DAV INSTITUNONS: MAHARASNTAAND GUJARAT

ZONE 6. For what value of mthe system of equatlons x+2y =5 and 3x +my =-15 has no solution
(UNDER THE AEGIS OF DAVCAE, DAVCMC, NEW DELHI) (a) 2 (b) 3 (c) 6 (d) 1
FIRST TERM EXAMINATION
z923-2024 7. Determine the value of ysatistylng both the equattonsx+6= yand 2x -y=4
(a) 2 (b) 10 c) 16 (d) 4
MATHEMATICS (041) -SET: A
Time Allowed: 3 Hours
Date: 01/09/2023 Muximum Marks: 0 8. Find the value of 'aa for which ax-6x-20 has equal roots
(b) 9
Generoltnstvcton;
1. This question paper has 5 sections A-E. 9. Whlch of the following could be the equatlon of a quadratic polynomlal
(a) (x+1)=(x-3)+5 (b) (%+2) =2x+3*-6
2. Section Ahas 20 MCOs carrying 1 mark each.
(c) x+9=3-2x () 1+*2x-+*4
3. Section Bhas S questions carrying2 marks each.
4. Section C has 6 questions carrying 3 marks each. 10. The sum of the squares of two consecutlve natural numbers is 313. The numbers are?
(a) 12, 13 (b) 13, 14 (c) 11,12 (d) 14, 15
S. Saction D has 4 questlns carrying 5 mark each.
11. If the mode of a data is 53 and mean is 33, then ts median is
6. Section Ehas 3 case-based question of 4 marks with subparts of values 1,1 and 2 (b) 39.66 (d) 37.15
marks esch (a) 39.23 (c) 38.41
respecthvely.
7. Al questions are compulsory. However, an internal cholce has been provided in 2 questlons of 2 marks, 12.Consider the folowing frequency distrlbution othe heights of 60 students of a class
2 questions of 3 marks and Zquestions of S marks. An internal choice has been provided inthe 2 marks Helght (in 150-155 155- 16O 160- 165 165- 170 170- 17S 175- 180
questions of Section E.
cm)
No. of 15 13 16 9
SECTION-A students
1. #x* 2x3x S; y Px3, then the HCF of (x y) is The surn of the lower limit of the modal cass and the upper limit of the median classis
(o) 24 (b) 12 (c)8 (d) 2 (a) 300 (b) 315 () 305 (d) 165

2. FHCF 225, 60) =225 x5 - 10x, then the value of xis 13. If the modal class of data glen below ls 10-15, then the value of is
(a) 111 (b)60 (c) 110 (d) 100 Classes 0-5 5-10 10- 15 15-20 20-25
Frequency 7 6 4
3. Find a qusdratic polynomial, whose zeroes areS and 6 (a) f<8 (b) f28 (c) f=7 (d) fs7
(a) -30 (b) x*x-30 (c)**+30 {d) **30
14. In AABC, AB =6 cm and DE | BC such that AE AC, then find the length of AD
4. e andß are the zeroes of apolynomial y² -4/3x +3, then the value of a +f aß is (a) 2cm {b) 2.5 chn (c) 1 cm (d) 1.5 cm
(a) 4/3-3 (b) 4V3 +3 (c) 4/3 (d} 12/3
S. The graph of y=plxj is given below. Write the zeoes of the polynomlal p

