SEBA Class 10 Sample Paper 2023 General Maths

Sample Paper 2023
Total no of DLIE
printed pages:
Pre-Final Assessment Examination-2022
Class X
Subject: General Mathematics
Full marks : 90 Time: 3 hours

Pass marks : 27
the questioms)
(Ihe jigures in the margin imdicate full marks for
Unless stated otherwise, use T=-

SECTION : A ( 1 )

Choose the correct answer.

1. If 4225 = 65 then V42.25 is equal to

q 4225 =65 3, (OCE 42.25

(b) 6.5 (c) 0.65 (d) 0.045
(a) 65

2 The value of V8+ V27 + V64 is

8 + V27+V64 za
(b) 7 (c)8 (d) 9
(a) 6
24 is 1
3. The product of HCF and LCM of 4, 12 and

4, 12 24 1I.T AT T.3 RRF
(C) 288

(a) 24 (b) 48 (c) 96

1 (PTO)

4. Given positive integers a and b there exist unique integers g
and r satisfying a = bq +r, where 1

7 q 5rI TICG a =
bq + r TG
(a) 0 <r <b (b) 0 Sr <<b
(c) 0 <r sb (d) 0 Srsb
5. The product of the zeroes
of the polynomial 3x2+ 11x-3
S
1
3x2 +llx -3 MDA *71
PA
-11
(a) 3
(b) 3 c)1 (d)-1
6. Under what condition will ax2 +bx + c =
0 be a quadratic
equation? 1
5 6 HCT ax + bx +c = 0 401 aTG 4 RA?

(a) a> 0 (b) a<0 (c) a = 0 (d) a * 0
7. The 20th term of the AP 10, 7,4,.... is 1
10, 7, 4, .. FARA 091ocoR 20 MTI Z-
(a) 47 (b)-47 (c)67 (d)-67
8. AABC ARQP. IfAB =
3.8 cm, BC =
6 cm,
CA 3 3cm, QP = 12 cm then PR = ?

AABC ARQPIz AB =3.8 Bf, BC = 6 B . ZA =

3-/3 , QP = 12 Bf. PRa AM Z -

(a) 7.6 cm (b) 6 cm (c)63cm (d)3.8 cm

2 (Contd.)

99. If the circumference of a circle is 44 cm, then its arca is-I

(a) 276 cm? ((5N.2)
(b) 44 cm* (5a.2)
(c) 176 cm? (CBf.)
(d) 154 cm' (BfM.)
10. Distance ofthe point (-4, 3) from the origin is 1

(4, 3CBR RI
(a) 3 (b) 4 (d) 7

11. Volume of hemi-sphere ofradius r is 1

2 4
2 (b) 47Tr? (d)nr3
(a) 3 (c)
12. If P(E) = 0.09 then the probability of the event "not E" is-

P(E) =0.09 (ET "E R" G1 TERO Ta-
(a) 0.09 (b) 0.81 )0.91 (d) 1.09

SECTION : B (11)

13. 5 persons can finish a piece of work in 20 days. How many
persons can finish the work in 1 day? 2

5 TR 20 ae a AAI ATS ATR

3 (PTO)

14. Pind the smallest perfect square number which is divisible bv
4,9 and 10. 2

15. Find the zeroes of the polynomial x -2 and verify the
relationship between zeroes and the coefficients. 2

16. Find the polynomial whose sum and product of zeros are

respectivelyand -1. 2

1
7-1.
3

17. Solve the equation. (FAT )
x-Sx + 6 =0
18. Find the number of terms of the following AP 2

7, 13, 19, 205

19. Find the value of (A G )
2tan 450 + cos 30° -4sin 600

3
20 If sinA=then find tan A.

sinA = (OT
4
tan Aa Gtmes
(Contd.)

21. The length of a tangent drawn from a point which is at a
distance of 5 cm from the centre of the circle is 4 cm. Find
the radius of the circle. 2

22. Two coins are tossed simultaneously. Then find the
probability of getting at least one tail. 2

23 One card is drawn from a well shufled deck of 52 cards.
Find the probability of getting a spade. 2
a RATNI 52 5 4R SI5E 437

SECTION: C (111)
24. Show that 3 is an irrational number. 3

25. Find the quadratic polynomial whosezeroes are-4 and.3

3

2
26. Solve the following pair of linear equations. 3

X -y 3

6
5 (PTO)

DI AE
Or/7
For which value of k will the following pair of linea
equations have unique solution? 3

