SEBA Class 10 Question Paper 2024 Maths

ASSAM BOARD
QUESTION
PAPER
2024

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Total No. of Printed Pages--31
B24-GM
Subject Code: C2 (EN/ASBN/BD/HN)

2024

GENERAL MATHEMATICS

Full Marks: 90
Pass Marks : 27

Time:3 hours
Candidates shall note that each question will be
multilingual, viz., in English / Assamese / Bengali /
Bodo I Hindi medium, for their ready reference. In case of
any discrepancy or confusion in the medium Il version,
the English version will be considered as
the authentic version.

The figures in the margin indicate full marks for the questions.
22
Unless stated otherwise, use T =
7

22
7

22
7

22
7

22
7

n02 [Contd.

(2 )

SECTION-A / / 1/hET/
Choose the correct answer :

1, The value ofy in the blank
space of the following table is 1

1 4 8
32 16

(A) 8 (B) 6
(C) 4 (D) 2

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

(A) 441 (B) 572
(C) 576 (D) 729

B24-GM/102A [Contd.

(3 )

3. If n is the cube root of n, then the value of n is 1

R m, n T,at n 414 ETI
(A) Vm (B) m
(C) m³ (D) m²
4. Given that the LCM of 306 and 657 is 22338. What is the LCM of
102, 306 and 657? 1

1| KE A, 306 F657 aA8. 22338. qfo 102, 306 IF 657

(PSRI ICR A 306 qR 657-43 1.3. 22338. 102, 306 4R 657-S
A1.3. A?
EH4 f 306 41T 657 fA T.AI. 22338. atI 102, 306 R0
657 A. 311.41, qI H| A?
306 3r 657 5 LCM 22338 ti A 102, 306 3¦t 657 l LCM ETI
(A) 102 (B) 22338
(C) 22338 x3 (D) 22338×102
5. Given two statements : 1
Statement (i): The square of any positive odd integer 2k+l is
always 1l more than a multiple of 8.
Statement (i): The square of anypositive odd integer 2k+ lis
always 1 more than a multiple of 4.

1aRI

1 aI

B24-GM/102A [Contd.

(4 )

HI4TqTEAqg 1 aifHI

Choose the correct alternative.

(A) Both (i) and (ii) are true

(i) 4R (i) iDR YOJ
(i) 3RT (ii) H-ta gK

(B) i) is true but (ii) is false
i) 0 (ii)
(i) (ii) J
(i) 31 2R IATA (ii) 3 TTY
(i) 4 o (ii) 34HCT
(C) (i) is false but (ii) is true
(i) (ii)
(i) fe (ii) 0
(i) 341 CTY 4 (ii) 3| 2K

B24-GM/102A [ Contd.

(5 )

(D) Both (i) and (ii) are false

(i) qR (ii) FD SPJ
(i) 3RT (ii) r t TY
(i) 3n (ii) i 34

6. Under what condition will px + gx+ rx +s= 0 be a cubic
equation? 1

pxs +qx*+ rx+s=0 qôi fais AR137?

(A) p/g, r and s are all non-zero

P, q, r RsA8R A
p, q, r AR0 s IAAI ifrg' 3I

(B) pz0 and qz0

p0 4R qz0
pz04RÌ g=0
pz0 Rqz0
(C) p 0or q 0
p 0|gz0
pz0T g0
pz0 dl qz0
p 034T g0

(D) p 0

B24-GM/102A [Contd.

(6 )

. When* is real number, the graph of the cubic polynomial &r°-1 1

(A) does not intersect the
x-axis

(B) intersects the x-axis at
exactly one point

(C) intersects the x-axis at two distinct points

(D) intersects the -axis at three distinct points

B24-GM/102A [Contd.

(7)

8. If the of linear equations a1+3y+ c=0
pair and
4x +by+ c2 =0 has a unique solution, then 1

(A) a =3, b9 = 4 (B) aË = 12, b, =1
(C) aj = 4, b, =3 (D) aj = 5, b =1

9. The coordinates of any point on the -axis are 1

(A) {z, 0) (B) (0, y)
(C) (x, *) (D) (*, y)

10. The sum of the zeroesS of the quadratic polynomial
p(*)= 4x-1 is 1

tTÀ fACTeUhai p(*) = 4x?-1f nfra'sft aTAIÈI A0T

(A) -1
(C) 2 (D) 4

B24-GM/102A [ Contd.

