Uttarakhand Board Class 10 Question Paper 2023 for Maths

Uttarakhand Board
Question Paper
CLASS 10

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Roll No. No. of printed pages ; I

031 23L (HGGI
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IT,IATHEMATICS

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Time:3Floursl I Max. Marks : 8O
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Directions : There are in all27 questions in this question paper. All questions are
cornpulsory.
( ii) rwt ig FEfRH 3id rt'6 sn[q siftaa f; t

Marks alloted to the questions are mentioned against them.
(iii) rdd qr{ 6t €sFT$-6 qfud aplr qgtsd r+< *frst
Read each question careftllly and answer to the point.
( iv) rrFT \iwr rc6ffia sq{ dt {s qE & r*6 srs b rf,R C qr{ frdB{
ftd w d r v& ko,ru 3ili+ r+<gRiloT ii ftRsst
euestion No. 1 is multiple choice question. Four options are given in
answer of each part of this question. Write correct option in your
answer book.
(v) ITQ;T{sr 1 6T rd-6 Erus s.F si6 6T tt qs{ €1gr z * g dtF EtF 3i6 &
t t
qr{ dt qqn €qr 10 16 tr6 d 3i6 b qr{ dt sr{ risr 17 21 H?F aN
t
3io b ss{ f;l ,rqq dwr 22 27 d6 fra 3i6 b qq{ St
Each part of question No. 1 carries one mark. Question No. 2 to 9
are of one ma!-k each. Question No. 10 to 15 are of two marks
each. Question No. 17 to 21 are of four marks each. Question No"
22 to 27 are of five marks each.
fs
(vi ) qwT-wr ii sqq rr{ 6Yg k6N q€t t ?rErft oftrrq sFii ti gidRm fr'ffi{
s-ff{ fu?Tr rrqr tl US sv+t iibrd u6 fratdq 6'r fr va< fifret
There is no overall choice in this question paper, however, an internal
choice has been provided in few questions. Attempt only one of the
given choices in such questions.
tll [P.r.o.

:,

1 (6) Frq ti 3TqR+q vqr t ' 1

In the following irrational number is :
(i) 0.12s (ii) zJI (iii) zJq (iv) JZ J8
(qq) sgqd x2 - 3 b E5<6l or cifrrffi{ drn ' 1

Sum of zeroes of the polynomial x2 - 3 will be :
(i) 0 (ii) zJi (iii) 3 (iv) -3
(rT) qfr ffi rrrtt<R ffi mr nqi r{d 3n+ 1 t, d\' tss'r eEt trd drn , 1

If the nth term of an A.P. is 3n+1, its 8th term will be :
(ii) 24 (iii) 2s (iv) 26
1

1

If sin a = ), the value of cos A will be :

(i) o (ii) i (iii) + (iv) +
(E) frgail (4, 5) sfq (0, e) 6l Frnrt ET-& tqT b qw ftE b FIfu6 dt , 1

The co-ordinates of the rnid point of the line joining the points (4, 5) and
(6,9) will be :
(i) (1, 2) (ii) (s, 7) (iii) (s, 2)
(iv) (7, 7)
(a) frsffiqBrga\#5dTs4 ' eb3T$Tdfrdl 5;.fr.$& effiisT3r{qrddrrr:
1

Sides of two similar triang les are in the ratio 4:9. Areas of these triangles
will be in the ratio :
(i) 2:3 (iii) 81 : 16
(ii) 4:e (iv) 16 : B 1
(u) qft Efla gqtdiq x2+kx-6= 6l 16 l[f, 1 t, a] t m qH frrn, 1

If one root of the quadratic equation x2+kx-6=0 is 1, the value of k will
be:
(i) 2 (ii) 3 (iii) s (iv) 6

231 (HGG) 12l

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(a) Eo' qit o) um dI{ tbm'r aror *t sicn srl *qr srq *i fi YrftrdFar 6}fr ' 1

A die is thrown once. The probability of getting an even number will be :

(i) i?..._111 (ii) ; (iii) ; (iv) ;

2 qRfq€sT #6laiqmrnffii-{Hiatqrsrstaenrfftr 1

The decimal expansion of the rational numb., # is terrninating or a

non-terminating rePeating.

3 fru-H ffif,{sr ax2+bx+c=O b {d fi rffr ffir dFt qft b'-+ac=o ? 1

What will be the nature of the roots of tl-ie quadratic equation axz+bx+c=0, if
b2-4ac=0 ?

4 m'r nat e-( mr *.ni
What will be the nth term of an A.P. 2, 4, 6, 8, --'---?

