CBSE Class 10 Mathematics Basics Question Paper 2020 Set 430-5-3

H$moS> Z§.
Code No. 430/5/3
amob Z§. narjmWu H$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$db at 10.15 a.m. From 10.15 a.m. to
10.30 a.m., the students will read
àíZ-nÌ H$mo n‹T>|Jo Am¡a Bg Ad{Y Ho$ Xm¡amZ the question paper only and
do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo & will not 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

.430/5/3 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. `{X q~Xþ (3, – 6) q~XþAm| (0, 0) VWm (x, y) H$mo Omo‹S>Zo dmbo aoImI§S> H$m _Ü`-q~Xþ h¡, Vmo
q~Xþ (x, y) hmoJm
(A) (– 3, 6)
(B) (6, – 6)
(C) (6, – 12)
3
(D) ( , – 3)
2

.430/5/3 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. If (3, – 6) is the mid-point of the line segment joining (0, 0) and (x, y),
then the point (x, y) is
(A) (– 3, 6)
(B) (6, – 6)
(C) (6, – 12)
3
(D) ( , – 3)
2

.430/5/3 3 P.T.O.

2. AmH¥${V-1 _| {XE JE d¥Îm _|, ñne©-aoIm PQ Ho$ g_mÝVa ItMr OmZo dmbr ñne©-aoImAm| H$s
g§»`m h¡

AmH¥${V-1
(A) 0
(B) AZoH$
(C) 2
(D) 1

3. {ÛKmVr g_rH$aU 4x2 – 6x + 3 = 0 H$m {d{dº$H$a (discriminant) h¡
(A) 12
(B) 84
(C) 2 3
(D) – 12
4. {ZåZ{b{IV ~ma§~maVm ~§Q>Z Ho$ {bE :
dJ© : 0–5 5 – 10 10 – 15 15 – 20 20 – 25
~ma§~maVm : 8 10 19 25 8

_mÜ`H$ dJ© H$s Cƒ gr_m h¡
(A) 15
(B) 10
(C) 20
(D) 25
3
5. `{X cos A = , 0 < A < 90 h¡, Vmo A ~am~a h¡
2
3
(A)
2
(B) 30
(C) 60
(D) 1
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2. In the given circle in Figure-1, number of tangents parallel to tangent PQ is

Figure-1
(A) 0
(B) many
(C) 2
(D) 1
3. The discriminant of the quadratic equation 4x2 – 6x + 3 = 0 is
(A) 12
(B) 84
(C) 2 3
(D) – 12
4. For the following frequency distribution :
Class : 0–5 5 – 10 10 – 15 15 – 20 20 – 25
Frequency : 8 10 19 25 8
The upper limit of median class is
(A) 15
(B) 10
(C) 20
(D) 25
3
5. If cos A = , 0 < A < 90, then A is equal to
2
3
(A)
2
(B) 30
(C) 60
(D) 1

.430/5/3 5 P.T.O.

6. {H$gr Ag§^d KQ>Zm Ho$ hmoZo H$s àm{`H$Vm h¡
(A) 1
1
(B)
2
(C) n[a^m{fV Zht
(D) 0

7. `{X a¡{IH$ g_rH$aUm| H$m EH$ `w½_ g§JV h¡, Vmo {Zê${nV aoImE±
(A) g_mÝVa h¢
(B) à{VÀN>oXr `m g§nmVr h¢
(C) h_oem g§nmVr hmoVr h¢
(D) h_oem à{VÀN>oXr hmoVr h¢
8. q~XþAm| (3, – 2) VWm (– 3, 2) Ho$ ~rM H$s Xÿar h¡
(A) 52 BH$mB©
(B) 4 10 BH$mB©
(C) 2 10 BH$mB©
(D) 40 BH$mB©
9. g§»`m 180 H$mo A^mÁ` JwUZI§S>m| Ho$ JwUZ\$b Ho$ ê$n _| ì`º$ H$aZo na {ZåZ àmßV hmoVm h¡ :
(A) 10  2  32
(B) 25  4  3
(C) 22  32  5
(D) 495

