CLASS 10 CBSE

MATH E MATICS - 100 MCQ

CBSE X
1. If the HCF(2520, 6600) = 40 and then x is equal to
LCM(2520, 6600) = 252 × k, then the (A) 1 (B) 2
value of k is
(C) 3 (D) 0
(A) 1650 (B) 1600
[CBSE 2024]
(C) 165 (D) 1625
[CBSE 2024] 6. If 3825 = 3x × 5y × 17z , then the value of
x + y − 2z is
2. The smallest irrational number by which (A) 0 (B) 1
√
20 should be multiplied so as to get a ra-
tional number, is (C) 2 (D) 3
√ √ [CBSE 2024]
(A) 20 (B) 2
√
(C) 5 (D) 5 7. The greatest number which divides 281 and
[CBSE 2024] 1249 , leaving remainder 5 and 7 respec-
tively, is
3. The HCF of two numbers 65 and 104 is 13.
(A) 23 (B) 276
If LCM of 65 and 104 is 40 x, then the value
of x is (C) 138 (D) 69

(A) 5 (B) 13 [CBSE 2024]

(C) 40 (D) 8 8. The LCM of three numbers 28, 44, 132 is

[CBSE 2024] (A) 258 (B) 231

4. A pair of irrational numbers whose product (C) 462 (D) 924

is a rational number is [CBSE 2024]
√ √ √ √
(A) ( 16, 4) (B) ( 5, 2)
9. If the product of two co-prime numbers is
√ √ √ √
(C) ( 3, 27) (D) ( 36, 2) 553 , then their HCF is
[CBSE 2024] (A) 1 (B) 553

5. If a = 22 × 3x , b = 22 × 3 × 5, (C) 7 (D) 79

c = 22 × 3 × 7 and LCM (a, b, c) = 3780, [CBSE 2024]

1
10. If the prime factorisation of 2520 is has infinitely many solutions, is
23 × 3a × b × 7, then the value of (A) −2 (B) 2
a + 2 b is:
1 1
(A) 12 (B) 10 (C) (D) −
2 2
(C) 9 (D) 7 [CBSE 2024]

[CBSE 2024] 15. The pair of linear equations x + 2y + 5 = 0

and −3x = 6y − 1 has
11. The LCM of the smallest prime number and
the smallest odd composite number is (A) unique solution
(B) exactly two solutions
(A) 10 (B) 6
(C) infinitely many solutions
(C) 9 (D) 18 (D) no solution
[CBSE 2024] [CBSE 2024]

12. Two positive integers m and n are expressed 16. If ax + by = a2 − b2 and bx + ay = 0, then
as m = p5 q2 and n = p3 q4 , where p and q the value of x + y is
are prime numbers. The LCM of m and n is
(A) a2 − b2 (B) a + b
(A) p8 q6 (B) p3 q2
(C) a − b (D) a2 + b2
(C) p5 q4 (D) p5 q2 + p3 q4
[CBSE 2024]
[CBSE 2024]
17. Two lines are given to be parallel. The equa-
13. In the given figure, graphs of two linear tion of one of these lines is 5x − 3y = 2.
equations are shown. The pair of these lin- The equation of the second line can be
ear equations is
(A) −15x − 9y = 5 (B) 15x + 9y = 5
(C) 9x − 15y = 6 (D) −15x + 9y = 5
[CBSE 2024]

18. Which out of the following type of straight

lines will be represented by the system of
equations 3x + 4y = 5 and 6x + 8y = 7 ?
(A) Parallel
(A) consistent with unique solution.
(B) Intersecting
(B) consistent with infinitely many solu-
(C) Coincident
tions.
(D) Perpendicular to each other
(C) inconsistent.
(D) inconsistent but can be made consistent [CBSE 2024]
by extending these lines.
19. The value of k for which the pair of equa-
14. The value of k for which the system of equa- tions kx = y + 2 and 6x = 2y + 3 has
tions 3x − y + 8 = 0 and 6x − ky + 16 = 0 infinitely many solutions,

