Math Assignment Ch1 Class X  Real Number System
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S N 
Question 
S N 
Question 
a 
650,
1170 Ans 130 
g 
4052 ,
12576 Ans 4 
b 
963,
657 Ans 9 
h 
136, 170 ,
255 Ans 17 
c 
592 ,
252 Ans 4 
i 
506 ,
1155 Ans 11 
d 
315 ,
198 Ans 9 
j 
1288 ,
575 Ans 23 
e 
180 ,
192 Ans 12 
k 
180, 252 ,
324 Ans 36 
f 
216 , 1176
Ans 24 
l 
184 , 230 , 276
Ans 46 
a 
156 
e 
10626 
b 
5005 
f 
364 
c 
7429 
g 
429 
d 
1008 
h 
169785 [ Ans
3²×5×7³×11] 

510
, 92 Ans HCF = 2, LCM =
23460 

336,
54 Ans HCF = 6, LCM = 3024 

225
, 450 Ans HCF = 225, LCM = 450 

1440
, 1800 Ans HCF = 360, LCM = 7200 

40,
36 , 126 Ans HCF = 2, LCM = 504 

25,
40 , 60 Ans HCF = 5, LCM = 600 

72,
80, 120 Ans HCF = 8, LCM = 720 

84,
90 , 120 Ans HCF = 6, LCM =
2520 
a 
Ans Terminating 0.45 
b 
Ans nonterminating but repeating decimal 
c 
Ans Terminating 
d 
Ans Terminating 
e 
Ans Terminating 
f 
Ans Terminating 40.6 
S N 
Questions 
6 
Show
that any positive even integer is of the form 4q or 4q + 2. 
7 
Show
that any positive even integers is of the form 6q, 6q + 2, 6q + 4. 
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. 
9 
Use E.D.A to show that cube of any
positive integer is either of the form 9m, 9m + 1, 9m +
8. 
10 
Given that LCM(989, 1892) is 43516,
find HCF. 
11 
HCF (45 and 105) = 15 find
their LCM 
12 
Given that LCM(77, 99) = 693. Find
HCF. 
13 
Given that HCF(x, 657) = 9 and
LCM(x, 657) = 22338. Find x. 
S N 
Questions 
S N 
Questions 
S N 
Questions 
a 
e 
i 

b 
f 
j 

c 
g 

d 
h 
S.NO. 
QUESTIONS 
Q 15 
If
HCF(6, x) = 2 and LCM(6, x) = 60. Find x. 
Q 16 
If
HCF(48, x) = 24 and LCM(48, x) = 144, find x. 
Q 17 
Check whether 12ⁿ can end with the
digit 0 ∀n ϵ N. 
Q 18 
Check whether 39ⁿ is divisible by
3. 
Q 19 
What is the exponent of 3 in the
prime factorization of 864. 
Q 20 
What is the HCF × LCM for 105 and
120. 
Q 21 
Can two numbers have 15 as their
HCF and 175 as their LCM ? Give reasons. 
Q 22 
If
HCF of 144 and 180 is expressed in the form 13m – 3 , then find the value of
m. 
Q 23 
If
HCF of 65 and 117 is expressible in the form 65n  117, then find the value
of n. 
Q24 
Find
the HCF of 65 and 117 and find the value of m and n if HCF = 65m + 117n 
Q25 
By Using EDA, find whether 847,
2160 are coprimes or not 
Q26 
Show that 2 x 3 x 4 x 5 x 6 x 7 +
5 x 6 is a composite number. 
Q27 
Write whether given a rational or an irrational number. Ans
Rational 
Q28 
Given The decimal expansion of above given number will terminate after how many places of decimals.
Ans 4 
S. No. 
QUESTIONS 
Q35 
If HCF of 81 and 237 be expressed as
81x + 237y then find the value of x and y Ans x =  38, y = 13

Q36 
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]

Q37 
What is the smallest number which,
when divided by 35, 56, 91 leaves remainder 7 in each case.
Ans 3647 
Q38 
Find the greatest number that will
divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
Ans 63 
Q39 
Find the greatest number which on
dividing 1657 and 2037 leaves remainder 6 and 5 respectively.
Ans 127 
Q40 
Find the greatest number of 6 digit
which is exactly divisible by 24, 15 and 36 Ans 999720

Q41 
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. 
Q42 
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. 
Q43 
Find the greatest number which when
divides 2011 and 2623 leaving remainder 9 and 5 respectively 
Q44 
Find the largest number which on
dividing 1251, 9377 and 15628 leaves remainder 1, 2, and 3 respectively. 
Q45 
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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