DAV BOYS SENIOR SECONDARY SCHOOL

GOPALAPURAM, CHENNAI-86
PERIODIC TESTI 2023-2024
MATHEMATICS
CLASS : X TIME : 3 Hrs
DATE : 28-07-2023 MARKS : 80
General Instructions;
1. This question paper consists of 38 questionSdividedinto5 sections. A, B, C, D and E.
2. Section A has 20 MCQs carrying 01 mark each
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 mark each.
5. Section D has 4 questions carrying
05 marks each.
6. Section E has 3 case based
values of 1,1 and 2 marks eachintegrated units Ofassessment (04 marks each) with sub-parts of
respectively.
7. All questions are compulsory.
However, an internalchoice in 2 questions of 5 marks, 2
questions of 3 marks and 2 questions of
2 provided. An intemal choice has been
provided in 2 marks questions of section marks has been
E.
8. Draw neat figure wherever
required.
SECTION A 20 x 1 = 20
If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a = 1

2 The LCM of the smallest two-digit number and the smallest 1

composite number is
a) 12
c) 20 d) 40

3 The sum of the exponents of prime factors in the factorisation of 196 1

is

4 If xy = 180 and HCF(x, y) = 3, then CM (x, y) is 1

a) 60 b) 540
c) 90 d) 54

l, 300 and B is an acute angle, then the value 1

of B is
a) 45 0 b) 600
c) 30 0 d) 78
0

6 3 chairs and 1 table cost 900; while 5 chairs and 3 tables cost 1
2100. If the cost of 1 chair is x and the cost of 1 table is y, then
the situation can be represented algebraically as:
 3y 900
a) 3x + y 900 b) x+
2100
sy 2100
900
c) 3x + y 900 d) x+3y
+ 3y 2100
2100
The given pair of "near equation the 1
n nonintersecting.Which Of
following is true?

b2
¯

8 Two lines are given to be

intersecting at a point. If the equation of one 1
of the lines is 3x—2y = 5, then
the equationof the second line can be

c) —12x+ By = 28 d) 12x-8y=20
9 The values of x and y satisfying the twoequations32x + 33y = 34 1
and 33x + 32y = 31 respectivelyare
b) —1,4
d) -1,2

10 If 3q = 6 and 2P 2q = 10, then the value of q is 1

11 The ratio in which the line segment joining (2, —3) and (5, 6) is divided 1
by the x axis is

1
12 The value of a, for which the point P G, 2) is the midpointof the line
segment joining the points Q(—5,4) and O) is

1
13 The distance between the points P( m•—n)and n) is
a) units b) (m + n) units

c) units d) units
r 14 If the ond points o a diameterOfn circlo aro
(—6.3) and (6, 1
the centro of tho circle is
a) (12,-7)
c) (0.3.5) d) (6, 3.5)

15 The coordinates of a point which

divides the line segment joining the I
points (6, 3) and (—4,S) in the ratio are

5)
16 If the distance between the
points (4,p) and (1,0) is 5, then the value 1
Ofpis

17 - = x sin 450cos 45 0 then x is 1

1 -1
2 2
3
c) 3
2
2

in &ÄBC right angled at B, sin . Then the value of cos C is 1

25
7 24
25
7
24 7
19 Direction: In each of the following(question19 and question 20), a 1
statement of Assertion is given followedby a statementof Reason.
Choose the correct one.
tan 60 0
Assertion: The value of cot 600
is 3.
Reason: The value of the expression (sin 0 0 —cos 00) is negative.
a) Both Assertion and Reason are true and Reason is the
correct explanation of Assertion.
b) Both Assertion and Reason are true but Reason is not
the correct explanation of Assertion.
c) Assertion is true but Reason is false.
d) Assertion is false but Reason is true.

20 Assertion: Ifx = x 7, 22 x 32x 5, z = x 52

and LCM = 25 x 34 x 52 x 7, then n = 4.
Reason: The value of z is 2025,
a) Both Assertion and Reason are true and Reason is the correct
explanation of Assertion.
 not the
b) Both Assertion and Reanon ttue
explanation of Assertion,
c) Assertion true but Reanon
d) Assertion is false but Roaoon in true.

