SEBA Class 10 Question Paper 2023 Maths

ASSAM BOARD
QUESTION
PAPER
2023

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Total No. of Printed Pages : 23
B23-GM
Subject Code : C2
(EN/AS/BN/BD/HN)

3047 734458

2023

GENERAL MATHEMATICS
Full Marks :90
Pass Marks : 27

Time: 3hours

Candidates shall note that each question will be multilingual, vic, in
English/Assamese/Bengal/Bodo/Hindi medium, for their ready reference.
In case of anydiscrepancy or confusion in the medium /version,
the English version will-be considered as the authentic version.

The figures in the margin indicate full marksfor the questions.

Unless stated otherwise, use =7

22

22

22

1 1738 Contd.

1.
SECTION-A//F-*
Choose the correct answer :..

(i) Ifx « y and when x =6
then y=30. Now ifx: =2 then the value of yis 1
I7x « y
x=6Ay=30 |
|x« y 4Rx =6,y=30 | af=2'yA4
gxy 34RÌ x=6 GrAIal y =304Ax=22Ay
TGx oc y 3t x =6 ,at y= 30 | |qfr=2
37G x= 2aay 61 417 T
(b) 15
(d) 20
(i1) Which of the
following is a square of an odd natural number "? 1

(a) 256 (b) 169
(c) 546 (d) 754

(üi) The value of /8 +/27+\/64 is 1

(a) 6 (b) 7
(c) 8 (d)9
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integers
that if a and b are any two positiVe
(iv) Euclid's division lemma states
such that
then there exist unique integers q and r

(a) a= bq+r, 0 Srsb (b) a =bq + r, 0 <rsb
)Wa= bqtr,0sr<b (d) a=bq +r, 0 <r<b
expansion of the
(v) The number of decimal places after which the decimal
43
rational number 24 x 53 will terminate.

43
24 x53

43
24x53

43
24x 53

D
43
24 x 53

(a) 3 (b) 4
(c) 1 (d) 5
3 3047
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(vi) If 1 is a zero of
the
b is polynomial P(r) =br² +4(b+ 1) + 1then the value of 1
P*) = br +4(b +1l) +15b ti I 3
bAAR4
PX) = br + 4(b + 1l) + 15fts gt taT 1
sg b-4 24
Y P) = bx + 4(b+ l) + 1
aaautaif à aug' 1I4T 3Holl b iH

(a)-y
(c) 0
(d) -4
(Vi1) If the sum and product of the zeroes of a
polynomial is polynomial are p and q then the
1

(a) x+ (p + q)x+ pq (b) -(p+ q)x- p4
(c) -(p+ qx +pq - pxtq

(viii) The condition that the line ax + by + c= 0passes through the origin is 1

ar + by + c=073t oAAJ A S| 6G 2L
ax + by + c=0zIST3TI Efarcif i-14 IGIS| T
tal ar +by +c= 0*4 feç JA
(a) a=0 (b; b=0
(dy c*0

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(ix) The coordinates of any point on y-axis is 1

(a)0,) (b) (x. 0)
(c) (r, x) (d) (x, y)
(x) One root of quadratic equation is 2 and the sum of the roots is 5 then the
equation is 1

(a), -Sr +6=0 (b) r2+ 5r-6=0
(c) - 5x -6=0 (d) x- 5x +2= 0
2. Choose the correct answer of the following :

ORO

(i) If, a, 2 are the three consecutive terms of an AP then the value of "a" is 1

4

4
5 a,
4

4
afz a. 2fehf AP f afAE TE} a 51 HH
7 5
(a) (b) 4

(c) (d) s

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= 6 cm, then
(ii) AABC is an isosceles triangle in which 2C = 90°. If AC
AB =?
AABC 4bi Efags ' LC =90° | AC = 6 a:A: N u
AB =?
AABC 4P0D AA0E fass Rtra C=9ne af AC = 6 F4. 2N OR
AB =?

GT 37IAB =?

AB =?

(al6y2 cm/R:A:/A.raftrèrt
(b, 6cma:R:/A.Aetvàut
(c) 2y6 cm/R:fA:/.A.Atyrèt
(d) 42 cm/Ca:f:/A.AAfA
(iii) The distance of (3, -2) from the
x-axis is
(3,-2) f<gt x qpgR0 7NT

(3, -2)far-T r-eaiSIM5814 HRAI^YI TP0H
(3, -2) fax-14 Azt
(a) 3
(b) V13
(c) 1

(iv) The ratio in which y-axis divides the line segment
joining the points (-2, 0)
and (4, 0) is 1
(-2,0) F(4.0)FRIÀ RNGP y.Q v IvÝi37
(-2, 0) 44R (4, 0) FRRI0 ANGA y.CFA S q | D
(-2, 0) 34RT (4, 0) qMIGI4 g1Gt GIÌ y ft arg A GeI4414

fägsi (-2. 0) 3tt (4. 0) t arà tGrdS y-3a fre 349TafAMTA
(a) 2:3 (b)A:2
(c) 1:4 (d) 2: | "
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3047

(v) A straight line which intersects a circle in two points is called -

(a) çhord (b) radius

(c) tangent (d) Secant

3
(vi) If sin A then tan A=? 1

sin A=w8 tan A=? DRO

3
Ai14 sin A= SGtan A=?

g sin A = tan A=?
3
af; sin A=, t tan A=?