10. e§Hw$ Ho$ {N>ÞH$ Ho$ AmH$ma Ho$ EH$ {Jbmg H$m gånyU© n¥ð>r` joÌ\$b h¡ (r1 > r2)
(A)  r1 l +  r2 l

(B)  l (r1 + r2) +  r22
1
(C) h ( r12 + r22 + r1r2)
3

(D) h 2  (r1 – r2 )2

àíZ g§»`m 11 go 15 _| [aº$ ñWmZ ^[aE &
11. `{X ~hþnX ax2 – 2x H$m EH$ eyÝ`H$ 2 h¡, Vmo ‘a’ H$m _mZ ___________ h¡ &
.430/5/3 6

6. The probability of an impossible event is
(A) 1
1
(B)
2
(C) not defined
(D) 0
7. If a pair of linear equations is consistent, then the lines represented by
them are
(A) parallel
(B) intersecting or coincident
(C) always coincident
(D) always intersecting

8. The distance between the points (3, – 2) and (– 3, 2) is
(A) 52 units
(B) 4 10 units
(C) 2 10 units
(D) 40 units
9. 180 can be expressed as a product of its prime factors as
(A) 10  2  32
(B) 25  4  3
(C) 22  32  5
(D) 495

10. The total surface area of a frustum-shaped glass tumbler is (r1 > r2)
(A)  r1 l +  r2 l

(B)  l (r1 + r2) +  r22
1
(C) h ( r12 + r22 + r1r2)
3

(D) h 2  (r1 – r2 )2

Fill in the blanks in question numbers 11 to 15.
11. If 2 is a zero of the polynomial ax2 – 2x, then the value of ‘a’ is ________ .

.430/5/3 7 P.T.O.

12. `{X Xmo Jmobm| H$s {ÌÁ`mAm| H$m AZwnmV 2 : 3 h¡, Vmo BZ Jmobm| Ho$ Am`VZm| H$m AZwnmV
_________ hmoJm &
13. {H$gr d¥Îm H$mo Xmo q~XþAm| na à{VÀN>o{XV H$aZo dmbr aoIm H$mo __________ H$hVo h¢ &
14. `{X  PQR H$m joÌ\$b eyÝ` h¡, Vmo q~Xþ P, Q VWm R ______________ h¢ &
15. g^r dJ© ____________ hmoVo h¢ & (gdmªJg_/g_ê$n)
àíZ g§»`m 16 go 20 _| {ZåZ{b{IV Ho$ CÎma Xr{OE :
16. EH$ {g¸o$ H$mo Xmo ~ma CN>mbm OmVm h¡ & XmoZm| ~ma {MV AmZo H$s àm{`H$Vm kmV H$s{OE &
17. 36 dJ© go_r n¥ð>r` joÌ\$b dmbo Jmobo H$s {ÌÁ`m kmV H$s{OE &
18. `{X – 6, x, 8 EH$ g_m§Va loT>r Ho$ H«${_V nX h¢, Vmo x H$m _mZ kmV H$s{OE &
AWdm
g_m§Va loT>r – 27, – 22, – 17, – 12,... H$m 11dm± nX kmV H$s{OE &
19. AmH¥${V-2 _|, ^y{_ Ho$ EH$ q~Xþ B go _rZma AC Ho$ {eIa H$m CÞ`Z H$moU 60 h¡ & `{X
_rZma H$s D±$MmB© 20 _r. hmo, Vmo _rZma Ho$ nmX-q~Xþ go Bg q~Xþ H$s Xÿar kmV H$s{OE &

AmH¥${V-2
20. _mZ kmV H$s{OE :
tan 40  tan 50
AWdm
`{X cos A = sin 42 h¡, Vmo A H$m _mZ kmV H$s{OE &
IÊS> I$
àíZ g§»`m 21 go 26 _| àË`oH$ àíZ 2 A§H$m| H$m h¡ &
1
21. `{X tan (A + B) = 3 VWm tan (A – B) = h¡, 0 < A + B  90, A > B, Vmo
3
A VWm B Ho$ _mZ kmV H$s{OE &

