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CLASS-IX, MATHEMATICS [NUMBER SYSTEM], PRACTICE SHEET –M-02[XI AMU ENT-2015]
Which one of the following is a true statement:
(a)
1 is prime
(b)
1 is composite
(c)
1 is neither prime nor composite
(d)
1 is either prime or composite
Q.2.
Pick up the true?
(a)
Every whole number is a natural number
(b)
Every integer is a rational number
(c)
Every rational number is an integer
(d)
Every rational number is a whole number
Q.3.
For basic operations of natural numbers, which of the following is valid:
(a)
Additional & multiplication
(b)
Additional, subtraction and multiplication
(c)
Addition, subtraction, multiplication and division
(d)
Division & multiplication
Q.4.
The set of natural numbers is closed with respect to:
(a)
Additional and multiplication only
(b)
Multiplication only
(c)
Division only
(d)
Subtraction only
Q.5.
Which of the following numbers is closed with respect to addition subtraction,
multiplication and division:
(c)
Set of all numbers
(a)
Set of rational numbers
(b)
Set of natural numbers
(d)
Set of integers
Q.6.
The set of negative integers is closed with respect to:
(c)
Subtraction only
(a)
Additional only
(b)
Multiplication only
(d)
None
Q.7.
Rational numbers are “closed” with respect to:
(a)
Addition and multiplication only
(b)
Addition and subtraction only
(c)
Addition, multiplication and subtraction
(d)
Addition, multiplication, subtraction and division
Q.8.
The sum, difference, quotient and products of irrational numbers are:
(a)
Are always rational numbers
(b)
Are always irrational numbers
(c)
May be rational or irrational
(d)
None of these
Q.9.
The distance between − 7 and |−7| in a number line is:
(a)
−7
(c)
14
(d)
−14
(b)
+7
Q.10. Identify a rational number:
(c)
e
(a)
π
(d)
0.10100111011110
(b)
22/7
Q.11. An irrational number is always:
(a)
Non-terminating, non-recurring
(b)
Terminating, non-recurring
(c)
Non-terminating, recurring
(d)
Terminating, recurring
Q.12. 0.2353535 … … … … … … … can be represented as:
Q.1.
(a)
(b)
𝟐𝟑𝟑
𝟗𝟗𝟎
233
999
(c)
(d)
233
289
234
990
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Q.13.
Let A = {3, π, √2, 2/7, 3 + √7} The subset of A containing all the elements from it which are irrational numbers is:
(a)
Q.14.
Q.15.
Q.16.
Q.17.
Q.18.
(b)
{3, π, 2/7,3 + √7}
{3, 2/7}
(c)
{3}
(d)
π is a:
(a)
rational number
(b)
irrational number
tan π/6 is equal to:
(a)
√3
(b)
1/2
What is true about ‘e’:
(a)
e is a real number between 2 and 3
(b)
e is an example of irrational number
(c)
e stands for exponental
(d)
all the above is true
An irrational number is:
(a)
Terminating
(b)
Non-terminating but recurring
(c)
Non-terminating and non-recurring
(d)
Terminating but no non recurring
Which one of the following is rational?
(a)
Q.19.
(b)
Q.21.
(b)
Q.23.
Q.24.
63
complex number
whole number
(c)
(d)
1/ √2
1/ √𝟑
(c)
(√2 + √3)
(c)
489
119
(d)
997
The least among the following is:
(𝟎. 𝟐)𝟐
(a)
(b)
0.2
The correct expression of 6.40 in the form of p/q is:
(a)
Q.22.
2
(√2 + 2)
(c)
(d)
(d)
(b)
(𝟐 − √𝟐)(𝟐 + √𝟐)
The rational number for the recurring decimal 0.125125 … … . . is:
(a)
Q.20.