(8 )

11. The common difference of the AP /2, N8, /18, V32 is 1
V2, V8, V18, V32 sISA ESIfOCOK MA9 Z4
V2, V8, 18, V32 AIEA SsOft MIA9 IR
V2, V8, V18, /32 H mfafA THK
STfARI
HAR A V2, V8, 18, /32 A1 HÃ R aI
(A) greater than the
common difference of the AP 2, 4, 6, 8
2, 4, 6, 8A134 1stfbcoK
IAI ETOA yS7
2, 4, 6, 8 A134 2stojog
KIAA 1R (AF T9
2, 4, 6, 8 HHg anfaft
PeR
HYT-R At 2, 4, 6, 8 HIG 34 WRPfRfTG
"T
AfeA
(B) equal to the
common difference of the AP /32, J18, J8

(C) equal to the common
difference of the AP 50, V98, V162
V50, /98, V162 4I8S 2b KIAA Ies
4A
J50, V98, 162 HHgfr afA 0GR SKfaat qHA
HH1-R A¥ V50, /98, /162 HG4 qUT
(D) greater than the common difference of the AP 1

1 -1
0,
V2 V2
1
0,
V2
1
V2
1 1
0,

B24-GM/102A
[Contd.

(9 )
12. If the
base of a
by 10%,triangle
is increased by 10% and the altitude is
decreased then the new area of the triangle 1
10% p fRAI ' * taft
10% 21

3TIRIASà 10% HA

(A)
remains the same (B) decreases by 1%
1% '
1% 16
1% GHta
(C) 1% 4e I I
increases by 10% (D) increases by 11%
10% ifp<
10% 9 11% aifa
10% aA 11% 194
11% aia
10% 4¢ SIT
11% 4¢ I I
13. The point R divides the
line segment AB, such that AR
The ratio in which R =AB.
divides AB is 1
R RiS AB NGF AAYA SN 3
ICS AR=AB IRA AB
4

R RD AB aTS0bF
QNASA 3IGS AR= AB IR-4Z

Rfari AB Bra taf aK GIIH0
IIA ARAB
4
aTI
R 341 AB AIET aIIHY tgE4I H

B24-GM/102A [Contd.

( 10 )

R tag AB a H T8ffH 3
I Tf AR=AB aat I RI
4

(A) 3:1 (B» 3:4
(C) 4:3 (D) 4:7

14. P(-1,0) is the centre of a circle and
Q(2, 4) is a point on this circle.
Three other points on this circle are
1

(i) (-6, 0)
(ii) {-1 5)
(iii) (3, -3)
(iv) (0, -5)
Choose the correct alternative.

(A) Any three of the above

B24-GM/102A [Contd.

( 11 )
(B) (ii), (iii)
and (iv) only
A1Q (ii), (ii)
A1 (ii), (iii) F (iv)
(ii), (iii) 3 qR (iv)
hi (ii), (iü)(iv)
3 (iv)
341
(C) (1), (ii)
and (iii) only
AG (i), (ii) F
1Q i), (ii) 4R (ii)
(i), (ii) 3RT (iii)(iii)
ha (i), (ii) 3R 3AIET(iii)
(D) (), (iii)
and
A1Q (i), (iii) (iv) only
A(i), (iii) (iv)
4R (iv)
(i), (ii) 3AR (iv)
3ATEA'
a (), (iii) 3îr (iv)
15. The
longest chord of a circle is
called 1

(A) radius
(B) arc

(C) diámeter (D) major arc

B24-GM/102A [Contd.