2
 (A) is k = 3 (B) does not exist [CBSE 2023]
(C) is k = −3 (D) is k = 4
25. 3 chairs and 1 table cost 900 ; whereas 5
[CBSE 2023] chairs and 3 tables cost 2, 100. If the cost
of 1 chair is x and the cost of 1 table is y,
20. If the pair of equations 3x − y + 8 = 0 and then the situation can be represented alge-
6x − ry + 16 = 0 represent coincident lines, braically as
then the value of ’ r ’ is :
1 1 (A) 3x + y = 900, 3x + 5y = 2100
(A) − (B) (B) x + 3y = 900, 3x + 5y = 2100
2 2
(C) -2 (D) 2 (C) 3x + y = 900, 5x + 3y = 2100
(D) x + 3y = 900, 5x + 3y = 2100
[CBSE 2023]
[CBSE 2023]
21. The pair of equations x = a and y = b
graphically represents lines which are 26. The condition for the system of linear equa-
tions ax + by = c; lx + my = n to have a
(A) parallel
unique solution is
(B) intersecting at (b, a)
(C) coincident (A) am = bl (B) al = bm
(D) intersecting at (a, b) (C) al = bm (D) am = bl
[CBSE 2023] [CBSE 2023]

22. The area of the triangle formed by the line 27. The condition for which the pair of equa-
x y
+ = 1 with the coordinate axes is tions ax +2y = 7 and 3x + by = 16 repre-
a b
1 sent parallel lines is
(A) ab (B) ab
2 7
1 (A) ab = (B) ab = 6
(C) ab (D) 2 ab 16
4
(C) ab = 3 (D) ab = 2
[CBSE 2023]
[CBSE 2023]
23. If 2x + 3y = 15 and 3x + 2y = 25, then
the value of x − y is 28. Graphically, the pair of equations
−6x − 2y = 21 and 2x − 3y + 7 = 0
(A) -10 (B) 8
represents two lines which are
(C) 10 (D) -8
(A) intersecting exactly at one point
[CBSE 2023] (B) intersecting exactly at two points
(C) coincident
24. The pair of equations ax +2y = 9 and
(D) parallel
3x+ by = 18 represent parallel lines, where
a, b are integers, if : [CBSE 2023]

(A) a = b (B) 3a = 2 b 29. In an A.P., if the first term a = 7, nth term

(C) 2a = 3 b (D) ab = 6 an = 84 and the sum of first n terms

3
 2093 a20 − a15 = 20, is
sn = , then n is equal to
2
(A) 4 (B) 5
(A) 22 (B) 24
(C) 4d (D) 5 d
(C) 23 (D) 26
[CBSE 2024]
[CBSE 2024]
36. The common difference of the A.P.
30. nth term of an A.P. is 7n + 4. The common
1 1 − 4x 1 − 8x
difference is , , , . . . . . . . . . . . . . . . .. is :
2x 2x 2x
(A) 7n (B) 4 (A) −2x (B) -2
(C) 7 (D) 1 (C) 2 (D) 2x
[CBSE 2024] [CBSE 2024]

31. In an A.P., if the first term ( a) = −16 and 37. If the first three terms of an A.P. are
the common difference (d) = −2, then the 3p − 1, 3p + 5, 5p + 1 respectively; then the
sum of first 10 terms is value of p is :
(A) -200 (B) -70 (A) 2 (B) -3
(C) -250 (D) 250 (C) 4 (D) 5
[CBSE 2024] [CBSE 2024]

32. Which term of the A.P. −29, −26, −23, . . . .., 38. The number of terms in the A.P.
61 is 16? 3, 6, 9, 12, . . . , 111 is
(A) 11th (B) 16th (A) 36 (B) 40
(C) 10th (D) 31st (C) 37 (D) 30
[CBSE 2024] [CBSE 2024]

33. The common difference of an A.P. in which 39. The 14th term from the end of the A.P.
a15 − a11 = 48, is −11, −8, −5, . . . , 49 is
(A) 12 (B) 16 (A) 7 (B) 10
(C) -12 (D) -16 (C) 13 (D) 28
[CBSE 2024] [CBSE 2024]

34. The sum of first 200 natural numbers is 40. If k + 7, 2k − 2 and 2k + 6 are three consec-
(A) 2010 (B) 2000 utive terms of an A.P., then the value of k
is
(C) 20100 (D) 21000
(A) 15 (B) 17
[CBSE 2024]
(C) 5 (D) 1
35. The common difference of an A.P. in which
[CBSE 2024]

