SEBA Class 10 Question Paper 2022 General maths

Total No. of Printed Pages-19
B21-GMM

Subject Code:C2 EN/AS/BN/BD/HN)

Question Paper 2022
GENERAL MATHIEMATICS

Full Marks : 90
Pass Marks : 27 L

Time: 3 hours
Candidates shall notethateach question will be multilingual, viz, n
Englishl Assamese/Bengali/Bodo lHindi medium, for their ready reference
In case ofany diserepaney or confusion in the medium/version, the Engiisn
version will be considered as the authentic version.

The figures in the margin indicate full marks for the questions.

Unless stated otherwise, use T =

7

/30 Contd.

2
SECTION

-A /TT/-TT
T/ -ATETTI/ TT
ect answer :
c o r r e c t
ansu

Choose
the

of the following is not a
af the 1
1.
Which
perfect square
R ?

a) 441 (b) 572 (c) 576 Yd) 729

2. The value of is 1

3

a

(a)
8
(b)
16 (c)
8
12
vd 1681
12 81
3. The HCF of 135 and 225 is 1

1357 225 11.. T
135 97 225 43 11.3. I
135 3A 225 à.THI. T414
135 3 225 I 4. H. 3

(a) 303755 (6) 945 (c) 45 (d) 15

B21-GM/30DA [Contd.

3)
4. A bell
rings at every 18 seconds and at
e v e r y

60 seconds. If these two bells an
another bellf rings i n s t a n t ,

ring
then the bells will
simultaneouslya
an
at
sly
ring simultaneously
gD 18 CRTO A again after
OI 60 (T6
ug175

HTAR I 18 Hs 3TRM
TT AAÀ RM 60 vg
ES

(a) 30seconds /RTO/ GT / TVE/
60 seconds / (RUPO/
GTRS/US/T-3
(c) 90 seconds/ O / OTTE
/ TVEH
(d) 180 seconds/ (RTTO/ ATI
/HEUE/ Hs

5. Which of the following is a
polynomial? 1

(a) +2x +19 (b)+2x +19

(c) 1 (d) a +19
x+19

B21-GM/30A
Contd.

4

the followin
6. Consider pairs of linear equations 1

()3r +2y=5, 2x+3y 5
Ji) 4r-3y=9, 4x-3y =8
Choose the correct alternative.

(a) The pairs in i) and (i) are consistent / (i) ( i ) a AZR

(b) The pairs in (i) and (i) are inconsistent (i) IF (11) S

(c) The pair in () is inconsistent, whereas the pair in (i) is
consistent / (i) 7RTATDI TRSE, P (i) 7 ANDI RTE/ (i)-93

(d) The pair in (i) is consistent, whereas the pair in (i) is
inconsistent/ () TRTITRT, Pa (i) a AACDI7RE/()-

7. The number of roots of the equation (x +2)° = x° - 4 is
1
(x +2)
(x+2=*-4ARUm HR RI
x+2= x-4 FAA4T5f danfa srmfaHTA1 T47

Feiesrx+2 =-4 KOAT
(a) 4 6) 3 (c) 2 (d) 1

B21-GM/30A Contd.

5)
8. The first term of an AP is 4 and O n d i f f e r e n c ei s - 3 .

The fifth term 1s
o 4 H U-3
7 4 4R
7T13 K-3 , qA Rr-3 , T
a t fra Taara 4 4 3TPTER f-3

19
(a)-8 (6)-11 (c) 16 ad
respectively of a

9. D and E are points on the sides AB and AC respecth 5.4
.4 cm.
cm.
n, BC=5
triangle ABC. DE || BC,
DB =7-2cm,
AE =18 cm, B
AD is ||BC,
RIDE
ABC ay AB TF AC T A D EE R
FO D
7.2 cm, AE = 1-8 cm, EC = 5.4 cm. AD E
DB =

D E DE | BO;
ABC TaS AB 9R AC R
EC 5.4 cm. AD I
DB 7 . 2 cm, AE =18 cm,
=

AC 3TaaA A Htà D 3ATT
E HI41
ABC TEAATHA
AB R I
5.4 cm. AD
=7.2 cm, AE =1-8 cm, EC
=

fai DE || BC, DB
TI T
I YTT AB M AC
FA: fD at Efa
Tt1 ay ABC ,
7-2 cm, AE=1-8
cm 7 EC =5.4 cm
DE|| BC, DB
=

