# MCQ Questions Chapter 1 Real Numbers Class 10 Mathematics

Please refer to MCQ Questions Chapter 1 Real Numbers Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 1 Real Numbers in Class 10 Mathematics provided below to get more marks in exams.

## Chapter 1 Real Numbers MCQ Questions

Please refer to the following Chapter 1 Real Numbers MCQ Questions Class 10 Mathematics with solutions for all important topics in the chapter.

MCQ Questions Answers for Chapter 1 Real Numbers Class 10 Mathematics

Question. The remainder of any perfect square divided by 3 is
(a) 0
(b) 1
(3) Either (a) or (b)
(d) Neither (a) nor (b)

C

Question. The greatest five digit number exactly divisible by 9 and 13 is
(a) 99945
(b) 99918
(3) 99964
(d) 99972

B

Question. Find the HCF of 432 and 504 using prime factorization method.
(a) 36
(b) 72
(3) 96
(d) 108

B

Question. If p,q and r are prime numbers such that r = q + 2 and q = p + 2, then the number of triplets of the form (p,q,r) is
(a) 0
(b) 1
(3) 2
(d) 3

B

Question. Which of the following is always true ?
(a)The rationalising factor of a number is unique
(b)The sum of two distinct irrational numbers is rational
(3)The product of two distinct irrational numbers is irrational
(d) None of these

D

Question. Find the remainder when the square of any number is divided by 4.
(a) 0
(b) 1
(3) Either (a) or (b)
(d) Neither (a) nor (b)

C

Question. If the product of two irrational numbers is rational, then which of the following can be concluded ?
(a) The ratio of the greater and the smaller numbers is an integer
(b) The sum of the numbers must be rational
(3) The excess of the greater irrational number over the smaller irrational number must be rational
(d) None of these

D

Question. The LCM and HCF of two numbers are equal, then the numbers must be
(a) Prime
(b) Co-prime
(3) Composite
(d) Equal

D

Question. The sum of LCM and HCF of two numbers is 1260. If their LCM is 900 more than their HCF, find the product of two numbers.
(a) 203400
(b) 194400
(3) 198400
(d) 205400

B

Question. N is a natural number such that when N3 is divided by 9, it leaves remainder a. It can be concluded that
(a) a is a perfect square
(b) a is a perfect cube
(3) Both (a) and (b)
(d) Neither (a) nor (b)

B

Question. Find the remainder when the square of any prime number greater than 3 is divided by 6.
(a) 1
(b) 3
(3) 2
(d) 4

A

Question. If 1 ≤ k ≤ 25, how many prime numbers are there which are of the form 6k + 1 ?
(a) 15
(b) 16
(3) 17
(d) 18

B

Question. If a,b,c and d are four positive real numbers such that sum of a,b, and c is even and the sum of b,c and d is odd, then a2 − d2 is necessarily
(a) odd
(b) even
(3) prime
(d) Either (a) or (b)

A

Question. If HCF (72, q) = 12 then how many values can q take ? (Assume q be a product of a power of 2 and a power of 3 only)
(a) 1
(b) 2
(3) 3
(d) 4

B

Question. Find the HCF of 120 and 156 using Euclid’s division algorithm.
(a) 18
(b) 12
(3) 6
(d) 24

B

Question. What is the digit in the tens place in the product of the first 35 even natural numbers ?
(a) 6
(b) 2
(3) 0
(d) 5

B

Question. The LCM of 1/ 4 and 2/ 5 is
(a) 1
(b) 1/ 10
(3) 2
(d) 1/ 20

C

Question. The multiplicative inverse of (x + 1) + 1/ (x−1) is
(a) 1/ (x−1) + (x−1)
(b) (x−1) −1 (x+1)
(3) x-1/x2
(d) x+1/x 2

C

Question. Find the unit’s digit in the product of the first 50 odd natural numbers.
(a) 0
(b) 5
(3) 7
(d) None

B

Question. If n is a natural number, then 92n − 42n is always divisible by
(a) 5
(b) 13
(3) Both (a) and (b)
(d) Neither (a) nor (b)