.430/5/3 8

12. If the radii of two spheres are in the ratio 2 : 3, then the ratio of their
respective volumes is __________ .
13. A line intersecting a circle in two points is called a ___________ .
14. If ar ( PQR) is zero, then the points P, Q and R are ____________ .
15. All squares are __________ . (congruent/similar)

Answer the following question numbers 16 to 20 :
16. A coin is tossed twice. Find the probability of getting head both the times.
17. Find the radius of the sphere whose surface area is 36 cm2.
18. Find the value of x so that – 6, x, 8 are in A.P.
OR
Find the 11th term of the A.P. – 27, – 22, – 17, – 12, ... .
19. In Figure-2, the angle of elevation of the top of a tower AC from a point B
on the ground is 60. If the height of the tower is 20 m, find the distance
of the point from the foot of the tower.

Figure-2
20. Evaluate :
tan 40  tan 50
OR
If cos A = sin 42, then find the value of A.

SECTION B
Question numbers 21 to 26 carry 2 marks each.
1
21. If tan (A + B) = 3 and tan (A – B) = , 0 < A + B  90, A > B, then
3
find the values of A and B.

.430/5/3 9 P.T.O.

22. A§J«oµOr dU©_mbm Ho$ g_yh _| go EH$ dU© (Aja) `mÑÀN>`m MwZm OmVm h¡ & BgH$s Š`m
àm{`H$Vm hmoJr {H$ `h dU© (Aja) EH$ ñda (vowel) h¡ ?
23. x Ho$ {bE hb H$s{OE :
3 x2 + 14x – 5 3 = 0

24. {ZåZ{b{IV ~§Q>Z H$m _mÜ` kmV H$s{OE :
dJ© : 5 – 15 15 – 25 25 – 35 35 – 45

~ma§~maVm : 2 4 3 1

AWdm
{ZåZ{b{IV ~§Q>Z 100 H$_©Mm[a`m| Ho$ AmZo-OmZo Ho$ IMm] H$mo Xem©Vm h¡ :
ì`` (< _|) : 200 – 400 400 – 600 600 – 800 800 – 1000 1000 – 1200
H$_©Mm[a`m| H$s
21 25 19 23 12
g§»`m :
Bg ~§Q>Z H$m ~hþbH$ kmV H$s{OE &
25. Om±M H$s{OE {H$ Š`m {H$gr àmH¥$V g§»`m n Ho$ {bE g§»`m 6n A§H$ ‘0’ (eyÝ`) na g_mßV
hmo gH$Vr h¡ &
AWdm
150 VWm 200 H$m b.g. (LCM) kmV H$s{OE &

26. AmH¥${V-3 _|, ABC VWm XYZ Xem©E JE h¢ & `{X AB = 3 go_r, BC = 6 go_r,
AC = 2 3 go_r,  A = 80,  B = 60, XY = 4 3 go_r, YZ = 12 go_r VWm
XZ = 6 go_r h¡, Vmo  Y H$m _mZ kmV H$s{OE &

2 3 go_r 4 3 go_r

AmH¥${V-3
.430/5/3 10

22. A letter is selected at random from the set of English alphabets. What is the
probability that it is a vowel ?

23. Solve for x :
3 x2 + 14x – 5 3 = 0

24. Find the mean for the following distribution :
Classes : 5 – 15 15 – 25 25 – 35 35 – 45
Frequency : 2 4 3 1

OR
The following distribution shows the transport expenditure of
100 employees :
Expenditure
200 – 400 400 – 600 600 – 800 800 – 1000 1000 – 1200
(in <) :
Number of
21 25 19 23 12
employees :
Find the mode of the distribution.

