# Class 10 Maths Important Questions for Real Numbers

Given below are the Class 10 Maths Important Questions for Real Numbers
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
Question 1. Without actually performing division, state which of these number will terminating decimal expression or non terminating repeating decimal expression
1. 7/25
2. 3/7
3. 29/343
4. 6/15
5. 77/210
6. 11/67
7. 15/27
8.  11/6
9. 343445/140
Solution
Those rational number which can be expressed in form x/2m X5n    are terminating expression and those can not 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
867=225X3 +192
225=192X1 +33
192=33X5+ 27
33=27X1+6
27=6X4+3
6=3X2+0
So solution is 3
b) 8
Question 3. Write 10 rational number between
a) 4 and 5
b) 1/2 and 1/3
Question 4. Represent in rational form.
a) 1.232323….
b) 1.25
c) 3.67777777
Question 5
a) Prove that 2+√3 is a irrational number
b)  Prove that 3√3 a irrational number
Solution
a) Let’s take this as rational number
$\frac{a}{b}=2+\sqrt{3}$
Or
$\frac{a-2b}{b}=\sqrt{3}$
Since a rational number can’t be equal to irrational number, our assumption is wrong
b) Let’s take this as rational number
q=3√3
q/3=√3
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
b) Product of two prime number is always equal to their LCM
c) √3X √12 is a irrational number
d) Every integer is a rational number
e) The HCF of two prime number is always 1
f) There are infinite integers between two integers
g) There are finite rational number between 2 and 3
h) √3 Can be expressed in the form √3/1,so it is a rational number
i) The number 6n for n in natural number can end in digit zero
j) Any positive odd integer is of the form 6m+1 or 6m+3 or 6m +5 where q is some integer
Solution
1. True
2. True
3. False, as it is written as 6
4. True ,as any integer can be expressed in the form p/q
5. True
6. False,There are finite integer between two integers
7. False
8. False
9. False
10. True
Multiple choice Questions
Question 7 the HCF (a, b) =2 and LCM (a, b) =27. What is the value a X b
a) 25
b) 9
c) 27
d) 54
Solution (d)
LCM X HCF=aXb
Question 8. 2+√2 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) LCM (a, b) =aXb
b)HCF (a, b)= aXb
c) a=br
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 x2 =3  ,y2=9 , z3=27, which of these is true
a) x is a irrational number
b) y is a rational number
c) z is rational number
d)  All of the above
Solution (d)
Question 12 Find the HCF and LCM of these by factorization technique
a)  27,81
b) 120 ,144
c) 29029 ,580
Solution (a)
27= 3X3X3
81=3X3X3X3
HCF=27
LCM=81
b)
120=2X2X3X2X5
144=2X2X3X2x2X3
HCF=23X3=24
LCM=720
c)
29029=29X13X11X7
580=29X5X4
HCF=29
LCM=29X13X11x7X4X5=580580
Question 13. Find all the positive integral values of p for which  p2 +16 is a perfect square?
Solution
p2+16=q2
(q-p)(q+p)=16
So we have
Case 1
q-p=8 and q+p=2  which gives p=3
Case 2
q-p=4 and q+p=4 which gives p=0
Case 3
q-p=2 and q+p=8 which gives p=3
So the answer is 3 only