15. in AABC ~A EDF and AABC Is not similar to ADEF, then which of the following is not true?
() BC. EF= AC. FD (b) AB. EF u AC. DE
(c) BC. DE = AB. EF (d) BC: DE AB. FD
()3,-14 (b) 3, 2, 31,4 t) -3, -1, 2, 4 (d)3,-2, -1
 16. If tan =3 and is acute,
then fnd the value of 26 26. (a) Prove that v11 is SECTION-C
(a) 20° (b) 30° (c) 240
(d) 480 Iratlonal
OF
17. Glven that cos9 =the value of 3c
1+tantg
(a) 2 (b) 3 (d) 1 (b) Atraffic lights at three difterent road crossings
(c) 0 108 seconds respecthvely. If they change harige after every 48 seconds, 72 seconds and
18. If cotA= together again? simultaneously at 8 a.m,, at what tlme will théy change
then the value of (cosA - slnA) XcosecA
(a) 27. FInd the zeroes of thepoynomlal 6x-13x + 6
and vertfy the relatlonship between zeroes and
coefficdents óf polynomial.
DIRECTION: In the question numbers 19 and 20. a statement of assertion (A) Is followed bya statament
of Reason, Choose the 28. The sum of the numerator and the
correct optlons. denominator ofa fraction s 8. f3 is added to both nUmerator
and the denominator, the fractlon
a. Both A and B are true and R Is the correct
explanation for A.
b. Both A and Bare true and R Is not the correct
becomesFind the fractlon.
C. A ls true but RIs false.
explanation for A. 29. Nine times a two-digit number is the
same as twice the number obtalned by
d. Alsfalse but Ris trué. digits of the number. If one's digit of the
number exceeds the other by 7, Findinterchanging
the number.
the

19. Statement (A): f(x) = 2x-3x+7 is a polynomial In the 30. (a) The marks of students in a test were
varlable x of degree 4 recorded as under:
Statement (R): The highest power of x in a polynomial of f(x) is called the degree of the Marks% 20-30 30-40 40-50 50-60 60-70 70-80 80-90
polynomial f(x. No of Students 9 12 18 15 6
20. Statement (A): If one root of the quadratic equaion Find the mean marks by assumed mean method.
of k is 2.
6x-x-k=0 is, then the value
OR

Statement (R): The quadratic equation ax+ bx+c=0, a# 0 has atmost twO roots, (b) Find the value of f from the gven data If ts
mode is 6S
Class |0- 20 20-40 40-60 60-80 80-100 100-12o
SECTION- B Frequency 8 12 6
21. (a) Find the quadratic polynomial whose zeroes are Where frequency 6,8, f and 12 are In ascending order.
3+V2 and3 2
OR 31. If sides AB and BC and AD medlan of a triangle ABC are
(b) Ifa. B are zeroes of the respectively
and QR and median PM of triangle POR Show that AABC~APQR proportional to the sides PQ
are 3a and 38
polynomial x-4x +3, then form a quadratic polynomial whose zeroes
SECTION-D
22. Sove for x
4x+- - 32. (a) Determine graphically the coordinates of the vertices of a trlangle the
23. Had Anita scored 10 more are yx,ys4x, **y=5
equations of whose sides
marks in her
wOuld have been the square of her actualmathematics test qut of 30 marks, 9 tímes these narke OR
marks, How many marks did she get In the test? (b) Solve the following system of linear aquatlons graphlcally:
24. (a) Fe s an acute angle and sin =COs , find the 3x +y-12 «0andx-3y+6= 0
value of 3tarr29 +2
OR sin6+ cos -1 Shade the region bounded by these lines and xaxds.
(b) f cos40x)=sin 30, find value of cot (25° +x).
25. Prove that 1 - coc'a
1+coreCa COseca
33. An incomplete
variable
distribution20-30
10-20
s ghven below
30-40 40-50 50-60 60-70
Frequency12 30 65 25
70-80
18 1. What will be the distance covered by Shyam's car In two hours?
You are iren that the median valuels 46 and the total
number of tems is 230. Using the median
formula, fIll up
te missing frequencies. 2. If the quadratic equation in terms of speed of Soham's car be x+5x- 500, what wlIlbe the
34.(a) State and prove Basic Proportionalty Valve of the discriminart.
OR
Theorem 3. What s the speed of Soham's car?
(b) Through the midpoint M of the slde CD of a
parallelogram ABCD, the line BM OR
is drawn Intersecting AC at Land AD produced to E, Prove that EL = 2BL
How much time Shyam took to travel 400 km?
35. If tan+sin = m and tan8-sin@ n, show that m² - n 4mn
CASE STUDY 3
SECTION-E
36. The Growing Power of Electrlcty: Explorlng Energy Consumption
CASE STUDY- 1
As the prefterred form of energy consumption, electricity plays a vital role ln our daly lves.
Seminar for Sublect Educators Across the globe, the demand for electrlcity continues to surge, outpaclng population growth.
A seminar is being conducted by an Educatlonal Organlzation, where the participants wil be educators This surge has resulted In an increase In the average amount of electricty consumed per
of different subjects. The number of participants In Hindl, English and Mathematics are 60, 84 and person, also known as per-caplta electricity consumptlon. Seeking to better understand this
108 trend, a comprehenshve survey was conducted within a colony, reaching out to 56 familes.
respectively. Answer the following questions: The following tables gives the weekky consumptlon of electricity of these familles

