--
DELHI PUBLIC SCHOOL BANGALORE NORTH
ACADEMIC SESSION 2024-2025
PRE-BOARD EXAMINATION •
SETA
CLASS:X
. ! I
DURATION: 3 hours
'
SUBJECT: MATHEMATICS MAX MARKS: 80
GENERAL INSTRUCTIONS:
Read the following instructions carefully and follow them
1. This question paper contains 38 questions.
2. This Question paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Question no. 1 - 18 are multiple choice questions (MCQs) and questions no. 19 and
20 are Assertion -Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 2 marks
each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 3 marks each.
6. In Section D, Question no. 32-35 are long answer (LA) type questions, carrying 5 marks each.
7. In Section E, Question no. 36-38 is case study-based questions carrying 4 marks each with sob parts
of the values of 1,1 and 2 marks each respectively.
8. All questions are compulsory. However, and internal choice in 2 Question of Section B, 2 Questions
of Section C and 2 Questions of Section D has been provided. An internal choice has been provided
in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
2;
10. Taken:= wherever required if not stated.
11. Use of a calculator is not permitted.
SECTION A
..a:' A library receives a shipment for a series of encyclopaedias. The shipment includes volumes
31 - 40..These encyclopaedias arrive in a box and are not ordered. One encyclopaedia is 1
picked at.random from the box without looking into it. What is the probability that the
volume of the encyclopaedia picked is a multiple of2 OR 5?
I 5 6 7
a) 10 b) 10 ul!f 10 d) io
;r. The pair of equations x + 2y + 5 = 0 and - 3x - 6y + 9 = 0 has
a) a unique solution 1
b) exactly two solutions
c) infinitely many solution
~no solution
In the quadratic equation 6x 2 - gx + 2 = 0 the sum of the rooJs is ~qual to three times their
product. What is the value of g? :-• • •,.•., t , 1
°1 ) :':.i -11)
a) -6
_,
b) - c) 1 ···c. ~,,4
6
1
6"' • • 2• b h zeros of 2 .and -:1, and .a>O,, Gwen this
-ct A quadratic equation Y = ax + x + c as --'--~t P? 1
information, which of the following could be the graph of....,.Jr'-- •
b)
y y .
c) • d)
The cylindrical bumps on top of Lego blocks are called m,ak,
Pragun has built a solid inverted Lego pyramid as shown ia6e~-·Diemuolm rcS1bwls 1
in successive floors forms an arithmetic progression. Praguti Fcma.Gltt6dtcfhcm.moftbe
number of studs used in the first p floors given by ( 6p2 - ]f,). IBW waqt , _ . me 6ere
on the 5th floor - -· --
(NOTE: The figure is only for visual representation)
a) 140 b) 88 c)64
If a and pare the zeroes of the quadratic polynomial / (x) = r 1 - x -- I dlca Ille value 1
0
r!+!.- p·
p a , IS
«~i
_ ~
_,<a . tf _) -,
~ - •·f
_1, ,I :. ,
1 ... lf
a JV' 1-
_-' t
.. \. lt .. f -I IC. .
• C'
q '
a) !.!. c) 4 411
'
'-----'--- ---------- -----·---- ---------- L-.111
2
r.
In the given figure PA and PB ·
cm If L APB = ' h are two tangents drawn lo the circle with centre O and radius
5 600, t en the length of PA is:
• . 1
-tvm~o
I - .ct
{3 r 5
p
-'f3
~ · rA
~
5
--..ar .[J b) 5,/3 c)
/0
./J d) 10
.¥ Raghav drew the following figure on a board where a circle is inscribed in a quadrilateral.
1
p
then he wrote the following relationship.
i) ZW + WX = XY + YZ
ii) ZY + WX = ZW + YX
a) only i $Only ii c) both i and ii d) neither i nor ii
A circle of radius 5 units has its centre at ( -2, 2). The point ( -6, Y{ !i;s o~t~cgtie._
Which of these could be the value of y? , ~ fo-\ 1..- \ ~ ~, i, ; "\ ~-t '-'
a) -3 b) I c) 5 d)6 l.... u4'-'-' ~ t \
\ 6 -\ -1 \ll ,..- 1,.. o
'
A (5,3), B (1,4) and C( 8,5) are the coordinates of the vertices ofa triangle. '-\~- "'~ ..~ ~,---:, !)