( 12 )

16. If 5x = sec and 5
= tan, then the value of 1

f 5x = seco 5
F tan0 , (98

q 5x = sec q4R 5 = tan0 , SRG 1

gt 5x = seco 34R 5 =tan , I

aft 5x = sech 3ir 5 tan ,

(A) 5
(B)
(C) 0 (D) 1

17. If the length of the tangent drawn from a point Q to a circle is
24 cm and the distance of from the centre of the circle is 25 cm,
then the radius of the circle is 1

25 cm TUPIK E'a

25 cm AYeDA UK A

fAsUSTY Q fari HATAI 25 cm

25 cm gr ja arft
(A) 7 cm (B) 12 cm
(C) 15 cm (D) 24-5 cm

B24-GM/102A [Contd.

(( 13 )

18. If twocubes each of volume 64 cm are joined end to end, then the
surface area of the resulting cuboid is 1

(A) 160 cm2 (B) 176 cm 2

(C) 128 cm 2 (D) 192 cm2

19. If the median of the data 25, 30, +30, 35 + x, 40 + * arranged in
increasing order is 35, then the value of x is 1

BPG ACI BAII 25, 30, x+30, 35+x, 40+ *3 TAT 35 2a,

URA A MYR 25, 30, x +30, 35+ x, 40 +*-4 4 35 A,

25, 30, x+30, 35+x, 40 +x

stAGAH wa 3jehs 25, 30, x +30, 35 +x, 40 +*1 AG 35 Ix

(A) 35 (B)5

(C) 25 (D) 10

B24-GM/102A [Contd.

( 14 )

Lne probability of getting aprime number greater than 2 in a
single throw of a die is

(A) 1
(B)
6
(C)
(D)

Z1, Ifthe area of a
trapezium is 1350 m and the sum of the lengths of
its parallel sides is three
trapezium is
times the height, then the height of the
1

HRqrHA gei 1350 m R fer 3Tanfavrf I3AEA

(A) 20 m
(B) 10 m
(C) 60 m (D) 30 m

B24-GM/102A
[Contd.

( 15 )

22. "The smallest perfect square number which is divisible by 4, 9 and
10 is 1

4, 9 R 10 Hat t ai y

(A) 144 (B) 900 (C) 3600 (D) 360

Z3. lf the sum of the zeroes of f(x) = kx-8x +6 is 4, then the value
of k is 1

f(x)= kx-&x +6-4g Aft 44, RKA k- AP A
f(x)= kx-8x +6A ufura'A aAI 4r , 3I k AH11

(A) 6 (B) & (C) 2 (D) 1

24. If a quadratic polynomial Chas two different zeroes, then the
number of points in which the graph of the polynomial will
intersect the x-axis is 1

fadfza m?

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

B24-GM/102A [Contd.

( 16 )

40. Which of the following equations is a linear equation in one
variable? 1

(A) 2x =3y (B)-3*+5=0
(C) 3x +y=0 (D) 33+7=8t-2

26. The pair of equations kx +2y=5 and 3x
solution if +y=1 will have a unique
1

kx +2y =5 4 3x+y=1taf A9 a9 g^ AT41
QA UIF
kx + 2y =5 3R 3x+y=1 anft 4ArUs f Vq HaGAR ArA

(A) k=0 (B) k 6
(C) #=2 (D) k=3

27. The number of roots of the equation (* +2) = -4 is 1

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

B24-GM/102A ( Contd.

( 17 )

28. Which of the following equations has two real and equal roots? 1

(A) 3a+14x -5 =0 (B) 4x4+2x-1=0
(C) 9x-6x+1=0 (D) x -5x +4=0

29. In an AP, the first term and last term are l and 11 respectively. If
the sumn of the terms in the AP is 36. then the number of terms is 1

(A) 6 (B) 8-D (C) 10 (D) 12

30. 42 is a term of which of the following arithmetic progressions? 1

(A) 92, 86, 80, (B) 102, 95, 88, ..
(C) 2, 6, 10, (D) 0, 8, 16, ..

B24-GM102A [ Contd.

