CBSE Class 10 Mathematics Basics Question Paper 2020 Set 430-4-3

H$moS> Z§.
Code No. 430/4/3
amob Z§. narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð
Roll No. >na Adí` {bIo§ &
Candidates must write the Code on the
title page of the answer-book.

ZmoQ> NOTE
(I) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV (I) Please check that this question
n¥ð> 19 h¢ & paper contains 19 printed pages.

(II) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS (II) Code number given on the right
>Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na hand side of the question paper
{bI| & should be written on the title page of
the answer-book by the candidate.
(III) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| (III) Please check that this question
>40 àíZ h¢ & paper contains 40 questions.
(IV) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go (IV) Please write down the Serial
nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Number of the question in the
Adí` {bI| & answer-book before attempting it.
(V) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ >H$m (V) 15 minute time has been allotted to
g_` {X`m J`m h¡ & àíZ-nÌ H$m {dVaU read this question paper. The
nydm©• _| 10.15 ~Oo {H$`m OmEJm & question paper will be distributed
10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db at 10.15 a.m. From 10.15 a.m. to
10.30 a.m., the students will read the
àíZ-nÌ H$mo n‹T>|Jo Am¡a Bg Ad{Y Ho$ Xm¡amZ question paper only and will not
do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo & write any answer on the
answer-book during this period.

J{UV (~w{Z`mXr)
MATHEMATICS (BASIC)

{ZYm©[aV g_` : 3 KÊQ>o A{YH$V_ A§H$ : 80
Time allowed : 3 hours Maximum Marks : 80
.430/4/3 1 P.T.O.

gm_mÝ` {ZX}e :
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m g»Vr go nmbZ H$s{OE :
(i) àíZ-nÌ Mma IÊS>m| _| {d^m{OV {H$`m J`m h¡ – H$, I, J Ed§ K & Bg àíZ-nÌ _|
40 àíZ h¢ & g^r àíZ A{Zdm`© h¢ &

(ii) IÊS> H$ _| àíZ g§»`m 1 go 20 VH$ 20 àíZ h¢ Ed§ àË`oH$ àíZ EH$ A§H$ H$m h¡ &
(iii) IÊS> I _| àíZ g§»`m 21 go 26 VH$ 6 àíZ h¢ Ed§ àË`oH$ àíZ Xmo A§H$m| H$m h¡ &

(iv) IÊS> J _| àíZ g§»`m 27 go 34 VH$ 8 àíZ h¢ Ed§ àË`oH$ àíZ VrZ A§H$m| H$m h¡ &

(v) IÊS> K _| àíZ g§»`m 35 go 40 VH$ 6 àíZ h¢ Ed§ àË`oH$ àíZ Mma A§H$m| H$m h¡ &
(vi) àíZ-nÌ _| g_J« na H$moB© {dH$ën Zht h¡ & VWm{n EH$ -EH$ A§H$ dmbo Xmo àíZm| _|, Xmo-Xmo
A§H$m| dmbo Xmo àíZm| _|, VrZ-VrZ A§H$m| dmbo VrZ àíZm| _|, Mma-Mma A§H$m| dmbo VrZ àíZm|
_| Am§V[aH$ {dH$ën {XE JE h¢ & Eogo àíZm| _| Ho$db EH$ hr {dH$ën H$m CÎma {b{IE &
(vii) BgHo$ A{V[aº$, Amdí`H$VmZwgma, àË`oH$ IÊS> Am¡a àíZ Ho$ gmW `Wmo{MV {ZX}e {XE JE h¢ &

(viii) H¡$bHw$boQ>a Ho$ à`moJ H$s AZw_{V Zht h¡ &

IÊS> H$
àíZ g§»`m 1 go 20 VH$ àË`oH$ àíZ 1 A§H$ H$m h¡ &
àíZ g§»`m 1 go 10 _| ghr {dH$ën Mw{ZE &
1. AmH¥${V-1 _|, J«m\$ _| {XImE JE ~hþnX p(x) Ho$ eyÝ`H$m| H$s g§»`m h¡