AD 1 HA& (d) 1:2 cm
3-6 cm (c)24cm
(a) 4:8 cm (b) 1
and (-a, -6) is
distance between
the points (a, b)
10. The
HT
(a, b) F (-a, -6) R7 D
AY AIT
(a, b) 4 (-a, -b) R T
f a H-AA TtA TTEI AT
(a, 6) 3TT (-a, -b)
-b) e t
fRgt (a, 6) st (-a,
(b) 4a2+b2
(a) 2a+82

(d) 2(a +6)
(c) 0

TContd.
B21-GM/30A

6

edge1s 1
. The surface area of a cube is 600 m2. The length ofeach

(d) 5 m
(a) 15 m b) 101m c) 8 m

12. What is the probability of getting a number 9 in
a single throw Or
1
a die?

(a) (b) 1 (c) d) 0

SECTION-B/*TT/ RI/G-ETT/G-Tm
13. The length of a rectangle is three times its breadth. If the area of
the rectangle is 432 cms, find its perimeter. 2

432 cm2 ael, aA Hrdfë fersh faga I

B21-GM/80A I Contd.

7

irectly as y, and a
6 when value
1 4 I f r va

of y
when *
= 2. y=30, ther
,then find
the
2

R =6; (OCR

a, y 4 A51 y=30 x =6;
JRA
30

34T y= 30 =2 TA
H = = 6;
31 *

zfex 3it y HITUTaI 6, 3Tx=6 Tm 74y=30, a y *

15. Solve the following pair of linear equations 2

0-2x+0 3y =1.3
0.4x+05y =2.3

16. The product of two consecutive positive integers is 306. Find the

integers.

B21-GM30A Contd

8
progressionion: 2
«of
17. number
Find the
number
terms of the following a r i t h m e t i c

AReraft 3faH fag

7, 13, 19, ., 205
at D
A line intersects the sides AB and AC
aa
of a triangle AB AE
18. AD 2
respectively, and is parallel to BC. Prove that AB
A AC
AC
PCo
D E T
457AR ABC Ta9 AB W AC
Ts A
AE
RTE BC NIB47 I aT
AB AC P5 R
E R
93PIT CAR1 ABC TayT AB 4 AC a E CA D 4TR
AD AE
CRTiD BC 97 AIBAT I 2RII SI 64
AB AC
ziH FiSIT ABC 3GTfqqnfa AB 3TÀAC
TETfat 5Ttà D ARIE
AE
B
AB MAC T1 3541: D 3it E
sta
TEI fAyT ABC 1
&a I BC HHiat 1 fera f fA AE
AB AC

(1 sin0)(1-sin0)
19. If cot0= then evaluate
8 (1+ cos0)(1-cos®)

C (1+ sin)-Sint) qA AeN FÄI
cot (1+ cos)(1-cos6)

cot R
(1+ sin6)1-sin)
a A fAa TA
8 (1+ cose)1-cos6)

fagcot8 8
7 (1+ sin1-Sint) f AH EAI
(1+ cos6)(1-cos6)

zt cot8= (1+ sin8)d-Sin) HA fAITI
(1+ cos6)(1-cos6)

B21-GM/30A I Contd.

9

20. If sin(x + y)
= , cos(x -

y) = v3
and x <90°, then
>y,
find x and y. 0°<x+.
cos(x -y)=Y3
sin(x +y) ,
* 90°, (o
x>y, 0°< x+Y

sin(x+y) =1, cos(r -y)= V3
4RX>y, 0<x+Y 90, TR

g sin(r+y)=1, cos(x--)= ARI x>y,
, 0 ° s x + y <9 0 , T
0°<x+y<90,

afe sin(x+ y) =
1, cos(x -y) =3 7 x>y,
>y, 0°<x+y< 90°,
0°<x+ySS

21. If the tangents PA and PB from a point P to a circle with centre O

inclined to each other at an angle of 80, then find ZPOA. 2

80° CI T, O ZPOA AA FI

T 9 P 4 (ITT O E 9 T PA 9R PB
R 80° M FA, URTA LPOA RAR F

T HTHR f P ATa o AiHi aa aeaA PA 3TT PB Aitsa aim

I R PÀo a ft za R PA R PB RI-TITi VFR 80
7 d, LPOA I
B21-GM/30A Contd.

