SEBA Class 10 Sample Paper 2024 Maths

CLASS 10
SAMPLE PAPER
2024

@aglasem

Total no. p
Examination-2023-24
Class : X
Subject : Mathematics
Full marks : 90 Time :3 hours
Section-A
(Ouestions No. 1to 45 carries 1 mark each)
(e at 1{ t 45ta esj* s t yeytt* 1)

1. Which one of the following is a rational nümber?

V2 V3
(a) (b) (c) ()
W6
2. The number of natural numbers between 18 and 19² is

(a) (b) 38
39 (c) 37 (d) 36
3. Given that LCM (306, 657) = 22338, then HCF (306,
657) is
306 $ 657 .At.O 22338 TG 306 657 4

(a) 306(b) 9 (c) 657 () 8
4. The product of zeroes of x' -9 is

(a) -9 (b) 3 (c) 9 (d) -3
Which of the following is a polynomial?

(a) (b) x +1

$.
X-3
1
(c) x'+5x+6 (d) x²- 5x + 4

1 PT0.

6. Under what condition one zero of ax + bx tc will be
reciprocal of the other ?
f 5Ð It$ ax? + bx + c fagS qEVA gbi sU
yjacDK fopy ?
(a) a = 0 (b) b #0 (c) a = c (d) a # c
7. The common difference ofan AP whosen term =3n+7is
AAq QD sto no4 7 =3n + 7
(a) 2 (b) 3 (c) 4 (d)-2
8. tan0 - sec =?
1
(a) (b) -1 (c) 1 () 2
9. The distance between (p, ) and p, -9 is
(p, ) s(-, -) f At KYE
(a) 2(p+) (b) 0

(c) 4p+q' (d) 2 Vp+q'
10. 20 x 30 x 40=?
(a) -1 (b) 0 (c) 1 (d) 234
11. J17424 =?
(a) 12 (b) 132 (c) 11 (d) 1452
12. Factors of x² - 5x + 6 are
x² - 5x + 6 Get* -
(a) (x - 2), (x- 3) (b)(x + 2), (x - 3)
() (x-2), (x + 3) (d) (x + 2), (x + 3)
13. H.C.F. of 405 and 2520 is
405 *2520 .A1.5. 7
(a) 56 () 45 (c) 9 (d) 405
14. Ifpx)=x'+7x+ 10is a polynomial, then sum of zeroes is

q px) =x'+ 7x + 10 qb E7 3, 58

(a) 7 (b) -7 (c) 10 (d) -10
Contd.

15. Graphically the pair of equations 6x -3y + 10 =0,
2x -y+9=0represents two lines which are
6x-3y + 10= 0, 2x - y+9=0 i I A LG a

(a) Intersecting at one point (b) Coincident

(c) Parallel (d) Intersecting at two points

16. If thelines 3x +2ky =2,2x +5y + 1=0are parallel,then
the value of k is
af 3x + 2ky = 2, 2x+ 5y + 1=0 R0 Tu 84,
2 15
44(a) (b) 5 (c) 4 (d) 2
17. The roots of quadratic equation
2x' 6x +3 = 0 are
2x?- 6x +3 =0 AÝi -
(a) Real and equal (b) Real and unequal

Not real (d) Non real and equal

18. The 11" term of an AP-3, -%, 2...is
-3, -,,2.
2

(a) 28 (b) 22 (c) -38 (d) -48
19. Allsquares are- ( 7 a 6 )
(a) Congrurent (4A) (b) Similar ( )

(c) Both (a) and (b) (d) None of these
((a) fs (b) qA0D0E) (}IKK qbie )
3 PI.0.

25. A die is thrown once, the probability of getting an even
number is

2 5
(a), 3 (b) 1 (c) 6 (d)
26. If two positive integers a and b are written as a = p'g and
b= pq; p, qare prime numbers, then is HCF (a, b) is

(a) p'q (b) pq (c) pq? (a) p'q'
26
27. =?
4+3
(a) 4- 3 (b) 8 -23
(c). 4 + V3 (d) &+ 23
28. If a, Bare zeros of the polynomial f(x) x²+ x+1, then
1.1
the value of+ is
1 1
f(x)= x² +x+ 1 arfCD a ysB t + B

(a) -1 (b) 1 (c) 2 (d) -2
29. Which of the following pairs of inear cquations in two
variables has no solution?

(a) 2x + 3y =7 (b) 2x + 3y =7

3x -2y =7 4x - 6y= 14
(c) 2x + 3y = 7 (d) 2x + 3y = 7
4x + 6y=7 4x + 6y= 14

5 PT:O.

polynomial are 2, and-.
2 then
ofa quadratic
30. Iftwozeroespolynomial will be
the quadratic

x? - 4
(b) x+ 44
(a)
x²- 4x (d) x²+t 4x
(c) 4 and seventh term is
AP, the common difference is
31. In an
term is
4,then the first

(c) 28 (d) 30
(a) 24 (b) 26
the diagonals of arhombus are 16cm and 12
32. The lengths of the side of the rhombus is
cm. Then the length of
cm * 12 cm RDR
qDi T $® yu GA 16

(c) 10cm (d) 12 cm
(a) 6 cm (b) 8 cm
Ifthe distance betwecn the points (4, p) and (1, 0) is 5, then
33.
the value of p is
(4, p) T(1,0) 04 AGY9 53, (9S p A

(b) 3, -3 (c) 5, 5 (d) 3, 5
(a) 4, -4
34. If sin 9= ,then the value of cos is ( < 900) is
b

af sin =b 98 cos® (0 < 90) AA 24
a
b
(a) (b) Vb-a?