which of the following types of triangles will ABC be 1 \. I~ .,\A~•
a) Equilateral triangle ~.~ .\-J \·-
b) Scalene right-angled triangle "J l ~ J I
c) Isosceles right-angled triangle .} . ~
•
I
d) Isosceles acute angled triangle
1 5 tan2 A - 5 sec2 A - I is equal to
a) - 6 b) -5 (c) I (d) 4 1
22 (Sin 60° + cos 30°) + (sin 30° + cos 60°) is equal to 1
(a) 0 (b) 1+2✓3 (c) ,/J - / (d) 1+✓3
3 From an external point M, a tangent MA is drawn to a circle. The number of tnngcnts 1
throu h M arallel to MA is
3
r
(a) 2 (b) more than 2 (c) l (d) 0 }
X A card is selected at random from a deck of 52 cards. Find the probability M t h e ~ l ~
card is red face card. l
3 3
a) u b) s2 c)l d)~
S2
g A solid spherical ball fits exactly inside the cubical box of side 2a. The volume ofdie ball 1
IS
i
16 3
a)
3 rra
32 J
c)
3 1ra
~ The volume of right- circular cone whose area of the base is 156cm2and VUlical beigbt is 1
8cm, is
3
a) 2496cm b) l248cm3 c) l664cm3 d) 416cm1
-0 The mean of five observations is 14. If the mean of firstthree observations is 14 aad dal 1
of the last three observations is l 7,then the third observation is
a) 23 b)l9 c)l8 d)l7
-18 The median of the following observations arranged in ascending order is 13 1
3,7,8,x+l,x+3, 12, 15, l8Thevalueofx.is
a) l O b) 11 c) 12 d) I]
DIRECTIONS : In the question numbers 19 and 20, a statement of Assertion (A) is followed
by a statement of Reason (R). Choose a correct option out of the following:
a) Both Assertion(A) and reason(R) are true, and reason( R) is the c o r r e c t ~
of Assertion(A).
b) Both Assertion(A) and reason(R) are true, and reason( R) is not theoom!d:oqpftnmriY£m
of Assertion(A).
c) Assertion (A) is true but reason ( R) if false.
d) Assertion (A) is false but reason ( R) if true.
.t'9 Assertion (A): Area of the square inscribed in a circle of radius r is
2r 2 sq.units
Reason (R): Area of major segment of a circle = Area of the circle - Afi2 of minor-
segment
40 Assertion (A) : If HCF of 510 and 92 is 2, then LCM of 510 and 92 is 32460 1
Reason (R): For any two positive integers a and b, HCF(a, b) x LCM (a, b) ~ c )( fJ
SECTIONS
If the points(x, y) is equidistant from the points (a+ b, b -a) and (a - b,a + ii}. Pm\-;cthat 2
bx=ay
J-----..;l---,,~- ------------:-::-- ---=---:::----:-;- "7""-;::-;--:-:--- -:------=----·-
.P' /fwo tanks contain 504 and 735 litres of milk respectively. Find the maximum capaci1y of a z
container which can measure the milk of either tank an exact number of times [
OR :I
In a school there are two sections, namely A and B, of class X. There a."t: 30 ~ in
section A and 28 students in section B. Find the minimum number of bot.'!l--s n.>qumL~ ibr
their class library so that they can be distributed equally among students "..r section A or
1-~~S~ec::::.!.:.ti~on'..!....:::B_ _ _ _ _---=---=--~:- ----::--------- ----·-··-···---- -.---
If sec A + tan A = x, then find tan A in terms of x l
L.....__jL__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ - · - - ~
...... 2/
4
From a group of2 boys and 3 girls, two children are selected at random. Find the probability
such that 2
i) at least one boy is selected.
ii) both the selected children are girls.
OR
bag contains tickets numbered 11, 12, 13 ... .30. A Ticket is taken out from the bag at
random. Find the probability that the number on the drawn ticket.
is a multiple of 7
.. is reater than 10 and a multi le of 5
In what ratio does the point P( - 4,y) divide the line segment joining the points A(- 6, 10)
and B(3, - 8) if it lies on AB. Hence find the value of y. 2
SECTION C
Shown below are two circles with centres p and Q. Diameter ST is 6 cm. Find the area of
the shaded region
3
OR
hown below is a circle with centre 0. PQR is an equilateral triangle of side length 12 cm.
Find the area of the shaded region in terms of 7t.
Prove that 4 - 5-fj is an irrational number.