( 18 )

Ol In a AABC, XY || BC, If AB = 4BX and YC=2 cm, then the value
of AY is
1
AABC XY | BC, q AB = 4BX F YC =2cm , (98 AY? AR

AABC SXY | BC. AB = 4BX aR YC =2 cm , RKA AY-4A

AABC TA XY | BC. st AB= 4BX 3IK YC = 2 cm , 34oll AY&

AABC , XY | BCt t AB= 4BX ¦t YC = 2 cm , al AY ai HH

(A) 4/cm (B) 6 cm
(C) 5 cm
(D) 8 cm

32. If CM and RN are respectively the
and if AABC ~ APQR, then which ofmedians of AABC and APQK
the following is correct? 1
CM RN GA AABC F APQRA A , F
AABC ~ APQR A, C8 VoR APOI 9%?
CM qR RN GA AABC qR
APQR-4 qYIAI , qR
AABC ~ APQR 3A, DRG ACGA GPAD ?
g CM 3AR RN i f AABC R APQRA àH a 3Ar
AABC ~APQR AAT, Hol IERÍf 4 ?
qie CM 3R RN sHI: AABC Â APQR qfan sr aft
AABC~ APQR, a fA-H H?
(A) AAMC ~ APNR (B) AAMC - APRN
(C) AAMC ~ ANRP (D) AAMC ~ ARNP

B24-GM102A
[Contd.

((19 )

38. The coordinates of the point A, where AB is adiameter of the circle
whose centre is (2, -3) and B is (1, 4), are 1

QT q IM AB. RYAKE (2, -3) FB4 EISF (1, 4) AAR

4IS CON IM AB. PEA EIRF (2, -3) 4R B-4g AIKF (1, 4) A

TR }arfA GIAI AB. fref raft faEIAI (2, -3) rà B afa farrI
(1, 4) R i A A graf faI TÌA

(1, 4) Afarg I fA}Rs aT

(B) (2, 8)

(C) (3,/-10) (D) (-2, 3)

34. The ratio in. which the point (-4, 6) divides the line segment
joining the points A(-6, 10) and B(3, -8) internally is 1

(-4, 6) OICAA(-6, 10) F B(3, -8) A RROF ofos 1

(-4, 6) frft A(-6, 10) R B(3, -8) KAIN aNOF sftos 1

(-4, 6) fara A(-6, 10) Tà) B(3, -8) fart araAHY ETG0-ara zfrt

(-4, 6) farz A(-6, 10) st B(3, -8) fag irt tards frH qua
fanaa n?

(A) 3:2 (B) 2:3
(C) 7:2 (D) 2:7

B24-GM/102A [Contd.

(20 )

35. If sin A= cos33°, A 90°. then the value of A is 1
I7 sin A= cos33°, A <90° , CU8 A4AA
AIT sin A = cos330, A < 90° 24, 9A
A-4g AA 24
gG sin A= cos33°, A < 90° , 4ocllA HH1 A
YTG sin A= cos38o su A < 90° A 1 H4 EMTN
(A) 90° DMO (B) 33º
(C) 27° (D) 570

36. If atan = x, bcot = y,
then the value of xy is 1
7 atan=x, bcot9 =y ,
08 y{ \1 24
7 atan=x, bcot0 = y N,
DRA xy -43 41 24
atan8 = x, bcot0 = y t, Hoi xy A 4HIAP
utt atan9 = x, bcot0= y, xy 47 TI
(A) a+b
(B) -1
(C) 1
(D) áb
37. If tangents PA and PB drawn
from point P
centre 0 are inclined to each other at an angle to a circle with
value of ZPOA is of 80, then the
1

(A) 60° (B) 50°
(C) 70° (D) 80°

B24-GM/102A
[Contd.

(21 )

38. The degree measure of the angle at the centre of a
circle of
radiusr is 9, The length of an arc of the sector is 1

(A)
90° (B)
180°
(C) rnr
270° (D)
360°

39. The number of tangents drawn through a point inside a circle is 1

(A) 0 (B) 1 (C) 2 (D) 3

40. If the circùmference of a circle is 22 cm, then the area of a
quadrant of the circle is 1

gft ÄGfA Arft feHTAT 22 cm

77 cm2
(A) 77 cm (B)
2

(C) (D) 77 cm2
8 4

B24-GM102A [ Contd.

