CBSE Class 10 Mathematics Real Numbers MCQs Set D

Question: If the product of two numbers is 149058 and HCF of these numbers is 21 then how many pairs of these numbers are possible?
a) 1
b) 2
c) 3
d) 4
Answer: b

Question: For P ∈ N, 34^p − 24^p is always divisible by
a) 15
b) 5
c) 13
d) Both 5 and 13
Answer: d

Question: The unit value of 100¹⁰⁰⁶ − 5 is
a) 0
b) 1
c) 2
d) 3
Answer: b

Question: The decimal expansion of the rational number 12879 / 1250 will terminate after:
a) One decimal place
b) Two decimal places
c) Three decimal places
d) Four decimal places
Answer: d

Question: The greatest number of 5 digits exactly divisible by 15, 24, and 36 is
a) 99620
b) 99720
c) 99968
d) 99960
Answer: b

Question: For any odd natural number n, (√3)⁴ⁿ + (√2)⁴ⁿ is always divisible by
a) 5
b) 7
c) 17
d) 13
Answer: d

Question: Which among the following statements is not true?
a) The square of any odd integer is of the form 4q + 1, for some integer q.
b) For any odd integer p, p² − 1 is divisible by 8.
c) If p and q are both odd positive integers, then p² + q² is even and divisible by 4.
d) For any natural number n, n¹² cannot end with the digit 0 or 5.
Answer: c

Question: Which one among the following statements is true?
a) The remainder when the square of any number is divided by 4 is 1 or 0.
b) There is no natural number for which 4 ends with digit zero.
c) A positive integer n is prime, if no prime p less than or equal to √n divides n.
d) All of the options
Answer: d

Question: If LCM and HCF of two numbers are equal, then the numbers will be
a) Composite
b) Prime
c) Equal
d) Co-prime
Answer: c

Question: Which of the following is the greatest prime factor in 527527?
a) 17
b) 11
c) 13
d) 31
Answer: d

Question: If I is a positive integer then I² will be in the form of
a) 4m for some integer m
b) 8m for some integer m
c) 4m + 1 for some integer m
d) Both 4m for some integer m and 4m + 1 for some integer m
Answer: d

Question: For any natural number n, 2(2n + 1)² − 1 is always divisible by
a) 2
b) 4
c) 8
d) All of the options
Answer: d 

Question: The value of (27)^3p - (13)^3p ends in ______ (where p is a natural number)
a) 0
b) 4
c) 6
d) Either 4 or 6
Answer: d

Question: Which of the following is always true?
a) The sum or difference of a rational and an irrational number is rational.
b) Every irrational number is a surd.
c) The product or quotient of a non-zero rational number and an irrational number is irrational.
d) All of the options
Answer: c

Question: The number 3¹³ − 3¹⁰ is divisible by
a) 2 and 3
b) 3 and 10
c) 2, 3 and 10
d) 2, 3 and 13
Answer: d

Question: If p is a single-digit natural number and the unit digits of 4^p and p are same, how many possibilities can p assume?
a) 2
b) 3
c) 4
d) 5
Answer: b

Question: When 2²⁵⁶is divided by 17, the remainder is
a) 1
b) 16
c) 14
d) None of the options
Answer: a

Question: The largest number that divides 70 and 125 leaving remainders 5 and 8 respectively is
a) 13
b) 9
c) 3
d) 585
Answer: a

Question: The rational number 0.1343434... is equal to
a) 134 / 999
b) 134 / 990
c) 133 / 999
d) 133 / 990
Answer: d

Question: The sum of exponents of prime factors in the prime factorization of 196 is
a) 3
b) 4
c) 5
d) 2
Answer: b

Question: Which of the following statement is true?
a) Every point on the number line represents a rational number.
b) Irrational numbers cannot be represented by points on the number line.
c) 22/7 is a rational number.
d) None of the options.
Answer: d

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

Question: The decimal expansion of the rational number 33/22.5 will terminate after
a) one decimal place
b) two decimal places
c) three decimal places
d) more than 3 decimal places
Answer: b

Question: The least number which is a perfect square and divisible by 16, 20, and 24 is
a) 240
b) 1600
c) 2400
d) 3600
Answer: d

