Uttarakhand Board Class 10 Sample Paper 2024 Maths

Uttarakhand Board

SAMPLE
PAPER


2024

sM srill.{- 2024
oHT-10
.rFra (Mathematics)- (ost)
Wrtn 80
Tlslq : g qtt Maximum Marks : 80
Time: 3 hours
27 qPq t I r{fi qY-q 3rFrfld S t
ftdqr- (i) {q{ tr{a-qain frall qa
27 questions in this question paper' All
questions are
Directions- There are
comPulsorY'
(ii) sr-d qrus altun t
*# iq iit*no 316questions t

Marks allotted to the are mentioned against them'

(iii) e#; ,=, d
-qq{do ozn w5fun €ftf t

"Eq "9<
to the point'
Read each question carefully and answer
,, .Eftffi'r=o-gt gs qs{ d u-f,t
'ft-fi-fl 6 '.d-o *r-sgtrdfiT d
(iv) tr= €cqT
q qN fa-m-n ft\'w
t *St 31q-fi siilq
frtur r
'
question. Four options are given in answer
Question No.1is multiple choice
ofeachpartofthisquestion.Writecorrectoptioninyouranswerbook'
(v)ge{{{[email protected].+fitrn.ggfieroorBrqq{€CqTztgilfi
go3]-6dgPqtt9.T{{[email protected]
q-rq q-@T rz t 21' ;'' d qr{ d t q.T{ €sT 22 d 27
dfifr-qGmdsq-{Bl '"
"*
EachpartofquestionNo.lcarriesonemark.QuestionsNo.2togareof
onemarkeach.QuestionNo.l0to16areoftwomarkseach.QuestionNo'
lTtoZtareoffourmarkseach,QuestionsNo'22to2Tareoffivemarks
t
q+qq qi o1{ fr-f,-n q-Si oeilft oftqq ,-rn t
tuit ffihq=-q, d
srdtrfi {a-"n-fl qila ft-* t r qeqi d d-{d q-fi fffi-iq
'* t8
or fi sf,{ fiftq t

Thereisnooverallchoiceinthisquestionpaper/however,aninternal
of the given
Attempt only one
choice has been provided in few questions.
choices in such questions
-;

Fmfr.fu-a q ii 3NR-iq s-cqT t-
1
1. (a)
(i) 22 / 7 (ii) Tr (iii) V4 (iv) flt t 6t"i TSf
in the fbllorving irrational number is-
(t) 22t7 (ii) z (iii) VZ (iv) None of them

Rqrq qfi-fi-inT 2x2 - 4x * 3 =
(b)
0 @l ft-E-qn-qx B- 1

(i) 16 l\i) 24 (iii),- I {iv) 3
Descriminent of quatit'atic equation 2x'-4r+3:0
is-
(i) 16 fit) 24 (iii) - 8 (iv) 3

L

(c) cot 60" 4T q1T t- 1

(i) 1 VT
1.
(ii) .--: (iii) (iv) slqR?ilBa
Va
Value of cot 60" is-
(i) 1 (ii) a (iii) rltr (iv) Not defined

(d) q$K ,'-3 d 3['q-qi oT xlT-q3 6]qT- 1

(i) o (ii) v3 (iii) 3 (iv) -3
Procluct of zeroes o1'the polynomial x2-3 will be-
(i) 0 (ii) \E (iii) 3 (iv) -3

(e) fr.S (2, -4) @t x 3T&T t {ft B- 1

(i) -4 (ii) 0 (iii) 2 (iv)-Z
Distance of'point (2. -4) from x axis is-
(i) -4 (ii) 0 (iii) 2 (iv)-2

(f) qrql<N ffi +, 10, 16, 22, ......... eT $rf,d q-( E)Tl- 1

(i) 32 (ii) 28 (iii) 40 (iv) 34
The 7tr'term of'AP: 4. i0. 16. 22. ......... will be-
(i) 32 (ii) 28 (iii) 40 (iv) 34

(e) {tftrd qdql qn Hft-f,dT B- 1

(i) 3 (ii) 2 (iii) 1 (iv) 0
Probability of a dellnite event is-
(i) 3 (ii) 2 (iii) 1 (iv) o

(h) foS.rq fu", q nallnc de,r AD/DB:2/3 t, qR pc:6 t-fr n) aB o-r
qrq d-qT- 1

(i) 3 (ii) 4 (iii) 6 (iv) 5
ln thc tlgtrrc l)E ll LX an.l
ffi = i if EC:6cm, value of AE will be-
(i) 3 (ii) 1 (iii) 6 (iv) s
r
\.

A

B C

y.2- z +fr izrTd dsTr 10 +S GTTqtq .qI{{ d ioq fl GTr{kFi sra o-Rg? 1

Q.2- Find the volume of a cylinclel having height 7cm^ and base diameter 10 cm.

9.3- q-R tun n:i, Ai cos r\ O-T qr{ Sld O-tl I 1

q.3- If tan A:1find cos A
5

y.4- r{qr<r ffi z, rc, rc 205 q q-qi of q-sT gro o-tr t 1

Q.+- Find tire number of teurs of the AP 7 , 13, 19.. . . . . .205.