5 fug (r, 4) fr x-3{Eilt$ ffirffil 1

What will be the distance of the point (3, 4) from x-axis?

6 qft u6 Tn # qRB 6n *ft *, d rse FIEn ror drftr 1

If the circumference of a circle is 6n cm, what will be its radius?
7 t
Tn b qrr{ fum ffir fr€ qtr w futrS saf Mi fi* ar sofr f;a 1

How many tangents can be drawn to a circle from a point lying out side the
circle?

8 3d6dt 4, 6, g, 8, 2, 7 6l rTltg ffil *rn? 1

What will be the mean of the data 4, 6, 3, 8, 2,7 ?

9 ffifua p-d r'A 3691 ffi qr€r*F dqr t? 1

What is the median of the following given data?
L4, L5, !8,2L,25,27,31, 35, 38.

231 (HGG) t3I I P.r.o.

10,3fiTrflTUIqgugfrfuar<rwffi12,15st{zt6-ILCMgradBgl2
Find the LCM of the intege rs !2, 15 and 27
by-using the prime factorisation
method.

Find the roots of the quadratic equation
x2+x-6=0'

2
L2. furflfu'
Show that :
tan 480 tan 230 tan 420 tan 670 = 1

13. fr-€c (5, -6) sfi< t-r, -4) dT ffi qrd ttr.rws o1 v-els fuu $wd tt m46o tFklT 2
*l joining the points (5, _6) and
In what ratio the Y-axis divides the line segment
(;1, -4)?
L4. d dedrq gn161ffi s tft der 3 tfr dl C Tn
d rs #dr d ffir$ srd dBs
*mE"#wf or&frr
Two concentric circles are of radii 5 cm and 3
cm. Determine the length of the
chordofthelargercirclewhichtouchesthesmallercircle.
3rerEl / oR
uffi fr-€ A t, ET) ud5 Ta b bts t s tfr (a u< d, ga q-{ sqf ttr-r d dEr$ + tft tt
gefr Dffiiaradfret
5 cm from the center of the
The length of a tangent from a point A, at distance
circle, is 4 cm. Determine the radius of the circle'

ls. * n* s{T-ofr c qR pQllRs t, a fu6 o1tss fu I
poQ - rson tl 2

In the given figure, if PQllRS, prove that a PoQ -
ASOR '

R

P
o

a
S

t4l

231 (HGG)

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€.r

16. 116 ?t& t s nrn sf{ s 6r& rte dr gtr Qtd d t rm iia urqoor FIorfr arfr tt $Hfrt
vrfu'odT mr t fu td mro dP 2

In a bag there are 3 red balls and 5 black balls. A ball is drawn at random from
the bag. What is the probability that the ball drawn is red?

3flcEil / OR
52 qdiS srd rorq t th& qfr u6 Tr$ ii t rry wr Frorf,r wor tl aro rIT b ensnd
dr qrq 6ri fr srftrodr ara dftnut
One card is taken out from a well-sh uffled deck of 52 cards. Find the probability
of getting a king of red colour.

L7 . FrrqftTRrd Hfraxuiib gru ai ro dhs ' 4

Solve the following pair of equations :
23 -2
r/x {Yr-
-f-

49 1
T- r-
{x {Y

18. u6 W t s60 ftrft d dr aq 6Tft tr qfr q-5 s ffi1qdT stRrd
uir nrrr qrf, EII?T

atfi, dqtr$cnrd 1 duroqir*rtrftt trrn.Sfrqrmardfrfrsl 4

A train travels 360 Krn with a uniform speed. If the speed had been SKnn/hour
more, it would have taken t hour less for the same distance. Find the speed of
the train.

3Telfl / oR
3 E{ Td (6qFI # sng tad dl atr Effi'rl sf{ 3i-{ t s E$ qqilq 3Trg & elffiq sT Eh{r
I tr rod rdrn;T 3ilg srd dfrer
The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5

years from now Find his present age.
'r 1.

231 (HGG) t5I I P.T.O.

le. fugfrHs 4

Prove that :
(sin A + cosec A)' + (cos A + sec A), = 7 + tan2 A * cotz A

zo. zrfr R(-s, 7), B(-4, -5), c(-1, -6) 3lR D(4, s) m agfs ABCD b aft{ d, d {s
rrg{amr Sxnmsnotftret 4
If A(-5,7),8(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral
ABCD, find the area of this quadrilateral,

21. ffi ffiqr ktrr 3.s tft Erd tro qTF b sTrorq 6'r t, d rS Btrr ard ro srdTir& T{
smqrtfratt rsfrqdtfrHq$ffi 15 5 tfitr rsffif
orrrqotgdq f{tFm
aradrBut 4
A toy is in the form of a cone of radius 3,5 cm rnounted on a hemisphere of
same radius, The total height of the toy is 15.5 cm. Find the total suface area
of the toy.