4
41. Two A.P.s have the same first term. The tan(θ + φ) is
common difference of the first A.P. is -3 and √ 1
(A) 3 (B) √
of the second A.P. is -5 . The difference of 3
the 6th term of the second A.P. from that (C) 1 (D) not defined
of the first A.P. is [CBSE 2024]
(A) 2 (B) -8
47. If cos(α + β) = 0, then value of
(C) -10 (D) 10  
α+β
cos is equal to
[CBSE 2024] 2
1 1
42. If a, b, c form an A.P. with common differ- (A) √ (B)
2 2
ence d, then the value of a − 2b − c is equal √
(C) 0 (D) 2
to
[CBSE 2024]
(A) 2a + 4 d (B) 0
(C) −2a − 4d (D) −2a − 3d 48. If sin θ = cos θ, (0◦ < θ < 90◦ ), then value
of (sec θ · sin θ ) is
[CBSE 2024]
1 √
(A) √ (B) 2
43. If the sum of the first n terms of an A.P 2
be 3n2 + n and its common difference is 6, (C) 1 (D) 0
then its first term is [CBSE 2024]
(A) 2 (B) 3 1
 
θ
49. If sin θ = 1, then the value of sin is
(C) 1 (D) 4 2 2
1 1
[CBSE 2024] (A) √ (B) √
2 2 2
3
44. If tan θ = , then cos2 θ − sin2 θ = 1
4 (C) (D) 0
2
7
(A) (B) 1 [CBSE 2024]
25
−7 4 50. If tan2 θ + cot2 α = 2, where θ = 45◦ and
(C) (D)
25 25 0◦ ≤ α ≤ 90◦ , then the value of α is
[]
(A) 30◦ (B) 45◦
45. If sin θ = cos θ, then the value of (C) 60◦ (D) 90◦
tan2 θ + cot2 θ is
[CBSE 2024]
(A) 2 (B) 4  
10 1
(C) 1 (D) 51. The value of sin θ +
2
is
3 1 + tan2 θ
[2021 C] (A) 0 (B) 2
√
3 1 (C) 1 (D) −1
46. If cos θ = and sin φ = , then
2 2 [CBSE 2024]

5
   
cos2 θ 1 58. sec2 θ − 1 1 − cosec2 θ is equal to
52. 2
− , in simplified form, is
sin θ sin2 θ
(A) 1 (B) -1
(A) tan2 θ (B) sec2 θ
(C) 2 (D) -2
(C) 1 (D) -1
[CBSE 2023C]
[CBSE 2023]
59. From a point on the ground, which is 30 m
53. sec θ when expressed in terms of cot θ, is away from the foot of a vertical tower, the
equal to angle of elevation of the top of the tower is
1 + cot2 θ √ found to be 60◦ . The height (in metres) of
(A) (B) 1 + cot2 θ
cot θ the tower is
√ √ √ √
1 + cot2 θ 1 − cot2 θ (A) 10 3 (B) 30 3
(C) (D)
cot θ cot θ (C) 60 (D) 30
[CBSE 2023]
[CBSE 2024]
54. The distance between the points ( a cos θ +
60. At some time of the day, the length of the
b sin θ, 0) and (0, a sin θ − b cos θ ), is
shadow of a tower is equal to its height.
(A) a2 + b2 (B) a2 − b2 Then, the Sun’s altitude at that time is
√ √
(C) a2 + b2 (D) a2 − b2 (A) 30◦ (B) 45◦
[CBSE 2020] (C) 60◦ (D) 90◦
3 [CBSE 2024]
55. If sec x + tan x = , then sec x − tan x =
4
3 4 61. If a vertical pole of length 7.5 m casts a
(A) (B)
4 3 shadow 5 m long on the ground and at the
(C) 3 (D) None of these same time, a tower casts a shadow 24 m
long, then the height of the tower is
[]
  (A) 20 m (B) 40 m
56. cos4 A − sin A on simplification,
4
(C) 60 m (D) 36 m
gives
[CBSE 2024]
(A) 2 sin2 A − 1 (B) 2 sin2 A + 1
(C) 2 cos2 A + 1 (D) 2 cos2 A − 1 62. The ratio of the length of a pole and its
√
shadow on the ground is 1 : 3. The angle
[CBSE 2024] of elevation of the Sun is
 
57. 2 cos2 θ 1 + tan2 θ is equal to (A) 90◦ (B) 60◦
(A) 0 (B) 1 (C) 45◦ (D) 30◦
(C) 2 (D) 3 [CBSE 2024]
[CBSE 2023] 63. In the given figure, AT is tangent to a circle

6
 centred at O . If ∠CAT = 40◦ , then ∠CBA (A) 65◦ (B) 57.5◦
is equal to
(C) 67.5◦ (D) 32.5◦
[CBSE 2024]

66. In the given figure, if PT is a tangent to a

circle with centre O and ∠TPO = 35◦ , then
the measure of ∠x is :