(a) (b) 3

(d)

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(vi) If TP and TQ are
the two
ZPOQ = 110° then tangents to a circle with centre 0 so that
ZPTQ is equal to

PTQ AIAT

ZPTQ
4Qg
TP R
POQ = 110°, 3e PTO HHH GI

(a) 60
(c) 80°
(d)90°
(viii) If the surface area of a cube is 486 cm²
then its volume is - 1

(a) 81 cmR:RA.A. AR? RA?
(b) 243 cmaR.Aafe dA?
(c) S29 cm³(a::.A,AA
(d) 729 cm³(8:A:3/(A Att

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(ix) The median and mode of a data are 33 and 45 respectively. Then its mean is 1

(a), 30 (b) 33
(©)7 (d) 35
(x) The probability of getting a number 8 in a single throw of a die 1

(az (b) 3
(c) 1

3. Answer the following as directed :

faena anfcà fh a:

(i) What is the area of a rhombus whose lengths of diagonals are 8 cm and
4 cm ? 1

4 ?
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so as to geta
ind the smallest number by which 27 should be multiplied 1
rational number.

(ii) What is product of the zeroes of 4x2+8x? 1

(iv) Ifn is the degree of the polynomial p(x) then what is the number of zeroes
of p(r) ? 1

(v) Write true or false :
Ox+0.y +k=0, (k* 0) is a linear equation. 1

Ox+ 0.y +k=0 (k*0), gbi taR A

Or + 0.y +k= 0 (k+ ) 4 tta* A

Ox + 0.y + k=0 (k* 0) 34T44gaiT HHTS I

Ox +0.y+ k=0 (k*0) as tfguHteUI
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(vi) Find the number of solutions of the equations
X-4y +6=0 and 3x12y +18 =0
x-4y +6=0 3x 12y+ 18 = 0 NAARTf |
x-4y + 6=0 4 3x- 12y+ 18 = 0 A19(AA FAN0AK ARRT Afg 0|
x-4y +6= 0HR 3r- 12y+ 18 = 0HH14Tf HIqHAIEA fHIfEAI
r-4y +6 = 03t 3x - 12y + 18 =0Htui i AgI I A I

(vii) What is the condition if the roots of the equation x'+ px +
q=0 are real
and unequal ? 1

(vii) What is the value of cif the roots of the equation ar+ bx +c=0 are equal ?
ar? + br +c=0 DK 4A Ýi 4 A c A f ?

(ix) What term of the A.P 2,4,6, 8 ..... will be 50 ?
2,4, 6, 8 .....gtobRfAHO4 s 50 atfK ?
2, 4. 6. 8.... 2ODA PU ARI$ 750 13?

2,4,6, 8......gfi fA H faciaa 50 ?
AP 2,4, 6.8 ......1 ht HI y 50 BI?
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(X) How
sum ismany
78? terms of the A.P. 24,
21, 18, .. must be taken so that their
24, 21, 18, .....

24, 21, 18,
4AsfvOR
24, 21, 18, ...... Q3
fbfg u
78 GA ? ....He unuf aàà
T fE
HTt
AP 24, 21, 18, ... q4TtI
4
Answer in short : enrt qin 78 T?

(1) In a
triangle
EC =? AABC, DE|BC. If AD = 1.5 cm, DB
qti fags =3 cm, AE = lcm
then
AABC EDE || BC |
2::N SI EC=? AD =1.5 R:A:, DB =3 :^:, AE =
1
AD1g AABC S DE | BC | 3fF
AD =1.5 A.A., DB=3
À., AE=1
H 3SIRYAAABC ATA
AE= 1A T3GTEC = ? DE | BC I AD = 1.5 A, DB =3 TH,
5 aNIABC DE| BC
, t EC |ft AD =1.5A, DB =3 sr
=? AE =1 t
(ii)) In AABC and APQR, AB BC CA
QR PRPO then what is the triangle, similar to
APQR ?
AB 1
z1 AABC F APQR BC CA
QR PR PO , (03 APQR ASS
fagrcot f ?
AABC R APOR AB BC CA
A
QR PRPO , RT APQR -4 g

yG AABC ÌAPOR A AB_ BC CA
QR PR PO
3TeifHI 4?
AB BC
AABC À3 APOR ,
À, - ,
QR PR APOR HEY
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3047

(ii)) What are the co-ordinates of the mjd-point of the line
joining the points
(-2, S) and (8, -3)? 1

(-2, 5) F(8, -3)RAI GK ATTARF f ?
(-2, 5)<4R (8, -3) RTT AI TTRYA zKF ?
(-2, 5) 3TRT (8, -3) faqA gIA Ttferaf eaf frerAI HT?