25. Check whether 6n can end with the digit ‘0’ (zero) for any natural
number n.
OR
Find the LCM of 150 and 200.

26. In Figure-3,  ABC and  XYZ are shown. If AB = 3 cm, BC = 6 cm,
AC = 2 3 cm,  A = 80,  B = 60, XY = 4 3 cm, YZ = 12 cm and
XZ = 6 cm, then find the value of  Y.

2 3 cm 4 3 cm

Figure-3

.430/5/3 11 P.T.O.

IÊS> J$
àíZ g§»`m 27 go 34 _| àË`oH$ àíZ 3 A§H$m| H$m h¡ &
27. 4 go_r, 5 go_r VWm 6 go_r ^wOmAm| dmbo EH$ {Ì^wO H$s aMZm H$s{OE & {\$a BgHo$ g_ê$n
EH$ Am¡a {Ì^wO H$s aMZm H$s{OE {OgH$s ^wOmE± nhbo {Ì^wO H$s g§JV ^wOmAm| H$s 2 JwZr
3
hm| &
AWdm
2.5 go_r {ÌÁ`m H$m EH$ d¥Îm It{ME & BgHo$ Ho$ÝÐ go 8 go_r Xÿa pñWV EH$ q~Xþ P
br{OE & d¥Îm na q~Xþ P go ñne©-aoIm `w½_ H$s aMZm H$s{OE &
28. `{X Xmo g_m§Va lo{T>`m| 23, 25, 27, ... VWm 5, 8, 11, 14, ... Ho$ nd| nX g_mZ h¢, Vmo n
H$m _mZ kmV H$s{OE &
29. AmH¥${V-4 _|, AB Am¡a CD Ho$ÝÐ O dmbo d¥Îm Ho$ Xmo nañna bå~ ì`mg h¢ VWm OD N>moQ>o
d¥Îm H$m ì`mg h¡ & `{X OA = 7 go_r h¡, Vmo N>m`m§{H$V ^mJ H$m joÌ\$b kmV H$s{OE &

AmH¥${V-4
AWdm
AmH¥${V-5 _|, 7 go_r ^wOm dmbo dJ© ABCD Ho$ n[aJV EH$ d¥Îm ItMm J`m h¡ & N>m`m§{H$V
^mJ H$m joÌ\$b kmV H$s{OE &

AmH¥${V-5
.430/5/3 12

SECTION C
Question numbers 27 to 34 carry 3 marks each.
27. Construct a triangle with its sides 4 cm, 5 cm and 6 cm. Then construct a
2
triangle similar to it whose sides are of the corresponding sides of the
3
first triangle.
OR
Draw a circle of radius 2.5 cm. Take a point P at a distance of 8 cm from
its centre. Construct a pair of tangents from the point P to the circle.
28. If the nth terms of two A.P.s 23, 25, 27, ... and 5, 8, 11, 14, ... are equal,
then find the value of n.
29. In Figure-4, AB and CD are two diameters of a circle (with centre O)
perpendicular to each other and OD is the diameter of the smaller circle.
If OA = 7 cm, then find the area of the shaded region.

Figure-4
OR
In Figure-5, ABCD is a square with side 7 cm. A circle is drawn
circumscribing the square. Find the area of the shaded region.

Figure-5

.430/5/3 13 P.T.O.

30. {gÕ H$s{OE {H$ EH$ d¥Îm Ho$ n[aJV ItMo JE MVw^w©O H$s Am_Zo -gm_Zo H$s ^wOmE± d¥Îm Ho$
Ho$ÝÐ na g§nyaH$ H$moU A§V[aV H$aVr h¢ &
31. H¥$îUm Ho$ nmg EH$ go~m| H$m ~mJ h¡ {OgHo$ gmW EH$ 10 _r.  10 _r. gmBµO H$m EH$
{H$MZ JmS>©Z h¡ & CgZo Cgo EH$ 10  10 {J«S> _| ~m±Q>H$a Cg_| {_Å>r VWm ImX S>mbr h¡ &
CgZo q~Xþ A na EH$ Zt~y H$m nm¡Ym, q~Xþ B na Y{ZE H$m nm¡Ym, q~Xþ C na ß`mO H$m nm¡Ym
VWm q~Xþ D na EH$ Q>_mQ>a H$m nm¡Ym bJm`m h¡ & CgH$m n{V am_ {H$MZ JmS>©Z H$mo XoIH$a
Vmarµ\$ H$aVm h¡ VWm H$hVm h¡ {H$ A, B, C VWm D H$mo {_bmZo na dh em`X EH$ g_m§Va
MVw^w©O ~Z OmE & ZrMo {XE JE {MÌ H$mo Ü`mZnyd©H$ XoIH$a {ZåZ{b{IV Ho$ CÎma Xr{OE :

