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Math Assignment Ch-1 Class X | Real Numbers

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

For complete explanations and basics related to the number system: Click Here

Math Assignment Chapter 1 Class X : Real Number System

Level - 1
Q1- Define Fundamental theorem of Arithmetic’s, HCF & LCM  .
Solution:  Fundamental theorem of Arithmetic’s :
Every composite number can be expressed as the product of primes and this factorization is unique, irrespective of their order.
HCF : HCF is the product of common factors with smallest powers.
LCM : LCM is the product of all factors with largest powers.
Q2) Express the following as the product of primes.
a) 156      b)  5005      c) 7429     d) 1008    e) 364    f) 429   g) 288    h)  424  i) 10626 
Question 3:  Use FTA & Find HCF & LCM of the following
i) 510 , 92        Ans HCF = 2,  LCM = 23460
ii) 336, 54        Ans  HCF = 6,  LCM = 3024
iii) 225 , 450     Ans HCF = 225, LCM = 450

iv) 96 and 120.    Ans:  HCF = 24, LCM = 480

v) 1440 , 1800    Ans HCF = 360, LCM = 7200
vi)  18180 and 7575    Ans HCF = 505, LCM = 90900
vii)  40, 36 , 126    Ans HCF = 2, LCM = 2520
viii) 25, 40 , 60  Ans HCF = 5, LCM = 600
ix) 72, 80, 120  Ans HCF = 8,  LCM = 720
x) 84, 90 , 120  Ans HCF = 6,  LCM = 2520
xi)   28,  44, 132     Ans HCF =  4      LCM = 924 

Question 4: If the product of two co-prime numbers is 553, then their HCF is :  Ans: 1

Question 5 If two positive integers p and q can be expressed as p = 18a2b4 and q = 20a3b2, where a and b are prime numbers, then find LCM(p, q) 

Ans :  LCM = 180 a3b4    HCF = 2a2b2      

Question 6: If ‘p’ and ‘q’ are natural numbers and ‘p’ is the multiple of ‘q’, then what is the HCF of ‘p’ and ‘q’ ?     Ans HCF = q, LCM = p

Question 7: Given that LCM(989, 1892) is 43516, find HCF.
Ans 43
Question 8: HCF (45 and 105) = 15  find their LCM
Ans: 315
Question 9: Given that LCM(77, 99) = 693. Find HCF.
Ans: 11
Question 10: Given that HCF(x, 657) = 9 and LCM(x, 657) = 22338. Find x.
Ans 306
Question 11:  Prove the following are irrational number

S N

Questions

S N

Questions

S N

Questions

a

e

i

b

f

j

c

g

k
equation

d

h

lequation 
Question 12: If HCF(6, x) = 2 and LCM(6, x) = 60. Find x.    Ans 20
Question 13: If HCF(48, x) = 24 and LCM(48, x) = 144, find x.   Ans 72

Question 14: If the HCF (2520, 6600) = 40 and LCM (2520, 6600) = 252 x k, then find the value of k ?   Ans: k = 1650

Question 15: If a = 22 x 3x , b = 22 x 3 x 5, c = 22 x 3 x 7 and LCM(a, b, c) = 3780, then find the value of x  ?       Ans : x = 3

Question 16: The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x then find the value of x  ?    Ans:  x = 13

Question 17: The ratio of HCF to LCM of the least composite number and the least prime number is :    Ans: 1 : 2

Question 18: Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers ?

Ans: x = 30, Required numbers are 60 and 90, HCF = 30

Question 19: Check whether 12ⁿ can end with the digit 0 n ϵ N.
Question 20: Can the number (15)n, n being a natural number, end with the digit 0 ?
Question 21: What is the exponent of 3 in the prime factorization of 864.
Ans: In the prime factorisation of 864 the Exponent of 3 is 3
Question 22: What is the HCF × LCM for 105 and 120.    Ans: 12600

Question 23: HCF x LCM for the numbers 40 and 30 is :  Ans 1200

Question 24: Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons.
Answer: 175 is not divisible by 15, so it is not possible to have two numbers which have 15 as their HCF and 175 as their LCM
Note: LCM is always the multiple of HCF. So if we divide LCM of two numbers  by their HCF then remainder should be zero.
Question 25: Show that 2 x 3 x 4 x 5 x 6 x 7 + 5 x 6 is a composite number.
Hint: Composite Numbers: The numbers which have more than two factors are called composite numbers.
Question 26: Show that the number  5 x 11 x 17 x 3 x 11 is a composite number.
Question 27: Write whether        is a rational or an irrational number.           
Ans Rational number

Hint: Simplify the above number we get a rational number

Question 28: What is the smallest number which, when divided by 35, 56, 91 leaves remainder 7 in each case.      Ans 3647
Question 29: Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.     Ans 63

Question 30: Find the greatest number which divides 281 and 1249, leaving remainder 5 and 7  ?    Ans : 138

Question 31: Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively.         Ans 127
Question 32: Find the greatest number of 6 digit which is exactly divisible by 24, 15 and 36
Ans 999720
Question 33: 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.     Ans: 75 cm
Question 34: Find the greatest number which when divides 2011 and 2623 leaving remainder 9 and 5 respectively.    Ans 154
Question 35: Find the largest number which on dividing 1251, 9377 and 15628 leaves remainder 1, 2, and 3 respectively.    Ans 625
Question 36
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

Question 37

Three bells ring at intervals of 6, 12 and 18 minutes. If all the three bells rang at 6 a. m., when will they ring together again ?

Ans: LCM = 36 minutes, Three bells rang again at 6:36 A.M.

Question 38

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next ?

Ans: LCM = 432 second = 7minutes 12 seconds.Three bells rang again at 7h : 07 min : 12 sec

Question 29 (Case Study Based Question)

Teaching mathematics through activities is a powerful approach that enhances students understanding and engagement. Keeping this in mind, Ms. Mukta planned a prime number game for class 5 students. She announces the number 2 in her class and asked the first student to multiply it by a prime number and then pass it to the next student. Second student also multiplied it by a prime number and passed it to third student. In this way by multiplying to a prime number, the last student got 173250

Now, Mukta asked some questions as given below to the students:

(i) What is the least prime number used by students ?  Ans: 3

(ii)  (a) How many students are in the class ? Ans: 7 Students

                                         OR

       (b) What is the highest prime number used by students ?  Ans: 11

(iii) Which prime number has been used maximum times ? Ans: 5


QUESTIONS DELETED FROM CBSE SYLLABUS

* Q1- 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 2
Show that any positive even integer is of the form 4q or 4q + 2.
* Question 3
Show that any positive even integers is of the form 6q, 6q + 2, 6q + 4.
* Question 4
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 5
Use E.D.A to show that cube of any positive integer is either of the form 9m,  9m + 1,  9m + 8.
* Question 6
If HCF of 144 and 180 is expressed in the form 13m – 3 , then find the value of m.
Ans 3
* Question 7
If HCF of 65 and 117 is expressible in the form 65n - 117, then find the value of n.
Ans   n = 2
* Question 8
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 9
By Using EDA, find whether 847, 2160 are co-primes or not
Ans Yes these are co-prime because their HCF = 1
* Question 10

Given    The decimal expansion of above given number will terminate after how many places of decimals.

Ans 4

* Question 11
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 12
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 13
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]

THANKS FOR YOUR VISIT
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