{𝛑, √𝟐, 𝟑 + √𝟕}
(c)
(d)
640
(c)
99
𝟔𝟒𝟎
(d)
𝟏𝟎𝟎
2
6/3 √2
𝟏𝟐𝟓
𝟗𝟗𝟗
125
990
0.24
0.4
64640
1000
646
99
The most appropriate statement about a number line is:
(a)
It represents all integers
(b)
It represents all the whole numbers
(c)
It represents both rational and irrational numbers
(d)
It represents all real numbers
First to discover irrational numbers was:
(c)
Aryabhatta
(a)
Pythagoras
(b)
Cantor and Dedekind
(d)
Archimedes
Arc (APB) is a semicircle. P is a point on the circumference from where a perpendicular PO is drawn on the diameter AB suc
OB = x ∶ 1, then the relation between x and y is:
(a)
1
x
P
1
+ =1
y
(b)
(c)
x2 + y2 = 1
y = √𝐱
(d)
x = √y
y
A
x
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O
1
B
Q.25.
Q.26.
The multiplicative inverses of 2 + √3 is:
(a)
2 −√𝟑
(b)
−(2 + √3)
(c)
(d)
If x = 2 + √3, then the value of x + is:
x
(a)
(b)
I only
II only
If x =
√5+1
If
√7−√5
5−3√2
2+√3
2−√3
7
7
= +
2+√3
+
√3−1
√3+1
If √2 = 1.414, then
7
3+√2
1
(a)
(b)
Q.38.
−
0.577
0.202
(c)
6, √35
(d)
7, √5
(c)
(d)
34, −3
None
(c)
4−√3
(d)
16−√𝟑
(c)
(d)
1.584
None
1
√5
equals to:
(c) 0.441
(d) 0.347
1
√6−√5
+
1
√5−√4
−
1
√4−√3
+
1
√3−√2
−
1
√2−√1
0
1
If 28√x + 1426 =
(a)
(b)
(c)
(d)
equal to:
1.586
1.585
If √5 = 2.236, then
√7−√6
9
11
simplies to:
(a) 0.447
(b) 0.437
Q.37.
(c)
(d)
, then the values of a and b are:
0
1
(a)
(b)
Q.36.
b√2
2−√3
(a)
(b)
Q.35.
a
43, −30
43, 30
+
Both I and II are incorrect
None is incorrect
= a + b√35, then the respective value of a and b are:
6, −√35
6, 1
5+3√2
(c)
(d)
is:
√0.414
√7+√5
(a)
(b)
Q.34.
√2+1
4√3
2−3√3
, then the value of x 2 + y 2 is:
1.414
(a)
(b)
Q.33.
√5+1
√2−1
Find the sq. root of
If
√5−1
√5 + 1
13/6
(a)
(b)
Q.32.
and y =
√5−1
(a)
(b)
Q.31.
None
1
(a)
2√3
(c)
(b)
4
(d)
Q.27. A number which lies on a number line is:
(a)
Rational number, not irrational number
(b)
Irrational number, not rational number
(c)
Other than rational or irrational number
(d)
A real number
Q.28. Which of the following is a rational:
(a)
Radius of a circle with circumference 1/π
(b)
Circumference of a circle with radius 1/𝛑
(c)
Area of a circle with radius 1/π
(d)
Radius of a circle with area 1/π
Q.29. Consider the following statements,If r is rational and s is irrational, then
I.
r + s and r – s are irrational numbers
II.
r.s and r/s are irrational numbers
which statements is/are incorrect:
Q.30.
1
2−√3
444
676
3
4
simplifies to:
(c)
−1
(d)
√𝟕 − √𝟏
(c)
(d)
256
None
of 2872, then x is equal to:
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Q.39.
√(7 + 3√5)(7 − 3√5) = … … … … … … …
4
3
(a)
(b)
Q.40.
3 125
√
8/5
5/8
0.0002
0.002
√10 + √25 + √108 + √154 +
Q.43.