3
Prove that (sin 40 - cos 0 + J)cosec 0
4 2
=2
3
If a and pare roots of a polynomial x 2
- 5 = 0, fonn a polynomial whose roots are
~~~ 3
a
In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2
marks more in Mathematics and 3 marks less in English, the product would hav·e been 3
210. Find her marks in the two subjects.
5
.,
I .
I
I '
JI{ Shown below is a circle with centre O_. YX is the i.angent to die cildlc at Y•
x.:
i) Prove that L1ZWY ~ .1ZYX
ii) Using part i), find the length ofZV.
OR
the following figure if ABIIDC andACandPQ intersectcadt cda'attkpmllO ,
prove that
OA.CQ = OC.AP
p
o,.__ _ _.,___ _ _ _ _.::w, C
SECTIOND
M 1 Prove that the lengths of tangents drawn liom an external poimt 1D 21 circle~ rqnal
3
• Two tangents TP and TQ are drawn to a cildc with centre O fromn m Odclaal point T.
Prove that LPTQ = 2LOPQ
2
T
I
I ~ 5
Calculat~ the mode and the median of the. following frequency distribution table.
~/
Class above above above above above
above above
interval 25 35 45 55 85
65 75
No.of students 52 47 37 17 ,8 2 0
IL OR
,YThe mean of the following distribution is 50, but the frequencies x and y in classes 20-40
and 60-80 respectively are missing. Find the missing frequencies.
CLASS FREQUENCY
0 -20 17
20-40 X
40-60 32
60- 80 y
80 - 100 19
TOTAL 120
5
Solve graphically the pair of linear equations.
3x - 4y + 3 = 0 and 3x + 4y - 21 = 0. Calculate the area of the triangle formed by the
lines so drawn and the x-axis. And shade the triangular region.
OR
'"/or what values of 'm' and 'n' does the following pair oflinear equations have an infinite
number of solutions?
3x + 4y = 12 and
m(x + 2y) - n(x - 2y) = 5m - 1
~ An aeroplane when flying at a height of 4500 metres from the ground passes vertically
above another aeroplane at an instant when the angles of elevation of the two aeroplanes s
from the same point on the ground are 60° and 45° respectively. Find the vertical distance
between the two planes at that instant.(use ..fJ =1.73)
1
SECTION E
J6 Tamper~prooftetra-packed milk . h' security.
• guarantees both tireshness and
uncompromised quality, preserving the nutritional values wit man m
d aking CD& cmmres
Thiii!laudmWe I I
choice for health-conscious individuals.
5cm
500 mL milk is packed in a cuboidal container of dimensions 15 cm x 8 cm ~ .Saa.
These milk packets are then packed in cuboidal cartons of dimensions 30 CDJ x 12 ODJ "-
1~ c~. Based on the above given information, answer the following questiom:
~)Jld the volume of the cuboidal carton.
0'!:!9w ~uch milk can the cup (as shown in the figure) hold? 1
(.MiT(a) Fmd the total surface area of a milk packet. 1
OR
2:
Ill b How man milk ackets can be filled in a carton ?
37 A school has decided to plant some endangered trees on 51st World EnYBWiill!#OMG ~ in
the nearest park. They have decided to plant those trees in few concentric cimdm-rowssoch
that each succeeding row has 20 more trees than the previous one. The fi~ ciitttdar miw bas
50 trees. .
Based on the above given information, answer the following questions :
(i)1-low many trees will be planted in the !0th row ? . _,,
(J.i}1-!ow many more trees will be planted m the 8th row than m the 5th row , ~
(i.iij{a) If3200 trees are to be planted in the park, then how many rows areo~"sr 1
OR
1
(iii) (b) If 3200 trees are to be planted in the park, then how many trees ai! i1iW k#l tsi.) he
planted after the 11th row ? 2 i
L__l_____ _____ _____ _____ _____ _____ _____ ____.___,t
8
In the figure given below, a folding table is shown:
. .I
I
A'-------c
The legs of the table are represented by line segments AB and CD intersecting at 0. Join
AC and BD. Considering tabletop is parallel to the ground, and OB= x, OD= x + 3,
OC = 3x + 19 and OA = 3x + 4,
answer the following questions :
~ Prove that Ii OAC is similar to Ii OBD. 1
(i i}-J>r.ove that ~
AC
=£!!.
BD 1
(iij}'(a) Observe the figure and find the value ofx. Hence, find the length of OC.
OR 2
(iii) (b) Observe the figure and find ;i .
ALL THE BEST
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