AmH¥${V-1
(A) 3
(B) 2
(C) 1
(D) 4

.430/4/3 2

General Instructions :
Read the following instructions very carefully and strictly follow them :
(i) This question paper comprises four sections – A, B, C and D. This question
paper carries 40 questions. All questions are compulsory.
(ii) Section A : Question Numbers 1 to 20 comprises of 20 questions of one mark
each.
(iii) Section B : Question Numbers 21 to 26 comprises of 6 questions of two marks
each.
(iv) Section C : Question Numbers 27 to 34 comprises of 8 questions of three marks
each.
(v) Section D : Question Numbers 35 to 40 comprises of 6 questions of four marks
each.
(vi) There is no overall choice in the question paper. However, an internal choice
has been provided in 2 questions of one mark, 2 questions of two marks,
3 questions of three marks and 3 questions of four marks. You have to attempt
only one of the choices in such questions.
(vii) In addition to this, separate instructions are given with each section and
question, wherever necessary.
(viii) Use of calculators is not permitted.
SECTION A
Question numbers 1 to 20 carry 1 mark each.
Choose the correct option in question numbers 1 to 10.
1. In Figure-1, number of zeroes of the polynomial p(x), shown in the graph are

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

.430/4/3 3 P.T.O.

2. EH$ nmgo H$mo EH$ ~ma \|$H$m OmVm h¡ & EH$ {df_ g§»`m AmZo H$s àm{`H$Vm h¡
(A) 1
1
(B)
2
4
(C)
6
2
(D)
6
3. k H$m _mZ {OgHo$ {bE g_rH$aU 3x – y + 8 = 0 VWm 6x + ky = – 16 g§nmVr aoImAm|
H$mo ì`º$ H$a|, h¡
1
(A) –
2
1
(B)
2
(C) 2
(D) –2
4. `{X sin A = cos A, 0  A  90 h¡, Vmo H$moU A ~am~a h¡
(A) 30
(B) 60
(C) 0
(D) 45
5. EH$ R>mog AY©Jmobo H$m Hw$b n¥ð>r` joÌ\$b h¡
(A) 3r2
(B) 2r2
(C) 4r2
2 3
(D) r
3
6. g_m§Va loT>r 5, 8, 11, ..., 47 H$m A§{V_ nX go (àW_ nX H$s Amoa) Xÿgam nX h¡
(A) 50
(B) 45
(C) 44
(D) 41
7. Xmo g_ê$n {Ì^wOm| H$s ^wOmAm| H$m AZwnmV 4 : 9 h¡ & BZ {Ì^wOm| Ho$ joÌ\$bm| H$m AZwnmV h¡
(A) 4:9
(B) 2:3
(C) 81 : 16
(D) 16 : 81
.430/4/3 4

2. A dice is thrown once. The probability of getting an odd number is
(A) 1
1
(B)
2
4
(C)
6
2
(D)
6
3. The value of k for which the equations 3x – y + 8 = 0 and 6x + ky = – 16
represent coincident lines, is
1
(A) –
2
1
(B)
2
(C) 2
(D) –2
4. If sin A = cos A, 0  A  90, then the angle A is equal to
(A) 30
(B) 60
(C) 0
(D) 45
5. Total surface area of a solid hemisphere is
(A) 3r2
(B) 2r2
(C) 4r2
2 3
(D) r
3
6. The second term from the end of the A.P. 5, 8, 11, ..., 47 is
(A) 50
(B) 45
(C) 44
(D) 41
7. Sides of two similar triangles are in the ratio 4 : 9. Areas of these
triangles are in the ratio
(A) 4:9
(B) 2:3
(C) 81 : 16
(D) 16 : 81
.430/4/3 5 P.T.O.

8. {X`m J`m h¡ HCF (156, 78) = 78 h¡, Vmo LCM (156, 78) H$m _mZ h¡
(A) 156
(B) 78
(C) 156  78
(D) 156  2

9. {ÛKmV g_rH$aU 2x2 – 4x + 3 = 0 H$m {d{dº$H$a (discriminant) h¡
(A) –8
(B) 10
(C) 8
(D) 2 2
AWdm
{ÛKmV g_rH$aU 2x2 – 4x + 3 = 0 Ho$ _yb h¢
(A) dmñV{dH$ VWm ~am~a
(B) dmñV{dH$ VWm {^Þ
(C) dmñV{dH$ Zht
(D) dmñV{dH$
10. q~XþAm| (– 1, – 3) VWm (5, – 2) Ho$ ~rM H$s Xÿar h¡
(A) 61 BH$mB©
(B) 37 BH$mB©
(C) 5 BH$mB©
(D) 17 BH$mB©

