Uttarakhand Board Class 10 Question Paper 2024 for Maths

UTTRAKHAND BOARD

Question Paper

<tnd. gfrd Ywi at riqsr 8 =

R.oll No. No. of printed Pages : 8

031 23-L (HGH)
2A24
rrerd
II,IATHEMATICS
g,{fq,3Uo}; t {s#6 : 80
Time:3Hoursl I Max. Marks : 80
fr{qr: (i) {s ewr-qr fr E'o 27 qq7 fll qrfr * srFrard dt

Dlrections: There are in ali 27 questions in this question p;per. All questions are
compulsory.
(ii) qvEt fE frerfRd si6 rqil HEgs stftd Sl
l4arks alloted to the questions are mentioned against them.
(iii) q-fu sy-{ m1 €qffim qB& aex g,.gtrd 5n{ fitssl
Read each question carefr-llly and answer to the point'
(ii,) ryr €reur r vfiotfr'c F{ tl 5s wq e r$d lous b sf,{ d uI{ frfifl
tlS ,Tu dr efr Fq.e-n 3Tq+ ffiqkdtr fi frfuE t

given in
Question No. 1 is multiple choice question. Four options are
answer of eaeh part of this question. Write correct option in your
answer book.
tt t
(v) srq €g'r 1 mT qd6 su-g u-.D stfi 6T vqq {reqr z g do Err 3i6 &
qqqdl qq;I €Eqr 10 + 1 6 E?F d std & sT{fl t qqqdEqr 17 t 21 {6 qK
3io & s'${ dl ss"{ risr 22 e 27 il6 frq 3i6 b eqq f;l
Each part of question No. 1 carries one mark. Question No' 2 to 9
'are of one mark each" Question No. L0 to 16 are of two marks
each. Question I\o. L7 to 21 are of four marks each' Question No'
22 to 27 are of five marks each.
(vi) {fl qs;T-q, fr wrq q-{ mt$ k6N =rfr * delrfr aftq.q sent ii sTaR6 fr-6-s
s,6rq fuqr rur *l tt$ uY{ttt bilf, r'ofu a'r fi rfl{ AiBul
There is no overall choice in this question paper, however, an internal
choice has been provided in few questions" Atternpt only one of the
given choices tn such questions.
t1l tPro

.l

1. (6) FrE{frfua d + srqRiq swr d, 1

In the following, irrational number is:

(i) J16 (ii) JE (iii) + (iv) 0.7s
5
(qq) ErR fum d-drd axz+bx+c b q<-o o sflT p
dt d (*+g) 6r qrq frn , .r

If cr and B are the zeroes of the quadratic polynomial ax2+bx+c, then the

-; q
a
(iii) -: (iv) :
d o
6r sdf Td *m, 1

5th term of the A.p. 10, 7, 4,....... will be:

(i) 1 (ii) -1 (iii) 2
(q) qfr sin o = cos o d e 51 qq $rn,
1

If sin 0 = cos 0, the value on 0 will be:
300 (iii) 45o (iv) 90o
x-3r&T cK furd frg b frfu6 f,, 1

Coordinates of the point on the x-axis are:

(i) (x, 0) (ii) (0, y) (iii) (x, y) (iv) (-x, -y)
qfr frffiil xz-6x+K=o b qtr qrli;T f; dr x 5-1rTrq *fi, 1

If the roots of the quadratic equation x2-6x+K=0 are equar, the varue
of K
will be:

(ii) 6 (iii; e (iv) Lz
(E) qR ansc fi ec=6 effi t a) ns ef< nc b ftq fr-u,il st ;1stflfi
tqilr of mryg
sft' 1

trf in AABC, BC=6 cm, then rength of the rine joining
the mid points of AB
and AC will be:

(ii) 3 cm (iii) 6 cm (iv) 12 cm
231 (HGH)
t21

(H) zrfr m=51ftu
6u sffi b fru qrezT 3il{ qrRror lrrpr: 12d 1s f;, d} 3ftFr qstrd'
+rr- 1
If for a given data, mean and median are 12 and L5 respectively,
then thier
mode will be -
(i) 2L (ii) 13. s (iii) 10 (iv) s
2 Wffi 26 3il{ 91 613rtnfrr gu1qqus frflel Axr HCF f,kT otfuf 1
Find the HCF of integer-s 26 and 91 by using the prime
factorisation method.
3 sq<R ffi Zr, 18, 15,.......... 6"r mtq Ht q( 0 d?
1
Which term of the Ap 21, 19, 15,.....". is 0?