(a)
(b)
𝐼𝑓 √3𝑛
(a)
(b)
𝑥𝑎 𝑐
𝑥
𝑥
(
xl
xm
xn n+l
× ( l)
x
(a)
(b)
0
1
(c)
(d)
𝑥𝑙
None
xq q+r−p
( r)
x
×(
xm m+n
xn
xr r+p−q
× ( p)
x
)
8
6
(c)
(d)
0
1
(c)
(d)
1
None
(c)
(d)
1
Zero
(d)
None
(c)
(d)
√2 > √4 > √6
3
4
√2 > √4 > √6
(c)
(d)
2
3
(b)
1
=
xp p+q−r
× ( q)
x
=
0
𝑥 𝑟+𝑝−𝑞
𝑥 𝑝 𝑝𝑞
( 𝑞)
𝑥
1
𝑥 𝑞 𝑞𝑟
. ( 𝑟)
𝑥
𝑥
𝑥
𝑥𝑟
. ( 𝑝)
1
𝑟𝑝
𝑥
=?
1
𝑝𝑞𝑟
1
−
𝑝𝑞𝑟
𝐼𝑓 𝑥𝑦𝑧 = 1, 𝑡ℎ𝑒𝑛
1
1+𝑥+𝑦 −1
+
1
1+𝑦+𝑧 −1
+
1
1+𝑧+𝑥 −1
0
1
1
(c)
𝑥+𝑦+𝑧
√√𝑎𝑏 −1 . √𝑏𝑐 −1 . 𝑐𝑎 −1 = … … … … …
(a) abc
(b)
1
𝑎𝑏𝑐
(c) 0
(d) 1
Which chronological order is correct:
𝟑
𝟒
(a)
√𝟒 > √𝟔 > √𝟐
4
Q.52.
(c)
(d)
2+𝑚2 +𝑛2
(a)
(b)
Q.51.
8
4
𝑥
l+m
)
(b)
Q.50.
(c)
(d)
𝑥𝑐 𝑏
x
𝑥 𝑎+𝑏+𝑐
(a)
Q.49.
𝑎
𝑥𝑏
1
Q.48.
0.02
0.2
( 𝑏) × ( 𝑐 ) × ( 𝑎) =
(a)
(b)
Q.47.
(c)
(d)
√225 = 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡𝑜:
11
9
= 729, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛 𝑖𝑠:
12
10
(a)
(b)
Q.46.
3/8
8/3
√√0.000064 =…………….
Q.42.
Q.45.
(c)
(d)
3
(a)
(b)
Q.44.
2
1
= …………………
512
(a)
(b)
Q.41.
(c)
(d)
3
(b)
√6 > √4 > √2
Which one of the following is the least prime no.:
(a)
0
(b)
1
Product of two co – prime is 119. Their L.C.M is:
(a)
119
3
4
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Data is in sufficient
Q.58.
(c)
More than 119
(d)
The H.C.F. of two co – prime numbers is:
(a)
Equals to their LCM
(c)
(b)
Lesser to their LCM
(d)
LCM of two prime numbers a and b (a > b) is 161, the value of a – b is;
(c)
(a)
16
(b)
-1
(d)
LCM of two prime numbers x and y (x > y) is 209, the value of x – y is;
(c)
(a)
8
(b)
-8
(d)
The word ‘algorithm” was derived from:
(a)
Logarithm
(c)
(b)
Al – gebr
(d)
Which of the following is irrational number:
(c)
(a)
𝝅
(d)
(b)
22/7
Which of the following is a rational number:
√𝟎. 𝟎𝟒
None
Q.59.
(a)
√2
(b)
√0.4
Which of the following is a non-terminating decimal expransion:
Q.53.
Q.54.
Q.55.
Q.56.
Q.57.
(a)
(b)
23
(c)
(d)
(c)
23 52
𝟏𝟐𝟗
(d)
𝟐𝟐 𝟓𝟕 𝟕𝟓
More than toi their LCM
Always equal to one
+1
0
7
11
Khwarizmi
Arithmetic
3.14
None
13
3125
154
420
Q.60.
Which of the following is irrational?
(a)
53.1234567
(c)
53.125125312
(d)
1234567
(b)
0.130130013000130000…..
Q.61. The rational number p/q will have terminating decimals if and only if the prime factor of q is in the form:
(a)
2m × 5n , m, n = 1,2,3,4 … … ..
