NCERT Class 10 Chapter 1 Real Numbers Official CBSE Board Sample Problems: Very Short Answer

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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