4 16 Eqrd vs6-€T sr-d d,1Bs pfirb
{m s slk _z dr 1
Find a quadratic equation whose roots are 5 and _2.

sin60ocos30o + cos60osin30o 6"t H];t AfO O1fref
1
Find the vaiue of sin60ocos30o + cos60osin30o,

6 fr$i (s, -6) srt< 1-r, -4) ai ffi drd tqrsus 6) y-3T&{ r(:1 b 3rdqm fr frqp
6-krr tt r or qrq Hra dfusr 1
The ratio in which y-axis divides the line segment joining
the points (5, _6) and
(-1, -4) is K:1. Find the value of K.
7 fr-fro1B.8,
1
Prove that:
(secA+ta nA) ( 1 -sinA) = cosA

8 BmT 21 tfr qrd Er6 Tf, h cm frssue 6T et{se
srd etBu, frrffor m}ur ooo tt
. --22 ffifu',)
7 I

1

Determine the area of a sector of a circle.with radius
21 cm, if angle of sector is
600.

( ttt
I taKe lr__lz)
\\"/

e. qfr p(r)=0.0s *, a)'r q-&, 6} rifu6-d1 aq.r d,ft? 1
If P(E)=0.05, what will be the pnobability of ,not E,?
231 (HGH) t 3I I P.T.O.

10. q'fr HCF(306,1314)=re fr LCM(306,1314) gro otHut 2
Ii HCF(30 6,L3t4)=18, find LCM(306,1314).

11. *fW fu :.,D u-o sqR3-q dwr tl 2

Show tltat 31) is an irrational number.

Lz. #{ ffi Erfr fu-trfr (M z * frerys 62 2

How many three-digit numbers are divisibleby 7?

L3. ABCD E6 lrtrrq d frqf Atsl iDC t nw Fflb ffi q{sm kg o q{ qftrdd orfr dr
qvlt$utu
#=# t' 2

ABCD is a trapezium in which ABIIDC and its diagonals intersect each other at

the point o. Show ,f',r. 99
ffi =
3Tzriil / OR
{
fr ryfr 3tr-6.fr d orllBC tt AD Er?T otBer
In the given figure DEllBC, Find AD.

A.

1.8 cm
D E

7.2cm 5,4 cm
t
B

14. s ftft fuqr erd E-6 E-a b kg e q{ wf ksr pq &< o d dr+ qrfr EE tqr t fug q
q-{
{s s-sr{ ffi d fu oq=13 tfrr pa frt ETE-r$ Fr-d 6}ftTs t 2
A tangent PQ at a point F of a circle of radius 5 cm meets a line through the
centre O at a point Q so that OQ=13 crn. Find the length of pe.

231 (HGH) 141

1s. furfrTfuH srcr.dr EiH il fr-d ws6 ert
m-m htBu " L
Find the rnedian class for
qLiency distribution-
drt 3rfrTrf,
Class intervai 0-5 5- 10 10-1 s 1 5-20 za-25
srriqrrnT
frequency 10 1n
1"5 L2 L\) I
I
16. zo qmt b cry H{6 fi 4 qmr sfi6 d I
rs HgF d * m sffi qTq@qT ft-sTmT alni di SH,_6t II
mrr qrfAorffi * fu qa .-re-e*qrs r&
**np .l I
I
A lot of 20 bulbs conra!n 4 defectlve
ones" One bulb is taken at rarrdbm f
lot. What will be the probability that from the I
this bulb will not be defective? I
I

I

$

I

3reril I OR
fufrTfud tb f
Wqsla-ndfrs, f
Solve the fottowing pair of linear equatioris
; {
3x 5y 1
2 3
X Y
5* 2 6

18. qtrqd d ss+ 26 ed eS *r r{ q}di mt
sng fqff itt ffi gqrqhrTsiq * s E{ qffirfl
seo
6T srdTlr, tt- o;i a-Aq,3,rg sr-fl difur
4
Rohan's mcther is 26 years older
than hisn. The product of their ages
' {[n years]
after 3 years from now wiil be 360"
Find Rohan,s present age.

231 (HGH)
t5I I p"T,o.

1s. qfr n efq e ffisf{t: (*2, -z) ell-< 12, -4) 6} d fd-€ p b Frdqri-6 an frfru anfu
o* = ae fi sfr{ p tqrsus AB q{ fura
+
61 4

if Aand B are (-2, -2) and (2, -4) respectively, find the co-srdinates of point P

; AB and P lies on the
such that nO = line segment AB.

4
zo. fuerffifu,
Prove that :
tanO+-=._-=1+SeCeCOSeC0
cot0
1-eot0 1-tan0
srerqr / oR
fu6ffiks'
Prove that:
cosA sin A
1-tanA 1-cotA
2L ffi 14 Sfi e#< sTr€xx # frtrr 6 tfi Er& t'o ottr m'<.g5* nff{ ii * $fr #ar$ 3ilr
fS suem drf,T u6 m6Efu qi$ Frsrd ftrqr fldr t r tq qA ds mI 3{r{i?FT wa dfru t

4

From a solid right circular cylinder with height 14 cm and radius of the base 6
em, a right circular cone of the same height and sanne base is removed. Find the
volume of the remaining solid.

