MP Board Class 10 Question Paper 2020 for Mathematics

Serial Number Roll No.

Total No. of Questions : 26

Total No. of Printed Pages : 16

• P-913
High School, Examination (Regular) - 2020
41 11
MATHEMATICS
(Hindi & English Versions)

Time : 3 Flours [ Maximum Marks : 100

4P1

(i) #1.ti 1;P"

(ii) stHict) 1 # 5 cicb 4q4Tz wchl t W9- t 1

(iii) APB vitch 6 # 26 it ait-ditc f q WT. t I

(iv) ,3-11" lo-114c-t fl-q-

Instructions :

(i) All questions are compulsory.

(ii) Question Nos. 1 to 5 are objective type questions.

(iii) Internal options are given in Question Numbers 6 to 26.

(iv) Draw neat and clean labelled diagram whenever required.

100 P-913 I 1

1x5=5
fi cb t foitr7

bi =__
ZT cri x+bi y+ci =0 UtTT
(i) a2 b2 c2

a2x + b2y + c2 — 0

(b) r cl)) I
(a) W" t;c1) 6) 4 ii

I (d) i 614 I
(c)

(ii) A.P. : 10, 7, 4,... tiT 10q1 trq

(a) 14 (b) 17

(c) —14 (d) —17

a 47 13 -er a + p ITN :
(iii) u1 ftEITff •Tfl-q ax2 +bx+c LRTJF

(a) --
a
(b)

a a
—b-
(d) —b
(c)

-qutrl ittit To 117 PA, PB TEO il3fTq t 80° cbl~i
(iv) ti c.t) P 0
t, LPOA Gitiqt

(a) 50° (b) 60°

(c) 70° (d) 80°

(v) ABC 47 BDE1 qcbit D .i
v BC W" 1:11)1T—N t I

f'13-0 ABC *t BDE i -qTER

(a) 2:1 (b) 1:2

(c) 4:1 (d) 1:4

2 111131N11111111111111U11111111111111131111111 P.T.O.
100 / P-913 1

Choose the correct option and write it :

cl
(i) When i3-= bl = , then the system of equation ai x + 1 1 0 and
a2 . b2 c2

(a) has unique solution. (b) has no solution.
(c) has two solutions. (d) has infinitely many solutions.
(ii) 10th term of the A.P. : 10, 7, 4,..., is

(iii) If a and p are the zeros of the quadratic polynomial ax2 + bx + c ,
then the value of a + is

(a) (b) —
a

a a
(c) (d)

(iv) If tangents PA and PB from a point P to a circle with centre 0 are inclined to
each other at angle of 80°, then ZPOA is equal to :
(a) 50° (b) 60°
(c) 70° (d) 80°
(v) ABC and .BDE are two equilateral triangles such that D is the mid-point of
BC. Ratio of the areas of triangles ABC and BDE is

(a) 2:1 (b) 1:2
(c) 4:1 (d) 1:4

100 / P-913 I HIEN 11 HIM 11111311 00 I 3 UV 111 1111 [ P.T.O.

1 x 5=5
2 -ftr it ch. VA ct;li,-N :

(1) 4-0-9- i 3-1Tzra-9- m-r tv t1
Es,) .
(ii) RA mtil;1 i'r Wit vrtii-it t4L-1131)' -fir 76Z:Wd=fek --"T q 41 t 1

(iii) ter t rTt Lct) 3•ITTITF4

3 11Thir +

(iv) r chi chi 'TO-

(v) itqf tm ft—i
=g-R m—t-th
Fill in the blanks :
(i) Formula of volume of cylinder is rY
ND
(ii) The sum of the probabilities of all -the elemary events of an experiment
is
(iii) There is an empirical relationship between the measures of central tendency :
3 Median = Mode + o'D

(iv) Formula of area of the circle of radius r ism
(v) A tangent to a circle intersects it in LC, point.

i art Ply : 1x5=5
3 ciRqd
o
(i) f sl I ZcI I tclI J Nt CI 411 4 Tizif GI kit (711
c,11 c4 • 614t

r = r

(iii) ti
c 2 771-q 3T1114) 3-1-R4 7r t. I

(iv) -4711 Ar cbl y P14icb cb6c11 tI

(v) • -,[5, tug. tc?-11 t

100 / P-913 1 4 111111111(1 11111 OM 1111 1 11 111 11111 111111111 P.T.O.

