CBSE Class 10 Mathematics Theory (Std) Question Paper 2020 Set 30-4-3

H$moS> Z§.
Code No. 30/4/3
amob Z§. narjmWu H$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> 23 h¢ & paper contains 23 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 (‘mZH$) – g¡ÕmpÝVH$
MATHEMATICS (STANDARD) – Theory

{ZYm©[aV g_` : 3 KÊQ>o A{YH$V_ A§H$ : 80
Time allowed : 3 hours Maximum Marks : 80
.30/4/3 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$s{OE :
(i) `h àíZ-nÌ Mma IÊS>m| _| {d^m{OV {H$`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| _| VWm 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$m h¡ &
àíZ g§»`m 1 go 10 VH$ ~hþ{dH$ënr` àíZ h¢ &
ghr {dH$ën Mw{ZE &
1. EH$ ~§Q>Z H$m ‘mܶ VWm ‘mܶH$ H«$‘e… 14 VWm 15 h¢ & AV… ~hþbH$ H$m ‘mZ hmoJm
(A) 16
(B) 17
(C) 18
(D) 13

2. {ÛKmV g‘rH$aU x2 – 4x + k = 0 Ho$ Xmo {^Þ dmñV{dH$ ‘yb hm|Jo ¶{X
(A) k=4
(B) k>4
(C) k = 16
(D) k<4

.30/4/3 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.
Question numbers 1 to 10 are multiple choice questions.
Choose the correct option.

1. The mean and median of a distribution are 14 and 15 respectively. The
value of mode is
(A) 16
(B) 17
(C) 18
(D) 13

2. The quadratic equation x2 – 4x + k = 0 has distinct real roots if
(A) k=4
(B) k>4
(C) k = 16
(D) k<4
.30/4/3 3 P.T.O.

3. EH$ g‘m§Va loT>r H$m àW‘ nX 5 h¡ VWm A§{V‘ nX 45 h¡ & ¶{X g^r nXm| H$m ¶moJ\$b
400 hmo, Vmo nXm| H$s g§»¶m h¡
(A) 20
(B) 8
(C) 10
(D) 16
AWdm
EH$ g‘m§Va loT>r – 15, – 11, – 7, ..., 49 H$m 9dm± nX h¡
(A) 32
(B) 0
(C) 17
(D) 13

4. q~Xþ A(– 5, 2) VWm q~Xþ B(4, 6) H$mo Omo‹S>Zo dmbo aoImI§S> H$m ‘ܶ-q~Xþ P  a , 4  h¡ &
8 
‘a’ H$m ‘mZ h¡
(A) –4
(B) 4
(C) –8
(D) –2

5. ~hþnX p(x), {OgH$m J«m’$ AmH¥${V-1 ‘| {X¶m J¶m h¡, Ho$ eyݶH$m| H$s g§»¶m h¡
(A) 4
(B) 3
(C) 5
(D) 1

AmH¥${V-1
.30/4/3 4

3. The first term of an A.P. is 5 and the last term is 45. If the sum of all the
terms is 400, the number of terms is
(A) 20
(B) 8
(C) 10
(D) 16
OR
The 9th term of the A.P. – 15, – 11, – 7, ...., 49 is
(A) 32
(B) 0
(C) 17
(D) 13

a 
4. Point P  , 4  is the mid-point of the line segment joining the points
8 
A(– 5, 2) and B(4, 6). The value of ‘a’ is
(A) –4
(B) 4
(C) –8
(D) –2

5. The number of zeroes for a polynomial p(x) whose graph is given in
Figure-1, is
(A) 4
(B) 3
(C) 5
(D) 1

Figure-1

.30/4/3 5 P.T.O.

