MATHEMATICS ASSIGNMENT
CHAPTER-1 [NUMBER SYSTEM] CLASS X
Mathematics assignment for class X chapter 1 Real Numbers with answers and hints for the solution. Extra questions of chapter 1 real number class X
Math Assignment Chapter 1 Class X : Real Number System
Q1- Define Euclid’s division lemma ,
HCF, LCM & fundamental theorem of Arithmetic’s.
Q2) Find the HCF of the following by using EDA .
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a
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650,
1170 Ans 130
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g
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4052 ,
12576 Ans 4
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b
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963,
657 Ans 9
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h
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136, 170 ,
255 Ans 17
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c
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592 ,
252 Ans 4
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i
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506 ,
1155 Ans 11
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d
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315 ,
198 Ans 9
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j
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1288 ,
575 Ans 23
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e
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180 ,
192 Ans 12
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k
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180, 252 ,
324 Ans 36
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f
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216 , 1176
Ans 24
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l
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184 , 230 , 276
Ans 46
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Question 3: Express the following as the
product of primes
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a
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156
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e
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10626
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b
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5005
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f
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364
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c
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7429
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g
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429
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d
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1008
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h
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169785 [ Ans
3²×5×7³×11]
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Question 4: Use FTA & Find HCF & LCM
of the following
a) 510 , 92 Ans HCF = 2, LCM = 23460
b) 336, 54 Ans HCF = 6, LCM = 3024
c) 225 , 450 Ans HCF = 225, LCM = 450
d) 1440 , 1800 Ans HCF = 360, LCM = 7200
e) 40, 36 , 126 Ans HCF = 2, LCM = 2520
f) 25, 40 , 60 Ans HCF = 5, LCM = 600
g) 72, 80, 120 Ans HCF = 8, LCM = 720
h) 84, 90 , 120 Ans HCF = 6, LCM = 2520
Q5- State whether the following
are terminating or non-terminating, if terminating then convert these
into decimals.
a) 
Ans Terminating 0.45 b) 
Ans non-terminating but repeating decimal c) 
Ans Terminating d) 
Ans Terminating e) 
Ans Terminating f) 
Ans Terminating 40.6 Question 6
Show that any positive even integer is of the form 4q or 4q + 2.
Question 7
Show that any positive even integers is of the form 6q, 6q + 2, 6q + 4.
Question 8
Use E.D.A to show that square of any positive integer is either of the form 3m, 3m + 1 for some integer m.
Question 9
Use E.D.A to show that cube of any positive integer is either of the form 9m, 9m + 1, 9m + 8.
Question 10
Given that LCM(989, 1892) is 43516, find HCF.
Ans 43
Question 11
HCF (45 and 105) = 15 find their LCM
Question 12
Given that LCM(77, 99) = 693. Find HCF.
Question 13
Given that HCF(x, 657) = 9 and LCM(x, 657) = 22338. Find x.
Ans 306
Question 14: Prove the following are irrational
number
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Level - 2
Question 15
If HCF(6, x) = 2 and LCM(6, x) = 60. Find x.
Ans 20
Question 16
If HCF(48, x) = 24 and LCM(48, x) = 144, find x.
Ans 72
Question 17
Check whether 12ⁿ can end with the digit 0 ∀n ϵ N.
Question 18
Check whether 39ⁿ is divisible by 3.
Question 19
What is the exponent of 3 in the prime factorization of 864.
Question 20
What is the HCF × LCM for 105 and 120.
Question 21
Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.
Question 22
If HCF of 144 and 180 is expressed in the form 13m – 3 , then find the value of m.
Ans 3
Question 23
If HCF of 65 and 117 is expressible in the form 65n - 117, then find the value of n.
Ans n = 2
Question 24
Find the HCF of 65 and 117 and find the value of m and n if HCF = 65m + 117n
Ans m = 2, n = - 1
Question 25
By Using EDA, find whether 847, 2160 are co-primes or not
Ans Yes these are co-prime
Question 26
Show that 2 x 3 x 4 x 5 x 6 x 7 + 5 x 6 is a composite number.
Question 27
Write whether given a rational or an irrational number.
Ans Rational
Question 28
Given 
The decimal expansion of above given number will terminate after how many places of decimals.
Ans 4
LEVEL - 3
Question 29 If HCF of 81 and 237 be expressed as 81x + 237y then find the value of x and y
Ans x = - 38, y = 13
Question 30
Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively . Ans 204
[Hint 28 – 8 = 20, 32 – 12 = 20, Required No = LCM(28, 32) -20]
Question 31
What is the smallest number which, when divided by 35, 56, 91 leaves remainder 7 in each case. Ans 3647
Question 32
Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively. Ans 63
Question 33
Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively. Ans 127
Question 34
Find the greatest number of 6 digit which is exactly divisible by 24, 15 and 36
Ans 999720
Question 35
Show that one and only one out of n, n + 4, n + 8, n + 12, n + 16 is divisible by 5. Where n is any positive integer.
Question 36
Length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Find the length of the longest rod which can measure the three dimensions of the room exactly.
Question 37
Find the greatest number which when divides 2011 and 2623 leaving remainder 9 and 5 respectively
Ans 154
Question 38
Find the largest number which on dividing 1251, 9377 and 15628 leaves remainder 1, 2, and 3 respectively.
Ans 625
Question 39
On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps.
Ans 360
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