àíZ g§»`m 11 go 15 _| [aº$ ñWmZ ^[aE &
11. {H$gr ~mø q~Xþ go d¥Îm na ItMr JB© ñne©-aoImAm| H$s bå~mB`m± __________ hmoVr h¢ &
12. {ÛKmV ~hþnX t2 – 16 Ho$ eyÝ`H$m| H$m `moJ\$b _________ h¡ &
13. q~XþAm| (– a, a) VWm (– a, – a) Ho$ ~rM H$s Xÿar __________ h¡ &
14. g_rH$aU x2 + bx + c = 0 Ho$ _yb ~am~a h¢, `{X ___________ h¡ &
15. 100 àojUm| dmbo EH$ ~§Q>Z Ho$ ‘go H$_ àH$ma’ H$m VmoaU VWm ‘go A{YH$ àH$ma’ H$m VmoaU
q~Xþ (58, 50) na à{VÀN>oX H$aVo h¢ & Bg ~§Q>Z H$m _mÜ`H$ __________ h¡ &
.430/4/3 6

8. Given that HCF (156, 78) = 78, LCM (156, 78) is
(A) 156
(B) 78
(C) 156  78
(D) 156  2

9. The discriminant of the quadratic equation 2x2 – 4x + 3 = 0 is
(A) –8
(B) 10
(C) 8
(D) 2 2
OR
Roots of the quadratic equation 2x2 – 4x + 3 = 0 are
(A) real and equal
(B) real and distinct
(C) not real
(D) real
10. The distance between the points (– 1, – 3) and (5, – 2) is
(A) 61 units
(B) 37 units
(C) 5 units
(D) 17 units

Fill in the blanks in question numbers 11 to 15.
11. The lengths of the tangents drawn from an external point to a circle are
___________ .
12. In the quadratic polynomial t2 – 16, sum of the zeroes is __________ .
13. The distance between the points (– a, a) and (– a, – a) is ___________ .
14. The roots of the equation, x2 + bx + c = 0 are equal if __________ .
15. For a given distribution with 100 observations, the ‘less than’ ogive and
‘more than’ ogive intersect at (58, 50). The median of the distribution is
___________ .
.430/4/3 7 P.T.O.

àíZ g§»`m 16 go 20 _| {ZåZ{b{IV Ho$ CÎma Xr{OE :
16. x-Aj na Cg q~Xþ Ho$ {ZX}em§H$ kmV H$s{OE Omo q~XþAm| (2, 3) VWm (5, – 6) H$mo Omo‹S>Zo
dmbo aoImIÊS>> H$mo 1 : 2 Ho$ AZwnmV _| {d^m{OV H$aVm h¡ &
17. ^y{_ Ho$ EH$ q~Xþ C go, Omo _rZma Ho$ nmX-q~Xþ go 60 _r. H$s Xÿar na h¡, _rZma AB Ho$
{eIa H$m CÞ`Z H$moU 30 h¡, O¡go {H$ AmH¥${V-2 _| {XIm`m J`m h¡ & _rZma H$s D±$MmB©
kmV H$s{OE &

AmH¥${V-2
18. g_m§Va loT>r 7, 4, 1, – 2, ... H$m 26dm± nX {b{IE &
19. AmH¥${V-3 _|, Ho$ÝÐ O dmbo d¥Îm na EH$ ñne©-aoIm PT ItMr JB© h¡ & `{X
 POT = 75 hmo, Vmo  OTP H$m _mZ kmV H$s{OE &

AmH¥${V-3
20. `{X cosec  = 5 h¡, Vmo cot  H$m _mZ kmV H$s{OE &
4
AWdm
sin 42 – cos 48 H$m _mZ kmV H$s{OE &
IÊS> I$
àíZ g§»`m 21 go 26 VH$ àË`oH$ àíZ 2 A§H$m| H$m h¡ &
21. `{X tan 2A = cot (A – 18) h¡, Ohm± 2A VWm (A – 18) XmoZm| Ý`yZ H$moU h¢, Vmo A H$m
_mZ kmV H$s{OE &
.430/4/3 8

Answer the following question numbers 16 to 20 :

16. Find the coordinates of the point on x-axis which divides the line segment
joining the points (2, 3) and (5, – 6) in the ratio 1 : 2.