6. {X¶m J¶m h¡ {H$ q~Xþ A(1, 2), B(0, 0) VWm C(a, b) ñ§maoIr h¢ & {ZåZ{b{IV g§~§Ym| ‘| go
a VWm b Ho$ ~rM H$m H$m¡Z-gm g§~§Y ghr h¡ ?
(A) a = 2b
(B) 2a = b
(C) a+b=0
(D) a–b=0

7.  H$m Eogm ‘mZ {OgHo$ {bE sin (44 + ) = cos 30 h¡, hmoJm

(A) 46
(B) 60
(C) 16
(D) 90

8. a¡{IH$ g‘rH$aUm| y = 0 VWm y = – 6 Ho$ ¶w½‘ H$m EH$
(A) A{ÛVr¶ hb h¡
(B) H$moB© hb Zht h¡
(C) AZoH$ hb h¢
(D) {g’©$ EH$ hb (0, 0) h¡

9. EH$ W¡bo ‘| 3 bmb, 5 H$mbr VWm 7 g’o$X J|X| h¢ & Bg W¡bo ‘| go EH$ J|X H$mo ¶mÑÀN>¶m
{ZH$mbm OmVm h¡ & {ZH$mbr JB© J|X H$mbr Zht h¡, BgH$s àm{¶H$Vm h¡
1
(A)
3
9
(B)
15
5
(C)
10
2
(D)
3

.30/4/3 6

6. It is being given that the points A(1, 2), B(0, 0) and C(a, b) are collinear.
Which of the following relations between a and b is true ?
(A) a = 2b
(B) 2a = b
(C) a+b=0
(D) a–b=0

7. The value of  for which sin (44 + ) = cos 30, is

(A) 46

(B) 60

(C) 16

(D) 90

8. The pair of linear equations y = 0 and y = – 6 has
(A) a unique solution
(B) no solution
(C) infinitely many solutions
(D) only solution (0, 0)

9. A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the
bag at random. The probability that the ball drawn is not black, is
1
(A)
3
9
(B)
15
5
(C)
10
2
(D)
3

.30/4/3 7 P.T.O.

10. AmH¥${V-2 ‘|, ¶{X TP, TQ Ho$ÝÐ O dmbo {H$gr d¥Îm na ItMr JB© Xmo ñne©-aoImE± Bg àH$ma
h¢ {H$  POQ = 115 h¡, Vmo  PTQ ~am~a h¡
(A) 115
(B) 57·5
(C) 55
(D) 65

AmH¥${V-2
AWdm
EH$ d¥Îm na {H$gr ~mø q~Xþ Q go ItMr JB© ñne©-aoIm H$s bå~mB© 5 go‘r h¡ VWm q~Xþ Q
H$s d¥Îm Ho$ Ho$ÝÐ go Xÿar 8 go‘r h¡ & d¥Îm H$s {ÌÁ¶m h¡
(A) 39 go‘r
(B) 3 go‘r
(C) 39 go‘r
(D) 7 go‘r
àíZ g§»`m 11 go 15 _| [aº$ ñWmZ ^[aE &
11. q~XþAm| (a, b) VWm (– a, – b) Ho$ ~rM H$s Xÿar _________ h¡ &
12. {ÌÁ¶m 8 go‘r dmbr YmVw H$s EH$ JmobmH$ma J|X H$mo {nKbmH$a 8 g‘mZ AmH$ma H$s N>moQ>r J|X|
~ZmB© JB© h¢ & àË`oH$ ZB© J|X H$s {ÌÁ¶m ___________ go‘r h¡ &
2  5
13.  
 3  EH$ _________ g§»¶m h¡ &
 
14. _mZ br{OE {H$  ABC   DEF VWm BZ {Ì^wOm| Ho$ joÌ’$b H«$‘e… 81 go‘r2 VWm
144 go‘r2 h¢ & ¶{X EF = 24 go_r h¡, Vmo ^wOm BC H$s bå~mB© _________ go_r hmoJr &

15. ¶{X tan A = 1 h¡, Vmo 2 sin A cos A = _________ .
.30/4/3 8

10. In Figure-2, TP and TQ are tangents drawn to the circle with centre at O.
If  POQ = 115 then  PTQ is
(A) 115
(B) 57·5
(C) 55
(D) 65

Figure-2
OR
From an external point Q, the length of the tangent to a circle is 5 cm and
the distance of Q from the centre is 8 cm. The radius of the circle is

(A) 39 cm

(B) 3 cm

(C) 39 cm

(D) 7 cm

Fill in the blanks in question numbers 11 to 15.
11. The distance between the points (a, b) and (– a, – b) is _________ .