( 22 )

ne volume and surface area of asphere are equal. The diameter of
the sphere is

(A) 3units (B) 6 units
34
6 4$
D 6 4$
3yfe 6ayfe
3z61 6 5-A1$
(C) 2 units
(D) 4 units
2q
4 q$
2 q$
44F
2rufe
4Hryfe
2 51$
4 3418

42. The ratio of the volume of a
cone and a cylinder having same
radius and height is
1

(A) V3:1 (B) 1:3
(C) 1:2 (D) 3:1

B24-GM/102A [Contd.

( 23 )

43. If the difference of median and mode is 24, then the difference of
mean and median is 1

(A) 10 (B) 12 (C) 14 (D) 13

44. A number is selected from the first 100 natural numbers. The
probability that the number is divisible by 8 is 1

8 1 1
(A) (B) (C) (D)
25 25 DD 6 100

45. Which of the following cannot be the probability of an event? 1

H| 1
(A) 0-225 (B) 0-6 (C) 1-2 (D)
3

B24-GM/102A [Contd.

(24 )

SECTION B/ / /G -algt/T-MI

46. /Factorise : 4x +1 2

GeTG* RNT AI : 4x +1
fag-fnft fafr : 4*+1
yurGSA ffY : 4x+1
*wo ropes are of lengths 64 cm and 80 cm, Both are to be cut into
Pieces of equal length. What should be the maximum length of the
pieces?

A foA I3ISUI ift 64 cm A 80 cm. aya4 HHH SAIA yai

48. If B and Q are acute angles of right angled triangles ABC and
PQR such that sin B= sinQ, then prove that /B = ZQ. 2

sin B= sin,(0(8 11 I ZB =Q.

NA sinB= sinQ, VRIA EA19 RAI A ZB= LQ.
gf GHf 3aIfH ABC R PQRA B 34R ZQ RI GGI TH
IEr sin B=sinQ, IRHA GTIH B = LQ.

ZB= ZQ.

B24-GM/102A [Contd.

(25 )

49. In APQR, right angled at Q. PQ =3cm and
PR=6 cm. Determine
LQPR and PRQ. 2

APQRI Q AÜI 90°. z PQ =3 cm q PR=6 cm, (o8 ZQPR

APQR- Q Aio 90°. zf PQ =3 cm q PR=6 cm, ORA
ZQPK

APQR & Q GAI 90°, gfa PÌ=3cm 34RT PR=6 cm, 34tl ZQPR
HRI ZPRQ fagil
APQR GT Q HHCATU PQ=3 cm 3Âr PR =6 cm , a ZQPR 0N
PRQ TA AfI

50. Two dice, one blue and one grey, are thrown at the same time.
Write down all the possible outcomes. What is the probability that
the sum of the two numbers appearing on the top of the dice is 13? 2

B24-GM/102A [Contd.

( 26 )

/ ducing them to a pnir c>f'
1.
51 •,/.olve the following pair of equations by re
· lmear equations : ~ "NTtfA ~ : '

~ ~ ' l ~ ~ ~ ' 1 ~<Ti~~~ "NTtfA <f¾.<TI :
b ~ ' 1 Cll!tll/,IC<li" ~ ~ ' 1 c@m "m~. metl41~ -rrr,;ro; om ~
....,, .... . ..,•~ •~~., :
~

~ tl'll'R~1~q,'mJl m;ra mw3llft "ijlfR ~ Im~~~ :
f.ii:;i~f©o ~41cfi<o, ~c m~ wftcti{OT ~ ~qH,
I

7x - 2y == 5, ~ == 15
xy xy

. . . . t gers the sum of whose
52· Fmd two consecutive odd positive in e '
squares is 290.
1jyT ~ ~~ ~~ ~~ ~~~ ~'8~ ~ q~ ~~~ 290.
1jfu ~ ~~ ~'i'f m ~~~ ~~~ ~ ~ ~ ~~ ~~ 290.
lIT,R ~ ~~ ~'U '{7T' 3l-l~' ll@ ~ ' ~ Gf1fci)(F{ ~1-:lli:P ll~41
290.