zz. u6 3nqa a5T dlTsm s ilf $-sr$ 6q d fl-dr t, qfr sflfr m6"r$ 5 $5.r$ 6q 6{ ft Hr&
* sfu M s F6r$ dEI fi alfi tr qR 6q ffir$ oi s gffi 3it{ # o} z 6mr$ sdT e
fr *H6d G7 ffif rmr-$ aq Hrdr *l 3lrqrT # AqrE mra #Bel '
The area of a rectangle gets reduced by 9 square units, if its length is reduced br
S units and hreadth is increased by 3 units. If we increase the length by 3 uni',-s
and the breadth by 2 units, the area increases by 67 square units. Find the
dimensions of the rectangle"

3lerdrr / oR
23r (FrGh{} I6I

a

str#ffi$ ffi
The sum of the digits
$#,*,
6r + uqr, H-@T b 3isr
m) wru+ +

of a two-digit number
twice the number obtained is 9. Arso nine times
by reversing the order this number. is
of the digits. Find the
numben
6
23' v+16 ilqlq q{ *u
+qT{ of urrir w furfr
d sfEm m* s ffi# d mofu
s.r s**w ooo t
qe'r 300 d finT
dl +". a fu{ *ffi,,o,
1o q$
The shadow of a tower
standing on a revel g.roo 5
sun's artitude is 30o rhan is found to be 40 m ronger
when ,, ,l uno. Derermine
;l}.,n" the height of rhe

24
;Smry.S?, i*ffif, -rr eik e w ff w q{tr{ p
rrd,

;?"::.:::T;: ."ii'H,:[:jj;I[;1;T,T,: cm rhe,angen,s a, p ano I
3teftil / oR
rso *fr du.d_drfl
16 ds6T.ms mi E_6
w+) b s'r€r{ S qt I a
$ffi# ffi uF t; t o'* .1 r*$ # t, # ++=s
frsqlg*= d arm
*l'o + m-sb 61 Brqr

;::J#,T'*:#:.:;j:#:[]:#:,_:T 'he base of a ,amp.pos, a, a
length of his shadow eter above the ground,
after 4 seconds find the

* BC q{ um
HHA::*P fu D sq rox turo t tu zno c = tanc 8r Gyrf$u
side Bc or a triansre
;i: :I,::::rthe ABc such rhar
24pc=ZBAC. ,nn,:
26' o)s cq.5 ffi b srox
-, *
*'ffi
q-{ 116 pis
ry eruqr<}fra"d, oB d-dirfirr

ffi-H *;Tffi .r*s,, * * fu rq ,* ;sn.+ 'TFT
u,1

jilTJ:ffi
3,
:iffi ;::":,J::1J riil:l.i:, con ica, top,f the rre,s t nl h a

;";;"; ;,,' derermine ,n| T,.::';;:il"::#'ffii
I,H[T:n"J:',.,
231 (HcH)
3[eIEn / OR
171
I P.T.O.

qq 1200 m-r ft1tT 3ffi4 6Te dt q+rro Eilsss
h-mT 12 *fi. Er& um W dt atr$ ftdr *-q
mr elxnm ara ffiul
A ehord of a circle of nadius L2 cm subtends an angle of 1"200 at the centre"
Find

the area of the corresponding segment of the circle.

27. Fqftfua 3ffi 6T qTEil sl-f, fr1ffiu ' 5

Find the rnean of the following data :

e"rf si-fl{TcT 15*25 25*35 3 5-45 45- 55 55-65 65-75 7 5-85
i
I

Class interval
L.

I
I

I
I

I dI{qKfr,T 6 7 t 4 2 1

I
frequency I

*****

231 {HGH} I8I

I

RollNo.
arysqlq

QUESTION PAPERS
GET PREVIOUS YEAR QUESTION PAPERS FOR ALL CLASSES FOR CBSE, ISCSE, ISC AND ALL ALL
STATE BOARDS HERE AT

Andhra Pradesh Board Question Papers
BOARD
WISE Assam Board Question Papers
Bihar Board Question Papers
Chhattisgarh Board Question Papers
Goa Board Question Papers
Gujarat Board Question Papers
Haryana Board Question Papers
Himachal Pradesh Board Question Papers
J&K State Board Question Papers
Jharkhand Board Question Papers
Karnataka Board Question Papers
Kerala Board Question Papers
Madhya Pradesh Board Question Papers
Maharashtra State Board Question Papers
Manipur Board Question Papers
Meghalaya Board Question Papers
Mizoram Board Question Papers
Nagaland Board Question Papers
Orissa Board Question Papers
Punjab Board Question Papers
Rajasthan Board Question Papers
Tamil Nadu Board Question Papers
Telangana State Board Question Papers
Tripura Board Question Papers
Uttarakhand Board Question Papers
Uttar Pradesh (UP) Board Question Papers
West Bengal (WB) Board Question Papers