4x + ky + 8 = 0

2x2y+2 0
27. The sum of the reciprocals of Rehman's ages (in years) 3 years

ago and 5 years from now is.Find his present age. 3
3
7 3 3R T57 5 RA TR (1K0)

3
28. If the 3rd and the 9th terms of an AP are 4 and 8
respectively which term of this AP is zero? 3

29. Finda relation between x and y such that the point (x, y) is

equidistant from the point (3, 6) and (-3, 4). 3
x y AT 6 GiHea MTE (x, y) D i (3, 6) TT

-3, 4) TOR 1 ATAO I
30. Find the ratio in which the line segment joining A(1,-5) and
B(4, 5) is divided by the x-axis. Also find the co-ordinates
of the point of division. 3

A(1, -5) 7B(4, 5) RTRTAII AI87 x-UTR

(Contd.)

31. Prove that (any one) 3

sin 2sin' 0
) tan 0
2 cos'0- cos0
sec6-1
cOs ece-cot0
i) sece+1

32 The wheels of a car are of diameter 80 em each. How many
complete revolutions does each wheel make in 10 minutes
when the car is travelling at a speed of 66 km per hour?3

TT aocoI bR 10 ffADos
af os 66 A.
Find the
33 The length of the minute hand of a clock is 14 cm.
3
area swept by the minute hand in 5 minutes.

SECTION : D (T*1*N)
subtract 1 from the
34. If we add 1 to the numerator and
denominator a fraction reduced to 1. It becomes i f we
2
the fraction? 4
only add 1 to the denominator. What is

7 (PTO)

DI

Or/e1

of K does the pair of linear equations ivon
For which values
solutions? 4
many
below has infinitely

kx + 3y (k - 3) =0
12x +ky -k =
00
DE || AC
35. In the given figure
D
and DF | AE
Prove that

BF BE B E 4
FE EC
DE || AC DF || AEI
7E1b-

BF BE
FE EC
Or/T7
and PQR
medians of triangles ABC
If AD and PM are
respectively where
AABC ~
APQR, prove that

AB AD

PQ PM
PCA AD UE PMI
ABC PQR 9Y 7b J
AB AD

AABC APQR, (ORY CNIM A1 A PQ PM

8 (Contd)

36./ A quadrilateral ABCD is drawn to
circumscribe a circle. Prove that D R
AB +CD=AD + BC

Q

AB +CD =AD + BCc A P B

Or/31
Two tangents TP and TQ are drawn to a circle with centre
O from an external point T.
Prove that ZPTQ =
2LOPQ

B zAI C A A PTQ =
220PQ
37. Draw a line segment of length 10 cm and divide it in the ratio
3:2. (Write steps of construction) 4

Or/RT
Draw a triangle ABC with side BC=6 cm, AB=5 cm and
LABC= 60°. Then construct a triangle which is similar to
3
AABC whose sides are of the corresponding sides of
4
AABC. (Write steps of construction) 4
BC = 6 . , AB = 5 (bfa, I ZABC = 60° TT ABC 4

R AABC qAR

9 (PTO)

SECTION: E (A11)

38, A tent is in the shape of a cylinder surmounted by a conical
top. If the height and diameter of the cylindical part are
2.1 m and 4 m respcctively and the slant height of the top is
2.8 m, find the area of the canvas used for making the tent.
Also find the cost of the canvas of the tent at the rateof
Rs. 500 per m (note that the base of the tent will not be
covered with canvas). 5

R RIRIA G5U 2.8 , COC 47|6(G

Or/wT
A solid toy is in the form of a hemispher surmounted by a
right circular cone. The height of the cone is 2 cm and the
diameter of the base is 4 cm. Determine the volume of the

toy.Ifa right circular cylinder circumscribes the toy, find the
difference of the volumes of the cylinder and the toy. (Take
T 3.14). 5

CB T f 4 bA. ITODR T Aa

(T 3.14 (1T1)

10 (Contd)

39. The following table shows the ages of the patients in a
hospital during a year.

Age(inyear) 5-15 15-25 25-35 35-45 45-55| 55-65
Number of
patients 6 11
21 23 14 5
Find the mean and mode of the given data.

Or/ekT
The median of the following data is 525. Find the values of
x and y if the total
frequency is 100. 5

1RtO 100
Class interval Frequency
(Cat AA) (314R141)
0 100 2
100 200
200 300 X

300 4000 12
400 500 17
500 600 20
600 700
700 800 9
800 900o 1
900 1000 4

11