12. A spherical metal ball of radius 8 cm is melted to make 8 smaller
identical balls. The radius of each new ball is _________ cm.

2  5
13.  
 3  is _________ number.
 

14. Let  ABC   DEF and their areas be respectively 81 cm 2 and 144 cm2.
If EF = 24 cm, then length of side BC is _________ cm.

15. If tan A =1, then 2 sin A cos A = _________ .

.30/4/3 9 P.T.O.

àíZ g§»`m 16 go 20 _| {ZåZ{b{IV Ho$ CÎma Xr{OE >&
229
16. {H$VZo Xe‘bd ñWmZm| Ho$ ~mX n[a‘o¶ g§»¶m H$m Xe‘bd {Zê$nU gm§V hmoJm ?
2  57
2

17. AmH¥${V-3 ‘|, AB VWm CD CZ Xmo d¥Îmm| H$s C^¶{ZîR> ñne©-aoImE± h¢ Omo EH$-Xÿgao H$mo q~Xþ
D na ñne© H$aVo h¢ & ¶{X AB = 8 go_r hmo, Vmo CD H$s bå~mB© kmV H$s{OE &

AmH¥${V-3
18. {X¶m J¶m h¡ {H$ _.g. (HCF) (135, 225) = 45, Vmo b.g. (LCM) (135, 225) kmV
H$s{OE &
19. AmH¥${V-4 ‘|, AÀN>r Vah go VZr hþB© EH$ 20 ‘r. bå~r añgr, ^y{‘ na grYo bJo I§^o Ho$
{eIa go ~§Yr h¡ & ¶{X ^y{‘ ñVa Ho$ gmW añgr Ûmam ~Zm¶m J¶m H$moU 30 H$m hmo, Vmo I§^o
H$s D±$MmB© kmV H$s{OE &

AmH¥${V-4
20. Xmo nmgm| H$mo EH$ gmW ’|$H$m OmVm h¡ & BgH$s ³¶m àm{¶H$Vm h¡ {H$ XmoZm| nmgm| na AmZo
dmbr g§»¶mAm| H$m JwUZ’$b 1 hmo ?
.30/4/3 10

Answer the following question numbers 16 to 20.

16. After how many decimal places will the decimal representation of the
229
rational number terminate ?
2  57
2

17. In Figure-3, AB and CD are common tangents to circles which touch each
other at D. If AB = 8 cm, then find the length of CD.

Figure-3

18. Given that HCF (135, 225) = 45, find the LCM (135, 225).

19. In Figure-4, a tightly stretched rope of length 20 m is tied from the top of
a vertical pole to the ground. Find the height of the pole if the angle made
by the rope with the ground is 30.

Figure-4

20. Two dice are thrown simultaneously. What is the probability that the
product of the numbers appearing on the top is 1 ?

.30/4/3 11 P.T.O.

IÊS> I$
àíZ g§»`m 21 go 26 VH$ àË`oH$ àíZ 2 A§H$m| H$m h¡ &

21. {ZåZ{b{IV ~§Q>Z H$m ~hþbH$ kmV H$s{OE :
dJ© : 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100

~ma§~maVm : 10 8 12 16 4

AWdm
{ZåZ{b{IV ~§Q>Z go ‘mܶH$ kmV H$s{OE :
dJ© : 500 – 600 600 – 700 700 – 800 800 – 900 900 – 1000

