#Class 9 #MCQ #Chapter_1 #Number_Systems.pdf

Maths Learning Centre, Jalandhar
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https://www.youtube.com/@MathematicsOnlineLectures Class IX: Number System Mathematics
LEVEL - I
1. The product of any two irrational numbers is:
(a) always an irrational number (b) always a rational number
(c) always an integer (d) sometimes rational, sometimes irrational
2. The decimal expansion of the number 2 is:
(a) a finite decimal (b) 1.41421
(c) non-terminating recurring (d) non-terminating recurring
3. Which of the following is irrational?
(a)
4
9
(b)
12
3
(c) 7 (d) 81
4. The value of 23.43 is in the form of
p
q , is
(a)
232
99
(b)
2320
99
(c)
232
9
(d)
2320
9
5. The value of 1.999... in the form ,
p
q
where p and q are integers and 0

q , is
(a)
19
10
(b)
1999
1000
(c) 2 (d)
1
9
6. The number obtained on rationalising the denominator
1
7 2

is
(a)
7 2
3

(b)
7 2
3

(c)
7 2
5

(d)
7 2
45

7.
1
9 8

is equal to
(a)  
1
3 2 2
2
 (b)
1
3 2 2

(c) 3 2 2
 (d) 3 2 2

8. The value of
32 48
8 12


is equal to
(a) 2 (b) 2 (c) 4 (d) 8
9. If 2 1.4142,
 then
2 1
2 1


is equal to
(a) 2.4142 (b) 5.8282 (c) 0.4142 (d) 0.1718
10. 4 2
2
2 equals
(a)
1
6
2

(b)
6
2
(c)
1
4
2 (d) 26
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11. The product 3 4 12
2 2 32
  equals
(a) 2 (b) 2 (c) 12
2 (d) 12
32
12. If 2 3 2 3
,
xy a yz b
  and 2 3
zx c
 then 3
z equals :
(a)
4
2
bc
a
(b)
4
2
b c
a
(c)
4 4
2
b c
a
(d)
4
2
ab
c
13. If
2
2 9 1
3 81
x x
 
 , then x is:
(a)
1
4,
2
(b)
1
2,
4
(c) 2, 1 (d) Both (a) and (b)
14. If 7 6
 
A and 6 5
 
B , then
(a) A > B (b) A = B (c) A < B (d) 
A B
15. The value of
1
5 2 6

is
(a) 2 (b) –1 (c) 3 2
 (d) 1
16. The value of expression
0 1
1 3 1
3
(0.6) (0.1)
3 3 1
2 2 3

 


     
 
     
     
is
(a)
3
2

(b)
2
3
(c)
3
2
(d)
9
4
17. The decimal expansion of the rational number 2
33
2 .5
will terminate after
(a) one decimal place (b) two decimal place
(c) three decimal place (d) more than 3 decimal places
18. For some integer m, every even integer is of the form
(a) m (b) m + 1 (c) 2m (d) 2m + 1
19. For some integer q, every odd integer is of the form
(a) q (b) q + 1 (c) 2q (d) 2q + 1
20. n2
– 1 is divisible by 8, if n is
(a) an integer (b) a natural number (c) an odd integer (d) an even integer
21. The product of a non-zero rational and an irrational number is
(a) always irrational (b) always rational (c) rational or irrational (d) none
22 If
6
3 2 3
3 2 2 3
 

a then a is
(a) –2 (b) +2 (c) 3 (d) –3

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23. Value of  
1
3 4
1 1
3 3
5 8 27
 
 

 
is
(a) 2 (b) 5 (c) 3 (d) 4
24. Value of  
3
2
4
(256)

 is
(a)
1
2
(b) 2 (c) 3 (d)
1
3
25. Value of
1
3 3 3 2
(1 2 3 )
  is
(a) 2 (b) 3 (c) 5 (d) 6
LEVEL - II
26. The value of
1 1
1 1 1 1
a a
a b a b
 
   

 
is
(a)
2
2 2
b
b a

(b)
2
2 2
a
2b a

(c)
2
2 2
2a
b a

(d)
2
2 2
2b
b a

27. If
1
x
2 3


, then the value of 3 2
x 2x 7x 5
   is
(a) 1 (b) 2 (c) 3 (d) 4
28. If
2 5
a
2 5



and
2 5
b
2 5



, then the value of 2 2
a b
 is
(a) 144 5 (b) 144 5
 (c) 5 (d) 144
29. The value of
2n 3 n 2
n 1 2/3
7 (49)
((343) )
 


is equal to
(a) 39
 (b) 42
 (c) 44
 (d) 45

30. Value of
1 1 1
1 2 2 3 3 4
 
   +
1
4 5

+
1 1
5 6 6 7

  +
1 1
7 8 8 9

 
(a) 2 (b) 3 (c) 4 (d) 5
31. Find the value of
160 160 160 160 160 160
2 7 7 12 17 12 17 22 22 27 27 32
    
