CBSE Class 10 Mathematics Real Numbers MCQs Set 05

Question: The L.C.M. of 3465 and 5460 is
a) 181080
b) 180180
c) 108108
d) 108801
Answer: b

Question: Find the least number of bundles if 117 books (45 Math and 72 Physics) are packed such that each bundle contains the same number of books of the same subject.
a) 8
b) 11
c) 13
d) 9
Answer: c

Question: If a = 2³ × 3, b = 2 × 3 × 5, c = 3ⁿ × 5, and LCM(a, b, c) = 2³ × 3² × 5, then n =
a) 1
b) 2
c) 3
d) 4
Answer: b

Question: A rectangular metal piece 360 cm by 280 cm is cut into identical square pieces. The number of square pieces formed is
a) 126
b) 20
c) 40
d) 63
Answer: d

Question: The circumferences of the front and rear wheels of a tricycle are 120 cm and 90 cm respectively. After how many revolutions will marked points on both wheels touch the ground again together?
a) 6, 8
b) 3, 4
c) 9, 12
d) 1, 4
Answer: b

Question: What is the value of x if LCM(x, 18) = 36 and HCF(x, 18) = 2?
a) 1
b) 2
c) 3
d) 4
Answer: d

Question: Which of the following statements is/are not correct?
a) 73/54 is a non-terminating repeating decimal.
b) If a = 2 + √3 and b = √2 − √3, then a + b is irrational.
c) If 19 divides a³, then 19 divides a, where a is a positive integer.
d) Product of LCM and HCF of 25 and 625 is 15625.
Answer: a

Question: The terminating decimal among the following is
a) 141/1000
b) 17/30
c) 271/90
d) 53/343
Answer: a

Question: Three bulbs glow at intervals of 24, 36 and 54 seconds respectively. If all glow together at 8:00 a.m., when will they glow again simultaneously?
a) 8:30:36 a.m.
b) 8:03:36 a.m.
c) 8:36:03 a.m.
d) 8:36:30 a.m.
Answer: b

Question: Which of the following is not correct?
a) There are infinitely many even primes.
b) Let ‘a’ be a positive integer and p a prime number such that a² is divisible by p, then a is divisible by p.
c) Every positive integer different from 1 can be expressed as product of power of 2 and odd number.
d) If p is a prime, then √p is irrational.
Answer: a

Question: If p₁ and p₂ are two odd primes such that p₁ > p₂, then p₁² − p_2² is
a) an even number
b) an odd number
c) an odd prime number
d) a prime number
Answer: a

Question: Find the largest number which divides 120, 224 and 256 exactly.
a) 8
b) 6
c) 4
d) 5
Answer: a

Question: What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?
a) 15
b) 16
c) 9
d) 5
Answer: b

Question: For some integer m, every even integer is of the form
a) m
b) m + 1
c) 2m
d) 2m + 1
Answer: c

Question: The product of unit digit in (795 − 358) and (795 + 358) is
a) 8
b) lies between 3 and 7
c) 6
d) lies between 3 and 6
Answer: a

Question: Given that LCM(91, 26) = 182, then HCF(91, 26) is
a) 13
b) 26
c) 17
d) 9
Answer: a

Question: What is the value of –0.235 as a rational number?
a) 233/900
b) 233/990
c) 235/999
d) 235/990
Answer: c

Question: If p, q are two consecutive natural numbers, then HCF(p, q) is
a) p
b) q
c) 1
d) pq
Answer: c

Question: On dividing a natural number by 13, the remainder is 3; on dividing the same number by 21, the remainder is 11. If the number lies between 500 and 600, the remainder on dividing by 19 is
a) 4
b) 6
c) 9
d) 13
Answer: a

Question: A class of 20 boys and 15 girls is divided into n groups so that each group has x boys and y girls. What are the values of x, y and n respectively?
a) 3, 4 and 8
b) 4, 3 and 6
c) 4, 3 and 7
d) 7, 4 and 3
Answer: c

Question: If m = n² – n, where n is an integer, then m² – 2m is divisible by
a) 20
b) 24
c) 30
d) 16
Answer: b

Question: The unit digit in the expression 55⁷²⁵ + 735⁸¹⁰ + 228⁵³ is
a) 0
b) 4
c) 5
d) 6
Answer: d

Question: Which of the following statement(s) is/are always true?
a) The sum of two distinct irrational numbers is rational.
b) The rationalising factor of a number is unique.
c) Every irrational number is a surd.
d) None of the options
Answer: d

Question: If 1/7 = 0.142857…, a repeating decimal with six different digits, and x is the sum of the first three such n for which 1/n = 0.abcdef… with different digits, what is x?
a) 20
b) 21
c) 41
d) 42
Answer: c

Question: Product of two co-prime numbers is 117. Their LCM should be
a) 1
b) 117
c) Equal to their HCF
d) Lies between 1 to 117
Answer: b

Question: If 14 (1 x 2 x 3 x 4 x 5 ................A 10 x 14) and B 19 (1 x 2 x 3 x 4 x 5 ................10 x 19) then which one of the following is/are correct? 
(i) B – A is a prime number.
(ii) B + A is a composite number.
(iii) A is a composite number.
(iv) B is a prime number.
a) Both (i) and (ii)
b) Both (ii) and (iii)
c) Both (iii) and (iv)
d) All (i), (ii), (iii) and (iv)
Answer: b 

True or False:

Question: Every fraction is a rational number.
Answer: True 

Question: √2 and √3 are irrational numbers.
Answer: True

Question: The number of irrational numbers between 15 and 18 is infinite.
Answer: True

Question: Every composite number can be expressed (factorised) as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur.
Answer: True

Question: The quotient of two integers is always a rational number.
Answer: False

Question: Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ r < b.
Answer: True

Question: If x = p/q is a rational number, such that the prime factorisation of q is of the form 2ⁿ5ᵐ, where n, m are non-negative integers, then x has a decimal expansion which is terminating.
Answer: True

Question: 1/0 is not rational.
Answer: True

Question: Any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5, where q is some integer.
Answer: True 

Match the Following :   

Question:   
     Column-I                                                                                                             Column-II
(A) H.C.F of the smallest composite number and the smallest prime number            (p) 6
(B) H.C.F of 336 and 54                                                                                              (q) 5
(C) H.C.F of 475 and 495                                                                                            (r) 2
Answer: (A) → (r); (B) → (p); (C) → (q)

Question:  
  Column-I                                                                   Column-II
(A) 551/23 × 56 × 79                                               (p) a prime number
(B) Product of ( √5 – √3) and (√ 5 + √3) is              (q) is an irrational number
(C) √5 – 4                                                                (r) is a terminating decimal representation
(D) 422/23 × 54                                                       (s) is a non-terminating but repeating decimal representation
Answer: (A) → (s); (B) → (p); (C) → (q); (D) → (r)