(A) 70◦ (B) 50◦

(C) 65◦ (D) 40◦
[CBSE 2024]

64. In the given figure, tangents PA and PB to

the circle centred at O , from point P are (A) 110◦ (B) 115◦
perpendicular to each other. If PA = 5 cm,
(C) 120◦ (D) 125◦
then length of AB is equal to
[CBSE 2024]

67. In the given figure, O is the centre of the

circle. MN is the chord and the tangent ML
at point M makes an angle of 70◦ with MN.
The measure of ∠MON is :

√
(A) 5 cm (B) 5 2 cm
√
(C) 2 5 cm (D) 10 cm
[CBSE 2024]

65. In the given figure, PT is tangent to a circle

with centre O . Chord PQ subtends an angle
of 65◦ at the centre. The measure of ∠QPT
is
(A) 120◦ (B) 140◦
(C) 70◦ (D) 90◦
[CBSE 2024]

68. In the given figure, AB and AC are tangents

to the circle. If ∠ABC = 42◦ , then the
measure of ∠BAC is :

7
 71. In the given figure, RJ and RL are two tan-
gents to the circle. If ∠RJL = 42◦ , then the
measure of ∠JOL is :

(A) 96◦ (B) 42◦

(C) 106◦ (D) 86◦
[CBSE 2024]
(A) 42◦ (B) 84◦
69. In the given figure, QR is a common tangent
to the two given circles touching externally (C) 96◦ (D) 138◦
at A . The tangent at A meets QR at P . If [CBSE 2024]
AP = 4.2 cm, then the length of QR is :
72. In the given figure, PA and PB are two tan-
gents drawn to the circle with centre O and
radius 5 cm . If ∠APB = 60◦ , then the
length of PA is :

(A) 4 · 2 cm (B) 2 · 1 cm
(C) 8.4 cm (D) 6.3 c
[CBSE 2024]
5 √
(A) √ cm (B) 5 3 cm
70. A chord of a circle of radius 10 cm subtends 3
a right angle at its centre. The length of the 10
chord (in cm ) is : (C) √ cm (D) 10 cm
3
[CBSE 2024]

73. In the given figure, PQ is tangent to the cir-

cle centred at O. If ∠AOB = 95◦ , then the
measure of ∠ABQ will be

√ √
(A) 5 2 (B) 10 2
5
(C) √ (D) 5
2
[CBSE 2024]

8
 (A) 47.5◦ (B) 42.5◦ (A) QR (B) PR
(C) 85◦ (D) 95◦ (C) PS (D) PQ
[CBSE 2023] [CBSE 2023]

74. In the given figure, PQ is a tangent to the 77. In the given figure, AB is a tangent to the
circle with centre O . If ∠OPQ = x, circle centered at O. If OA = 6 cm and
∠POQ = y, then x + y is ∠OAB = 30◦ , then the radius of the circle
is

√
(A) 45◦ (B) 90◦ (A) 3 cm (B) 3 3 cm
√
(C) 60◦ (D) 180◦ (C) 2 cm (D) 3 cm
[CBSE 2023] [CBSE 2023]

75. In the given figure, TA is a tangent to the 78. In the given figure, AC and AB are tangents
circle with centre O such that OT = 4 cm, to a circle centered at O. If ∠COD = 120◦ ,
∠OTA = 30◦ , then length of TA is then ∠BAO is equal to

√
(A) 2 3 cm (B) 2 cm
√ √ (A) 30◦ (B) 60◦
(C) 2 2 cm (D) 3 cm
(C) 45◦ (D) 90◦
[CBSE 2023]
[CBSE 2023]
76. In the given figure, the quadrilateral PQRS
circumscribes a circle. Here PA + CS is 79. In the given figure, PA and PB are tangents
equal to : from external point P to a circle with centre
C and Q is any point on the circle. Then the
measure of ∠AQB is

9
 (A) 62 12 2◦ (B) 125◦ (A) 0.89 (B) 52%
(C) 55◦ (D) 90◦ 1 1
(C) % (D)
13 0.89
[CBSE 2023]
[CBSE 2024]
80. The length of the tangent drawn from a
85. One card is drawn at random from a well
point P, whose distance from the centre of a
shuffled deck of 52 playing cards. The prob-
circle is 25 cm , and the radius of the circle
ability that it is a red ace card, is
is 7 cm , is
1 1
(A) (B)
(A) 22 cm (B) 24 cm 13 26

(C) 25 cm (D) 28 cm 1 1
(C) (D)
52 2
[CBSE 2023] [CBSE 2024]

