SEBA Class 10 Sample Paper 2023 Advanced Maths

Sample Paper 2023
Total no of printed O8 DLIE
pages

Pre-Final Assessment Examination-2022
Class: X
Subject: Advanced Mathematics
Full marks : 90 Time: 3 hours
SECTION:A
Question numbers 1(a) to 1(j) each question carries 1 mark

1. In each of the following questions four answers are
providea
of which only one is correct. Choose the correct answer.

a) Let A and B be two sets. If n(A U B) = 90 and
n(B-A) = 38, then n(A) = ?

1, A B 7o RRIOI Z n(A u B) = 90
n(B- A) = 38, COT n(A) = ?

)48 28 52 iv) 90
b) Let A= {1,3.}, B {2,3, 5}. C {1, 3, 4,
= =

6}. The
number of elements in A x B x C is

A = {1, 3,}, B {2,3, 5}, C {1,=

3,4, 6}. =

Ax BxC I CR RI TI--
)9 24 ) 48 iv) 224
c) The value of 1 +i8+is + i is

i) 2 n)i m)-1 iv 0

(PTO)

d) Let a, b, q be three positive integers such that division
of a by b gives a = bq + t, where r is an integer. Then

7 , a, b, q ob1 A9 RY RRI U ba a
a 1 P a = bq + r ( S | (OTT

) 0 <r<b 0sr<kb
m) 0 <r sb iv) 0sr<b
e) The two roots of ax? + c =0 (a + 0) are
ax+ c 0 (a *0}3 T-
) Real (TA) imaginary( )
m) irrational (wAAR) iv) None (91G R)
I f log(2.345) 0.3701, then antilog (3.3701) = ?
ff log(2.345) = 0.3701, cE antilog (3.3701) = ?

)23.45 234.5 ii) 0.02345 iv-2345
g I f log 2 0.3010, then log 2=?
log 2 =0.3010, CTTlog 2=?
i) 0.03010 i) 0.003010
in) 1.3010 0.1505
h x.|14, thenx ?
If |15 = =

a15 x.|14, COU x =?
14 i) 15 iv) 1

Value of cos 2250is
cos 225° N

3
iil) A
1
i)-

2 (Contd)

DILIE

)
)The gradient of the line joining the points (0, 4) and
6 , 2) is
(0,-4) 4 (-6, 2) -y I HRCANS) Ca14 HATO1 &
- m) 2 iv)-2

SECTION:B
Each question carries 2 marks
(Question numbers 2 to 9)
eto aA NTIRT 2 (2 T*7 27 * 9T)

I n a class of 90 students, 60 students play vqlleyball, 53
students play badminton and 35 students play both the
games. Find the number of students who donot play any one
of the two games.
90 9D1 ga 60 A a , 53 A AUATA
3 5 TA TADI CRTTR (RTI NTT 9

3 Simplify: ( |) :

11
4for positive integer n show that

(1-i9| =2

5 I f the difference of the two roots of x't px + q=0 is 1,

then show that p? + 4q2 =
(1 +2q)
x+px + q=0 i 7D 1 T YTa

p+4q = (1 +2q)
3 (PTO)

Without repetition of digits, howmany 4-digit numbers can be
formed with the digits 1, 3, 5, 7, 9?
7 g e 4 t e 1, 3, 5, 7, 9 TROUTA 46) T

I n a triangle ABC, AC =
4.8 cm and AB =
7.2 cm. The
internal bisector of ZA intersects BC at X. If BX = 1.5 cm,

then find BC.
AABC AC =4.8 cm AB = 7.2 cml ZA
T e T BCT XRqT C T BX = 1.5 cm.