SXer.rT / oR
qr+ t 3ttFm qt m tffit6l-{ sfT d 5 ++ qrs drT Es rhmr BFrr rrdrTt Edq b 3rrem
6'r q1s 10 *fr tt qfr rhmr f,otd, {dT dr C ql* 6'r Hr fudrr EE sn}rna
A sphere of diameter 5 cm is dropped into a cylindrical vessei partly filled with
water. The diameterof the base of the vessel is 10 cm. If the sphere is completely
submerged, by how much will the level of water rise?

22. t:-6 qrq 10 dt C ern b sftEm 30 Bfi dsfi €trr b srgga 44 m
urfr tr 1s de C ra
40 fufr elnr b qfrFn ud ss ffi
ffiT b srg6'm arfi tr €n<T fi qr?T dsr;Tra 6t ftrq
u...............rfr
{ qTrT Hkr dhet s
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,
it can Eo 40 km upstream and 55 km downstream. Determine the speed of the
stream and that of the boat in still water,

3[erqr / oR
qfr ffi Frg b 3ivr 3flr F{ #itt z *s frq1 osg, a} aa fr a arfr tr qft 3iqT slk

6{ at{tfi s EiE frsr Hrs, dr aa i * a.m tr ra Frq srd dfrer
231 (HGc) t6I

a

A fraction becomes
fi, ,r2 is added to both the numerator and the denominator.
If, 3 is added to both the numerator and the denominator it Oecornes
f . Find
the fraction.

23. 1 .5 fro rTkrT t6 cr.stb.r 30 fio #t rcn qrq t Fs $ T{ rrff tt rq E6 gt q-dq bt 3ilr
srf,r * ils snd 3fq t r+ry b fuqr< o.r r+rn o.ror goo t ooo d ar+r dr caFs fu rt
tl-+q d BiR fuilS qft ro ffiftF{ rqr tt
s
A 1.5 m tall boy is standing at some distance from a 30 rn tall building. The angle
of elevation from his eyes to the top of the building increases from 300 to 600
as he walks towards the building. Find the distance he walked towards the
building.

24. Ei6 fufr ABC il{r$u hsc BC=G tft, AB=s +ft olk_znsc=600 a}i fr< !m
ftIg
ol dBs, furd wrs bl rirm 6t dr
=gqr
Draw a triangle ABC with side^ABC
Tir.,3ii us * s
BC=6 crn, AB=5 cm and ZABC=600. Then construct
a triangle whose sides u."
ABC.
f times of the corresponding sides of the triangle
3ferqr / oR
5 effi Bilr b w'Til q-{ ufi d wf M dfrs, dr q-{si 600 b m}q w gst dr
Draw a pair of tangents to a circle of radius 5 cm which are inclined
to each
other at an angle of 600.

2s. fra rrd hJd ABC b vfr{ a t ec q{ sar rr{rT erq BC 61 Eg o rR Fs ror< sffia
6rerT t fu ps=3cD dt fue dfru fu zRs, = 2AC2+ acz tt 5
The perpendicular from A on side BC of a given triangle ABC intersects
BC at D
such that DB=3CD. prove that 2AB2 = 2ACZ + BC2
A

B
231 (HGG)
t7l I P.r.o.

26. arKI 7 S Ermr zo fi 116{r tr6 WTi q}dr arar t sfr #
t frdffi €$ frrS 5} sqn sq
t Bafloq zz fr x 1a * 116 il{fiT srr.rT rrrn tl gs rgdt
qrff dffi
ara dtsur
5
A 20 m deep well with diameter 7 m is dug and the eafth from digging is evenly
spread out to form a platform 22 m x 14 m. Find the height of the platform.

/ oR
3[erdrr

uffi vrg b frFo,, sil +s tft #aT t, b m # frsqTs 28 t* sil-r z t* fl r ts6r 3Tr.kFr

Hrd frBet (n =
f Anur
The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm.

Calculate its volume. (take
" = |l
27 . ffifuc affi 6r sgar6 Erd dfrs,
Find the mode of the following data :

sf srtr{rd 1 0-20 20-30 30-40 40-50 s0-60 60-70 70-80
Class interval

qRqr{flI L2 19 6 10 9 6 5

Frequency

*****

231 (HGG) t8l

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