     
(a) 17 (b) 15 (c) 13 (d) 11
32. Radhica has two ribbons which are 80 cm and 96 cm long. She has to cut them into equal pieces to
make bows. What is the length of the longest piece of ribbon that she can cut, so that no ribbon is
wasted?
(a) 16 (b) 15 (c) 14 (d) 13

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33. ln a problem involving division, the divisor is eight times the quotient and four times the remainder. If
the remainder be 12, then the dividend is
(a) 400 (b) 342 (c) 300 (d) 450
34. If 3 3 3 3
1 2 3 ... 10
    = 3025 then 4 + 32 + 108 + … + 4000 is equal to
(a) 1200 (b) 12100 (c) 12200 (d) 12400
35. If 3 3
x 4 2 1
   , then the value of 2 3
3 3 1
x x x
  is
(a) 1 (b) 0 (c) 1 (d) 3
3 3
36. If 60a
= 3 and 60b
= 5, then the value of  
1 a b
2 1 b
12
 
 is
(a) 60 (b) 3 (c) 2 (d) 5
37. If
7 5
x
7 5



, then the value of  
2017
2
x 12x 1
  is
(a) 1 (b) 0 (c) 1
 (d)
1
8
38. If N = 1 + 11 + 111 + ….. + 1111111111
The sum of digits of N is in the form of ab. Average of a and b is
(a) 3 (b) 4 (c) 6 (d) 5
39. The value of 3 3
20 14 2 20 14 2
   is
(a) 2 2
 (b) 2 2
 (c) 4 (d) 4
40. (Oddeven + evenodd) + even is always:
(a) either even or odd (b) even (c) odd (d) None of these
41. X, Y, Z are distinct integers, X and Y are even and ‘Z’ is odd. Also ‘Y’ is a negative number and X
and Z are positive: Which of these is not true?
(a) (X - Y)3
Z2
is even (b) (X + Z)
2
Y is negative and even
(c) (X + Y + Z)
3
Y
3
is odd (d) (X - Z)
2
Y
2
is even
42. If ax = b, by = c, cz = a, then find the value of xyz
(a) 0 (b) 1 (c) 2 (d) None of these
43. If N is a natural number, then how many values of ‘N’ are possible such that
 
2
15 13 36
 
N N
N
is
also a natural number
(a) 8 (b) 9 (c) 10 (d) 6
44. Find the values of x and y such that the number 56129137X51Y is divisible by 88
(a) 2, 2 (b) 4, 2 (c) 4, 4 (d) none of these

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1 1 2 1 1 2
1 1 1 1
3 3 3 3 3 3
2 2 2 2
(a b )(a b ) (a b )(a a b b )
     
(a) 1 (b) a (c) 2a (d) b
2 9
3
3
3 2
1 3 4 2
4 16 x x
9 16 x 2 3
 
  
  
   
47. What is the remainder when 784 is divided by 2402?
48. What is the remainder in
643
2
?
96
49. What are the last two digits of x,
if x = (113 + 123 + 133 + 143)(573 – 553)
(a) 00 (b) 30 (c) 40 (d) 55
50. Find the remainder if 3040 is divided by 17
(a) 16 (b) 1 (c) 4 (d) 17
51. x = remainder when (1! + 2! + 3! + … 100!) is divided by 15. Find x
(a) 3 (b) 4 (c) 5 (d) 9
52. What is the remainder when 7413 – 4113 + 7513 – 4213 is divided by 66?
(a) 2 (b) 0 (c) 1 (d) 65
53. What is the remainder when 82361 + 83361 + 84361 + 85361 + 86361 is divided by 7?
54. 3324 – 1724 is atleast divisible by
(a) 450 (b) 800 (c) 40,000 (d) 250
55. Find the unit digit of 269 × 368 × 767
56. Find the unit digit of
8
9
12
23
7
(a) 7 (b) 9 (c) 1 (d) 3
57. What is the right most non-zero digit of the number N where N = (6! + 7! + 8! + 9! + 10!)131!?
(a) 2 (b) 3 (c) 4 (d) 6
58. What is the unit’s digit of
1781 + 2781 + 3781 + …… + 9781
(a) 1 (b) 3 (c) 5 (d) 7
59. How many zeroes are there at the end of 200!