81. If the probability of a player winning a game 86. Two dice are rolled together. The probabil-
is 0.79 , then the probability of his losing the ity of getting the sum of the two numbers
same game is : to be more than 10 , is
(A) 1.79 (B) 0.31 1 1
(A) (B)
9 6
(C) 0.21% (D) 0.21
7 1
(C) (D)
[CBSE 2024] 12 12
[CBSE 2024]
82. From the data 1, 4, 7, 9, 16, 21, 25, if all the
even numbers are removed, then the proba- 87. A box contains cards numbered 6 to 55 . A
bility of getting at random a prime number card is drawn at random from the box. The
from the remaining is : probability that the drawn card has a num-
2 1 ber which is a perfect square, is
(A) (B)
5 5 7 7
(A) (B)
1 2 50 55
(C) (D)
7 7 1 5
(C) (D)
[CBSE 2024] 10 49
[CBSE 2024]
83. Two dice are rolled together. The probabil-
ity of getting sum of numbers on the two 88. A box contains cards numbered 6 to 55 . A
dice as 2,3 or 5, is card is drawn at random from the box. The
7 11 probability that the drawn card has a num-
(A) (B)
36 36 ber which is a perfect square, is
5 4 7 7
(C) (D) (A) (B)
36 9 50 55
[CBSE 2024] 1 5
(C) (D)
10 49
84. Which of the following is not probability of [CBSE 2024]
an event?

10
89. Two dice are thrown together. The proba- [CBSE 2024]
bility that they show different numbers is
1 5 94. The probability of getting a bad egg in a lot
(A) (B) of 400 eggs is 0.045. The number of good
6 6
1 2 eggs in the lot is
(C) (D)
3 3 (A) 18 (B) 180
[CBSE 2024]
(C) 382 (D) 220
90. The probability of guessing the correct an- [CBSE 2024]
x
swer to a certain test question is . If the
6
probability of not guessing the correct an- 95. Two dice are tossed simultaneously. The
2 probability of getting odd numbers on both
swer to this question is , then the value of
3 the dice is
x is
6 3
(A) 2 (B) 3 (A) (B)
36 36
(C) 4 (D) 6 12 9
(C) (D)
[CBSE 2024] 36 36
[CBSE 2024]
91. If a digit is chosen at random from the dig-
96. From the letters of the word "MOBILE", a
its 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability
letter is selected at random. The probability
that this digit is an odd prime number is
that the selected letter is a vowel, is
1 2
(A) (B) 3 1
3 3 (A) (B)
4 5 7 6
(C) (D) 1 1
9 9 (C) (D)
[CBSE 2024] 2 3
[CBSE 2024]
92. Two coins are tossed simultaneously. The
probability of getting at most one tail is 97. The probability of throwing a number
1 1 greater than 2 with a fair die is
(A) (B)
2 4 2 1
(A) (B)
3 3 3
(C) (D) 1
4 1 5
(C) (D)
[CBSE 2024] 2 6
[CBSE 2024]
93. A bag contains 3 red balls, 5 white balls and
7 black balls. The probability that a ball 98. One ticket is drawn at random from a bag
drawn from the bag at random will be nei- containing tickets numbered 1 to 40 . The
ther red nor black is probability that the selected ticket has a
1 1 number which is a multiple of 7 is
(A) (B)
3 5 1 1
(A) (B)
7 8 7 8
(C) (D)
15 15

11
 1 7 [CBSE 2024]
(C) (D)
5 40
[CBSE 2024] 101. The probability of getting a chocolate
flavoured ice cream at random, in a lot of
99. What is the probability that a num-
600 ice creams is 0.055. The number of
ber selected randomly from the numbers
chocolate flavoured ice creams in the lot is
1, 2, 3, . . . , 15 is a multiple of 4 ?
4 6 (A) 33 (B) 55
(A) (B)
15 15 (C) 11 (D) 44
3 5
(C) (D) [CBSE 2024]
15 15
[CBSE 2024] 102. Two dice are thrown at the same time and
the product of the numbers appearing on
100. All queens, jacks and aces are removed from
them is noted. The probability that the
a pack of 52 playing cards. The remaining
product of the numbers lies between 8 and
cards are well-shuffled and one card is picked
13 is
up at random from it. The probability of
that card to be a king is : 7 5
(A) (B)
36 36
1 1
(A) (B) 2 1
10 13 (C) (D)
3 3 9 4
(C) (D) [CBSE 2024]
10 13

12