(iv) If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the
vertices of a
parallelogram, taken in order then what is the value of P? 1
| A(6, 1), B(8, 2), C(9, 4) F D(P, 3) PD D S ADt

|14 A(6, 1), B(8, 2), C(9, 4) RDP, 3) fAg Aoo RK

A(6, 1), B(8, 2), C(9, 4) 3TRT DP, 3)farzta feTesIEA 5ft frfefA
farat r t 3HsI P f A1H 4I GH ?
att teg A(6, 1), B(8, 2), C(9.4) 3t D(P, 3) y6 HHiGt aaa yft zeft H4

(v) Value of tan 48° tan 23° tan 42° tan 67° =?
tan 48° tan 23° tan 42° tan 67° =? 1
tan 48° tan 23° tan 42° tan 67° 4g =?
tan 48° tan 23° tan 42° tan 67° HH = ?
tan 48° tan 23° tan 42° tan 67° 1HH =?

(vi) What is the value of 2 tan²45° + cos?30° - sin 60°? 1
2 tan² 45° + cos 30°- sin² 60° ?3
2 tan² 45° + cos 30°- sin 60° 4A ?
2 tan² 45° + cos' 30°- sin² 60° f HHI HT ?
2tan² 45° + cos² 30°- sin² 60° T HH I ?

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(Y)What is the distance between two paralleltangents drawn on acircle of
radius 4 cm ?

(vii)The length of a tangent from a point A at distance 5 cm from
the centre ol
the circle is 4 cm. Find the radius of the 1
circle.

IBISUI 4 AfA |GTAGfEAI

(ix) The length of the minute hand of a clock is 14 cm. Find the area swept by
the minute hand in 5 minutes. 1

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(x) If the difference between circumference and diameter of a circle is 30 cm
then what is the radius of the circle ? use T=
-) 1

7

S. Fill in the blanks choosing the correct option from the
brackets : alternatives given in the

URO

(i) If the volume of a sphere is 288 T cm² then radius of the sphere is
(6 cm/7 cm/ 8cm/ 10 cm) 1

(68::/7 a:A:/ 8a:A:/ 10 :A:)

(6 A.A/7AÂ/8 AA/ 10 AA)

(6 Af/7f/ 8 af/ 10 Af)

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circumferenceof
Ithe
(i) The curved surface area of a cylinder is 2200 cm and 1
the base is 220 cm. The height of the cylinder is
(4 cm/1 cm/10 cm 3 cm)

(4 a:Â:/|CR:R:/10,.:/3 R:M:)
faf 220

(4G1./1.AN0A.A/3.A)

(4t/1/I0 Af/3 AfA)
q5 ysty 4a 2200 cm² s 3U â qt 220 cm dTH

(4 /1 rIo 3)

(ii) If the mean of x, x+ 3, x+ 6, x + 9 and .x + 12 is 10 then value of x
.(5/4/9/ 8) 1

1x,r+3.x+6,+9 *r+ 12 AS 10 O8Y AA
(5/4/9/8)

x,x+3, x+ 6, x+9 qRr+ 12-43 TKI 10 N OAr-4 A 4
.(5/4/9/8)

(5/4/9/ 8)

(5/4/9/ 8)

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(iv) The probability of an imnpossible event is . (1/5/0/6) 1
.(1 /5/0/6)
(1/5/0/6)
.(1/5/0/6)
I(1/5/0/6)

(v) A die is thrown once. The probability of
getting a number less than 5 is
1.