Write True/False •in the folling :
00
(i) The cumulative frequ of a class is the frequency obtained by adding
the frequencies of all rthe classes preceding the given class.
(ii) Circumference of a cA.Re of radius r = 2ic r .
(iii) Any polynomial of degree 2 can have at most two zeros.
(iv) The distance of a poll% from the y-axis is called its y-coordinate.
• r••••„)
(v) AE is rational numbg?f,

4 i-er : 1x5=5
.Ft -T 'A'
(i) cos ec(90- 0) (a) 0

1
Vsec2 0 - tan2 0 (b) -

OD
(iii) sin 0° (0) sec 0
a)
(iv) tan 0 (d) .1
•
sin 0
(v) cos 45°
(e) cos 0
Match the correct column !co
Column 'A' co Column 'B'

(i) cos ec(90- 0) (a) 0

1
(ii) c 0 - tan2 0 (b)
-V 2

(iii) sin 0° (c) sec 0
(iv) tan 0 (d) 1

sin 0
(v) cos 45° (e) cos 0
100 / P-913 I 5 11111111111 111111 1111111111 011111111111111111111111111 I R1I'.°.

5 .W1 1;c4.) / cuct-ti -t-R fArq lx5=5

(i) triti-741-

x T y 4Ic cF ti+i)cbtui +-wig> .Fcr foitqt

wr «414,t) FIT ?Am

(iv) itErEd wilcbtui ax2 +bx+c =0 NN,tdcbt cb( foiti-71

(v) cq (x + 1)2 = 2(x —3) itEITff let.-)ut ?

Write the answers in one word/sentence of each :

(i) Write definition of the Line of sight.

(ii) Write the standard form of a linear equation of two variables x and y.

(iii) Write the general form of arithmetic progression.

(iv) Write the formula of the discriminant of the quadratic equation ax2 + bx + c = 0.

(v) Is (x +1)2 =2(x-3) a quadratic equation ?

6 titcmi 12, 15 atiT 21 +Jul-toys H.C.F. - IN7 I 2

Find the H.C.F. of 12, 15 and 21 using the prime factorisation method.

3itc41 / OR
35
-N-11 4 i sritzrr i t•4-d-r-4-4 titsm *1+-teict 5l tilt ti ici
50
TIT atma. 3Tfdc t

Without actually performing the long division, state whether the rational
35
number 5 will have a terminating decimal expansion or a non-terminating
0
repeating decimal expansion.

100 / P-913 ] 6 I 11111111 I 111E111111 11111 1111 1 11 I I 11111111111111 Il ! [ P.T.O.

7 TI:fq x2 —3 t
'1f47 I
Find the zeros of the polynomial x
2 —3 .
afer41 /OR
ft#1 p (x) p (x) ww 4r4 arre
Thrt Ttwr .o-m. W-
fkgr ti. p (x)
471

The graphs of y = p (x)
are given in figure below for some polynomials
p (x) .
Find the number of zeros of p (x) .

8 -k-latf (0, 0) ah
(36, 15) t ft• cbr) #1 .
ffiff Th-tf I
Find the distance between the points (0, 0) and (36, 15).

,3-TeNT / OR
x-3RT 'VT fk--1 .rN•q• (2, — 5) 30 (-2, 9) A- -friTvw
tI
Find the point on the x-axis which is equidistant from (2, — 5) and (-2, 9).

100 / P-913 I
7
i ngla[14111111111141111111641 [ P.T.O.

ITTT4 t iVIVIT A14 -q-N--zIT03:41 f4--1--OT 2
20 A"-'ft-qT:P=f6A 4 q .
9
, from
A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at randomr,
the lot. What is the probability that this bulb is defective ?
3T2r4i i OR
- ''t -crri -ti*I
vrd- -1:cy)
wr( %---
c d-
-r- v t 1 -q- -P-4qTr Ti- rr -griu w-c-4
4 mA -cr-
7- tri- robability of getting an odd number. t'),
A die is thrown once. Find the p (-0

1.:-...)
rciRt ThAt ?
Th-lq tt w=r 7-. f4--a-
.'-.)
tosses two different coins simultaneously. What is the probability that !, s)

Harpreet
she gets at least one head ?
3i 1 / OR

f "T Trit # -TUT f4Wrffl. WUT
3-1-41 .9W- T # % -tf "1- )
52 rcl-qt
"ff'41
SITU Th74 Mc't -51-0W-di
One card is drawn from a well-shuffled deck of 52 cards. Find the prol;ability

of getting a face card.

cosA 4R tan A 149
-4ft sin A=

3 A and tan A.
If sin A=—, calculate cos
4
WM I OR

t'fF'-7 A+B= 90°
TA tan A cot B ,
A + B = 90°
If tan A= cot B, prove that
I P.T.O.
8 1111111111111111111111M1111111111111111111111111
/ P-913 I

12 % A t fi-bft AB L; ,Uzi 3
1:77
4),-q (2, -3) %. Bt 1. 4411E (1, 4
tx)
Find the coordinates of a point A, wilt-re AB is the diameter of a circle whose
centre is (2, -3) and B is (1, 4). --.(1.1

aiaT4T / OR
ti
cz:>
K 9-r9- Id i T, q 4(8,if.,i;-13(K, -4) 4R C(2,-5) Titt t
co
EN.)
Find the value of K if the points-JA(8, 1) 4) and C (2, - 5) are
collinear.