17. The angle of elevation of the top of the tower AB from a point C on the
ground, which is 60 m away from the foot of the tower, is 30, as shown in
Figure-2. Find the height of the tower.

Figure-2

18. Write the 26th term of the A.P. 7, 4, 1, – 2, ... .

19. In Figure-3, PT is tangent to a circle centred at O. Find the value of
 OTP if  POT = 75.

Figure-3

5
20. If cosec  = , find the value of cot .
4
OR
Find the value of sin 42 – cos 48.
SECTION B
Question numbers 21 to 26 carry 2 marks each.
21. If tan 2A = cot (A – 18) where 2A and (A – 18), both are acute angles,
find the value of A.
.430/4/3 9 P.T.O.

22. {ZåZ{b{IV gmaUr EH$ df© _| AñnVmb _| ^Vu hmoZo dmbo amo{J`m| H$s Am`w Xem©Vr h¡ :
Am`w (dfm] _|) : 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65
amo{J`m| H$s g§»`m : 60 110 210 230 150 50

Bg ~§Q>Z H$m ~hþbH$ kmV H$s{OE &
23. {X`m J`m h¡ {H$ Xmo g§»`mAm| H$m _.g. (HCF) 11 VWm CZH$m b.g. (LCM) 693 h¡ &
`{X EH$ g§»`m 77 hmo, Vmo Xÿgar g§»`m kmV H$s{OE &
24. 32 go_r D±$Mr Am¡a AmYma {ÌÁ`m 14 go_r dmbr EH$ ~obZmH$ma ~mëQ>r aoV> go nyar Vah ^ar
hþB© h¡ & aoV H$m Am`VZ kmV H$s{OE & ( = 22 à`moJ H$s{OE)
7
25. AmH¥${V-4 _|,  ABC VWm  XYZ Xem©E JE h¢ & `{X AB = 3.8 go_r,
AC = 3 3 go_r, BC = 6 go_r, XY = 6 3 go_r, XZ = 7.6 go_r, YZ = 12 go_r
VWm  A = 65,  B = 70 hmo, Vmo  Y H$m _mZ kmV H$s{OE &

3 3 go_r 6 3 go_r

AmH¥${V-4
AWdm
`{X Xmo g_ê$n {Ì^wOm| Ho$ joÌ\$b ~am~a hm|, Vmo Xem©BE {H$ `o {Ì^wO gdmªJg_ hmoVo h¢ &
26. Xmo A§H$m| dmbr {H$VZr g§»`mE± 6 go {d^mÁ` h¢ ?
AWdm
EH$ g_m§Va loT>r _| `h {X`m J`m h¡ {H$ gmd© A§Va 5 h¡ VWm BgHo$ àW_ Xg nXm| H$m
`moJ\$b 75 h¡ & g_m§Va loT>r H$m àW_ nX kmV H$s{OE &
IÊS> J$
àíZ g§»`m 27 go 34 VH$ àË`oH$ àíZ 3 A§H$m| H$m h¡ &
27. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© Vme H$s EH$ JÈ>r _| go EH$ nÎmm `mÑÀN>`m {ZH$mbm
OmVm h¡ & {ZåZ{b{IV H$mo àmá H$aZo H$s àm{`H$Vm kmV H$s{OE :
(i) bmb a§J H$m ~mXemh
(ii) BªQ> H$s ~oJ_
(iii) EH$ B¸$m
AWdm
.430/4/3 10

22. The following table shows the ages of the patients admitted in a hospital
during a year :
Age (in years) : 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65
Number of
60 110 210 230 150 50
patients :
Find the mode of the distribution.
23. Given that the HCF of two numbers is 11 and their LCM is 693. If one of
the numbers is 77, then find the other number.
24. A cylindrical bucket, 32 cm high and with radius of base 14 cm, is filled
22
completely with sand. Find the volume of the sand. (Use  = )
7
25. In Figure-4,  ABC and  XYZ are shown. If AB = 3.8 cm, AC = 3 3 cm,
BC = 6 cm, XY = 6 3 cm, XZ = 7.6 cm, YZ = 12 cm and  A = 65,
 B = 70, then find the value of  Y.

