CBSE Class 10 Mathematics Real Numbers MCQs Set 07

Question. The sum of rational and irrational number is always
(a) Rational
(b) Irrational
(3) Both
(d) Can’t say

Answer: B

Question. A heap is to be formed with lots of 8, 10 and 15 pebbles of different colours. The smallest number of pebbles in the heap is
(a) 121
(b) 120
(3) 110
(d) 8

Answer: B

Question. The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then the other number is
(a) 20
(b) 28
(c) 60
(d) 80

Answer: D

Question. By what number must 1789 be divided to get a quotient 29 and remainder 49?
(a) 60
(b) 61
(c) 59
(d) 52

Answer: A

Question. The difference of the L.C.M. and H.C.F. of 210 and 55 is expressed as 210 x 6 + 55y. What is the value of 3 y ?
(a) 361
(b) 19
(c) 55
(d) 6859

Answer: D

Question. The equivalent rational form of 17.¯6 is
(a) 53 /3
(b) 88/ 5
(3) 44 /25
(d) None of the options

Answer: A

Question. The product of rational and irrational number is always
(a) Rational
(b) Irrational
(3) Both
(d) Can’t say

Answer: B

Question. The rational form of 2.74¯35 is
(a) 27161/ 9999
(b) 27/ 99
(3) 27161/ 9900
(d) 27161/ 9000

Answer: C

Question. Rational number between 2 and 3 is
(a) 1.5
(b) 1.6
(c) 1.7
(d) All of these

Answer: D

Question. A circular field has a circumference of 360 km. Two cyclists Sumeet and John start together and cycle at speeds of 12 km/hr and 15 km/hr respectively, a round the circular field. After how many hours will they meet again at the starting point?
(a) 100 hours
(b) 171 hours
(c) 120 hours
(d) 140 hours

Answer: C

Question. 961/ 625 is a
(a) Terminating decimal
(b) Nonterminating decimal
(3) Cannot be determined
(d) None of the options

Answer: A

Question. The number 5 − √5/ 5 +√ 5 is
(a) Rational
(b) Irrational
(3) Both
(d) Can’t say

Answer: B

Question. √7 + 4√3/2 equals to ________
(a) √2 + √6
(b) 2√2 + √6/2
(c) √2 + √6/2
(d) √3 + 2/4
(e) None of the options

Answer: B

Question. 28 mango trees, 42 apple trees and 21 orange trees have to be planted in rows such that each row contains the same number of trees of one variety only. The minimum number of rows in which the above trees may be planted
(a) 13
(b) 12
(3) 11
(d) 10

Answer: A

Question. The value of [(x^a−a−1)1/^a−1]^a/a+1 =
(a) x
(b) 1/x
(3) x^a
(d) 1/x^a

Answer: A

Question. Which of the following number do not have a terminating decimal representation :
(a) 7/ 50
(b) 19/ 1000
(c) 12 /105
(d) 113 /2500

Answer: C

Question. The HCF of two numbers, obtained in three steps of division, is 7 and the first 3 quotients are 2,4 and 6 respectively. Find the numbers.
(a) 175, 392
(b) 189, 392
(3) 168, 385
(d) None

Answer: A

Question. Given a = 3- √2 . and b = 3+√2 , which of the following is correct?
(a) a + b is irrational.
(b) a – b is rational.
(c) ab is rational.
(d) a/b is rational.

Answer: C

Question. When simplified, the product (1−1/3)(1−1/4))(1−1/5)……(1−1/n) equals ;
(a) 1/ n
(b) 2/ n
(3) 2(n−1)/ n
(d) 2/ n(n+1)

Answer: B

Question. Without actually performing the Song division, choose which among the following rational numbers will not have a terminating decimal expansion.
(a) 123/16
(b) 351/2⁷ x 5⁸ x 7¹⁸
(c) 32/28 x 59
(d) 833/49 x 2⁷

Answer: B

Question. Three measuring tapes are 64 cm, 72 cm, 96 cm, the shortest length that can measured by any one of the tapes exactly is
(a) 576
(b) 120
(3) 8
(d) 10.

