NCERT Class 10 Mathematics Real Number Formative Assessment CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 1. Without actually performing division, state which of these number will terminating decimal expression or non-terminating repeating decimal expression

Solution

Those rational number which can be expressed in form are terminating expression and those cannot be are non-terminating decimal expression

Terminating decimal: (a) , (d)

Non terminating repeating decimal: (b) , (c) , (e) , (f) , (g) , (h) , (i)

Question 2. Using Euclid՚s theorem to find the HCF between the following numbers

a) 867 and 225

b) 616 and 32

Solution

Using Euclid theorem

So solution is 3

b) 8

Question 3. Write 10 rational number between

a) 4 and 5

b) and

Question 4. Represent in rational form.

a) 1.232323 …

b) 1.25

c) 3.67777777

Question 5

a) Prove that is an irrational number

b) Prove that is an irrational number

Solution

a) let՚s take this as rational number

Since a rational number can՚t be equal to irrational number, our assumption is wrong

b) let՚s take this as rational number

Since a rational number can՚t be equal to irrational number, our assumption is wrong

Question 6 -True or False statement

a) Number of the form 2n + 1 where n is any positive integer are always odd number

Solution: True

b) Product of two prime number is always equal to their LCM

Solution: True

c) is a irrational number

Solution: False, as it is written as 6

d) Every integer is a rational number

Solution: True, as any integer can be expressed in the form p/q

e) The HCF of two prime number is always 1

Solution: True

f) There are infinite integers between two integers

Solution: False there are finite integer between two integers

g) There are finite rational number between 2 and 3

Solution: False

h) Can be expressed in the form , so it is a rational number

Solution: False

i) The number for n in natural number can end in digit zero

Solution: False

j) Any positive odd integer is of the form where q is some integer

Solution: True

Multiple-choice Questions

Question 7 the HCF (a, b) = 2 and LCM (a, b) = 27. What is the value

a) 25

b) 9

c) 27

d) 54

Solution (d)

Question 8. Is a

a) Non terminating repeating

b) Terminating

c) Non terminating non-repeating

d) None of these

Solution (c)

Question 9. If a and b are co primes which of these is true

d) None of these

Solution a and b

Question 10. A rational number can be expressed as terminating decimal when the factors of the denominator are

a) 2 or 5 only

b) 2 or 3 only

c) 3 or 5 only

d) 3 or 7 only

Solution (a)

Question 11. If , which of these is true

a) x is an irrational number

b) y is a rational number

c) z is rational number

d) All of the above

Solution (d)

Short answer question

Question 12. Find the HCF and LCM of these by factorization technique

Solution (a)

HCF = 27

LCM = 81

Question 13. Find all ′ the positive integral values of p for which is a perfect square?

Solution

So we have

Case 1

and which gives

Case 2

and which gives

Case 3

and which gives

So the answer is 3 only