3 3 cm 6 3 cm

Figure-4
OR
If the areas of two similar triangles are equal, show that they are
congruent.
26. How many two-digit numbers are divisible by 6 ?
OR
In an A.P. it is given that common difference is 5 and sum of its first ten
terms is 75. Find the first term of the A.P.
SECTION C
Question numbers 27 to 34 carry 3 marks each.
27. One card is drawn from a well-shuffled deck of 52 cards. Find the
probability of getting
(i) a king of red colour.
(ii) the queen of diamonds.
(iii) an ace.
OR
.430/4/3 11 P.T.O.

EH$ ~m°Šg _| 90 {S>ñH$ (discs) h¢ {OZ na 1 go 90 VH$ H$s g§»`mE± A§{H$V h¢ & `{X Bg
~m°Šg go EH$ {S>ñH$ `mÑÀN>`m {ZH$mbr OmVr h¡, Vmo BgH$s àm{`H$Vm kmV H$s{OE {H$ Bg
{S>ñH$ na A§{H$V hmoJr
(i) Xmo A§H$m| H$s EH$ g§»`m &
(ii) EH$ nyU© dJ© g§»`m &
(iii) 15 go N>moQ>r EH$ A^mÁ` g§»`m &
28. gr_m Ho$ nmg EH$ 10 _r.  10 _r. gmBO H$m {H$MZ JmS>©Z h¡, Omo CgH$s agmoB© Ho$ gmW
gQ>m hþAm h¡ & dh Cg 10  10 Ho$ {J«S> _| Hw$N> Eogr gpãµO`m± VWm O‹S>r-~y{Q>`m± CJmZm
MmhVr h¡ Omo CgH$s agmoB© _| amoO à`moJ hmoVr h¢ & dh Cg_| {_Å>r VWm ImX S>mbH$a Cg_|
q~Xþ A na har {_M© H$m nm¡Ym, B na EH$ Y{ZE H$m nm¡Ym VWm C na EH$ Q>_mQ>a H$m nm¡Ym
bJmVr h¡ &
CgH$s ghobr Hw$gw_ CgHo$ JmS>©Z _| AmVr h¡ VWm dhm± CJmE JE nm¡Ym| H$s gamhZm H$aVr h¡ &
dh H$hVr h¡ {H$ em`X `h nm¡Yo EH$ hr aoIm _| h¢ & ZrMo {XE JE {MÌ H$mo Ü`mZ go n‹T>H$a
{ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :

.430/4/3 12

A box contains 90 discs which are numbered from 1 to 90. If one disc is
drawn at random from the box, find the probability that it bears
(i) a two-digit number.
(ii) a perfect square number.
(iii) a prime number less than 15.
28. Seema has a 10 m  10 m kitchen garden attached to her kitchen. She
divides it into a 10  10 grid and wants to grow some vegetables and
herbs used in the kitchen. She puts some soil and manure in that and
sows a green chilly plant at A, a coriander plant at B and a tomato plant
at C.
Her friend Kusum visited the garden and praised the plants grown there.
She pointed out that they seem to be in a straight line. See the below
diagram carefully and answer the following questions :

.430/4/3 13 P.T.O.

(i) 10  10 {J«S> H$mo {ZX}em§H$ Aj boVo hþE, q~XþAm| A, B VWm C Ho$ {ZX}em§H$ kmV
H$s{OE &
(ii) Xÿar gyÌ `m {H$gr AÝ` gyÌ go Om±M H$aHo$ kmV H$s{OE {H$ Š`m `h q~Xþ ñ§maoIr
h¢ >&

29. 4 go_r {ÌÁ`m H$m EH$ d¥Îm It{ME & Ho$ÝÐ go 8 go_r H$s Xÿar na EH$ q~Xþ P A§{H$V
H$s{OE VWm q~Xþ P go d¥Îm na ñne©-aoIm `w½_ H$s aMZm H$s{OE &