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3047 (EN/AS/BN/BD/HN)
18 B23-GM
3ir Q
sin4TÀI 1PQ
= -0Q
3r 4 =7
HH,OP P GHE1 AOPQ
)COS 3RÌ sQ
in I af| PQ
= 0Q
- 7t =OPART G,G-IA 3ATA AOPQ
PfA
qR Ìsin A:IN: 1=
PQ -0QQR A: 7 =OP4R OA PAOPQ
43
qt Q
sin Ia:Â: 1=
PQ -0Q P:: =7 OP
IFASIA AOPQ
P
2
Q.
cos and Q
sin values
of
Determine
the cm. 1=
PQ OQand cm 7 =right-angled
OPP, at AOPQ, In 8.
irrational. is
-y3 th5at how 7.
2
-xyz
Z-7+7xy ilas:qUuGSA
fafR:Z-7+7xy
-xyz fEt
T:z-7+7xy-xyz RCARA Teaty
:z-7+7xy
xyz - tenN
Factorise:z-7+7xy
-xyz 6.
2
-At/T-AT SECTION

A > B.
1
B) = where 0° <A + BS 90° and
9. If sin (A - B) = cos (A +
2
find A and B.

<A +B<90° F A > B, (URA
f sin (A - B) =. cos (A + B)= ' 0°
A IF B I

17 sin (A - B)=,, cos (A + B) = IA 0° <A + B<90° qR A > B, ORA

A qRB PA0 |

g sin (A - B) = cos (A + B) = a 0° <A+ B< 90° 3TKT A>B 3 ociI A

utt sin (A - B) =. cos (A + B)=.0
2
<A+ B<90°, A >B ,at A 3tt B I

one is 1and other is 2).
10. Hari tosses two different coins simultaneously (say,
What is the probability that she gets at least one head ?

|1.,Solve : x+ y =14,x-y=4
AF0:ty= 14, x- y =4
A0 FA0:x+ y= 14,x-y=4
HTaysAT fEi :x+y- 14.x-y=4
BT AIMR:rty=14, x- y =4
19 3047
B23-GM (EN/AS/BN/BD/HN)

3
1
12. Find the roots of the equation 2,y +=2r.

3
13. How many two-digit numbers are divisible by 3?

14. S and T are points on sides PR and OR of APOR such that P= ZRTS. Show
3
that ARPQ ~ ARTS.
APQR < PR F QR TI2T G945 S FT FÜ K 5P =ZRTS I734l
ARPQ ~ ARTS |
APQR-4s PR 4R QR I9 GGA S 4R T t K0CS P = ZRTS ITIS
ARPQ ~ ARTS I
S3RT T39I APQR fA PR 3À QR 3TA1fRfA HIZTA A-A faret ra P= ZRTS I
faffe ARPQ~ARTSI
APQR ÁT yG130 PR 3R QR s A4:
ZP=ZRTS? I<iEsfs ARPQ ~ ARTS I
15. If A(-5, 7), B(- 4, -5), C(-1,-6) and D(4, 5) are the vertices of a quadrilateral,
Find the area of the quadrilateral ABCD. 3
zfAA(-5,7), B(-4, -5), C(-I, -6) F D(4, 5) frgseaGi abi bÊggA,
qA A(-5,7), B(-4, -5),C(-1, -6) 4R DI4, 5) fageA sot bygOK 3N,

gtA(-5, 7), B(-4, -5). C(-1,-6) 3Ì DI4, 5) sT rÁ 3TgTAAt artafAfar
afe A(-5, 7), B(-4.-5), C(-1,-6) 3r D(4, 5) V% T fá gHg aI

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circle, which touches
16. Prove that in two concentric circles, the chord of the larger
3
the smaller circle. is bisected at the point of contact.

17. Ahorse is tied to a peg at one corner of a square shaped grass field of side 15 m 3
by means of a 5 n long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m
(use T =3.14)

(T24 0N=3.14)

(ii)
PA0|(J23 (SÌ =3.14)

GIIH|(T=3.14 H)

3047
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face of a cubical wooden block
I8. Ahemispherical depression is cut out from one edge of the cube.
is equal to the
Such that the diameter "" of the hemisphere 3
Determine the surface area of the remaining solid.

19Atthe median of the distribution given below is 28.5. find the values of xand y. 3

Class interval/( qa Frequency/ARTT3i/

0- 10
10 20
20 -30 20
30 - 40 15
40 - 50
50 60 5
Totalgb/cAfbTrÁUgT 60

20/ Construct atriangle similar to a given triangle ABC with its sides equal to of
the corresponding sides of the triangle ABC ie. of scale factor. 4

5

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3

3TGTRrTABC 3M1g1Hft sherà3gfRrfAA

OR/t/ /vaI/ 3AI
Construct atriangle of sides 4 cm, 5 cm and 6 cm, and then a triangle similar to
itwhose sides are ; of the corresponding sides of the fist
triangle. (Write the
steps of construction.) 4
4 cm, 5 cm 6cm Qdi fgys Fo fRs KA7A RRA

3

(Ta1 qu ferfy )
21. find
Iftwoall zeroes of the polynomial 2r-3r-3r +6r - 2 are 2and 2 then
other zeroes. 4

ORO
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