Answer: A

Question. 1/7 , when expressed as a non-terminating and recurring decimal is given by :
(a) 0.142857
(b) 0.428571
(c) 0.857142
(d) None of the options

Answer: A

Question. The L.C.M. of 2³ × 3² × 5 × 11, 2⁴ × 3⁴ × 5² × 7 and 2⁵ × 3³ × 5³ × 7² × 11 is
(a) 2³ × 3² × 5
(b) 2⁵ × 3⁴ × 5³
(3) 2³ × 3² × 5 × 7 × 11
(d) 2⁵ × 3⁴ × 5³ × 7² x 11

Answer: D

Question. The L.C.M. of two numbers is 39780 and their ratio is 13 : 15 then the numbers are
(a) 273,315
(b) 2652,3
(3) 516, 685
(d) none of the options

Answer: B

Question. Rational number between √2 and √3 is
(a) √2 +√3/2
(b) √2 X √3 /2 ´
(3) 1.5
(d) 1.8

Answer: C

Question. Four bells begin to toll together and toll respectively at intervals of 5, 6, 8 and 12 seconds. How many times will they toll together in an hour excluding the one at the start
(a) 30
(b) 19
(3) 13
(d) 5

Answer: A

Question. Which of the following number is rational :
(a) √2 + 3
(b) (7 − √5) (7 +√5)
(c) 3/√5
(d) ( √3 − √7)²

Answer: B

Question. If x = 7 + 4√3 + , then the value of x² +1/ x² is
(a) 193
(b) 194
(3) 195
(d) 196

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
(3) 22/ 7 is a rational number
(d) None of the options

Answer: C

Question. The largest number that divides 588, 1999 and 1650 leaving 3, 10 and 12 respectively is ______
(a) 117
(b) 109
(c) 27
(d) 43

Answer: A

Question. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is
(a) 28
(b) 32
(3) 40
(d) 64

Answer: C

Question. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. The minimum distance each should walk so that each can cover the same distance in complete steps is
(a) 1260 cm
(b) 1920 cm
(c) 2242 cm
(d) 2520 cm

Answer: D

Question. If x = 7 + 4√3, then the value of √x +1/√x is
(a) 8
(b) 6
(3) 5
(d) 4

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
(e) None of the options

Answer: B

Question. The least number, which when divided by 48, 60, 72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is
(a) 11115
(b) 15110
(3) 15120
(d) 15210

Answer: B

Question. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is
(a) 1677
(b) 1683
(3) 2523
(d) 3363

Answer: B

Question. The product of two numbers is 960. If H.C.F. is 8, then the numbers are
(a) 24,40
(b) 8, 120 or 24, 40
(3) 8, 140
(d) None of the options

Answer: B

Question. The HCF of 405, 840 and 960 is
(a) 9
(b) 15
(c) 45
(d) None of the options

Answer: B

Question. Which of the following number have a terminating decimal representation :
(a) 7/ 80
(b) 3/ 345
(c) 8/ 17
(d) 5/ 224

Answer: A

One word Answer 

Question. Which number should be multiplied to ( √7 −√5) to get a rational number?
Answer: √7 + √5

Question. Write a rational number between √2 and √3 .
Answer: 1.42 (flexible)

Question. Write down the decimal expansion of 7 / 80 .
Answer: 0.0875

Question. If HCF (72, 120) = 24, then what is the LCM (72, 120) ?
Answer: 360

Question. Express 0.2545454…………..as a fraction in simplest form.
Answer: 14/55

Question. The decimal expansion of the rational no.43/2⁴5³ will terminate after how many places of decimal?
Answer: After 4 places of decimal.

Question. Write one rational and one irrational number lying between 0.25 and 0.32.
Answer: One rational number=26/100, one irrational no. =0.27010010001…

Question. Find the HCF of 65&117 and express it in the form of 65m+117n.
Answer: HCF =13

Question. Find the HCF and LCM of 6,72 and 120 using the prime factorization method.
Answer: HCF=6, LCM = 360

Question. Find the LCM & HCF of 26 and 91 and verify that HCF x LCM=product of the two numbers.
Answer: LCM = 182 HCF=13 Product =2366

Question. Check whether 6n can end with the digit 0, where n is any natural number.
Answer: No,6ⁿ cannot end with the digit 0.

Question. How many prime factors are there in the prime factorisation of 420.
Answer: 4

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

Question. If LCM (24, 80) = 240, then what is the HCF (24, 80)?
Answer: 8