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Important Questions
CBSE CLASS X
Mathematics
1. An ogive in used to determine
(a) mean
(b) median
(c) mode
(d) none of these .
2. If the sum of the zeros of the polynomial
is 1, then one of the value of k is
(a)
(b) - 14
(c) 2
(d) - 4
3. In a ∆ABC,D and E are points on the sides AB and AC respectively such that DE//BC .If AD=2.5cm,
BD=3.0 cm and AE = 3.75cm, then AC =
(a) 7.25 cm
(b) 8.25 cm
(c) 8.75 cm
(d) none
4. The mean
of a data, by step deviation method, is calculated by using the formula :
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5. In an equilateral triangle ABC, if AD ┴ BC, then
(a) 3/4 (b) 4/3 (c) 1/2 (d) 2/1
6. If the sum of ages of father and his son is 65 years and twice the difference of their ages is 50 years,
then age of father is
(a) 45
(b) 40
(c) 50
(d) 155
7. Write the lower limit of the median class in the following frequency distribution .
(a) 20
(b) 30
(c) 40
(d) none of these
8. If the length of the corresponding sides BC and QR of two similar triangles ABC and PQR are
respectively 6cm and 10cm, then the ratio of the areas of ∆ABC and ∆PQR is
(a) 3:5
(b) 9:25
(c) 25:9
(d) 5:3
9. is
equal to
(a) 0 (b) 1 (c) sinө + cosө (d) sinө − cosө
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10.
11. A quadratic polynomial f (x) has two zeros namelya &b .find f (x) if (α +β ) = 19 and (α - β) = 5
(a)
(b)
(c)
(d) none
11. The arithmetic mean of 1,2,3,…,n is
12. If in ∆ABC, AD ┴ BC, and BD : DA =DA : DC, then which of the following angle is a right triangle
(a) ∟ABC
(b) ∟BAC
(c) ∟CAD
(d) ∟BAD
13. - - 34.9 6 is a
(a) terminating decimal
(b)non terminating non repeating decimal
(c) non terminating repeating decimal
(d) none of these .
14. If ∆ABC is similar to ∆DEF such that BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm2. Determine
the area of ∆DEF.
(a) 96 sq cm
(b) 24 sq cm
(c) 72 sq cm
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(d) none
15. The mean of n observation is . If the first item is increased by 1, second by 2 and so on, then the new
mean is
(d) none of these
16. On dividing
by a polynomial g (x) , the quotient and remainder were
respectively . Then the polynomial g (x).
17. If α, β , γ are roots of polynomial 3x3 +5x2 + 8x + 2 find the value of
α-1, β-1 , γ-1
(a) - 4 (b) - 5 (c) - 8(d) none of these
18.
19. If α & β are the zeroes of the polynomial x2+3x-10 then
20. Which one of the following represents the median for the frequency distribution given below :
(a) 22.35
(b) 22.25
(c) 22.75
(d) 22.85.
21. A triangle ABC is right-angled at B, If sin(A - C) = 0 then the value of 2A + C is
(a) 90 0 (b) 135 0
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(c) 145 0 (d) 180 0
22. What must be subtracted from the polynomial
divisible by x2-4x+3.
(a) 2x – 3
resulting polynomial is exactly
(b) 2x + 3
(c) 3x +2
(d) none
23. If one root of the
(a) 0
is polynomia reciprocal of the other, then the value of k is
(b) 5
(c)1/6
(d) 6
24. If the mean and median of a set of numbers are 8.9 and 9 respectively, then the mode will be
(a) 7.2
(b) 8.2
(c) 9.2
(d) 10.2
25.
26. In the adjoining figure ABC is a right triangle, right angled at B. Ad and CE and the two medians
drawn from A and C respectively. If AC = 5 cm and
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cm, find the length
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27.
(a) 0
(b) 1
(c) -1
(d) 2
28. If cos(α + β ) =0, then sin(α −β ) can be reduced to :
(a) cosβ
(b) cos 2β
(c) sinα
(d) sin 2α
29. The value of a and b such that
(a) a = 5 , b = -7
((b) a = - 5 , b = 7
((c) a = 5, b = 7
((d) none .
30. In an isosceles triangle ABC ,If AC = BC and
(a) 450
(b) 60 0
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is divisible by
give the remainder 3x + 5
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(c) 90 0
(d) 300
31. If one zero of polynomial
seven times the other, then the value of k
(a) 5/3
(b) -5/3
(c) 5
(d) none .
32.
33.
