TOPIC: REAL NUMBERS (CLASS X)
MCQ
Q (1) The HCF of 96 and 404 is …….
(a) 1
(b) 2
(c) 3
(d) 4
Q (2) Which of the following is not an irrational number?
(a) 7√5
(b) √2+2√2
(c) (√7-3) - √7
(d) √3 +2
Q (3) Which of the following has a terminating decimal expansion?
23
(a)
200
17
(b) 9
8
(c) 75
3
(d) 35
Q (4) Which of the following has a non terminating repeating decimal expansion?
3
(a)
8
13
(b) 125
7
(c) 80
29
(d) 343
Q(5) HCF (306, 657) = 9, what will be the LCM ( 306, 657) ?
(a) 12338
(b) 22338
(c) 23388
(d) 22388
Q (6) Three bulbs red, green and yellow flash at internals of 80 seconds, 90 seconds and 110 seconds. All
three flash together at 8:00 am. At what time the three bulbs flash altogether again?
(a) 10:20 am
(b) 10:10 am
(c) 10:12 am
(d) 10:23 am
4
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, Q (7) Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together. After
how many hours will they next toll together?
(a) 2 hours
(b) 1 hour
(c) 4 hours
(d) 3 hours
Q (8) What is HCF of two consecutive natural numbers?
(a) 1
(b) 2
(c) 3
(d) 4
43
Q (9) After how many places, the decimal expansion of the rational number 24×53 will terminate.
(a) 1
(b) 2
(c) 3
(d) 4
Q (10) Find the least number which is divisible by the natural numbers from 1 to 10.
(a) 2250
(b) 2550
(c) 2520
(d) 2025
Q (11). Assertion: There are two numbers such that there HCF is 18 and LCM is 380.
Reason: The LCM must be divisible by HCF.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
13
Q (12). Assertion: The number 3125 have terminating decimal expansion.
𝑝
Reason: It is in the form of 2𝑚×5𝑛 where m and n are positive integers.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q (13) Assertion: The number 4 n cannot end with the digit zero, where n is a natural number.
5
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, Reason: The prime factorization of number 4 n have only the prime 2.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q(14) Assertion: The HCF of two numbers is 5 and their product is 150, then there LCM is 30
Reason: For any two positive integers a and b , HCF ( a,b) + LCM ( a,b) = a × b.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q(15) Assertion: 5 - √𝟑 is an irrational number.
Reason : Every Irrational number has a non terminating non recurring decimal expansion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
CASE STUDY
Case Study 1: There is a circular path around a sports field. Sonia takes 9 min to drive one round,
while Ravi takes 12 min for the same. Suppose they both start at the same point and at the same time,
and go in the same direction.
Q (16) After how many minutes will they meet again ?
(a) 36 min
(b) 12 min
(c) 2 min
(d) 5 min
Q (17) What will you find for getting the answer ?
(a) HCF
(b) LCM
(c) Prime factorization
(d) Square root
Q (18) If Ravi will take 20 minutes and Sonia takes same 9 min to complete one round, then after how
many minutes they will meet again ?
(a) 180 min
(b) 100 min
(c) 120 min
(d) 90 min
6
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, Case study 2: A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such
a way that each stack has the same number, and they take up the least area of the tray.
Q (19) What is the number of each barfi that can be placed in each stake?
(a) 40 barfis of each kind
(b) 30 barfis of each kind
(c) 20 barfis of each kind
(d) 10 barfis of each kind
Q (20) How many trays are required to keep all the barfi?
(a) 35
(b) 45
(c) 55
(d) 65
ANSWERS
MCQ
23 29
1. (d) 4 2. (c) (√7-3) - √7 3. (a) 200 4. (d) 343 5. (b) 22338
6. (c) 10:12 am 7. (d) 3 hours 8. (a) 1 9. (d) 4 10. (c) 2520
ASSERTION AND REASONING
11. Correct answer (D)
Justification: If LCM and HCF of two numbers are given then the LCM must be divisible by HCF. 380
is not divisible by 18 so that assertion is wrong.
12. Correct answer (A)
Justification: The prime factorization of the denominator must be in the form of 2 m × 5 n, then only
the Rational numbers have terminating decimal expansion. 3125 = 5 × 5 ×5 ×5× 5
13. Correct answer (A)
Justification: If the number 4 n; for any n, were to end with the zero, then it would be divisible by 2
and 5 both. This is not possible because 4 n = (2) 2n; so the only the prime in the prime factorization of
4 n is 2. The uniqueness of Fundamental Theorem of Arithmetic guarantees that there are no other
primes in the factorization of 4 n. So there is no natural number n for which 4 n ends with the digit zero
14. Correct answer (C)
Justification: For any two positive integers a and b , HCF ( a,b) × LCM ( a,b) = a × b.
30 × 5 = 150, so the assertion is correct but the reason is not correct.