(b)
𝟐𝐦 × 𝟓𝐧 , 𝐦, 𝐧 = 𝟎, 𝟏, 𝟐, 𝟑, 𝟒 … … ..
(c)
2m × 5n , m, n = 0,2, 4,6 … … ..
(d)
2m × 5n , m, n = 0,1,3,5 … … ..
Q.62. There are three numbers such that
The lcm (I, II) = 10
The lcm (II, III) = 50
The lcm (III, I) = 25 & lcm (I, II, III) = 50 and the product of the three numbers is 1250. Find the H.C.F (I, II, III):
Q.63.
Q.64.
Q.65.
Q.66.
Q.67.
(a)
10
(c)
4
(b)
25
(d)
5
According to euclid’s division lemma, given positive integers a and b, there exists whole numbers q and r satisfying:
(c)
a = bq + r, 0 ≥ 𝑟 > 𝑏
(a)
a = bq + r, 0 ≤ 𝒓 < 𝒃
(b)
b = aq + r, 0 ≤ 𝑟 < 𝑏
(d)
b = aq + r, 0 ≥ 𝑟 > 𝑏
There is a circular track around a play ground. Ahmad takes 21 minutes to drive one round of the field. While raj takes 14
minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After
how many minutes will they meet again at the starting point?
(a)
30 min.
(c)
15 min.
(d)
None
(b)
42 min.
If HCF (306,657) is 9, the LCM (306, 657) is:
(c)
22360
(a)
22338
(b)
22348
(d)
None
Additive identity is:
(c)
−1
(a)
0
(b)
+1
(d)
±1
Multiplicative identity is:
(a)
0
(c)
−1
(b)
2
(d)
1
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Q.68.
Additive inverse of f(x) is:
(a)
0
(b)
−f(x)
Q.69. Multiplicative inverse of f(x) is:
(a)
0
(b)
−f(x)
Q.70. Conjugate of 2 +√3 is:
(a)
2 + √3
(b)
2−√𝟑
Q.71. The solution of 4x – 3 < 2x + 5
Consist of all real numbers such that:
Q.72.
Q.73.
Q.74.
Q.75.
Q.76.
Q.77.
Q.78.
Q.79.
Q.80.
Q.81.
Q.82.
Q.83.
(c)
(d)
1/f(x)
1
(c)
(d)
1/f(x)
1
(c)
(d)
−2 + √3
None
(a) x < 3
(c) x < 4
(b) x > 3
(d) x > 4
let h(x) = HCF of two polynomials f(x) and g(x) l (x) = LCM of f(x) and g(x), then what is correct:
(a)
h(x) + l(x) = f(x) + g(x)
(c)
±h(x) × l(x) = g(x) × l(x)
(b)
h(x) × g(x) = l(x) × f(x)
(d)
𝒏𝒐𝒏𝒆 𝒊𝒔 𝒄𝒐𝒓𝒓𝒆𝒄𝒕
The solution of 2x – 5 < x – 3 consist of all real numbers such that:
(a)
x < −2
(c)
x > −2
(d)
x>2
(b)
x<2
The relation between x and y, if x divides y and y divides x, is:
(a)
x>y
(c)
x=y
(b)
x<y
(d)
None
Which of the following statements is correct:
(a)
If n is odd, (10)𝑛 − 1 is divisible by 11
(b)
If n is even, (𝟏𝟎)𝒏 − 𝟏 is divisible by 11
(c)
If n is odd, (5)𝑛 − 1 is divisible by 5
(d)
If n is even, (5)𝑛 − 1 is divisible by 5
When x = 1, the value of |2𝑥 − 1| + |𝑥 − 3| will be:
(a)
2
(c)
4
(d)
5
(b)
3
Which one is a complex number:
(c)
1−√3
√√√2
(a)
(d)
1 + √−𝟑
(b)
1 + √3
Which one of the following numbers has rational square root:
(a)
0.4
(c)
0.9
(d)
0.025
(b)
0.09
The sum of a complex number and its conjugate is:
(a)
An imaginary number
(b)
A conjugate number
(c)
A real number
(d)
May be real or may be imaginary depending on the numbers
1
1
𝑥
𝑥3
If 𝑥 + = √3, 𝑡ℎ𝑒𝑛 𝑥 3 +
is equal to:
(a)
0
(b)
2
If a + b + c = 0, then 𝑎3 + 𝑏 3 + 𝑐 3 is equal to:
(a)
0
(b)
3 abc
(c)
−3abc
(a2 + b2 + c 2 − ab − bc − ca)
(d)
If a = 11, b = 22, c = −33, then 𝑎3 + 𝑏 2 + 𝑐 3 is equal to:
(a)
−𝟑 × 𝟏𝟏 × 𝟐𝟐 × 𝟑𝟑
(b)
+ 3× 11 × 22 × 33
If a + b + c = 13, 𝑎2 + 𝑏 2 + 𝑐 2 = 69, find ab + bc + ca:
(a)
−50
(c)
(d)
4
6
(c)
(d)
47916
Zero
(b)
50
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(c)
Q.84.