cp
13 5 ci c.f.) art k P tqZ TcP1 PQ 0 A- I 3
(-..
ict) Qt 4ti 4cbi Pff-a\- OQ = 12 4-11. I PQ
LC>

A tangent PQ at a point P of a circle of radius 5 ctn meets a line through
the centre 0 at a point Q so that 0Q-# 12 cm. Find the length of PQ.
312T-41 /' OR
r an 4t 'i refttrkt 4-1*if GRIGR Otr t i
The lengths of tangents drawn from anC'external point to a circle are equal.

t->
14 t fq"--111 st)4-141": 19 1. . I \iti zi Id Q-N-7 3
• f'4:[*r trik-RT 4-11 17i1 tritRT-Eff 42, *IT
(sum
The radii of two circles are 19 cm. and 9 cm. respectively. Find the radius of
the circle which has circumference equal to the sum of the circumferences of the
two 'circles.
/ OR
10 (4cb 1-ct cri) lrqr -q trT Cb Ch) ti I 3tecff
ti I d (41 d -(N5 5Ta-
A-CW Z11d ltA7 I

A chord of a circle of radius 10 cm. subtends a right angle at the centre.
Find the area of the corresponding minor segment.

j0(± / P-913 I Intl 1110111M 111111111 1 11 111 OEM MI NI. I P.T.O.

15 f 1 b-sF 1;4) atcrit144 titgqi t I 4

Prove that 45 is irrational number.

3.1114T / OR

135 3 225 HCF old f'017 zftifig it31179. SP:43T

WA-7 I

Use Euclid's division algorithm to find the HCF of 135 and 225.

16 itEITff Wfq. x2 -2x-8 t *IN-q 41T PIRTO MIT TrItO

#44 -t tic-gm cm-,
\TI - M 41*

Find the zeros of the quadratic polynomial x2 -2x-8 and verify the relationship
between the zeros and the coefficients.

314-4T / OR

3x4 +6x3 -2x2 -10x-5 3TR:i Trlit Id 4IN7, q 3

5- :I
311T -1F
3

Obtain all other zeros of 3x 4 +6x - 2x2 -10x-5, if two of its zeros are 3

and - 3

100 / P-913 ] 10 11111111111111111111111111111111111111111111111111111 [

1. 7 k %-t:r Tim t fo7, litvw •k Ch) Cl ?

3x+y=1

(2k -1)x+(k-1)y=2k+1

For which value of k will the following pair of linear equations have no
solution ?
3x+y=1

(2k-1)x+(k —1)y .2k+1

3111-4T / OR

#1-(-T *:0 4 tsil t Qui 4 18 itt. 31-11M t I d '"IfA71

The larger of two supplementary angles exceeds th,e smaller by 18 degrees.
Find them.

18 f A.P. "9-41:1 Wq 5, 3t1 Ff tg 45 30 q i 400 t1 1c titsqi atT 4
tii 31-UT

The first term of an A.P. is 5, the last term is 45 and the sum is 400.
Find the number of terms and the common difference.

MT-4T / OR

10 3-tiT 250 t Alfq 4 4 t TTR" ?

How many multiples of 4 lie between 10 and 250 ?

100 / P-913 ] 11 111101111111111111111111111111111111111111111111111

28.5 itra7 It TIT t I 31'W1 31-fdl # 4
19 1.5 41-a7 #-4T v,ct) icb f
%(.g & k3.-V4‘1 --1crr 45° t I i'' .1=1-4t4)T-1-.

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation
of the top of the chimney from her eyes is 45°. What is the height of the

chimney ?
IND
T/ OR —1

n 20 lita7 At 8 ,c tr-T (1 c'R6 nil
"qkfl- .WE c.t) cbMicbit
4vr 31-r tA zrpa- t
t, ITT #t4 c=0

"a17 (1.1 RI I 'iii cb-lul 30° A-,"d)- 144 \;')-cu M1 *N71

A circus artist is climbing a 20 m long rope, which is tightly stretched and
tied from the top of a vertical pole to the ground. Find .the height of the pole,
if the angle made by the rope with the ground level. is' 30°.

44 4 1-tr W urm 4 4 Tira7 t, 4
20 #-41 6 14Z7 citc <1.)
W-11" 34t ff1:17;E ct) 1#97. c) A* 28 41-CT t I litITT 4

A vertical pole of length 6 m casts shadow 4 m long on the ground and
at the same time a tower casts a shadow 28 m long. Find the height of
the tower.

aTERT / OR

1.teb VIT-41- NI-J-7 ABC 4 `7T 2a 5I 3&=ft i C P1rtsi-ff-4

ABC is an equilateral triangle of side 2a. Find each its altitudes.

