NCERT Class 10 Mathematics Real Number Formative Assessment CBSE Board Sample Problems
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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