9.5- 3825 @i GT+lrw {u'rru"$ d Xurmn d sq fr zqqo of r 1

Q.s- Express 3825 as a proclr-rct olits prime factors.

2

IT.6- \-qt RqTf, q-gq-E fl( qifrr, ftRr-d plq-*) d q).T f,eil {UTqTF-f, F-qsI: o
q _\vs 61 1

Q.6- Find a qr-ract'atic poiynomial sum and products of its zeroes are 0 and rE respectively.

9.7- qI{, qr{fr efr-q q-$ilqD t sE-€T fufof t 1

Q.7- Write the relationship between Mean. Median and Mode

9.8- 9 seczA - 9 tanzA e-T qr{ qqT ElqT? 1

Q.8- What is the value of 9 sec2A - 9 tan2A?

s.e- fr"-3c (a. b) trsTT (-a.-b) d fr"q zhl $ srd qfifu\ | 1

Q.9- Find the distance betr,vecn points (a. b) and (-a, -b)
q.10- HC]F (336.541 :6 Rql t I LCM (336,54) sl( qafr\ I 2
Q.10- Given that HCF (336. 54) : 6. F-ind LCM (336, 54).

s.11- {gq( 4 u2 + 8 u d alqfr 5;6 otfu\ 3tq gl;q-ai .i- g"n-*" d +q d
Q.11- Find the zeroes of the rrolynomial 4 u2 + 8 u and verify the relationship between the
zeroes and coelfrcients.

v.12- tRfr dl lsLqry 16 -."lltf fu-i-trT q\-,1-zz E) 3ft XUTTE6 182 Ell 2
Q.12- Find tq,o numbers u'hose sum is 2l and procluct is 182.
geLqr oR

k oT qlq srd 6ei, ffi flf Eqro Rfif,flT 2x2+kx+3:0 d d qqFN {d
qrK 61'l
Find the value of k so that the quadratic equation 2x2+kx+3:0 have two equal roots.

IT.13-9fr *A q 3 dlcr si-{ 5 orfr +i dt Efi rtd q t 1 tE qqzeqT
Frmrfr ql-d) t I sEl-fr ql?,rfum-aT qqT B fu tE- z
(i) drfr 6i (ii) dIc{ r-e S
Q.13- A bag coritaius 3 red balls and 5 black baiis. A ball is drawn at random from the bag.
What is the probabiiity that the ball drawn is-
1i,t red 1ii.; not led.

y.14- Frr;Tfufu'fl rttwft t ,r e-zTr , d qtq Era .F-S- 2
Q.14- Find the values of x & ], in fbllo'nving table-
T( (Term) qNqr{ilI IIilft ql{ftr-r{ilf
(l-r'equency) (Cumulative Frequency)
2 6 6
4 .r 26
6 t4 50
8 28 v
10 15 93

3

s.15- fu-€ +-$ srqq B-E t Td q{ S-fr .d wqf tErcfr +t trqr$ qir-w d-fr
tt 2
Q.15- Prove that the lengths o1'tangents drawn fi'om an external point to a circle are equal.

s.16-ke.r} fun q qR i.ullce ai-< r-Nllco n) fr{.€ o_*t 2
Q.16- In the given f-rgule if LN4 l l Ce ana lX l lCO prove that-

AM AN
AB AD
A

D
3{etqT oR

R{ q\ fr"{ q qR AoDC - AoBA"
[Boc:r25" sir-{ LcD0:70", lnoc an-i
lnco 6-]- q"m s"ro df]r t
125'

in the given figtire ii' AODC AOBA, A
l,
Lgoc:tus" and lcno:7O". find Looc
ancl LDCO.

q.17-qR fixfr Ap d s?-Irr 7 qql oT qlq +g t si{ sarr 17 q-ET oT q}-rT 28e t
ai Elld ezTrr n qqT oT {h"qq-e gtd dfr\ I 4
Q.17- if the sum of llrst 7 terms of an AP is 49 and that of first 17 terms is 289. Find the
sum of'filst n terms.

q.1B-RT-€ @-t-- sin'4
L+cos A
- + '*loto
sin A -
z cosec A 4

stn A 1'+cos A
e.18- Prove that- \+cos A + sin A - 2 cosec A
31erfl-/ on

ft'€ ril- (sin A + cosec A)'+ (cos A + sec A)2 :7 + tan2A+ cot2A

Pror,'e tlrat- (sin A + cosec A)' + (cos A + sec A)2 :7 + tan2A+ cot2A

9.19- oi$ {ff{ gfr trM 3drH d en+_rq mT t, ffi
s!-{ \-fi gIs-dT
ila-q e{'qrtlts_f, t I erd-,i-d &-T qrs 14 c* B Gil-i ilT Ert{ of go fu
13 c* t'r w qdq @T 3nf,Pd gdq si:q-d ETf, dfrr | 4

Q.1e- A vessel is in the form of a hollow hemisphere mourtted by a hollow cylinder. The
diameter of the l-remisphere is 14 cm. and the total height of the vessel is 13 cm. Find
the inner suf'ace area o1'the vessel.