100 / P-913 ] 12 I 1111111111 111111111111111 1111 I 11111 VII 11101111

21 c.t) -Effer 31-16 d W, GN I GI t -crt- t 13---Ter cb) 45 *4. 4
uMl u,do 51)4-11,1d c171 4Yqcb-ff
c
Ilci.4tf* I
fx)
An umbrella 'has 8 rib4\-Arhich are equally spaced. Assuming umbrella to be
a flat circle of radius 45-c-)cm., find the area between the two consecutive ribs
of the umbrella.
/ OR
zired. u11In 3.1-Fr Yrt> 1c1 TIT'q ABCD y-4r 14 tp-it. cbl
m1T APD 3 BPC 3T4-1-fl- I

CD A
11

CO
IN)•D
(x)

Find the area of the shaded region in. given figure if ABCD is a square of side
14 cm. and APD and B_BC ,are semicircles.
co
co
"--1 A

1) C

100 / P-913 13 P.T.O.
11111111111111111111111111 1

itErra- wilcbtui 11' k r L,t1 I ITIffpia"IN-q 4 Gi tip t i 5
22

2x2 +kx +3=0
Find the values of k for. the following quadratic equation, so that they have
two equal roots :

2x2 +kx+3=0
W-F4T / OR

iF Rqd -141c1)1 tqt :

1
x — — =3, x # 0
x

Find the roots of the following equation :

1
x-- =3, x*0
x

23 f
•
cosA 1+sin A
sec
1 + sin A cos A
Prove that :

cos A 1 + sin A
— 2sec A
1+ sin A cos A •,.:
ziemt /OR

-trft A, B efr-t• C -Nip ABC „.etff:ct;lui , -itur- 4

(B+c)___
sin cos A
2 2

If A, B and C are interior angles of a triangle ABC, then show that

B+C A-
sin = cos —
2 2

100 / P-9 1 3 ] 14 11111111111 111 1111111111 11111 111 311E1 111111 1 P.T.O.

24 3 414). .) Ifit7 I fTal7 ;11-U IR 4-A 4 7 414).. .t1
Ter ITT ft-erd- 14s P etrT Q 4rf-4 I - -1'A 1-0 ITT 'JzPi ttgrq 'dikq I
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended
diameter each at a distance of 7 cm from its centre. Draw tangents to the
circle from these two points P and Q.

WI 1 OR
5 ., 6 *it 4R- 7 . c•t) NV' Thff* 3.117 14)
k;cb 31-R4 4 ttpii i f f v-rdf
7
trq fl

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle
7
whose sides are — of the corresponding sides of the first triangle. Also write
5
the steps of construction.

25 iiiso TqT4 q141 f \;)-cni 24 .4rit. arr1117 -14— rr 6 tgt. clrlt t PiT 5.
iiqi t I ict) tsit.. -4 1 t 3TWFT itzrr 4 -k- 1r Z11(1
I

A cone of height 24 cm and radius of base 6 cm is made up of modelling
clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

WIT / OR
qc41 r t c•t) tRV" Vcb tffff 3.1-WT f 1 al-4=-4-ffr
t Itft tRi-ffcI I 14 PA t- ati7 ‘ict)1 5 Th+i) %1
TserzrcT viicf .q§tN.71

A medicine capsule is in the shape of a cylinder with two hemispheres stuck
to each of its ends. The length of the entire capsule is 14 mm and the diameter
of the capsule is 5 mm. Find its surface area.

100 / P-913 J 15 P.T.O.
11E1111111111 I I I 311 11111 1111111111 1111111111111

50s564--4' Afq-T 4—A-Ter d ITT 5
26 itt %Ter

,:.,:...,
470 (TR-4 .4) 500-520 520--4540 540-560 560-580 580-600

12 ,14
t, 8 6 10
IFTRIf tl tiw

sAIWE 4rva- tf4- 470
Consider the following distribution of daily wages of 50 workers of a factory :

Daily wages (in Z) 500-520 520,540 540-560 560-580 580-600

Number of workers 12 14 8 6 10

Find the mean daily wages of the wOrkers of the factory.

zi-2171,j OR

14-.1 arFra-r - 4 i>4) iWrisr 44 4 4* v, -erfig?( N-rg 4)-1 qPi

airi (44 4) 5-15 15-25 '_25-35 35-45 45-55 55-65

trfiTt A titm 6 11 - 21 23 14 5

a4tl cl•k-1 a-TW 'Tr teVIM A-N-71

The following table shows the ages or the patients admitted in a hospital during
a year :

Age (in years) 5-15 15-25 25-35 35-45 45-55 55-65

Number of patients 6 11 21 23 14 5

Find the mode of the data given above.

100 / P-913 ] 16 I 1111111111 111 111 11111 111111111 11111111111 11111 1111111