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

a)

b)

c)

d)

e)

f)

g)

h)

j)

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

a)

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

Or

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

a)

b)

c)

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

a)

b)

c)

Solution (a)

HCF = 27

LCM = 81

c)

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