GT Wm~~~ Rcfil~~, ~ qJf ~ m7T 290 61
I

est per year.
53. A sum of r 1,000 is invested at 8% simple inter
interests
Calculate the interest at the end of each year . Do thes e
s making
form an AP? If so, find the interest at the end of 30 year
3
use of this fact.
1,000 ~ ~ 8% "Wf ~ ~ ~ ' i f ~ ~'a[ I ~ ~
~~
?~
~ ~'<l, 'if'Rl ~ I ~ ~\ ffl ~ 11ltf ~ ~~ ~ ~
ffl, ~, ~~ ~ 30 ~ ~ ~ ffl" f f.tcfu ~ I
1,000 msl <ll~W 8% ~ ~ ~ AA"cm'if ~ ~ I ~ q~~
ffi
~ ~?
~ ~ ~, 'if'Rl ~I~~, -"f~ faf ~~ ~ ~~ ~
Wt~ , ~, ~~ ~ 30 ~ ~ ~ fflct f.tcfu ~ I
'\ '\ A
<Slif!Rlf< 8% ~
• ~orrr.>tTrt-:! n ' '\ '\ R ' llcl -rr.rdt
'11<.l."1 ~ 1,000 'U «11 ~.,-11 ., ,., , Ji 1),f,l'l <SlieR ~iiHll
~'l\!t l

*
liHR§.:i, Wfi)u ~ liHij~ ~ ~ ;n? ~ mm, ~ ~ ~
30 ~ 'Jfl~.Jllllc:4 ~ ~ I
mtf t~
1,000 ~ ~ 8% ~ WffiUT ~ ~ 1l'{ ~ ~ TTml ~
~ fcficr-rr wrr? ~ ~ 'cfiT ~ ~ AP t? ~ ti
~ ~ cf;t m
~ ~ 30 ra t~ ~ q@ ~ 'cfiT ~m er~ , ·

B24-GM/102A [ Contd,

( 27)

54
• Prove that if one angle of a triangle is equal to one angle of
the other triangle and the sides including these angles are
proportional, then the two triangles are similar. 3

~'1 ~ Cl:l ~ ~tr ~~et◄ ~ ~'1 ~ ~ fJ!~et"' ~ ~~ ~ ~ ~
~ ~'lC~J,r ~ ~ <il~C~&I ~~ ~, ~~!UT~ I
~'1 ~ Cl:l ~ ~<15tu ~~C'Sfi:I ~~ ~'1 ~ ~ Qi~cet~ JI~ ~'ffl
~ ~ JI~~ ~ ~'l-a~ ~ ~ "ffl,-a~ ~~ ~, ~ ~ 1!fu
~I

~~nt~~~q;)urM ~~~~q;)ur~~m 3fR~-m
m,
cf;t "{jT@ ~ WiljqiRlcfi "ITT s,q,fu,a ~ fcf> GHT nl~ ~~I

55. Two opposite vertices of a square are (-1, 2) and (3, 2). Find the
coordinates of other two vertices. 3

JIUT ~.,fC'lfiJJ◄ ~~ ~~"'l_ !UT~'~ (-1, 2) ~ (3, 2). ~ ~4f<l"l_ ~
ffl~ ~'8QT I

JI~ ~-,fC'lfiCJl~ ~~ ir)~"'l_ ~ ~ ( -1, 2) JI~~ (3, 2). ffl in~"!_ ~
ffl~ C<ffl ~ I

lTI;ra apf ~~l~f-i TIT-A ~ ~ fat~li)(I (-1, 2) 3lTU (3, 2). W ~
~ fat~1i)(f.i ~ fattt H©~ ~ I

~ crT ~ G1 i4q{)a ffl ~ R~~ricfi (-1, 2) 3fR (3, 2) ~I 3R GT ffl ~
R~~licfi ~~I

B24-GM/102A [ Contd.

