CBSE Class 10 Real Numbers Sure Shot Questions Set 12

Exercise

Question. A rational number can be expressed as a terminating decimal if the denominator has factors
(a) 2, 3 or 5
(b) 2 or 3
(c) 3 or 5
(d) 2 or 5
Answer: (d) 2 or 5

Question. Rational number \( \frac{p}{q} \), \( q \neq 0 \), will be terminating decimal if the prime factorisation of q is of the form (m and n are non-negative integers)
(a) \( 2^m \times 3^n \)
(b) \( 2^m \times 5^n \)
(c) \( 3^m \times 5^n \)
(d) \( 3^m \times 7^n \)
Answer: (b) \( 2^m \times 5^n \)

Question. Which of the following is the decimal expansion of an irrational number?
(a) 4.561
(b) 0.12
(c) 5.010010001…
(d) 6.03
Answer: (c) 5.010010001…

Question. 2.35 is
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number
Answer: (b) a rational number

Question. A rational and an irrational number lying between 0.25 and 0.32 are respectively.
(a) 0.30, 0.3010203040...
(b) 0.20, 0.2010203040...
(c) 0.33, 0.3510203040...
(d) None of the options
Answer: (a) 0.30, 0.3010203040...

Question. The decimal expansion (without actual division) and its nature (terminating or non-terminating) of \( \frac{17}{8} \) will be
(a) Terminating after 2 places
(b) Non-terminating but repeating
(c) Non-terminating but non-repeating
(d) Terminating after 3 places
Answer: (d) Terminating after 3 places

Question. The decimal expansion (without actual division) and its nature (terminating or non-terminating) of \( \frac{15}{1600} \) will be
(a) Terminating after 6 places
(b) Non-terminating but repeating
(c) Non-terminating and non-repeating
(d) Terminating after 2 places
Answer: (a) Terminating after 6 places

Question. The decimal expansion (without actual division) and its nature (terminating or non-terminating) of \( \frac{64}{455} \) will be
(a) Terminating after 2 places
(b) Non-terminating but repeating
(c) Non-terminating but non-repeating
(d) Terminating after 3 places
Answer: (b) Non-terminating but repeating

Question. The \( 2^n 5^m \) (where n and m are non-negative integers) from of denominator of \( \frac{3}{5} \) and its decimal expansion respectively are
(a) \( 2^0 \times 5^1 \), 0.6
(b) \( 2^1 \times 5^0 \), 0.5
(c) \( 2^1 \times 5^1 \), 0.6
(d) \( 2^2 \times 5^0 \), 0.8
Answer: (a) \( 2^0 \times 5^1 \), 0.6

Question. The \( 2^n 5^m \) (where n and m are non-negative integers) form of denominator of \( \frac{13}{80} \) and its decimal expansion respectively are
(a) \( 2^3 \times 5^2 \), 0.1248
(b) \( 2^2 \times 5^3 \), 0.1698
(c) \( 2^4 \times 5^1 \), 0.1625
(d) None of the options
Answer: (c) \( 2^4 \times 5^1 \), 0.1625

Question. Assertion (A): The sum or difference of a rational number and an irrational number is irrational.
Reason (R): Negative of an irrational number is rational.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (c) Assertion (A) is true but reason (R) is false.

Question. Assertion (A): \( 5 + \sqrt{3} \) is an irrational number.
Reason (R): The sum or difference of a rational and an irrational number is always irrational.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Case Study Based Questions

The Army Day is celebrated on 15th January every year in India. The day is celebrated in the form of parades and other military shows in the national capital New Delhi as well as in all headquarters of army. Parade I: An Army contingent of 616 members is to march behind an army band of 32 members in parade. The two groups are to march in the same number of columns. Parade II: An Army contingent of 1000 members is to march behind an army band of 56 members in parade. The two groups are to march in the same number of columns.

Question. Number 616 can be expressed as a product of its prime factors as
(a) \( 2^1 \times 14^1 \times 22^1 \)
(b) \( 2^2 \times 11^1 \times 14^1 \)
(c) \( 2^3 \times 7^1 \times 11^1 \)
(d) \( 2^4 \times 7^2 \times 11^1 \)
Answer: (c) \( 2^3 \times 7^1 \times 11^1 \)

Question. The HCF of 32 and 616 is
(a) 8
(b) 16
(c) 18
(d) 12
Answer: (a) 8

Question. The LCM of 56 and 1000 is
(a) 6000
(b) 7000
(c) 8000
(d) 9000
Answer: (b) 7000

Question. Number 1000 can be expressed as a product of its prime factors as
(a) \( 2^3 \times 5^3 \)
(b) \( 2^2 \times 5^4 \)
(c) \( 2^4 \times 5^2 \)
(d) \( 2^3 \times 5^4 \)
Answer: (a) \( 2^3 \times 5^3 \)

Question. The maximum number of columns in which army can march is
(a) 6
(b) 10
(c) 12
(d) 8
Answer: (d) 8

Traffic Lights are used to control movement of traffics. They are installed at crossings and intersections of roads. Usually three different colours of lights (Red, Yellow and Green) are used to tell commuters what to do. The traffic lights at different road crossings change after every 48 seconds, 72 seconds and 120 seconds respectively.

Question. 120 can be expressed as a product of its prime factors as
(a) \( 2^3 \times 3^1 \times 5^1 \)
(b) \( 2^2 \times 3^2 \times 5^1 \)
(c) \( 2^2 \times 3^1 \times 5^2 \)
(d) \( 2^3 \times 3^2 \times 5^1 \)
Answer: (a) \( 2^3 \times 3^1 \times 5^1 \)

Question. The HCF of 48, 72 and 120 is
(a) 12
(b) 16
(c) 18
(d) 24
Answer: (d) 24

Question. The LCM of 48, 72 and 120 is
(a) 432
(b) 420
(c) 720
(d) 840
Answer: (c) 720

Question. If all the traffic lights change simultaneously at 7 : 30 : 00 hours, they will change again simultaneously at
(a) 7 : 42 : 00 hrs
(b) 7 : 52 : 00 hrs
(c) 7 : 36 : 00 hrs
(d) 7 : 46 : 00 hrs
Answer: (a) 7 : 42 : 00 hrs

Question. The [HCF × LCM] for the numbers 48, 72 and 120 is
(a) 17480
(b) 17280
(c) 12280
(d) 18280
Answer: (b) 17280