Question: Consider the following statements: For any integer n,
I. n² + 3 is never divisible by 17.
II. n² + 4 is never divisible by 17.
a) both I and II are true
b) both I and II are false
c) I is false and II is true
d) I is true and II is false
Answer: d

Question: In a seminar, the number of participants in Science, English, and Mathematics are 144, 180, and 192 respectively. What is the minimum number of rooms required if each room must have the same number of students of the same subject?
a) 38
b) 40
c) 43
d) 45
Answer: c

Question: Without actual division, choose which of the following rational numbers will not have a terminating decimal expansion.
a) 123/16
b) 351/(27×58×718)
c) 32/(28×59)
d) 833/49²
Answer: b

Question: What is the HCF of P = 1 + 3 + 5 + … + 21 and Q = 2 + 4 + 6 + … + 22?
a) 12375
b) 14175
c) 825
d) 925
Answer: b

Question: The least number which when divided by 15, 25, and 35 leaves remainders 5, 15, and 25 respectively is
a) 515
b) 525
c) 1040
d) 1050
Answer: a

Question: The sum of three non-zero prime numbers is 100. One of them exceeds the other by 36. The largest number is
a) 73
b) 91
c) 67
d) 57
Answer: c

Question: If n is an even natural number, then the largest natural number by which n(n + 1)(n + 2) is always divisible is
a) 6
b) 8
c) 12
d) 24
Answer: d

Question: Which of the following will have a terminating decimal expansion?       
a) 77/ 210
b) 23/ 30
c) 125 /441
d) 23/ 8
Answer: d

Question: Which of the following is an incorrect statement?
a) If √a + √b is an irrational number, then ab is also an irrational number.
b) The reciprocal of an irrational number is always an irrational number.
c) There are infinitely many rational numbers between any two irrational numbers.
d) 7 × 13 + 13 is a prime number.
Answer: d

Question: Which of the following will have a terminating decimal expansion?
a) 77/210
b) 23/30
c) 125/441
d) 23/8
Answer: d

Question: The largest non-negative integer k such that 24k divides 13! is
a) 2
b) 3
c) 4
d) 5
Answer: b

Question: A number lies between 300 and 400. If it is added to the number formed by reversing its digits, the sum is 888. If the unit’s digit and ten’s digit are swapped, the new number exceeds the original number by 9. What is the number?
a) 339
b) 341
c) 378
d) 345
Answer: d

Question: Euclid's division lemma: For any two positive integers a and b, a = bq + r. What condition must r satisfy?
a) 0 ≤ r ≤ b
b) 0 < r ≤ b
c) 0 ≤ r < b
d) 0 < r < b
Answer: c

Question: The H.C.F. of 6930 and 8085 is
a) 1155
b) 2205
c) 1515
d) 2025
Answer: a

Question: When a natural number x is divided by 5, the remainder is 2. When another number y is divided by 5, the remainder is 4. The remainder z when x + y is divided by 5 satisfies 2z−5/3 = ?
a) −1
b) 1
c) −2
d) 2
Answer: a

Question: Which of the following statements is not correct?
a) Every integer is a rational number.
b) The sum of a rational number and an irrational number is an irrational number.
c) Every real number is rational.
d) Every point on a number line is associated with a real number.
Answer: c

Fill in the Blanks :

Question: 35/50 is a ..................... decimal expansion.
Answer: Terminating

Question: The exponent of 2 in the prime factorisation of 144 is ...............
Answer: 4

Question: √5 is a/an ............... number.
Answer: Irrational

Question: An .............. is a series of well-defined steps which gives a procedure for solving a type of problem.
Answer: Algorithm

Question: An ........... is a proven statement used for proving another statement.
Answer: Lemma

Question: LCM of 96 and 404 is ..................
Answer: 9696

Question: 6 + √2 is a/an ............... number.
Answer: Irrational

Question: HCF of 6, 72 and 120 is ..............
Answer: 6

Question: 1/√2 is a/an ............... number.
Answer: Irrational

Question: 156 as a product of its prime factors is .............
Answer: 2² × 3 × 13

Question: 7√5 is a/an ............... number.
Answer: Irrational