~ma§~maVm : 36 32 32 20 30

22. AmH¥${V-5 _|, H$moB© V§~y EH$ ~obZ Ho$ AmH$ma H$m h¡ {Og na EH$ e§Hw$ Aܶmamo{nV h¡ &
~obZmH$ma ^mJ H$s D±$MmB© 2·1 ‘r. VWm e§ŠdmH$ma ^mJ H$s {V¶©H$ D±$MmB© 2·8 ‘r. h¡ & XmoZm|
^mJm| H$s EH$g‘mZ {ÌÁ¶m 2 ‘r. h¡ & Bg V§~y H$mo ~ZmZo ‘| à¶w³V H¡$Zdg (canvas) H$m
joÌ’$b kmV H$s{OE & ( = 22 à`moJ H$s{OE)
7

AmH¥${V-5

23. x Ho$ {bE hb H$s{OE :
14x2 + 17x – 6 = 0

.30/4/3 12

SECTION B

Question numbers 21 to 26 carry 2 marks each.

21. Find the mode of the following distribution :

Classes : 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100

Frequency : 10 8 12 16 4

OR

From the following distribution, find the median :

Classes : 500 – 600 600 – 700 700 – 800 800 – 900 900 – 1000

Frequency : 36 32 32 20 30

22. In Figure-5, a tent is in the shape of a cylinder surmounted by a conical
top. The cylindrical part is 2·1 m high and conical part has slant height
2·8 m. Both the parts have same radius 2 m. Find the area of the canvas
22
used to make the tent. (Use  = )
7

Figure-5

23. Solve for x :

14x2 + 17x – 6 = 0

.30/4/3 13 P.T.O.

24. Xmo g‘ê$n {Ì^wOm| Ho$ n[a‘mn H«$‘e… 30 go_r VWm 20 go_r h¢ & ¶{X EH$ {Ì^wO H$s EH$
^wOm 9 go_r b§~r h¡, Vmo Xÿgao {Ì^wO H$s g§JV ^wOm H$s b§~mB© kmV H$s{OE &
AWdm
AmH¥${V-6 _|, PQR EH$ g‘H$moU {Ì^wO h¡ {OgH$m H$moU P g‘H$moU h¡ & QR na q~Xþ M
Bg àH$ma pñWV h¡ {H$ PM  QR h¡ & Xem©BE {H$ PQ2 = QM  QR.

AmH¥${V-6
25. no‹S> bJmZo H$m A{^¶mZ
EH$ J«wn hmD$qgJ gmogmBQ>r Ho$ 600 gXñ¶ h¢ {OZHo$ Ka H¢$ng ‘| h¢ VWm CÝhm|Zo Zd df© Ho$
Adga na no‹S> bJmZo H$m A{^`mZ {ZíM¶ {H$¶m & à˶oH$ Ka H$mo BÀN>mZwgma EH$ nm¡Ym
bJmZo H$mo {X¶m J`m & {d{^Þ àH$ma Ho$ nm¡Yo, Omo bJmE JE Wo, dh h¢
(i) Zr‘ – 125
(ii) nrnb – 165
(iii) H«$sna – 50
(iv) ’$bm| Ho$ nm¡Yo – 150
(v) ’y$bm| Ho$ nm¡Yo – 110
CX²KmQ>Z-g_mamoh na, BZm‘ XoZo Ho$ {bE, `mÑÀN>`m EH$ nm¡Ym MwZm J¶m & Cn`w©³V AZwÀN>oX
H$mo n‹T>H$a {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :
MwZo JE nm¡Yo H$m {ZåZ{b{IV hmoZo H$s àm{¶H$Vm ³¶m h¡ ?
(i) ’$bm| H$m EH$ nm¡Ym AWdm ’y$bm| H$m EH$ nm¡Ym
(ii) Zr‘ H$m nm¡Ym AWdm nrnb H$m nm¡Ym
26. ‘mZ kmV H$s{OE :
2 sin 68 2 cot 15
  3 tan 40 tan 45 tan 50
cos 22 tan 75
.30/4/3 14

24. The perimeters of two similar triangles are 30 cm and 20 cm respectively.
If one side of the first triangle is 9 cm long, find the length of the
corresponding side of the second triangle.
OR
In Figure-6,  PQR is right-angled at P. M is a point on QR such that PM
is perpendicular to QR. Show that PQ2 = QM  QR.