(i) {ZX}em§H$ Aj Ho$ ê$n _| 10  10 {J«S> H$m Cn`moJ H$aVo hþE q~XþAm| A, B, C VWm
D Ho$ {ZX}em§H$ kmV H$s{OE &
(ii) kmV H$s{OE {H$ Š`m ABCD EH$ g_m§Va MVw^w©O h¡ `m Zht &
32. {gÕ H$s{OE {H$ :
cos A 1  sin A
  2 sec A
1  sin A cos A

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

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30. Prove that the opposite sides of a quadrilateral circumscribing a circle
subtend supplementary angles at the centre of the circle.

31. Krishna has an apple orchard which has a 10 m  10 m sized kitchen
garden attached to it. She divides it into a 10  10 grid and puts soil and
manure into it. She grows a lemon plant at A, a coriander plant at B, an
onion plant at C and a tomato plant at D. Her husband Ram praised her
kitchen garden and points out that on joining A, B, C and D they may
form a parallelogram. Look at the below figure carefully and answer the
following questions :

(i) Write the coordinates of the points A, B, C and D, using the
10  10 grid as coordinate axes.

(ii) Find whether ABCD is a parallelogram or not.

32. Prove that :
cos A 1  sin A
  2 sec A
1  sin A cos A

33. Prove that 3 is an irrational number.
.430/5/3 15 P.T.O.

34. Xmo g§»`mAm| H$m AÝVa 26 h¡ VWm ~‹S>r g§»`m, N>moQ>r g§»`m Ho$ VrZ JwZo go 4 A{YH$ h¡ &
g§»`mE± kmV H$s{OE &
AWdm
x VWm y Ho$ {bE hb H$s{OE :
2 3 5 4
 = 13 VWm – =–2
x y x y

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

35. Xmo nmZr Ho$ Zb EH$ gmW EH$ hm¡µO H$mo 9 3 K§Q>m| _| ^a gH$Vo h¢ & ~‹S>o ì`mg dmbm Zb
8
hm¡µO H$mo ^aZo _|, H$_ ì`mg dmbo Zb go 10 K§Q>o H$_ g_` boVm h¡ & àË`oH$ Zb Ûmam
AbJ-AbJ hm¡µO H$mo ^aZo H$m g_` kmV H$s{OE &
AWdm
EH$ Eogo Am`VmH$ma nmH©$ H$mo ~ZmZm h¡ {OgH$s Mm¡‹S>mB© CgH$s bå~mB© go 3 _r. H$_ hmo &
BgH$m joÌ\$b nhbo go {Z{_©V g_{Û~mhþ {Ì^wOmH$ma nmH©$ {OgH$m AmYma Am`VmH$ma nmH©$
H$s Mm¡‹S>mB© Ho$ ~am~a VWm D±$MmB© 12 _r. h¡, go 4 dJ© _rQ>a A{YH$ hmo & Bg nmH©$ H$s
bå~mB© Am¡a Mm¡‹S>mB© kmV H$s{OE &
36. 32 go_r D±$Mr Am¡a AmYma {ÌÁ`m 18 go_r dmbr EH$ ~obZmH$ma ~mëQ>r aoV go ^ar hþB© h¡ &
Bg ~mëQ>r H$mo ^y{_ na Imbr {H$`m OmVm h¡ Am¡a Bg aoV H$s EH$ e§ŠdmH$ma T>oar ~ZmB© OmVr
h¡ & `{X e§ŠdmH$ma T>oar H$s D±$MmB© 24 go_r h¡, Vmo Bg T>oar H$s {ÌÁ`m VWm {V`©H$ D±$MmB©
kmV H$s{OE &
37. EH$ ZXr Ho$ nwb Ho$ EH$ q~Xþ go ZXr Ho$ gå_wI {H$Zmam| Ho$ AdZ_Z H$moU H«$_e: 30
Am¡a 45 h¢ & `{X nwb {H$Zmam| go 10 _r. H$s D±$MmB© na hmo Vmo ZXr H$s Mm¡‹S>mB© kmV
H$s{OE & ( 3 = 1.73 à`moJ H$s{OE)
38. {ZåZ{b{IV ~ma§~maVm ~§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 70 – 80