Va'-b? Jb'-a2
() (d)
b

6 Contd.

1
35. If sinA and cosB=,then value of A+ B is
2

1
zf sinA = aF cosB=, C98 A+ BA T
22 2

(a) 60 (b) 900 (c) 100° (d) 120°
36. Froma point Q, the length of the tangent to a circle is 24 cm
and the distance of Q form the centre is 25cm. Find the
radius of the circle.

t Q Y25 cm gecDR MI fA?
(a) 5 cm (b) 6 cm (c) Fem (d) 8c
37. If tangents PA and PB from a point P to a circle with centre
Oare inclined to each other at angle of 80", then the
measure of ZPO0A is

(a) 400 (b) 50° (c) 60° (d) 900
38. The area of a sector of a circle with radius 6cm and angle
of the sector is 600

132 7
(a) cm? (b) 132 cm?
7

132
(c) 132 cm? (d) cm²
22

7 PI.0.

39. The surface area of twospheres are in the ratio 1 :2, then
the ratioof their volumes is

(a) 1: 2 (b) 1: J2 (c)1:242 ( t:8
40. Find the median when it is given that mode and mean of a
distribution are 9 and 7.5 respectively.

(a) 9 (b) 8 (c) 7.5 (d) 7
41. Two coins are thrown together. The probability of getting
two heads is

1 1
X (c) 4 (d) 1
a) 2
(b) 3
42. If x= 2sin 0, y= 2cos0 - 2, then x + y =?
q X =2sin0, y =2cos0 -2, (5G xt y= ?
a) (b) 1 (c) 2 (d) 4
43. If aand ß are zeroes of f(x) = px'- 2x + 3p and a +ß=
aß, then the value of p is
zfa as B, f(x) = px'- 2x + 3p E7 aIcog t
a + B = aß, (0S p
3
a) 2
(c) 6 (d) 1
44. If xtan 60° cos 60°= sin60 cot 600, find x'.

a x tan 60° cos 60°= sin60° cot 60°, ( 9 X
1
(a) (b) 2 (c) V3 (d) 1

Contd.

45. On what condition px + qx +r0 has no real roots ?
b6 tCF px² + qx +r= 0fats AIACDA GAIA

(a>4qr (b) p² < 4qr
(c) q < 4pr (d) '> 4pr
Section-B
(Questions No. 46 to 51 carries 2 marks each)

46. Factorise (e* RC )
(l+ m)² - (|- m
47. Find the roots of 3x? 5x + 2 =0
3x- 5x +2= 0 COK y AN 0I
48. Provethat7is irrational.

49. In fi, PO | RS, then prove that APOQ~ ASOR.
P

APOQ ASOR.
Q
1- tan 0
50. If 3cot = 4, find the value of
1+ tan 0
1- tan 0
3cot0 =4, (9CS 1+ tanA
51. If tan (A + B) = /3 and
11
tan (A -B) = 0° <A+ B< 90, A> B, then find A
and B.
1

af tan (A + B) = 3 *tan (A - B) = Ai
0<A + B<90°, A> B, COI A BA |

PT.O.

Section -C
(Questions No. 52 to 58 carries 3 marks each)
(e aR 524 t 58a ecojF e euiK$ 3)
52. Use Euclid's division lemma to show that the square of any
positive integer is either of form 3m or 3m + 1 for some
inteser m.

Or/IAI
The sum of two digits of a two digit number in 9. Also, nine
times this number is twice the number obtained by reversing
the order of the digits. Find the number.

1
53. Solve ( ) X+-=25+
25
Or/aAI
1 1 11
Solve ( )
X
+4 X-7 30
54. Which term of the AP 121, 117, 113....is its first negative
ten?
121, 117, 113....4 sfoco R g s4G01
55. Find a relation between x and y such that the

point (x, y) is
equidistant from the points (3, 6) and (-3, 4).
x y* y A Ao# Glast s(x, y)
feooi (3, 6)

10
Contd.

Or/
Prove that ( )
cOs sin 0
= sin 0+ cos
1-tan 0 1-cot 0
56. Two concentric circles are of radii 5cm and 3cm. Find the
length of the chord of the larger circle which touches the
smaller circle.

57. Agulab jamun, contains sugar syrup up to about 30% of its
volume. Find approximately how much syrup would be found
in 45 gulab jamun, cach shaped like a cylinder with two
hemisphereical ends with length Scm and diameter 2.8cm.

58. The following data gives the distribution of total monthly
house hold expenditure of 200 families of a village. Find the
model monthly expenditure of the families.

Expenditure (In Rs) No.of families
(6 bo)
1000 - 1500 24
1500 - 2000 40
2000- 2500 33
2500 - 3000 28

3000 - 3500 30
3500 4000 22
4000 4500 16
4500 - 5000 7

11 PTO.

Section - D
(Questions No. 59 to 61 carries 4 marks each)
(et aR 59 t 617A eOJF qOj0$ 4)
59. Obtain allother zeros of 2x+-3x' -3x'+ 6x -2 if two of
are /2 and-/2.
its zeroes are

60. Construct a triangle similar to a given triangle ABCwith its
sides equal to 4 of the corresponding sides of triangle ABC.
(Write the steps of construction)

3
4

61. The diagonals AC and BD of atrapezium ABCD with
AB || DC intersect each other at O. Show that.
OA OB
OC OD
ABCD AfaA AB ||DC, AC * BD quA O

OA OB
OC OD
Or/
Prove that the tangents drawn at the ends of a diameter of
circle are parallel.

12
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