# 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