~ma§~maVm : 7 14 13 12 20 11 15 8

.430/5/3 16

34. The difference between two numbers is 26 and the larger number exceeds
thrice of the smaller number by 4. Find the numbers.

OR
Solve for x and y :
2 3 5 4
 = 13 and – =–2
x y x y

SECTION D

Question numbers 35 to 40 carry 4 marks each.

3
35. Two water taps together can fill a tank in 9
hours. The tap of larger
8
diameter takes 10 hours less than the smaller one to fill the tank
separately. Find the time in which each tap can separately fill the tank.

OR
A rectangular park is to be designed whose breadth is 3 m less than its
length. Its area is to be 4 square metres more than the area of a park
that has already been made in the shape of an isosceles triangle with its
base as the breadth of the rectangular park and of altitude 12 m. Find
the length and breadth of the park.

36. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled
with sand. This bucket is emptied on the ground and a conical heap of
sand is formed. If the height of the conical heap is 24 cm, then find the
radius and slant height of the heap.

37. From a point on a bridge across a river, the angles of depression of the
banks on opposite sides of the river are 30 and 45, respectively. If the
bridge is at a height of 10 m from the banks, then find the width of the
river. (Use 3 = 1.73)

38. Draw a ‘less than’ ogive for the following frequency distribution :

Classes : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80

Frequency : 7 14 13 12 20 11 15 8

.430/5/3 17 P.T.O.

39. `{X {H$gr {Ì^wO H$s EH$ ^wOm Ho$ g_m§Va AÝ` 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 AÝ` Xmo ^wOmE± EH$ hr
AZwnmV _| {d^m{OV hmoVr h¢ &
AWdm
AmH¥${V-6 _|, g_~mhþ {Ì^wO ABC _|, AD  BC, BE  AC VWm CF  AB h¢ & {gÕ
H$s{OE {H$ 4 (AD2 + BE2 + CF2) = 9 AB2.

AmH¥${V-6
40. ~hþnX p(x) = 3x4 – 4x3 – 10x2 + 8x + 8 Ho$ AÝ` eyÝ`H$ kmV H$s{OE, `{X 2 VWm
– 2 , BgHo$ Xmo eyÝ`H$ {XE JE h¢ &

AWdm
~hþnX g(x) = x3 – 3x2 + x + 2 H$mo ~hþnX x2 – 2x + 1 go {d^m{OV H$s{OE VWm
{d^mOZ EoëJmo[aÏ_ H$s gË`Vm H$s Om±M H$s{OE &

.430/5/3 18

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

OR
In Figure-6, in an equilateral triangle ABC, AD  BC, BE  AC and
CF  AB. Prove that 4 (AD2 + BE2 + CF2) = 9 AB2.

Figure-6

40. Find other zeroes of the polynomial

p(x) = 3x4 – 4x3 – 10x2 + 8x + 8,

if two of its zeroes are 2 and – 2 .

OR

Divide the polynomial g(x) = x3 – 3x2 + x + 2 by the polynomial
x2 – 2x + 1 and verify the division algorithm.

.430/5/3 19 P.T.O.