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60. (3x – 2y) : (2x + 3y) = 5 : 6 then one of the values of
2
3 3
3 3
x y
x y
 

 
 

 
is:
(a)
1
25
(b) 5 (c)
1
5
(d) 25
MULTIPLE CORRECT ANSWER TYPE
This section contains multiple choice questions. Each question has 4 choices (A), (B), (C), (D), out
of which ONE or MORE is correct. Choose the correct options.
61. Which is not the rationalizing factor of 1 + 2 3
 ?
(a) 1 + 2 3
 (b) 2 (c) 4 (d) 1 2 3
 
62. Evaluate
2
3
1
64

 
 
 
(a) 4 (b) 16 (c) 32 (d) 4
1
2
63.
n 3 n
(2n 2)
2 2(2 )
2



when simplified is
(a) 1 - 2(2n
) (b) 2n+3
-
1
4
(c) n 1
3
2  (d) n 2
6
2 
64. Which of the following is not the value of b in
3 1
a b 3
3 1

 

(a) 2 (b) –1 (c) –3 (d) 4
65. Which of the following is equal to
5 2 5 2
5 2 5 2
 

 
(a) 8 5 (b) 8 5
 (c) 5 2 (d) 320

MATRIX MATCH TYPE
66. Match the column
Column I Column II
(A) Integer (p) positive integer
(B) Zero (q) Irrational number
(C) natural number (r) whole number
(D) sum of a rational and irrational number (s) rational number
(a) (A- p), (B - r), (C - q), (D – s) (b) (A- s), (B - r), (C - p), (D – q)
(c) (A- r), (B - s), (C - p), (D – q) (d) (A- s), (B - q), (C - p), (D – r)

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Column I Column II
(A)
1
2 3

(p) 2
(B) 641/2
(q) 561/2
(C) 161/4
(r) 8
(D) 71/2
81/2
(s) 2 - 3
(a) (A- p), (B - r), (C - q), (D – s) (b) (A- s), (B - q), (C - p), (D – r)
(c) (A- r), (B - s), (C - p), (D – q) (d) (A- s), (B - r), (C - p), (D – q)
Column - I Column - II
(A) If
3
2
x  , the value of
1 1
1 1 1 1
x x
x x
 

   
(p)
9
4
(B) If  
x
x x
x x x
 , then the value of x is (q)
4
3
(C) If
5 1 5 1
,
5 1 5 1
a b
 
 
 
then the value of
2 2
2 2
a ab b
a ab b
 
 
(r)
1
8
(D) For what value of ‘a’ is
2
1
4
x x a
  a perfect square (s)
7
3
(a) (A- s), (B - p), (C - q), (D – r) (b) (A- p), (B - q), (C - r), (D – s)
(c) (A- r), (B - s), (C - p), (D – q) (d) (A- r), (B - s), (C - p), (D – q)
(A) If 3 2 2
x   , then the value of
6 4 2
3
1
x x x
x
  
is (p) 2
(B) Value of
1
x
x
 when 3 2 2
x   (q) 1.4
(C) Value of
1 1
2 2
1 1
3 4
(6.25) (0.0144) 1
(0.027) (81)
 

is (r) 4
(D) Value of 2 2 2 ...
   is (s) 204
(a) (A- s), (B - p), (C - q), (D – r) (b) (A- p), (B - q), (C - r), (D – s)
(c) (A- r), (B - s), (C - p), (D – q) (d) (A- r), (B - s), (C - p), (D – q)

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(A) Value of    
3 3
3 2 2 3 2 2
 
   (p) 330
(B) Value of
1 1
2 3 5 2 3 5

   
is (q) 7
(C) Value of
2 2 2 2 2
6 7 8 9 10
7 4 3 4 2 3
   
  
is (r)
1
2
(D) 11 112 343
n   , then the value of n is (s) 198
(a) (A- s), (B - p), (C - q), (D – r) (b) (A- s), (B - r), (C - p), (D – q)
(c) (A- p), (B - q), (C - r), (D – s) (d) (A- r), (B - s), (C - p), (D – q)
INTEGER ANSWER TYPE
The answer to each of the questions is a single-digit integer, ranging from 0 to 9.
71. Express 0.99999 ….. in the form
p
q ,
72. Evaluate 255
260
- 297
´ 218
.
73. If 25x-1
= 52x-1
- 100, find the value of x.
74. If
   
2 n
n 2 n/2
3m 3
9 3 3 27 1
3 2 27


  


then the value of m - n.
75. Find the value of x, if 5x-3
.32x-8
= 225.
76. If 272n – 1
= (243)3
, then find the value of n
77. Find the value of 3 3 8 7 4 3
   
78. Find the value of      
 
2 2
3 3 3 3 3
3.5 2.5 3.5 8.75 2.5
  
79. Evaluate:
1/2
9/4 2
2
4 2.2
8
2 2
 
 
 
 
 
 
 
 
80. Find the value of ‘a’ of 3 3/2 2
5 5 5 5 5a
 
  

#Class 9 #MCQ #Chapter_1 #Number_Systems.pdf

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#Class 9 #MCQ #Chapter_1 #Number_Systems.pdf