15.
7
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MCQ
Q (1) The HCF of 96 and 404 is …….
(a) 1
(b) 2
(c) 3
(d) 4
Q (2) Which of the following is not an irrational number?
(a) 7√5
(b) √2+2√2
(c) (√7-3) - √7
(d) √3 +2
Q (3) Which of the following has a terminating decimal expansion?
23
(a)
200
17
(b) 9
8
(c) 75
3
(d) 35
Q (4) Which of the following has a non terminating repeating decimal expansion?
3
(a)
8
13
(b) 125
7
(c) 80
29
(d) 343
Q(5) HCF (306, 657) = 9, what will be the LCM ( 306, 657) ?
(a) 12338
(b) 22338
(c) 23388
(d) 22388
Q (6) Three bulbs red, green and yellow flash at internals of 80 seconds, 90 seconds and 110 seconds. All
three flash together at 8:00 am. At what time the three bulbs flash altogether again?
(a) 10:20 am
(b) 10:10 am
(c) 10:12 am
(d) 10:23 am
4
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, Q (7) Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together. After
how many hours will they next toll together?
(a) 2 hours
(b) 1 hour
(c) 4 hours
(d) 3 hours
Q (8) What is HCF of two consecutive natural numbers?
(a) 1
(b) 2
(c) 3
(d) 4
43
Q (9) After how many places, the decimal expansion of the rational number 24×53 will terminate.
(a) 1
(b) 2
(c) 3
(d) 4
Q (10) Find the least number which is divisible by the natural numbers from 1 to 10.
(a) 2250
(b) 2550
(c) 2520
(d) 2025
Q (11). Assertion: There are two numbers such that there HCF is 18 and LCM is 380.
Reason: The LCM must be divisible by HCF.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
13
Q (12). Assertion: The number 3125 have terminating decimal expansion.
𝑝
Reason: It is in the form of 2𝑚×5𝑛 where m and n are positive integers.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q (13) Assertion: The number 4 n cannot end with the digit zero, where n is a natural number.
5
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, Reason: The prime factorization of number 4 n have only the prime 2.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q(14) Assertion: The HCF of two numbers is 5 and their product is 150, then there LCM is 30
Reason: For any two positive integers a and b , HCF ( a,b) + LCM ( a,b) = a × b.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
Q(15) Assertion: 5 - √𝟑 is an irrational number.
Reason : Every Irrational number has a non terminating non recurring decimal expansion.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
CASE STUDY
Case Study 1: There is a circular path around a sports field. Sonia takes 9 min to drive one round,
while Ravi takes 12 min for the same. Suppose they both start at the same point and at the same time,
and go in the same direction.
Q (16) After how many minutes will they meet again ?
(a) 36 min
(b) 12 min
(c) 2 min
(d) 5 min
Q (17) What will you find for getting the answer ?
(a) HCF
(b) LCM
(c) Prime factorization
(d) Square root
Q (18) If Ravi will take 20 minutes and Sonia takes same 9 min to complete one round, then after how
many minutes they will meet again ?
(a) 180 min
(b) 100 min
(c) 120 min
(d) 90 min
6
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, Case study 2: A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such
a way that each stack has the same number, and they take up the least area of the tray.
Q (19) What is the number of each barfi that can be placed in each stake?
(a) 40 barfis of each kind
(b) 30 barfis of each kind
(c) 20 barfis of each kind
(d) 10 barfis of each kind
Q (20) How many trays are required to keep all the barfi?
(a) 35
(b) 45
(c) 55
(d) 65
ANSWERS
MCQ
23 29
1. (d) 4 2. (c) (√7-3) - √7 3. (a) 200 4. (d) 343 5. (b) 22338
6. (c) 10:12 am 7. (d) 3 hours 8. (a) 1 9. (d) 4 10. (c) 2520
ASSERTION AND REASONING
11. Correct answer (D)
Justification: If LCM and HCF of two numbers are given then the LCM must be divisible by HCF. 380
is not divisible by 18 so that assertion is wrong.
12. Correct answer (A)
Justification: The prime factorization of the denominator must be in the form of 2 m × 5 n, then only
the Rational numbers have terminating decimal expansion. 3125 = 5 × 5 ×5 ×5× 5
13. Correct answer (A)
Justification: If the number 4 n; for any n, were to end with the zero, then it would be divisible by 2
and 5 both. This is not possible because 4 n = (2) 2n; so the only the prime in the prime factorization of
4 n is 2. The uniqueness of Fundamental Theorem of Arithmetic guarantees that there are no other
primes in the factorization of 4 n. So there is no natural number n for which 4 n ends with the digit zero
14. Correct answer (C)
Justification: For any two positive integers a and b , HCF ( a,b) × LCM ( a,b) = a × b.
30 × 5 = 150, so the assertion is correct but the reason is not correct.
15.
7
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