C

Question. There are 20 balls. The balls are numbered consecutively starting from anyone of the numbers from 1 to 20. For any case, the sum of the numbers on all the balls will be a/an
(a) odd number
(b) even number
(3) prime number
(d) Cannot say

B

Question. Which pair of numbers below are twin primes ?
(a) 8 and 9
(b) 2 and 3
(3) 3 and 7
(d) 41 and 43

D

Question. Which of the following values are even ?
(a) 21 + 18 + 9 + 2 + 19
(b) 34 × 28 × 37 × 94 × 12712
(c) 33 × 35 × 37 × 39 × 41 × 43
(d) 11 × 11 × 11 × 11 × 11 × ….
(e) 110
(f) 39 − 24
(a) a,b,c
(b) d,e,f
(3) b
(d) a,b,d,e

C

Question. If n is an odd natural number, 32n + 22n is always divisible by
(a) 13
(b) 5
(3) 17
(d) 19

A

Question. What is the number in the units place of (763)84 ?
(a) 1
(b) 3
(3) 7
(d) 9

A

Question. If the numbers a − b and a + b are twin primes, then a and b are necessarily
(a) Twin primes
(b) Co-primes
(3) Cannot say
(d) None

B

Question. The HCF of all the natural numbers from 200 to 478 is
(a) 2
(b) 1
(3) 478
(d) 3

B

Question. If n is any natural number, then 6n − 5n always ends with
(a) 1
(b) 3
(3) 5
(d) 7

A

Question. Find the greatest number that divides 59 and 54 leaving remainders 3 and 5 respectively.
(a) 3
(b) 7
(3) 8
(d) 5

B

Question. Find the unit digit in the expansion of (44)44 + (55)55 + (88)88.
(a) 7
(b) 5
(3) 4
(d) 3

A

Question. Ashok has two vessels which contain 720 ml and 405 ml of milk respectively. Milk in each vessel is poured into glasses of equal capacity of their brim. find the minimum number of glasses which can be filled with milk.
(a) 45
(b) 35
(3) 25
(d) 30

C

Question. Find the digit in the units place of (676)99.
(a) 9
(b) 2
(3) 4
(d) 6

D

Question. The LCM of 5 63 , , 1252 and 4 17 is
(a) 60
(b) 1 60
(3) 180
(d) None

A

Question. Find the number of factors of 1080.
(a) 32
(b) 28
(3) 24
(d) 36

B

Question. The LCM of two numbers is 1200. Which of the following cannot be their HCF ?
(a) 600
(b) 500
(3) 200
(d) 400

B

Question. If the number 2345p60q is exactly divisible by 3 and 5, then the maximum value of p + q is
(a) 12
(b) 13
(3) 14
(d) 15

B

Question. If a = 1/ 3−2√2 , b = 1/ 3+ 2√2 + then the value of a3 + b3 is
(a) 194
(b) 196
(3) 198
(d) 200

C

Question. Mukesh bought 3 apples, 5 bananas and 7 custard apples for certain amount (which is even). The cost of apples, bananas and custard apples could be (in Rs.)
(a) 5,7,9
(b) 9,8,6
(3) 2,4,5
(d) 9,10,11

D

Question. In a class there are 72 boys and 64 girls. If the class is to be divided into least number of groups such that each group contains either only boys or only girls, then how many groups will be formed ?
(a) 17
(b) 34
(3) 24
(d) None

A

Question. The absolute value of 25 − (25 + 10) + 25 ¸ 125 × 25 is
(a) − 5
(b) 3
(3) 15
(d) 5

D

Question. Rahul wanted to type of first 180 natural numbers. Find the number of times he had to press the numbered keys.
(a) 384
(b) 432
(3) 416
(d) 448

B

Question. If the seven digit number 4567 X 75 is divisible by 15 then find the least possible value of X.
(a) 2
(b) 1
(3) 0
(d) 3

A

Question. A rational number can be expressed as a terminating decimal if the denominator has factors
(a) 2 or 5
(b) 2 ,3 or 5
(3) 3 or 5
(d) None of these

