1.If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of ‘m’ is
a) 3
b) 1
c) 4
d) 2
2. Which of the following is false:
a) H.C.F.(a,b) × L.C.M.(a,b)=a×b
b) H.C.F.(p,q,r) × L.C.M.(p,q,r)=p×q×r
c) H.C.F.(p,q,r) = 1; if p,q,r are prime numbers
d) L.C.M.(p,q,r) = p×q×r; if p,q,r are prime numbers
3. The LCM of x and 18 is 36. The HCF of x and 18 is 2. What is the number x?
a) 3
b) 4
c) 1
d) 2
4. Which of the following is not a rational number?
a) √16
b) √8
c) √9
d) √25
5. 0.515115111511115…………. is
a) an irrational number
b) a prime number
c) a rational number
d) an integer
6. The decimal expansion of 21242124 will terminate after
a) None of these
b) 1 decimal place
c) 2 decimal places
d) 3 decimal places
7. If 9^{x+2} = 240 + 9^{x}, then the value of ‘x’ is
a) 0.3
b) 0.2
c) 0.1
d) 0.5
8. The multiplicative inverse of zero
a) does not exist
a) is 1/0
c) is 1
d) is 0
9. Every prime number has exactly _______ factors
a) 4
b) 2
c) 3
d) more than 4
10. The exponent of 3 in the prime factorization of 864 is:
a) 4
b) 2
c) 8
d) 3
Real Number Chapter  1 Quiz 3 Class 10th
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Question 1 of 10
1. Question
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of ‘m’ is
Correct
First find the HCF of 65 and 117
117 = 65 x 1 + 52
65 =52 x 1 + 13
52 = 13 x 4 + 0 (zero remaindr)
therefore HCF (117 , 65) is 13
now
∴ 65m – 117 = 13
⇒ 65m = 13 + 117
⇒ 65m = 130
⇒ m = 2Incorrect
First find the HCF of 65 and 117
117 = 65 x 1 + 52
65 =52 x 1 + 13
52 = 13 x 4 + 0 (zero remaindr)
therefore HCF (117 , 65) is 13
now
∴ 65m – 117 = 13
⇒ 65m = 13 + 117
⇒ 65m = 130
⇒ m = 2 
Question 2 of 10
2. Question
Which of the following is false:
Correct
H.C.F.(p,q,r) × L.C.M.(p,q,r) ≠ p×q×r
This condition is applied on HCF and LCM of two numbers (either (p, q).or (q, r) or (r, p)
For three numbers p,q and r the formula is differentIncorrect
H.C.F.(p,q,r) × L.C.M.(p,q,r) ≠ p×q×r
This condition is applied on HCF and LCM of two numbers (either (p, q).or (q, r) or (r, p)
For three numbers p,q and r the formula is different 
Question 3 of 10
3. Question
The LCM of x and 18 is 36. The HCF of x and 18 is 2. What is the number x?
Correct
We know that LCM x HCF = First number x Second number
HCF (x, 18) x LCM (x, 18) = 18x
2 x 36 = 18x
∴ x = (36×2)/18
= 4Incorrect
We know that LCM x HCF = First number x Second number
HCF (x, 18) x LCM (x, 18) = 18x
2 x 36 = 18x
∴ x = (36×2)/18
= 4 
Question 4 of 10
4. Question
Which of the following is not a rational number?
Correct
√16= √4 x √4 = 4 is a rational number
√9 = √3 x √3 = 3 is a rational number
√25 = √5 x √5 = 5 is also a rational number
but √8 is not a rational number
because √8 =2√2
and √2 is an irrational number
therefore √8 is also an irrational number.Incorrect
√16= √4 x √4 = 4 is a rational number
√9 = √3 x √3 = 3 is a rational number
√25 = √5 x √5 = 5 is also a rational number
but √8 is not a rational number
because √8 =2√2
and √2 is an irrational number
therefore √8 is also an irrational number. 
Question 5 of 10
5. Question
0.515115111511115…………. is
Correct
0.515115111511115…………. is an irrational number because it is nonrepeating decimal expansion.
Incorrect
0.515115111511115…………. is an irrational number because it is nonrepeating decimal expansion.

Question 6 of 10
6. Question
The decimal expansion of 21/24 will terminate after
Correct
21/24 = 7/8 = 7/2^{3} Here, in the denominator of the given fraction the highest power of prime factor 2 is 3, therefore, the decimal expansion of the rational number 7/2^{3} will terminate after 3 decimal places.
Incorrect
21/24 = 7/8 = 7/2^{3} Here, in the denominator of the given fraction the highest power of prime factor 2 is 3, therefore, the decimal expansion of the rational number 7/2^{3} will terminate after 3 decimal places.

Question 7 of 10
7. Question
If 9^{x+2} = 240 + 9^{x}, then the value of ‘x’ is
Correct
⇒ 9^{x+2} = 240 + 9^{x}
⇒ 9^{x}9^{2} = 240 + 9^{x}
⇒ 9^{x}(81−1) = 240
⇒ 9^{x} = 3
⇒ 9^{x} = 9^{1/2}
⇒ x = 1/2 =0.5Incorrect
⇒ 9^{x+2} = 240 + 9^{x}
⇒ 9^{x}9^{2} = 240 + 9^{x}
⇒ 9^{x}(81−1) = 240
⇒ 9^{x} = 3
⇒ 9^{x} = 9^{1/2}
⇒ x = 1/2 =0.5 
Question 8 of 10
8. Question
The multiplicative inverse of zero
Correct
All numbers except zero have a multiplicative inverse because we cannot multiply any number by it to get 1.
Incorrect
All numbers except zero have a multiplicative inverse because we cannot multiply any number by it to get 1.

Question 9 of 10
9. Question
Every prime number has exactly _______ factors
Correct
Prime numbers are the numbers which have only two factors, i.e., 1 and number itself.
Incorrect
Prime numbers are the numbers which have only two factors, i.e., 1 and number itself.

Question 10 of 10
10. Question
The exponent of 3 in the prime factorization of 864 is:
Correct
Prime factorization of 864 = 32×27
= 2^{5}×3^{3}
Therefore the exponent of 3 in the prime factorization of 864 is 3Incorrect
Prime factorization of 864 = 32×27
= 2^{5}×3^{3}
Therefore the exponent of 3 in the prime factorization of 864 is 3