30. {gÕ H$s{OE {H$ 3 EH$ An[a_o` g§»`m h¡ &

31. AmH¥${V-5 _|, 10 go_r {ÌÁ`m dmbo d¥Îm H$s EH$ Ordm AB Ho$ÝÐ na g_H$moU ~ZmVr h¡ &

AmH¥${V-5
kmV H$s{OE
(i) {ÌÁ`I§S> (sector) OAPB H$m joÌ\$b
(ii) bKw d¥ÎmI§S> APB H$m joÌ\$b ( = 3.14 à`moJ H$s{OE)

32. 5 n|{gbm| VWm 7 noZm| H$m Hw$b _yë` < 250 h¡ O~{H$ 7 n|{gbm| VWm 5 noZm| H$m Hw$b
_yë` < 302 h¡ & EH$ n|{gb VWm EH$ noZ H$m _yë` kmV H$s{OE &
AWdm
{ZåZ{b{IV g_rH$aU `w½_ H$mo dO«-JwUZ {d{Y go hb H$s{OE :
x – 3y – 7 = 0
3x – 5y – 15 = 0

33. {gÕ H$s{OE {H$ :
1 – cos 
(cosec  – cot )2 =
1  cos 

.430/4/3 14

(i) Write the coordinates of the points A, B and C taking the 10  10
grid as coordinate axes.
(ii) By distance formula or some other formula, check whether the
points are collinear.

29. Draw a circle of radius 4 cm. Take a point P at a distance of 8 cm from
the centre and construct a pair of tangents from point P to the circle.

30. Prove that 3 is an irrational number.

31. In Figure-5, a chord AB of a circle of radius 10 cm subtends a right angle
at the centre.

Figure-5
Find
(i) Area of sector OAPB
(ii) Area of minor segment APB. (Use  = 3.14)

32. 5 pencils and 7 pens together cost < 250 whereas 7 pencils and 5 pens
together cost < 302. Find the cost of one pencil and that of a pen.

OR

Solve the following pair of equations using cross-multiplication method :
x – 3y – 7 = 0
3x – 5y – 15 = 0

33. Prove that :
1 – cos 
(cosec  – cot )2 =
1  cos 

.430/4/3 15 P.T.O.

34. AmH¥${V-6 _|, EH$ {Ì^wO ABC Ho$ AÝVJ©V EH$ d¥Îm Bg Vah ItMm J`m h¡ {H$ dh
^wOmAm| BC, CA VWm AB H$mo H«$_e… q~XþAm| P, Q VWm R na ñne© H$aVm h¡ & `{X
AB = 10 go_r, AQ = 7 go_r, CQ = 5 go_r hmo, Vmo BC H$s bå~mB© kmV H$s{OE &

AmH¥${V-6
AWdm
AmH¥${V-7 _|, Ho$ÝÐ O dmbo EH$ d¥Îm na ~mø q~Xþ T go Xmo ñne©-aoImE± TP VWm TQ ItMr
JB© h¢ & {gÕ H$s{OE {H$  PTQ = 2  OPQ &

AmH¥${V-7
IÊS> K$
àíZ g§»`m 35 go 40 VH$ àË`oH$ àíZ 4 A§H$m| H$m h¡ &
35. EH$ ~mëQ>r e§Hw$ Ho {N>ÞH$ Ho$ AmH$ma H$s h¡ & Bg ~mëQ>r Ho$ {ZMbo VWm D$nar d¥ÎmmH$ma {gam|
H$s {ÌÁ`mE± H«$_e… 10 go_r VWm 20 go_r h¢ VWm BgH$s D±$MmB© 30 go_r h¡ & Bg ~mëQ>r
H$s Ym[aVm kmV H$s{OE & ( = 3.14 à`moJ H$s{OE)
AWdm
6 _r. Mm¡‹S>r Am¡a 1.5 _r. Jhar EH$ Zha _| nmZr 10 {H$_r/K§Q>m H$s Mmb go ~h ahm h¡ &
30 {_ZQ> _|, `h Zha {H$VZo joÌ\$b H$s qgMmB© H$a nmEJr `{X qgMmB© Ho$ {bE 4 go_r
Jhao nmZr H$s Amdí`H$Vm hmoVr hmo ?