A

Question. The only prime number which is even is
(a) 2
(b) 4
(3) 6
(d) none of these

A

Question. The value of 23.¯435.2 + is
(a) 2395/ 990
(b) 2527/ 99
(3) 5169/ 990
(d) 2837/ 99

D

Question. If 2 = x + 1/ 1+ 1/3 + 1/ 4 , then value of x is
(a) 12 /17
(b) 13 /17
(3) 18 /17
(d) 21 /17

D

Question. If R “Every fraction is a rational number” and T “Every rational number is a fraction”, then which of the following is correct?
(a) R is True and T is False.
(b) R is False and T is True.
(3) Both R and T are True.
(d) Both R and T are False.

A

Question. 5.2 is equal to
(a) 45/ 9
(b) 46/ 9
(3) 47/ 9
(d) None of these

C

Question. For any two rational numbers A and B, which of the following properties are correct?
(i) A < B (ii) A = B
(iii) A > B
(a) Only (i) and (ii) are correct.
(b) Only (ii) and (iii) are correct.
(3) Only (ii) is correct.
(d) All (i), (ii), (iii) are correct.

D

Question. If x = 3 +√2/ 3−√2 and y = 3−√2/ 3+√2  , the value of (x + y) is
(a) 306/ 49
(b) 484/ 49
(3) 22/ 7
(d) 73/ 7

C

Question. The GCD of 144, 418 and 112 is ;
(a) 2
(b) 4
(c) 8
(d) 12

A

Question. The least number that is divisible by all the numbers between 1 and 10 (both inclusive) is:
(a) 252
(b) 2520
(c) 1260
(d) none of these

B

Question. The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, the other number is :
(a) 2075
(b) 870
(c) 87
(d) 435

D

Question. The HCF of 2048 and 960 is :
(a) 32
(b) 64
(c) 128
(d) none of these

B

Question. If the sum of two numbers is 1215 and their HCF is 81, the total number of such pairs is :
(a) 2
(b) 3
(c) 4
(d) 5

C

Question. Which of the following number is given by 0.1236 :
(a) 17/ 275
(b) 34/ 550
(c) 34 /275
(d) 13/ 825

C

Question. The prime factorisation of 468 is :
(a) 2 × 33 × 13
(b) 22 × 3 × 13
(c) 22 × 32 × 13
(d) none of these

C

Question. If HCF of 374 and 255 is H and H = 255m + 374n then the value of m – n is equal to _____
(a) 3
(b) 4
(c) 5
(d) 1
(e) None of these

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 √π less than or equal to n divides n.
(d) All the above
(e) None of these

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, 2 p – 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, n 12 cannot end with the digit 0 or 5.
(e) None of these

C

Question. Choose which one among the following statement is incorrect?
(a) HCF of two co-primes a and b is 1.
(b) LCM of two co-primes m and n is mn.
(c) By using Euclid’s division lemma for two numbers 155 and 345, we get 345 = 155 × 2 + 35.
(d) The remainder, when the square of any prime number greater than 3 is divided by 6, is 1.
(e) None of these

E

Question. If I is a positive integer then (I)2 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 (a) and (c)
(e) None of these

D

Question. The decimal expansion of the rational number 12879/1250 will terminate after:
(a) One decimal places
(b) Two decimal places
(c) Three decimal places
(d) Four decimal places
(e) None of these

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 (b) or (c)
(e) None of these

D

Question. If the LCM Of (480,672) = 3360, find H.C.F. of (480,672).
(a) 75
(b) 69
(c) 67
(d) 96

D

Question. Find the number which when divided by 43 leaves a remainder 32 and gives a quotient 25.
(a) 1045
(b) 1107
(c) 1150
(d) 1105

B

Question. Sandeep donated 75 glucose biscuits and 45 monaco biscuits to the students of a class. These are to be packed in identical packets. The two type of biscuits are to be packed separately and each containing the equal number of biscuits. Find the least number of glucose and monaco biscuit packets respectively.
(a) 5, 15
(b) 5, 3
(c) 2, 3
(d) 3, 2