34. If α , β , γ are the zeros of the polynomial
35. In ∆ABC, AD is a median. Then
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equal to
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36. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep
together at 12 noon, at what time will they beep again for the first time ?
(a)12.20 pm (b)12.12 pm
(c)12.11 pm (d) none of these
37. A point ‘D’ is on the side BC of an equilateral triangle ABC such that . DC =1/4 BC Then
38.
39. If α , β are the zeros of the polynomial
(a) 1
(b) -1
( c) 0
(d) None of these
40. The average of 11 results is 50. If the average of the first six result is 49 and that of the last six is 52,
then the sixth result is
(a) 53
(b) 54
(c) 55
(d) 56
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41. A ladder reaches a window which is 12m above the ground on one side of the street, keeping the foot
at the same point , the ladder is turned to the other side of the street to reach a
window 9 m high. The width of the street if the length of the ladder is 15 m is
(a) 10m (b) 15m
(c) 21 m (d) 25 m
42. The largest number which divides 70 and 125 leaving remainder 5 and 8 respectively is :
(a) 13
(b) 65
(c) 875
(d) 1750
43. The graph of y = 1 is a line parallel to the
(a) x − axis
(b) y − axis
(c) both x and y axis
(d) none of these
44. If A is an acute angle in a right ∆ABC, right angled at B, then the value of sin A+ cos A is :
45. Two equilateral triangles have the sides of lengths 34 and 85 respectively. The greatest length of tape
that can measure the sides of both of them exactly is
(a) 34
(b) 17
(c) 51
(d) none of these
46. Remaining zeroes of
(a) – 1 , 1 (b) 1 , 1 (c) -1 , -1 (d) none
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if two of its zeroes are
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47. P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm, PB = 6 cm, AQ = 5 cm
and QC = 10 cm, find k if BC = k PQ.
(a)1 (b) 2
(c) 3 (d) none
48. If α & β are the zeroes of the polynomial
49.
form the polynomial whose zeroes are
then the value of x + y is
(a) 2
(b) 3
(c) 1/2
(d) 1
50. In right angled triangle ABC, AC= b, BC = a, AB = c and
(a) cx
(b) 2cx
(c) 2c/x
(d) 2x/c
51. The three angles will be
(a) 200 ,400 ,1200
(b) 300 ,600 ,900
(c) 450 ,405 ,900
(d) 1100 ,400 ,500
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52. If α and β are the zeroes of the polynomial
53.
then sum of their reciprocals is :
is equal to
(a) 2cosq
(b) 2sinq
(c) 0
(d) 1
54. The product of a non-zero rational and an irrational number is
(a) always irrational
(b) always rational
(c) rational or irrational
(d) one
55. In ∆ABC and ∆DEF, if
(a) ∆AABC ~ ∆ADEF
(b) ∆AABC ~ ∆AEDF
(c) ∆AABC ~ ∆AFED
(d) ∆AABC ~ ∆AEFD
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56.
is equal to
(a) 3
(b) 4
(c) 8
(d) 5
57. L.C.M. of a and b, if ab=1050 and H.C.F. of a and b is 15, is
(a) 60
(b) 70
(c) 80
(d) 75
58. If tan2A= cot( A - 18 0 ) , then the value of A is
(a) 18 0
(b) 36 0
(c) 24 0
(d) 27 0
59. If the system of equations kx +15y = 0 and 3x + 5y = 0 has a non-zero solution, then
(a) k = 0
(b) k = 9
(c) k ≠ 0
(d) k = 15
60. In fig. , if D is mid - point of BC, the value of
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(a) 2 (b) ¼ (c) 1/3 (d) ½
61. If the H.C.F. of 210 and 55 is expressible in the form 210×5 - 55y, then y=
(a) 17
(b) 18
(c) 19
(d) 20
62. Students of a class are made to stand in rows. If one student is extra in a row,there would be 2 rows
less. If one student is less in a row there would be 3 rows more. Then the number of
students in the class is
(a) 96
(b) 64
(c) 60
(d) none of these
63. The express sin A in terms of cot A is :
64. Prime factorization of the denominator of the rational number 34. 12345 is of the form:
(a) 2m ×5n where m, n are integers
(b) 2m ×5 n where m, n are positive integers
(c) 2m ×5n where m, n are non-negative integers
(d) denominator has factors other then 2 or 5
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65. A number between 10 and 100 is eight times the sum of its digits. If 45 is subtracted from it, the digits
are reversed. Then the number is
(a) 27
(b) 72
(c) 92 (
d) none of these
66. The zeros of a quadratic polynomial
are α and β .Then tje valus of m if
(a) 6
(b) 5
(c) -6
(d) -3
67. In the following frequency distribution table, write the values of ( a, b, c , d ) is
(a) ( 7 , 6 , 20 , 24 )
(b) ( 6 , 7 , 20 , 24 )
(c) ( 7 , 20 , 24 , 20 )
(d) ( 6 , 7 , 24 , 20 )
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68. If one zero of
is reciprocal of the other, then b =
2
69. The zeroes of 5x − 7x + k are sin A, cos A. Then the value of k is ,
(a) 12/7
(b) 7/12
(c) 12/5
(d) 5/12
70. If α ,β are the zeroes of
then
71. The algebraic sum of the deviations of a frequency distribution from its mean is
(a) always positive (b) always negative (c) O (d) a non-zero numbe
72. If the product of two zeros of the polynomial
73. If
then the value of
( a) 3
( b ) 1/ 2
(c)1/3
( d ) none of thèse
74.