.430/4/3 16

34. In Figure-6, a circle is inscribed in a  ABC touching BC, CA and AB at
P, Q and R respectively. If AB = 10 cm, AQ = 7 cm, CQ = 5 cm, find the
length of BC.

Figure-6

OR
In Figure-7, two tangents TP and TQ are drawn to a circle with centre O
from an external point T. Prove that  PTQ = 2  OPQ.

Figure-7

SECTION D
Question numbers 35 to 40 carry 4 marks each.

35. A bucket is in the form of a frustum of a cone of height 30 cm with the
radii of its lower and upper circular ends as 10 cm and 20 cm
respectively. Find the capacity of the bucket. (Use  = 3.14)
OR
Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of
10 km/hr. How much area will it irrigate in 30 minutes if 4 cm of
standing water is needed ?

.430/4/3 17 P.T.O.

36. {ZåZ{b{IV ~§Q>Z Ho$ {bE, ‘go H$_ àH$ma’ H$m VmoaU It{ME :
dJ© : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70

~ma§~maVm : 8 5 7 14 18 6 2

37. EH$ aobJm‹S>r EH$g_mZ Mmb go 360 {H$_r H$s Xÿar V` H$aVr h¡ & `{X `h Mmb
5 {H$_r/K§Q>m A{YH$ hmoVr, Vmo dh Cgr `mÌm _| 1 K§Q>m H$_ g_` boVr & aobJm‹S>r H$s _yb
Mmb kmV H$s{OE &
AWdm
Xmo dJm] Ho$ joÌ\$bm| H$m `moJ\$b 468 dJ© _r. h¡ & `{X CZHo$ n[a_mnm| H$m A§Va 24 _r.
hmo, Vmo XmoZm| dJm] H$s ^wOmE± kmV H$s{OE &
38. ~hþnX – x3 + 3x2 – 3x + 5 H$mo ~hþnX x2 + x – 1 go {d^m{OV H$s{OE VWm {d^mOZ
EoëJmo[aÏ_ H$s gË`Vm H$s Om±M H$s{OE &
AWdm
~hþnX p(x) = 2x4 – 3x3 – 3x2 + 6x – 2 Ho$ AÝ` eyÝ`H$m| H$mo kmV H$s{OE `{X BgHo$ Xmo
eyÝ`H$ 2 VWm – 2 kmV h¢ &
39. EH$ noS>ñQ>b Ho$ {eIa na 3.6 _r. D±$Mr _y{V© bJr h¡ & ^y{_ Ho$ EH$ q~Xþ go _y{V© Ho$ {eIa
H$m CÞ`Z H$moU 60 h¡ Am¡a Cgr q~Xþ go noS>ñQ>b Ho$ {eIa H$m CÞ`Z H$moU 45 h¡ &
noS>ñQ>b H$s D±$MmB© kmV H$s{OE &
40. {gÕ H$s{OE {H$ {H$gr g_H$moU {Ì^wO _| H$U© H$m dJ©, AÝ` Xmo ^wOmAm| Ho$ dJm] Ho$
`moJ\$b Ho$ ~am~a hmoVm h¡ &

.430/4/3 18

36. Draw a ‘less than’ ogive for the following distribution :
Class : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70

Frequency : 8 5 7 14 18 6 2

37. A train travels 360 km at a uniform speed. If the speed had been 5 km/hr
more, it would have taken 1 hour less for the same journey. Find the
original speed of the train.
OR
Sum of the areas of two squares is 468 m2. If the difference of their
parameters is 24 m, find the sides of two squares.
38. Divide polynomial – x3 + 3x2 – 3x + 5 by the polynomial x2 + x – 1 and
verify the division algorithm.
OR
Find other zeroes of the polynomial
p(x) = 2x4 – 3x3 – 3x2 + 6x – 2
if two of its zeroes are 2 and – 2.

39. A statue 3.6 m tall, stands on top of a pedestal. From a point on the
ground, the angle of elevation of the top of the statue is 60 and from the
same point, the angle of elevation of the top of the pedestal is 45. Find
the height of the pedestal.

40. In a right-angled triangle, prove that the square of the hypotenuse is
equal to the sum of the squares of the remaining two sides.

.430/4/3 19 P.T.O.