BC 1 Gat
8ABCD is a cyclic quadrilateral and the tangent at A to be
circle circumscribing the quadrilateral is parallel to BD.
Prove that CA is the bisector of DCB.
ABCD 01 5 b ARTs sl eDR fauia
BD ATKAI N A, CA, ZDCB 3 TAÍ}RBTI
Using the concept of the gradient of a line show that the
points (6, -1), (5, 0) and (2, 3) are collinear.
R1 ITTO 4111 RAT (TGt a (6, -1), (5, 0) q1
(2, 3) RaRDI 9THA I
SECTION : C
Each question carries 3 marks
(Question numbers 10 to 23)
aroT FTT 3 ( 7 107 23ta)

L I f A={3,5}, B ={1,2,4),
C= {3, 4, 6}, then showthat

(A x B) n {A C)
x
A x (Bn C)
=

(OT CTYGa
t A {3, 5}, B {1, 2, 4}, C {3, 4, 6}
=
=

A x (Bn C) =(A
x
B) n (A x C)
4
(Contd)

11. Let R be a relation defined as
R {(x. y)/x - y is divisible by 3 for x, y e Z}, show that

R is an equivalence relation.
R CDR AR T R = {(x, y)x, y E z 3 ITS X -y

12. If z = a + ib'and | Z +6| = | 2z + 3 |, then show that

2+b29
T Z a +ib | z+6 | =| 2z + 3 | COCE CTNG
a2+b2=9
130sing method of mathematical induction, show that :

2+22+23 +20 2(2 -), n e N.
For any integer a, show that
GCD (2a + 1, 9a + 4) = 1

1 1 . . (2a + 1, 9a +4) = 1 |

15Solve : (7AIK )

x
V1-x
there
16 In the number (0.0012)20 ; how many
zeros are

on the
between the decimal point and the first significant digit
12= 1.07918]
right side of decimal point? [Given that log

1 T l o g 12 = 1.07918]

5 (PTO)

Show that (C7931 a)
nP+r. "P r-
=
n+P
seated in a long
18. n how many ways 5 boys and 6 girls can be
bench so that each by will sit between two girls?

19. Find the value of 0. (900 <0
<270 )
6 Tsa : (909<0<270)
2sin0+V3cos6 +1 = 0
20. IfA+B+C 180°and sinA +sinB cosC
= =
0, then prove
that 2tanB + tanC =
0
T A +B +C 180° sinA + sinB cosC = 0, (OS
e1 a, 2tanB +tanC =0
2Show that ((7e a)
cos80+ cos40° - cos20° 0
22 Two circles touch each other internally at a point P. The
chord AB of the larger circle intersects the smaller circle at
the points C and D. Prove that CPA = ZDPB.

ZCPA =ZDPB
OrRAT
O is a point of the interior of AABC. The bisectors of
LAOB, BOC and 2COA meet AB, BC and AC at D, E

and F respectively. Show that
AD x BE x CF =DB x EC FA

6 (Contd)

AABC O 401 8 : RLAOB, ZBOC ZCOA
6 P A I A AB, BC 1 ACT D, E Fy

AD x BE x CF = DB x EC x FA

of
23. A line passes through the point (-3, 2). Find the equation
the line of the intercepts made by the line on the co-ordinate
axes are equal in magnitude and are of same sign.
qU (-3, 2)a TI RUTR 7a9 G e zi

SECTION : D
Each question carries 4 marks
(Question numbers 24 to 26)
a0 2 T T 4 (e T* 247 at 26cT)

24. z , =4 -

3i and z, =
i, then show that
z +

z,=4 3i 14 z, = z + i, CGTE CPYGT

+ cx + a 0 have a comon
25/If ax? + bx + c =0 and bx
=

root, then prove that
a + b + c = 0 or a = b = c

ax2+ bx + c = 0 bx? + cx+a =0 3 1 CCAROI

a +b + c =
0 a =b =
c

1 (PTO)

26. Reduce the
equation 3x + y +Z=0 to the normal
Hence find the inclination of the form
the origin on the line and also perpendicular drawn from
its length.

3x+y +z=0 ACDI T e RTI

Or/aRAT
Find the equation of
straight line in intercept form.

SECTION:E
Question numbers 27 and 28 each
question carry 5 marks
at9 a TT 5 (*7 27
a 28)
27. Show that for
any natural number n,
32-8n-1 is divisible by 64.
Ce EI S ARRU n 7 <1A I -

8n -

1,
64 NES
28 Prove that the internal bisector of the vertical
angle of a
triangle divides its base in the ratio of the other two sides.

8