10

contains 3 blue, 2 white and 4 red marbles. If a marble is
22. A box
drawn at
drawn at random
random irom the box, then what is the probability that it
white and (6) red? 2
will be

T47 (6)a ?

23. Mr. X and Mr. Y are two friends. What is the probability that both
will have (a) different birthdays and 6) the same birthday?
(Ignoring a leap year)

f4BR X T 4B Y TCAI TITAI (a) föa PATA (b) a TA
RIATR T1I ? (k 3 )

THTH TYTEFHT fg (Leap year RATA)

B21-GM/30A Contd.

11

SECTION-C/

24. Prove that 3+2V5 is irrational
3
211 a 3+25 qoAAN
21 SI A 3+2V5 itCAI

RAT TTH f 3+2W5 31 THtarfa

f f 3+2/5 qa aufu7 v

25. Find the quadratic polynomial whose 3
zeros are4 and 3

TI NT TE7 CBII -4 T , T A

26. Find the roots of the following equation 3

TTEA THTFATEfA tersrat fega

2x+7x+5V2 = 0

B21-GM/30A Contd.

12

consists of OU terms of which 3rd term is 12 and the last
27 An AP 3
106. Pind the 29th term.
term 1s

5051
9 ATCQ BUA Yu °HCDI 12 T u8 HCD1 106
TAIA I9|O

, 290 A

12 ARi a 7
TAÀ HTAQ STTAT HA 50 A I A THfa facisi
faeTT 106 P I , 29 fu facact ftg-

106 I H61
aau ye 12 3r sifa4
«
FHTR q1 4 50 i , frusi

ABCD with AB || DC
28. The diagonals AC and BD of a trapezium
A_OB 3
intersect each other at the point 0. Show that OD

BD TUITA O RTE R R TDRPG
ABCD GTNA AB ||DC, AC
IFYSTa A OB
OC OD
ABCD TA4 AB|| DC, AC RBD d O A
OA OB
OC OD

ABCD AHfA AB|| DC, AC 3AM BD zitm O faA3Ta
OB
OC OD

v EH ABCD, rad AB || DC, f i AC 3tr BD TR f43O

C OD

B21-GM/30A Contd

13

29. If Q(0,1) is equidistant from P(5, -3) find
the
-3) and R( then
3
value of x. Also, find the distances 6),
QR and PR

Q0,1) I P(5,-3) TR(x,6)7 M
aaT,
SI75gE QR TT PR TDI tfsI

Q(0,1) faG P(5, -3) 4R R(«,6) 43 (N AT,
TR
fA IC QR R PR 3Y0M A
74T7T-7T^T
ag Q0,1) far3m P(5, -3) 3 Rz,6)A tA ¥A

f Q0,1) fagai P(5, -3) 3tt R(x,6) TRE8, *

the
which divides the line joining
30. Find the coordinates of the point 3
in the ratio 2:3.
points (-1, 7) and (4, -3)

ACTS1 AAINOT 2:3 TGT
A KDK
17-1,7) S* (4, -3)

7KC1 ATVOT 2:3 MCE
51 1 RTUR
R-1,7) 4R (4, -3) 44

a r A AT FRA T k a 2:3 qUT3Ta
(-1,7) 34TRT (4, -3) fe-i

fargT (-1,7 31R (4, -3) T ftTÀ a

i
3H fa à Aeais aTa afrr,
aTaS 2:3 Ta fAATTa I

B21-GM/30A Contd.

14 )
3
Evaluate / Ni*
ii4
*/TA A FA1/ 4TA feEA/HTA T
31.
Sin 30°+ tan 45°-cosec 60
Sec 30°+ cos 60°+ cot 45°

circular field at the rate of
F 24 per
metre
is
32. The cost of encing a
of 0 - 5 0 per m
5,280. The
neld 18 to be ploughed at the rate 3
of ploughing the field.
Find the cost
45
TA 5,280
afsfADe 24 PI AT q7 JaP ° A

IPI
ASAT PTC 5,280
aft ADA 24 DRI IA G g e P ATCO AI

subtends a n angle of 60° at the
33. In a circle of radius 21 cm, a n a r c
centre. Find (a) the length of the a r c and (b) the a r e a of the sector
formed by the arc. 3

T4, 4 DI PT DI 60° I 1 GOTA
21 cmUPRA I

60° P I 1 T AI ORA

21cm PTE 3 , 4P 5I qejts E

B21-GM/30A [ Contd.