B

Question. The product of L.C.M. and H.C.F. of two numbers is 88288. If one of the numbers is 248, find the other number.
(a) 356
(b) 635
(c) 365
(d) 653

A

Question. Dimensions of a rectangle are (25 x 7)cmand (2 x 52 x 73 )cm . Express the area of the rectangle in prime factorization form.
(a) 2 x 5 x 7cm2
(b) 2 x 73 cm2
(c) 26 x 52 x 74 cm2
(d) 25 x 52 x 73cm2

C

Question. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
(a) 3
(b) 8
(c) 12
(d) 4

B

Question. Books in a library are stacked in such a way that they are stored subject wise and the stacks are of the same size. If there are 144 Geography books, 384 History books and 240 Economics books, in the library, in how many stacks can the books be arranged?
(a) 18
(b) 14
(c) 16
(d) 12

C

Question. If P = 1 .3. 5. 7………….21 and Q = 2 .4 . 6 . 8. 10…………22 then HCF of P and Q is ________
(a) 12375
(b) 14175
(c) 825
(d) 925
(e) None of these

B

Question. The value of (22)3m + (28)3m ends in ______{M ∈ N}  .
(a) 8
(b) 2
(c) 6
(d) 0
(e) None of these

D

Question. In a seminar, the numbers of participants in science, English and Mathematics are 144, 180 and 192 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.
(a) 38
(b) 40
(c) 43
(d) 45
(e) None of these

C

Very Short Answer and Question :

Question. By which smallest irrational number √28 be multiplied so as to get a rational number ?

√7

Question. LCM of two numbers is 2079 and their HCF is 27. If one of the numbers is 297, find the other number.

189

Question. Find the missing number in the following factor tree:

1001

Question. Find the (HCF x LCM) for the numbers 100 and 190 p.

19000

Question. If q/ p is a rational number (q ≠ 0). What is the condition on q so that the decimal representation of is terminating p/q ?

q is of the form 2n.5m, where m and n are non-negative integers.

Question. Given that LCM (26,169) =338, write HCF (26,169).

13

Question. State whether the number ( √2−√3 )(√2+√3 ) is rational or irrational justify.

Rational number

Question. Check whether 5x3x11+11 and 5×7+7X3 are composite number and justify.

Composite number and justification show that numbers are having more than two factors

Question. Express107 in the form of 4q+3 for some positive integer q.

4 X26+3

Question. Use Euclid’s division algorithm to find the HCF of 1288 and 575.

23

Question. Write whether the rational number 51/1500 will have at erminating decimal expansion or a non terminating repeating decimal expansion.

Terminating

Question. Give an example of two irrational numbers whose sum is a rational number.

2 −√3 and 2 + √3

Question. Find the HCF of 26 and 91.

13

Question. Give an example of two irrational numbers whose product is a rational number.

√2 and √8

(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : n2 + n is divisible by 2 for every positive integer n.
Reason : If x and y are odd positive integers, from x2 + y2 is divisible by 4.

A

Question. Assertion : Denominator of 34.12345. When expressed in the form , p/ q , q ≠ 0 is of the form 2m × 5, where m, n are non-negative integers.
Reason : 34.12345 is a terminating decimal fraction.

A

Question. Assertion : The H.C.F. of two numbers is 16 and their product is 3072. Then, their L.C.M = 162.
Reason : If a, b are two positive integers, then H.C.F × L.C.M. = a × b.

D

Question. Assertion : 2 is a rational number.
Reason : The square roots of all positive integers are irrationals.

C

Question. Assertion : If L.C.M. {p, q} = 30 and H.C.F {p, q} = 5, then p.q = 150.
Reason : L.C.M. of (a, b) × H.C.F of (a, b) = a.b.

A

Question. Assertion : 13/ 3125 is a terminating decimal fraction.
Reason : If q = 2n.5m where n, m are non-negative integers, then p/ q is a terminating decimal fraction.