Figure-6

25. Tree Plantation Drive
A Group Housing Society has 600 members, who have their houses in the
campus and decided to hold a Tree Plantation Drive on the occasion of
New Year. Each household was given the choice of planting a sampling of
its choice. The number of different types of saplings planted were :
(i) Neem – 125
(ii) Peepal – 165
(iii) Creepers – 50
(iv) Fruit plants – 150
(v) Flowering plants – 110
On the opening ceremony, one of the plants is selected randomly for a
prize. After reading the above passage, answer the following questions.
What is the probability that the selected plant is
(i) A fruit plant or a flowering plant ?
(ii) Either a Neem plant or a Peepal plant ?
26. Evaluate :
2 sin 68 2 cot 15
  3 tan 40 tan 45 tan 50
cos 22 tan 75

.30/4/3 15 P.T.O.

IÊS> J$
àíZ g§»`m 27 go 34 VH$ àË`oH$ àíZ 3 A§H$m| H$m h¡ &
27. {ZåZ{b{IV g‘rH$aU ¶w½‘ H$mo hb H$s{OE :
2 3 5 4
  11,  7
x y x y

AV… 5x – 3y H$m ‘mZ kmV H$s{OE &

AWdm

EH$ ZJa ‘| Q>¡³gr Ho$ ^m‹S>o ‘| EH$ {Z¶V ^m‹S>o Ho$ A{V[a³V Mbr JB© Xÿar na {Z^©a ^m‹S>m
gpå_{bV {H$¶m OmVm h¡ & 10 {H$‘r Xÿar Ho$ {bE ^m‹S>m < 75 h¡ VWm 15 {H$_r Xÿar Ho$ {bE
< 110 h¡ & {Z¶V ^m‹S>m VWm à{V {H$_r H$m ^m‹S>m ³¶m h¡ ? AV… 35 {H$‘r H$s Xÿar H$m
^m‹S>m kmV H$s{OE &

28. AmH¥${V-7 ‘|, O Ho$ÝÐ dmbo d¥Îm H$m ì¶mg AB h¡ VWm AC BgH$s EH$ Ordm h¡ &
 BAC = 30 h¡ & ¶{X q~Xþ C na ItMr JB© ñne©-aoIm, ~‹T>mE JE ì¶mg AB H$mo {~ÝXþ D
na à{VÀN>oX H$aVr h¡, Vmo Xem©BE {H$ BC = BD &

AmH¥${V-7

29. {gÕ H$s{OE {H$ :
sin   cos   1 1

cos   sin   1 sec   tan 

.30/4/3 16

SECTION C

Question numbers 27 to 34 carry 3 marks each.

27. Solve the pair of equations :

2 3 5 4
  11,  7
x y x y

Hence, find the value of 5x – 3y.

OR

Taxi charges in a city consist of fixed charges and the remaining charges
depend upon the distance travelled. For a journey of 10 km, the charge
paid is < 75 and for a journey of 15 km, the charge paid is < 110. Find
the fixed charge and charges per km. Hence, find the charge of covering a
distance of 35 km.

28. In Figure-7, AB is the diameter of a circle with centre O and AC is its
chord such that  BAC = 30. If the tangent drawn at C intersects
extended AB at D, then show that BC = BD.

Figure-7

29. Prove that :
sin   cos   1 1

cos   sin   1 sec   tan 

.30/4/3 17 P.T.O.

30. 5 go‘r, 6 go‘r VWm 7 go‘r ^wOmAm| dmbo EH$ {Ì^wO H$s aMZm H$s{OE & {’$a EH$ Aݶ

{Ì^wO H$s aMZm H$s{OE {OgH$s ^wOmE± nhbo dmbo {Ì^wO H$s g§JV ^wOmAm| H$s 2 JwZr
3
hm| &
AWdm
3 go‘r {ÌÁ¶m Ho$ EH$ d¥Îm na Eogr Xmo ñne©-aoImE± It{ME Omo nañna 60 Ho$ H$moU na PwH$s
hm| &