15
HTF EFA HaaT 21 cm HAÀ
(a) arcafa ITST ARI (6):aRAT T

fav 21 cm Tc hI Y5 ITY
60

Find the area of the sector of a circle
angle 30. Also, nd the area of the h radius 4 cm and of
(Use T=3.14)
cor nding major sector.
3
4 cm JPTYTS * 30° IA G1 3
fa fAeku i1 (7 =3-14
)
fArtu (T=3140 AT)
H'a4I 4 em 3R THEYTA HR

SECTION-D/-INT/ITRT/7-Em/ -4T
D
34. Find the zeroes of the
polynomialx*-3 and verify the relationship
between the zeroes and the coefficients.

-3 faaTariaiA afra'yat f s

-3 Ta

B21-GM/30OA [Contd

16

which values of following pair of linear
35. For
equations have,
and b does the 4
hnite number of solutions?

a 317b
7 HTAA
T a T 9TA?

374% 8M?
2x + 3y = 7, (a-b)x+(a+ b) y = 3a +b-2

a circle are
36. Prove that the tangents at the ends of a diameter of
parallel.

OR/ qeT/ T1/ aT/ 3 7 r
Prove that in two concentric circles, the chord of
the larger circle,
of contact.
which touches the smaller circle, is bisected at the point
Two concentric circles are of radii 5 cm and 3 cm. What is the length
circle? 3+1=4
of the chord of the larger circle which touches the smaller

TTpRTE TAT916T NI5cm 3 cm P A 1 &F T

frfrirenT ifae farcana aAÀ aR a I 5 em 31T 3 cm 7aafA MA

B21-GM/30A Contd.

17
37. Construct a triangle
similar to a
equal to of the given
4
the steps of
corresponding sides are
of rithe
any:triang
ABC with
ABC with its side
construction.) Plangle ABC. (Write

A
ABCayTCDA 1 1T7 2a
4P FA fays
ABC 4 71 ass
ABC fays T T98 r
AI (
ABC ATEFa4THA HTT
3ITafqrfA 3.
3TAT-4 ABC A HETA ATETq4T4
fe Ty faT ABC 3a (nTa
STUTtrfrt1)

SECTION-E / RI/ T/F-TRM/ F-HTT
38, A solid toy is in the form of a
circular cone. The height of thehemisphere surmounted by a right-
cone is 2 cm and the
the base is 4 cm.
Determine the volume of the toy. (Takediameter
3:14)
t =
o

5

HCT CRRI KPR | 2 cm 1 7 T 4 cm. oIDA
T N (7=3-14 4)

E0 O 2 cm R FA P 4 cm. AËR TN AN
(T=3-14 NCA)
CTgA TzA1 2 cm 31R EIHIA Ta3T 4 cm. F TR TI T

a (T=3-14 )
51 3TYTA Ta
4 cm TGi
IsT 2 cm 3r TUR ZH

f i (m =3-14 ifeg)
Contd.
B21-GM/30A

18
in a
following
tab.table shows the patients
admitted

39.
The
h
during a year:
ospital dur ges
of the
55-65
Agel i nyears) 45-55
5-15 15-25 25-35
35-45

5
Number of patientsN 23
14
6 11
21 5
Find
the mode of the data given above.

55-65
5-15 15-25 25-35 35-45
45-55

23 14 5
Cwr T L 6
11 21

CPI

CPRICAIT :
55-65
45-55
| 5-15 15-25 25-35 35-45

14 5
CTTR RIT 6 11 21 23

55-65
55-65
25-35 35-4545-55
&i (ateits4T) | 5-15 15-25
5
21 23 14
A a T 6611

25-35 35-45 45-55 55-65
15-25
5-15

21 23 14 5
6 11
iPri HT

[ Contd
B21-GM/30A

19

OR/ /91/ aT/ T
If the median of the distribution given below : find the
18 28-5, then 5
and y :
values ofr

Class interval / T/ Frequency/TKTOI

0-10 5
X
10-20

20-30

15
30-40

40-50
5
50-60
60
TiT
Total/ y/TD/ TÊ/

*

2-21
B21-GM/30A