NCERT Class 10 Chapter 1 Real Numbers Official CBSE Board Sample Problems: Very Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)
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Question
If HCF then find LCM
Solution
Product of numbers
LCM
Question
If 6.249 is expressed in the form, what can you say about q?
Solution
Since it is a terminating decimal, q is expressible in the form of where m and n are non-negative integers
Question
If is expressed in the form what can you say about q?
Solution
Since it is a repeating decimal, q is not expressible in the form of where m and n are non-negative integers
Question
Can end with the digit 0, for any natural number n. Justify your answer.
Solution
To end with 0, a number should be divisible by 10, i.e.. by 2 and 5. But 15 is not divisible by 2 so can not end with digit 0
Question
Without actual division, find the decimal representation of
Solution
Question
State the Fundamental Theorem of Arithmetic
Solution
Every composite number is expressible as a product of its prime factors. This prime factorization is unique except for the order in which the prime numbers occur.
Question
Is prime or composite? Justify
Solution
is composite as it is divisible by numbers other than 1 and itself
Question
Are the smallest prime and the smallest composite numbers coprime? Justify
Solution
Smallest prime. = 2
Smallest composite = 4
HCF = 2
Since they have a common factor other than 1, they are not coprime
Question
The product of the L. C. M and H. C. F of two natural numbers is 24. The difference of two numbers is 2. Find the numbers.
Solution
Let the numbers be a and b.
or 4
So the numbers are 4 and 6
Question
If two positive integers a and b are expressible in the form and ; p, q being prime numbers, then find the LCM (a, b) .
Solution
Question
Let
Be a rational number. Then x has decimal expansion which terminates:
Solution
After three places of decimal