3{ERT OR

4

a

fi T{ 3rrffr q Errffuf, qirl *zq-d srd f,*, qR C-q 0 or-A <}q}
@-T

ffiq gmii e B;ut\ Fqql: Tcrn duTT 14 crn B osrT LAlc:+o'tl 4
Fincl the ilrea ol'the shadeci region in figure. if ratio of the two concentric circles with
center O are 7ctn. and 14cm. respectively ind IAOC:40"

y.zo- ft--Sc (,-3" l0) eik 10, -8) o) ffi il-d i-{qrs-s C R-.5 (-1, 6) frttl
t
3qqrd fr"nfu-o 6{dT B? 4

e.20- Filc'l the ratio in rvhich the line segment joining the points (-3, 10) and (6, -8) is
divided b"v (-1. 6).

s.21- qffi d ra 6$- o.zx+ o.3y: 1.3 1 4

0.4r + 0.5"v :2.3

Q.21- Solve tire equation- 0.2r + 0.3,v : 1.3
0.4x + 0.5r,': 2.3

9.22- 7m 6i r-rqq d flTq{ t ddrd elqr d ftTs-{ qil B-izrq qtol oo" t 3fr-i
Elrd sr( or er{flq{ cp)-q 45" t I uq{ zht fu srd o1fuq I 5

@..22- Front rhe rop ol'a 7m. irigh building, the angle of elevation of the top of a cable tower
is (r0" anci angle of clepression of its foot is 45o. Determine the height of the tower.
3rzrur oR

\rfi 80.r d-S q-so d dt'i c.q 3rtq-i-qnt {flrFl dqr$ il-d d s*i
of gv tI sq EH eot d e.q q-sn d q-6 frS t *q d Brcr d
s;ry{ qi"T mqpT. 60o de-TT 3oo t, q++t ft1 fu en-t u-"1 t fug ot
qS sra frfu{ | 5
Tu,o l:roles of eclual heights are standing opposite each other on either side of the road,
u,hich is 80m. rvide. From a point between them on road, the angle of elevation of the
top of the poles are (r0" and 30o, respectir,ely. Find the height of the poles and the
distance of the point fiom the poles.
DRC
y.23- qm fd d qR,rd go z-dgn ABCD S-qT rrqT t I

R{6 -fr1ftr AB + ctD : AD + BCt s
S
Q.23- A quadlilateral ABCD is clralvn to circttmscribe a circle.
' Prol,e that- AB + CD - AD + BC

A P B

5

y.24- qfr qqmlq Bgu zn1 fu $rd G{TITN t z"* m.q"tlqR znuf t:cm ol
E\, al erq s) U$rq s;6 dfrr I s

Q.24- The altitude ola right triangle is 7cm. less than its base, if the hypotenuse is 13cm.
Fincl the other trvo sides.

3{erc{r oR

ftqrd H+fmruT ix2 - 4tEx + 4:0 d Id of sfft FrTa qrtfu\ I .rR Tdt
zDT GTRd.q d f,) s€ oro olfr{ I 5
Find thc. natlrre of the roots of the quadrate equation 3x2 - 4'l3x + 4:0, If the real
roots cxists, fincl tl-ren-r.

y.2s- ffifu'fl qn6rrq(T qdfl d fdq qttqfr Erd zh1fr\- 5

Q.25- Find the median fbr the fbllowing clata.
q,f
3T{NId
20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
(Class
Interval)
qEEr{d_i \
1 12 IT 16 20 i T6 10 08
(FreqLre ncy')

q.26-ft{€ qift{ fu qR far{fr E5-o o1 go Tql d {+l<N 3Fq E} 5crrcir o)
Frn-fltr.n fr--Egn qq s.ftdE 6{t d Tfr i-{qT d-* wq, a) er.qft\ t
Tdr{ w fi 3rjqrd fr"rrfu-d ei wfr di 5 t

Q.26- Prove that if a line is cllar,vn palallel to one side of a triangle to interest the other two
sides in distinct point, the other two sides are divided in the same ratio.

y.27- c{r{T 7nr 4TdT 20m TniT Tfr ryrT lg}-ET uraT B 3il{ E}{i i}
t
frqe o] e-qm !5q S-drtr{ 22m x 14 m 4TdT Tfr a{flT q{r+t rr+r tr
c
,' [n q{dt o1 dzr{ srd dfr\ | 5

Q.27- A 20m. deep rvell rvith cliameter 7m. is dug ancl the ea(h from digging is evenly
spread out to lbrln a platform 22 mX 14 ni. Find the height of the platform.

3{q7Lr OR

d"-d 2.4 cm. ei-q eqm 1.4 cm. sr& Td- Bts i-d-{ t t sqrq fu 3il-{ {S
qI{I 4Tf,r \ro QlqqoT{ dro o-re ftqT .alfl' t t tq ct gV dvr or ft-fiZ-dq
e{ l*fini ilo- q$q ehwd sro o1frr I

From a solid cviindeL u,hose height is 2.4 cm. and diarheter 1.4cm., a conical cavity of
the same height and same diameter is hollorvecl out. Find the total surface area of the
remaining solicl to the nearest cm2.

,(** **

6