Soctlon.B 5 N20 10
2
21 Check whether6" can end with tho digit0 any nurjibo(

(OR)
On a moming walk, three persona otop oft togothOCand thoir OtopO
measure 40cm.42cm and 45cm ronpoctivojy, mat in tho minimum
distance each should walk so that each can covor tho oamo diotanco
in complete steps
22 If x = a and y = b is the solution ot the pair Of oquationo 2
3x —Sy— 4 = O and 9x = 2y + 7, find tho valuoo Of a and b,
(OR)
The larger of the two supplementary angles oxcoodo tho sm0110fby
18 0. Find them.
23 Venfy that cos 60 0 = cos 2 0
30 -- sin 2 30 0 2

24 IfA=30 0 and B: 60 0 2
verifythatsin(A+B) = sin A cos B + cogA sin B
25 Find a relationbetweenx and y such that the point
equidistant from the points (7, 1) and (3,5).
Section -C 6 x 3 = 18
26 Prove that 3 + is an irrationalnumber. 3
27 4 3
A fraction becomes — if 1 is added to both numerator and
5'
denominator If, however, 5 is subtracted from both numerator and

denominator, then the fraction becomes mat is the fraction?

28 3
Solve:
2 3

29 3 sec ø—cosec O 1 3
If cot 0 = —
4 prove that sec O+cosecO

30 If sin(A + B) = 1 and cos(A —B) 00 < A + B 900,A > B then 3

find A and B.
(OR)
In a PQR, right-angledat Q, PQ z 3crnand PR=6crn Determine
R.
zQPR and zPRQ. Also find sin P + coo
31 If two vertices of a parallelogramABCD are A(3,2),B(—1,O)and ttE 3
diagonals bisect at (2,-5 ), find the Mher vertices C and D of the
parallelogram.
 Point P divides the Iino segment tho Points ) and B (5—8)
such that If p lies on the line 2x Y k O, find tho value

Section •D 4 5 e 20
32 tani 600+4 cod 450+3sec a00+Gcosi900 5
Evaluate.
cosec 300 •sec 600 —cot? 300
(OR)
In SPQR, right-angled at O. PR Q R 25 cm, and PQa 5 cm.
Determine the value of sin P. cog P and tan p.
33 Show that the points and D(6,2) are tho vortices 5
of a square.
34 In a two-digitnumber, the ten's digit is three times the unit's digit 5
\Vhen the number is decreased by 54, the digits are reversed. Find
the number.
(OR)
Draw the graphs of the equations x —y + 1 = O and 3x + 2y —12 = O.
Determine the coordinates of the vertices of the triangle formed by
these lines and the x-axis, and shade the triangular region.
35 Find the coordinates of the points which divide the line segment 5
joining 2, 2) and B(2, 8) into four equal parts.
Section-E
Q 36 to Q 38 are Case Study
a 4
36 In order to conduct sports day activities in the school, in
rectangularshaped school groundABCD, lines have been drawn
with the chalk powder at a distance of 1m each. 100 flower pots
have been placed at a distance of 1m from each other along AD, as
shown in the figure. Niharika runs —ththe distance AD on the

sewnd line and posts a green flag. Preet runs —ththe distance AD
on the eighth line and posts a red flag.

Answer the following:

(i) Find position of green flag. (1 mark)
(ii) Find the position of red flag. (1
mark)
(iii) Find between the flags. (2 marks)
(OR)
 If Rashmi has between the
to Post a blue nag exactlyhalfway
line segment where should she
joining tho two nags. thon
post her nag?
37 A book store 4
keeper gives books on has a
rent reading. He
variety of books in
his store related to fiction.stories, and quizzoS
etc.. He takes a
fixed charqo for the firsttwodays and an additional
charge for the
subsequent days. Balu paid 02 for a book kopt for 6
days. while Raju paid
e 16 for keeping
books for 4 days.

(Assume the fixed

charge be and additionalcharge (per day)
be æy )
i) Represent Balu's situation
algebraically. (1 mark)
Represent Raju's situation
algebraically (1 mark)
iii) Find the fixed charge and
the charge for each extra day.
(2marks)
(OR)
If both of them keep the book for 2 more days then
find the
total amount paid by both. (2marks)
38 Mathematics exhibitions are organized at the schools and 4
colleges to help the students to understandmathematics more
interestingly. Mathematics exhibitions are very important part of
the
mathematics curriculum.
To inculcate interest in mathematicsamong the students, a
mathematical exhibition is being conducted in a school and one of the
students is making a model of a factor tree.

2763

253

11

Answer the following.

(i) What will be the value of x. (1 mark)
(ii) What will be the value of y. (1mark)
(iii) Find LCM of y and z. (2marks)
(OR)
Find the HCF of x and z.