31. AmH¥${V-8 ‘| Xem©E AZwgma, N>m¶m§{H$V ^mJ H$m joÌ’$b kmV H$s{OE, Omo 7 go‘r {ÌÁ¶mAm|
dmbo Xmo d¥Îmm| Ho$ MVwWmªem| Ho$ ~rM C^¶{ZîR> h¡ &

AmH¥${V-8

32. {gÕ H$s{OE {H$ 5 EH$ An[a‘o¶ g§»¶m h¡ &

33. ¶{X {H$gr g‘m§Va loT>r Ho$ N>R>o nX H$m N>h JwZm BgHo$ Zm¡d| nX Ho$ Zm¡ JwZm Ho$ ~am~a hmo, Vmo
Xem©BE {H$ BgH$m 15dm± nX eyݶ h¡ &

34. q~XþAm| (3, – 1) VWm (6, 8) H$mo Omo‹S>Zo dmbo aoImI§S> H$mo g‘-{Ì^m{OV H$aZo dmbo q~XþAm|
Ho$ {ZX}em§H$ kmV H$s{OE &
AWdm
MVw^w©O ABCD H$m joÌ’$b kmV H$s{OE {OgHo$ erf©-q~Xþ A(1, 2), B(1, 0),
C(4, 0) VWm D(4, 4) na pñWV h¢ &

.30/4/3 18

30. Construct a triangle with sides 5 cm, 6 cm and 7 cm. Now construct
2
another triangle whose sides are times the corresponding sides of the
3
first triangle.

OR

Draw a pair of tangents to a circle of radius 3 cm which are inclined to
each other at an angle of 60.

31. Calculate the area of the shaded region common between two quadrants
of circles of radius 7 cm each (as shown in Figure-8).

Figure-8

32. Prove that 5 is an irrational number.

33. If 6 times the 6th term of an A.P. is equal to 9 times the 9th term, show
that its 15th term is zero.

34. Find the co-ordinates of the points of trisection of the line segment
joining the points (3, – 1) and (6, 8).

OR

Find the area of a quadrilateral ABCD having vertices at A(1, 2),
B(1, 0), C(4, 0) and D(4, 4).

.30/4/3 19 P.T.O.

IÊS> K$

àíZ g§»`m 35 go 40 VH$ àË`oH$ àíZ 4 A§H$m| H$m h¡ &

35. 7 ‘r. D±$Mo ^dZ Ho$ {eIa go EH$ Ho$~b Q>m°da Ho$ {eIa H$m CÞ¶Z H$moU 60 h¡ Am¡a BgHo$

nmX H$m AdZ‘Z H$moU 45 h¡ & Q>m°da H$s D±$MmB© kmV H$s{OE & ( 3 = 1·73 à`moJ
H$s{OE)

36. ~hþnX f(x) = 2x4 + 3x3 – 5x2 – 9x – 3 Ho$ Xmo eyݶH$ 3 VWm – 3 h¢ & Bg ~hþnX

Ho$ eof eyݶH$ kmV H$s{OE &
AWdm
eyݶH$m| H$s dmñV{dH$ JUZm {H$E {~Zm EH$ {ÛKmV ~hþnX ~ZmBE {OgHo$ eyݶH$ ~hþnX
5x2 + 2x – 3 Ho$ eyݶH$m| Ho$ ì¶wËH«$‘ hm| &

37. EH$ D$na go Iwbr ~mëQ>r Ho$ XmoZm| D$nar VWm {ZMbo d¥ÎmmH$ma {gam| H$s {ÌÁ¶mE± H«$_e…
40 go‘r Am¡a 20 go‘r h¢ VWm ~mëQ>r H$s JhamB© 21 go‘r h¡ & ~mëQ>r H$m Am¶VZ kmV

H$s{OE & gmW hr ~mëQ>r H$mo ~ZmZo ‘| à¶w³V YmVw ({Q>Z) H$s MmXa H$m joÌ’$b ^r kmV
H$s{OE & ( = 22 à`moJ H$s{OE)
7