is exactly divisible by (x2 - 1) Then the value of ‘a’ and ‘b’ are
(a) a = -1, b = -2
(b) a = 1, b = 2
(c) a = -1, b = 2
(d) a = 1, b = -2
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75. The mean of the median of 2, 8, 3, 7, 4, 6, 7 and the mode of 2, 9, 3, 4, 9, 6, 9, is
(a) 9
(b) 8
(c) 6
(d) 7.5
are ‘0’ the third zero is
76. Given that two of the zeroes of the cubic polynomial
(a) − b / a
(b) b / a
(c) c / a
(d) − d / a
77. π is
(a) rational (b) irrational (c) imaginary(d) an integer
78. There exist Infinite ……….. numbers between
.
(a) rational (b) irrational (c) real (d) All of a,b,c
79. If α, β are the zeros of the polynomial
(a) 1 (b) 2 (c)
80. If the arithmetic mean of 5, 7, 9 x is 9 then the value of x is
(a) 11
(b) 15
(c) 18
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(d) 16
81. If a , b are the zeros of the polynomial
82. The HCF of the smallest composite number and the smallest prime number.
(a) 1
(b) 2
(c) 4
(d) none of these
83. If
then find the value of λ is
(a) 0
(b) cos2 θ
(c) 1
(d) -1
84. If p, q are two co- prime numbers. HCF (p, q) is :
(a) p
(b) q
(c) pq
(d) 1
85.
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(a) 1
(b) - 1
(c) 2
(d) 0
86. If 29x + 37 y = 103 and 37x + 29y = 95, then :
(a) x = 1, y = 2
(b) x = 2, y = 1
(c) x = 2, y = 3
(d) x = 3, y = 2
87. Square of any positive integer is of the form.
(a) 3q +1
(b) 3q
(c) both a and b
(d) none
88. If ∆PQR is right angled at R, then the value of cos (P+Q) is
(a) 1
(b) 0
(c) ½
(d)
89. 1192 −1112 is
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(a) prime number
(b) composite
(c) an odd prime number
(d) an odd composite number
90. The empirical relationship among the Median, Mode and Mean of a data is :
(a) mode = 3 median + 2 mean
(b) mode = 3 median - 2 mean
(c) mode = 3 mean - 2 median
(d) mode = 3 mean + 2 median
91. If
sin(60 − α ) =1, then the value of a is
(a) 45 0
(b) 150
(c) 600
(d) 300
92. If the least prime factor of a is 3, the least prime factor of b is 7, then the least prime factor of (a+b) is
(a) 2
(b) 3
(c) 5
(d) 11
93. Decimal representation in the form of
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(a) 37330/ 111
(b) 37330/ 999
(c) 3733/ 999
(d) none of these
94. If sin θ = cos θ , then the value of 2 tan2 θ+sin2 θ-1
(a) 3 (b) 3 / 2 (c) 7/2 (d) none of these .
95. The decimal expansion of the rational number
will terminate after :
(a) 3 places (b) 4 places (c) 5 places (d) 1 place
96. If
and αis acute, then (3cosα - 4cos α ) is equal to :
(a) 0 (b) 1/2 (c) 1/6 (d) -1
97. Given that HCF (2520, 6600) = 40, LCM (2520, 6600) = 252× k , then the value of k is :
(a) 1650 (b) 1600 (c) 165 (d) 1625
98. If a, b are coprime, then a2,b 2are :
(a) Coprime (b)Not coprime (C) Odd numbers (d) Even numbers
99. If θ is acute and
then θ
(a) 600
(b) 300
(c) 900
(d) 450
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100.
The value of cos = 150 [Given
cos( α − β ) = cos α cos β+ sin α sin β
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