( 28 )

O from
56· Two tangents TP and TQ are drawn to a circle WI'th centre 3
an external point T. Prove that LPTQ = 2LOPQ. ·

~:l ~ T~ ~ 0 ~~ TP~ TQ ~~9P'f<fi U-TI ~'~ I ~'f
'fll elf L.PTQ = 2LOPQ.
_.,.1-x ~ ~ ~'f
~:l ~ T-~~ c~ 0 ~ ~ TP ul<l~ TQ ~ ~..,ft'."' .I
~ elf L.PTQ = 2LOPQ .
• ~ T ~ 0 ~ lffi'1 ~@-ifBii TP ~ TQ ~ ~ mm ~
~ I ~'©'@Tl{~ LPTQ = 2LOPQ.

~ ~ T "ij O ~ vf 1R TP ~ TQ en mi-~ ~ ~I . 5ll'.1lfolo
~~LPTQ = 2LOPQtl . ,

57. The cost of fencing a circular field at the rate of r 24 per metre ~s
r 5,280. The field is to be ploughed at the rate of r 0·50 per m · 3
Find the cost of ploughing the field.

~ ~ 24 ~ ~ ul~ 1'8l<fiM 9f~ ~ iirof ~ 5,280 ~ ffi
~ I 9f~~ ~ <l'iffelUM'!> 0·50 ~ ~ ~ <ll<l ~'lf I 9f~ffl ~ ~
mf.t'fu~I
~ ~ 24 ~ ~ ul~ 1>el<fil?l C~ <lT ~ ~ Ctr~~ ~
5,280~ ~~ICM~ < l ~ 0·50 ~ ~ ~ ~ afK'>f I
C~ ~ <ll-8~ ~ f.t'fu ~ I

lIT-m ~©-flit llil2ITTR' ~ ~ 'fH~l'i M21(1q 24 ut 5,280 -ti ~ I
llil?.Tmfil 'fH~l'i ~ M21(1q 0·50 ut- mR ~ ~ I "q;T~ ~ ~
~~-1©~ ~ I

*
m ~ 1R 24 ~ ~ G\ ~ ~-a1q;1< m
-ij ~ 3fu: ~ WTR ~ ~
s,2so ~ ~ ~ t1 m-ij ~ ~ ' I R ~ q7l ~ ~ o·5o ~ qil ~
amrrt1~m-ij~~~~~~~I

B24-GM/102A [ Contd.

( 29)
58. conical hole is
In a solid cylind
made. If th h _er of height 12 cm and radius 5 cm, a th t of the
cylinder the eight and radius of tho cone are same as_ . ag solid. 3
12 c , en find the total surface area of the remainm ..,
~~~ ~ 5 cm <Wflff~ l1Wl C'ifWl C4i1•~ ~ 111~ 15tlf~ '>~
~ ~ <Al ~'Cit I ~ --1~1,'GM ~ ~ <fJPftt{ C<lii\~lUi~ ~'i~ ~ ?;JJ,
i!C'iflUl~~~~I
12 cm ~ P.r ~ 45~
~ ~~ 5 cm ~~ ~ ~ ~ 11! "15tl1~
'-"~I~ ~ ~ I nQ. ~ __.., ~ \!il~Cal ~-~~
~~ 'ii, ..,;i:,11~ ~ ~~ <UPTI~ C<tii\•li&?t ~ l!l~-<. '

12 4. ~ ~C61~ NJl~61 ~ ~ I
cm'1'1 1v:m~ . - ~~
~'~ 5 cm tt'lg"('q ~ m;m 7tm ~ttfs·lc:t m;m ~
~7l'ln~ I ~ ~l~l"l ~~ 31ffi 'B'fflcTT ~t{if.i-ifi ~ ~ ' ~ ~
12 '""'.. ~«I~ Tfffi -P.n:;
,..,.~ =~~~-1n.11~fit~&~~ ~ I
~rn ~ ~ 5 cm ~ cfIB ~ om ~ -ij ~ • cfiT 1;cfi ~
~ ;:~~ ~ ~ ~ ~ ~ ~ ~ ~ i, m~ aF-fi • cfiT
~~I

t
59• Find th t Of
~ e med.ian of the following data which give the marks ou
3
J ' obtained by 100 students in a test :
Marks Obtained 20 29 28 33 42 38 43 25
Number of Students 6 28 24 15 2 4 1 20

~~~ 20 29 28 33 42 38 43 25
~ }f~W, 6 28 24 15 2 4 1 20

~ 0r-mn ~1fal<t>1fGc~ 100 ~ ~ 50 -i~C~n:1 R,~c?i 9fl'8Vf ~~ e&c~?i ~~
C"f-mJl ~ I ".J~ f.'tcfu ~ :

~<RT.:r.m 20 29 28 33 42 38 43 25
~}f~W, 6 28 24 15 2 4 1 20

B24-GM/1 02A [ Contd.