38. 600 {H$‘r H$s hdmB© ¶mÌm ‘|, Iam~ ‘m¡g‘ H$s dOh go EH$ hdmB© OhmµO H$s Mmb H$‘ H$a

Xr JB© & `mÌm H$s Am¡gV Mmb H$mo 200 {H$‘r/K§Q>m H$s Xa go KQ>mZo Ho$ H$maU C‹S>mZ H$m
g‘¶ 30 {‘ZQ> ~‹T> J¶m & Ama§^ ‘| hdmB© OhmµO H$s Am¡gV Mmb kmV H$s{OE &
AWdm

Hw$N> ì¶{³V¶m| ‘| < 9,000 g‘mZ ê$n go ~m±Q>o JE & `{X 20 ì¶{³V Am¡a hmoVo, Vmo à˶oH$
H$mo < 160 H$‘ {‘bVo & Ama§^ ‘| Hw$b {H$VZo ì¶{³V Wo ?

.30/4/3 20

SECTION D

Question numbers 35 to 40 carry 4 marks each.

35. From the top of a 7 m building, the angle of elevation of the top of a cable
tower is 60 and the angle of depression of its foot is 45. Determine the
height of the tower. (Use 3 = 1·73)

36. Obtain other zeroes of the polynomial

f(x) = 2x4 + 3x3 – 5x2 – 9x – 3

if two of its zeroes are 3 and – 3.

OR

Without actually calculating the zeroes, form a quadratic polynomial
whose zeroes are reciprocals of the zeroes of the polynomial 5x2 + 2x – 3.

37. A bucket open at the top has top and bottom radii of circular ends as
40 cm and 20 cm respectively. Find the volume of the bucket if its depth
is 21 cm. Also find the area of the tin sheet required for making the
22
bucket. (Use  = )
7

38. In a flight of 600 km, the speed of the aircraft was slowed down due to
bad weather. The average speed of the trip was decreased by 200 km/hr
and thus the time of flight increased by 30 minutes. Find the average
speed of the aircraft originally.

OR

< 9,000 were divided equally among a certain number of persons. Had
there been 20 more persons, each would have got < 160 less. Find the
original number of persons.

.30/4/3 21 P.T.O.

39. {ZåZ{b{IV ~§Q>Z H$mo ‘go H$‘’ àH$ma Ho$ ~§Q>Z ‘| ~X{bE VWm BgH$m VmoaU It{ME & AV…
~§Q>Z H$m ‘mܶH$ kmV H$s{OE &
àmßVm§H$ N>mÌm| H$s g§»¶m
20 – 30 4

30 – 40 10

40 – 50 12

50 – 60 14

60 – 70 8

70 – 80 3

80 – 90 4

90 – 100 5

40. ¶{X {H$gr {Ì^wO H$s EH$ ^wOm Ho$ g‘m§Va Aݶ Xmo ^wOmAm| H$mo {^Þ-{^Þ q~XþAm| na
à{VÀN>oX H$aZo Ho$ {bE EH$ aoIm ItMr OmE, Vmo {gÕ H$s{OE {H$ ¶o Aݶ Xmo ^wOmE± EH$ hr
AZwnmV ‘| {d^m{OV hmo OmVr h¢ &
AWdm

EH$ g‘H$moU {Ì^wO ‘|, {gÕ H$s{OE {H$ H$U© H$m dJ© eof Xmo ^wOmAm| Ho$ dJm] Ho$ ¶moJ\$b
Ho$ ~am~a hmoVm h¡ &

.30/4/3 22

39. Change the following distribution into ‘less than’ type distribution and
draw its ogive. Hence find the median of the distribution.

Marks Number of Students

20 – 30 4

30 – 40 10

40 – 50 12

50 – 60 14

60 – 70 8

70 – 80 3

80 – 90 4

90 – 100 5

40. If a line is drawn parallel to one side of a triangle to intersect the other
two sides in distinct points, then prove that the other two sides are
divided in the same ratio.

OR

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

.30/4/3 23 P.T.O.