1. In each room, If the same number of participants are to be seatedYnd all of them being in the same
subject, Find the maximum numbecpatletpans hatponi accommodated in each room.
2. Find the LCM of 60, 84 and 108.
Weekly consumption (in F0-1010-2020-30 30-40 40-50 50-60
3. What Is the minimum number of rooms required durtng theevent? uníts
OR
No. of famllies 16 12 |18
Explain whether 2x3 x5x17 +17 s acomposit number
37. CASE STUDY 2 Answer the Following questions:
1 Find the medlan dass of the above data.
An Excurlon to Lonavala: ATale of Frlendship and Speed
Embarlang on a memorable joumey, two close frdends, Soham and Shyam, along with their famlles, 2 And the modal class of the above data.
decided to travel to the picturesque destinatlon of Lonavala In thelr own cars. Soham's car gracefuly 3. Find the modal weekly consumption of electricity.
speeds along atz km/h, whlle Shyam's car outpaces Soham's by an additional Skm/h. Surprisingly, It OR
took Soham an extra 4hours to reach their shared destínation, completing the 400km journey.
Find the mean weeky consumptlon of electricity.
 |Not attnpti
97424 Mouday
: 9,12,13,33,32
)a)2A
2)a)L
3))2'47-30

))
22 222

D)

lo a) I2,13

4)dSch
13T527 2 1 313
2

= sihc
--lo

2a
tSy

22)
 12- 44e
12-= 4

25)

LHS
AT9.

THo)

n -n -fo o

S, -6

inhe

ll

aritbcnati) -9
 by

27)

-EI3)

3a(2x3)-2(22-)2o
(3-2)2-3) =0

Brodt not )

4+1
 (

4(xt3) 3(yr3)
-

3x t3y =24

3xt3 24
22)

a loytx) 2(loriy)
6

7y=7

2-4-7

gR M

jhe dagoras but each ohes

PM

A- = 26D. AD

A&8D
by SSS

AABCaER
He rond
32))_sety-keo
-x_3_45 3 o-3
y3_ 3 y32
35)

4-4Coe

4-4 CaA)

4 Vtone- Sa'o
4
 4e(roe)
4 tane e S2e

34)) BPT( 6asie Brgtelional Than lar shen a bnei dhaun

AE

A0

a(ADE) l ADxEE
ar (ODE)= lx
2
Ar0Bx Ef.

as CADE) : AE06

a(BDE) an (cgo

(ADE) =tADXEF

DB

an cED)
!AExD
 Henel Proved !
36)

No antapa in Matntes lo
2 (0284 2 l03 6O23x5
2 30 2 42 2 S4
3 15 3 2I 27
S S 3

mania he
2

i) CM =2x3s«7 3s
S 40
3280 324
3730

2x3xSxl77

3)

400 409

a(at5)
K00 (at) Soe o 2000 4nt20x
hiyo
2
+Sa -Soo =0.
+2s -202-Sogo

a-2)t2s=0

Sx 2

254200ß
20 2S

2oib