ODCO H$m joÌ\ ? 1

(ii) AOB H$m joÌ\$b kmV H$s{OE & 1

(iii) (H$) ABCD N>m`m§{H$V ^mJ H$m {gëd ? 2

AWdm
(iii) (I) Mmn CD ? 2

30/2/1 JJJJ Page 18

35. (a) Sides AB and BC and median AD of a triangle ABC are
respectively proportional to sides PQ and QR and median PM of
~
OR
(b) Through the mid-point M of the side CD of a parallelogram ABCD,
the line BM is drawn intersecting AC in L and AD (produced) in E.
Prove that EL = 2BL.

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

Case Study 1
36. In an annual day function of a school, the organizers wanted to give a
cash prize along with a memento to their best students. Each memento is
made as shown in the figure and its base ABCD is shown from the front
side. The rate of silver plating is 20 per cm2.

Based on the above, answer the following questions :

(i) What is the area of the quadrant ODCO ? 1

(ii) 1

(iii) (a) What is the total cost of silver plating the shaded part
ABCD ? 2
OR

(iii) (b) What is the length of arc CD ? 2

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 àH$aU AÜ``Z 2

37. EH$ H$m°\$s XþH$mZ _| H$m°\$s Xmo Vah Ho$ H$n _| namogr OmVr h¡ & EH$ H$n ~obZmH$ma h¡
{OgH$m ì`mg 7 cm VWm D±$MmB© 14 cm h¡ Am¡a Xÿgam H$n AY©Jmobr` AmH$ma H$m h¡
{OgH$m ì`mg 21 cm h¡ &

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

(i) ~obZmH$ma H$n Ho$ AmYma H$m joÌ\$b kmV H$s{OE & 1

(ii) (H$) ? 2

AWdm

(ii) (I) ~obZmH$ma H$n H$s j_Vm kmV H$s{OE & 2

(iii) ~obZmH$ma H$n H$m dH«$ n¥ð>r` joÌ\ ? 1

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 Case Study 2

37. In a coffee shop, coffee is served in two types of cups. One is cylindrical in
shape with diameter 7 cm and height 14 cm and the other is
hemispherical with diameter 21 cm.

Based on the above, answer the following questions :

(i) Find the area of the base of the cylindrical cup. 1

(ii) (a) What is the capacity of the hemispherical cup ? 2

OR

(ii) (b) Find the capacity of the cylindrical cup. 2

(iii) What is the curved surface area of the cylindrical cup ? 1

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 àH$aU AÜ``Z 3

38. H§$ß`yQ>a-AmYm[aV {ejU {H$gr ^r Eogr {ejU nÕ{V H$mo g§X{^©V H$aVm h¡ Omo gyMZm
àgmaU Ho$ {bE H§$ß`yQ>am| H$m Cn`moJ H$aVr h¡ & àmW{_H$ {dÚmb` ñVa na, _ëQ>r_r{S>`m
nmR> `moOZmAm| H$mo àX{e©V H$aZo Ho$ {bE H§$ß`yQ>a AZwà`moJm| H$m Cn`moJ {H$`m Om gH$Vm h¡ &
Ag_ Ho$ 1000 àmW{_H$ Am¡a _mÜ`{_H$ {dÚmb`m| na EH$ gd}jU {H$`m J`m Wm Am¡a
CZHo$ nmg {OVZo H§$ß`yQ>a Wo, CZHo$ AmYma na CÝh| dJuH¥$V {H$`m J`m Wm &

101 Am¡aBggo
H§$ß`yQ>am| H$s g§»`m 1 10 11 20 21 50 51 100
A{YH$
{dÚmb`m| H$s g§»`m 250 200 290 180 80
EH$ {dÚmb` H$m `mÑÀN>`m M`Z {H$`m J`m & Vmo :
(i) `mÑÀN>`m M`Z {H$E JE {dÚmb` _| 100 go A{YH$ H§$ß`yQ>a hmoZo H$s àm{`H$Vm
kmV H$s{OE & 1
(ii) (H$) `mÑÀN>`m M`Z {H$E JE {dÚmb` _| 50 `m 50 go H$_ H§$ß`yQ>a hmoZo H$s
àm{`H$Vm kmV H$s{OE & 2
AWdm
(ii) (I) `mÑÀN>`m M`Z {H$E JE {dÚmb` _| 20 go A{YH$ H§$ß`yQ>a Z hmoZo H$s
àm{`H$Vm kmV H$s{OE & 2
(iii) `mÑÀN>`m M`Z {H$E JE {dÚmb` _| 10 `m 10 go H$_ H§$ß`yQ>a hmoZo H$s àm{`H$Vm
kmV H$s{OE & 1

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 Case Study 3

38. Computer-based learning (CBL) refers to any teaching methodology that

makes use of computers for information transmission. At an elementary
school level, computer applications can be used to display multimedia
lesson plans. A survey was done on 1000 elementary and secondary
schools of Assam and they were classified by the number of computers
they had.

Number of 101 and

1 10 11 20 21 50 51 100
Computers more
Number of
250 200 290 180 80
Schools

One school is chosen at random. Then :

(i) Find the probability that the school chosen at random has more
than 100 computers. 1
(ii) (a) Find the probability that the school chosen at random has
50 or fewer computers. 2
OR
(ii) (b) Find the probability that the school chosen at random has
no more than 20 computers. 2
(iii) Find the probability that the school chosen at random has 10 or
less than 10 computers. 1

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