Yi ~ ,~-:•\ \, \\.:\_\ \ \ ;\\ 1,\:~_.\\.1.'..-~ .. \ \\,;,\ ~\''\,<'~-\_',.....,\v:;•,11/\'.; f'\',-~-:,_ r , ,,,,.,,
~' ~ •..:., \ , -;-, \. \·\ -~, '<\ -;-" V', \.?, ~;•,, -~,.'' · " '
,1
J
i
·;
( 30)

100 ~14<-llR' 1lt;m ~
7llt;lqfcf ~ ~ 50 ~ lJTGfq' m;r,WJ m .
~~~,~~:

42 38 43 25
~~ 20 29 28 33
2 4 1 20
q;uc?m'1>7~f.t ~ 6 28 24 15

. .; ~

f.li:.i~f©a ~ it 50 ~ ~ ~ m ~ 100 ~ ~ >ITTJ ~ c.-c11i.:. -rm: {I'
~~~:

"J1TfT ~ 42 38 43 25
20 29 28 33
4 1 20
mihftm 6 28 24 15 2

~O✓-a triangle ABC with sides BC =7 cm, LB = 4f, LA =105'·
; Then construct a triangle whose sides are times the
3
4
corresponding sides of MBC.
BC=7cm, LB= 45°, LA =105° ~ABC~ ~-:tar~ I~~
~UT~~~ <ll~C<ll<I -,~,, <1l~C<1F1<I i3 -8'l 1
. MBC1 rn?f

BC =7 cm, LB= 45°, LA =105° ~~~~ABC~ I~~
~~ Qi~IS/ ~ ~ ~-a~ MBC -~~ ~9f ~-a~ 4 -8'l 1
3

BC= 7 cm, LB= 45°, LA= 105° ~ ABC 1IT-ffi ~ 3lm91
~R~I~ MBC f.r ~ ~~ i ~ ~ 1IT-ffi ~~
3
3ffit9 I

1% ft~ ABC~,~ BC= 7 cm, LB= 45°, LA =105° "ITT! m
~ 1% ft~~~~ MBC ~ WIB ~m cl;t i ~ m,
3

B24-GM/102A [ Contd.

( 31 )

GI. If 0<, S ar e th /, po ly no m ial x 2 + bx + c, th en sh
ow
e ze ro es of th e
4
th at ~ is
zero of th e polynomial
ex 2 - (b 2 ~ 2c) x + c.
S a

+ bx + c ~~ ~
"J.'lf <>, ~ ~ , = ~
2 cq
>nil X
.
cx 2 (b2 J a_
- - 2 c) x + c~ ~ ~ i_ ;{ p
~~ ~ p ~, ~ ~'-!3 ~
~ x2 + bx + c
i_;{T a,
a
2 (b2 - 2 c )x + c ~ ~ ~i _; {T - .
ex - p
~ 'ffif~'an a, P~ , ~ 'tJi
ttlJR lgJ ffi lJ
~x + bx + c
2
~G l◄ •fl◄ if.)
a
~ 2 cfi 4Gl ◄•r t◄
.
IA 3lT p'
~. .._ Q ... ,.. '

- 2c )x +
2 '111t1 <:1111:i<lil
ex - (b
~ P ~ ' ol ~ ~
~ x + bx + c ~ ~ "GT
2 a,

qil ~~ a ~
cx - (b -2 c) x + c ~
2 2 I
p

** *

-= ~ ~ -
/
c, ~
,::2 ~ ,;

/~
ct z - 8, b:,., = ~/ e.z = -
'
T Pf - £:{ c- 1
= 8 ;:, b ~ = ~ = - 2 4 B
B2 4- G M /1 02 A

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