69
2
If p +
(a)
(b)
1
p2
(d)
75
1
= a and p − = b, then which of the following is correctly expresses:
p
𝐚 − 𝐛𝟐 − 𝟐 = 𝟎
a2 + b = 2
(c)
(d)
a2 − b2 = 1
a2 = b2
Q.85.
Give positive integers a and b, there exist unique integers q and r satisfying:
(a)
a = bq + r, 0 < b < r
(c)
b = aq + r, 0 ≤ r < b
(b)
a = bq + r, 0 ≤ r < b
(d)
b = ar + q, 0 ≤ b < r
Q.86. Euclid’s Division Lemma was known for a long time, but was first recorded in his book:
(a)
IV of Euclid’s Elements
(c)
VI of Euclid’s Elements
(b)
V of Euclid’s Elements
(d)
VII of Euclid’s Elements
Q.87. The word algorithm comes from the same of al-khwarizmi, in the 9th century who was:
(a)
Babylonian mathematician
(c)
Persian mathematician
(b)
Arabian mathematician
(d)
India mathematician
Q.88. Euclid’s algorithm is stated for:
(a)
Only positive integers
(b)
Only negative integers
(c)
Either positive integers or negative integers
(d)
Neither positive integers nor negative integers
Q.89. Euclid’s division algorithm can be extended for:
(a)
Negative integers only
(c)
All integers except zero
(b)
All integers only
(d)
None of these
Q.90. A number when divided by 61 gives 27 as quotient and 32 as remainder, the number is:
(a)
1569
(c)
1779
(b)
1689
(d)
1679
Q.91. By what number 1365 be divided to get 31 as quotient and 32 as remainder:
(c)
53
(a)
43
(b)
35
(d)
47
Q.92. The L.C.M. of 24, 36, 40 is:
(a)
460
(c)
340
(b)
540
(d)
360
Q.93. The H.C.F. of 144, 180, 192 is:
(a)
18
(c)
12
(b)
36
(d)
4
Q.94. The H.C.F. of two numbers is 23 and their L.C.M. is 1449. If one of the numbers is 161 then the other number is:
(a)
107
(c)
360
(d)
340
(b)
207
Q.95. If n is odd positive integer then 𝑛2 − 1 is divisible by:
(a)
6
(c)
8
(b)
7
(d)
5
Q.96. For any positive integer n, 𝑛3 − 𝑛 is divisible by:
(a)
5
(c)
4
(b)
3
(d)
6
Q.97. The largest number which divides 615 and 963 leaving remainder 6 in each case is:
(c)
79
(a)
87
(b)
67
(d)
59
Q.98. The largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively is:
(a)
96
(c)
112
(d)
74
(b)
138
Q.99. Given the H.C.F. (306, 657) = 9 then L.C.M. (306, 657) is:
(a)
22448
(c)
22338
(b)
33228
(d)
44338
Q.100. The H.C.F. of two numbers is 23 and their L.C.M. is 1449. If one of the numbers is 161, then the other number is:
(c)
320
(a)
207
(b)
360
(d)
240
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