CBSE Class 10 Mathematics Real Numbers MCQs Set 06

Question. Which of the following is a pair of co-primes ?
(a) (16, 62)
(b) (18, 25)
(3) (21, 35)
(d) (23, 92)

Answer: B

Question. 8 − 8 ×2,1/5 – 1,2/7/2-1/6-1/6 is equal to
(a) 6
(b) 2
(3) 4
(d) 8

Answer: C

Question. The value of 1/√3 +√ 2−1 + on simplifying upto 3 decimal places, given that √2 = 1.4142 and √6 = 2.4495 is
(a) 0.166
(b) 0.366
(3) 0.466
(d) 0.566

Answer: C

Question. π is
(a) Rational
(b) Irrational
(3) Imaginary
(d) An integer

Answer: B

Question. In a school, the duration of a period in junior section is 40 minutes and in senior section is 60 minutes. If the first bell for each section rings at 9 a.m., when will the two bells ring together again?
(a) 10:45 a.m.
(b) 10:15 a.m.
(c) 12:00 p.m.
(d) 11:00 a.m.

Answer: D

Question. M The prime factorization of two numbers are 3² x 7³ x 11 and 3 x 7² x 11³ x 17 . Which of the following is a common factor of the numbers? 
(a) 1683
(b) 5831
(c) 1089
(d) 539

Answer: D

Question. 0.0¯18 can be expressed in the rational form as
(a) 18/ 1000
(b) 18/ 990
(3) 18/ 9900
(d) 18/ 999

Answer: D

Question. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is
(a) 6
(b) 9
(3) 15
(d) 21

Answer: A

Question. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is
(a) 3
(b) 13
(3) 23
(d) 33

Answer: C

Question. The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case, is
(a) 8739
(b) 9831
(c) 9834
(d) 9893

Answer: B

Question. The greatest number of 6 digits exactly divisible by all the numbers between 1 and 10 (both inclusive) is _________
(a) 997920
(b) 999768
(c) 999660
(d) 999760
(e) None of the options

Answer: A

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. The largest number which divides 133 and 245 leaving a remainder 5 is
(a) 17
(b) 15
(3) 8
(d) 16

Answer: D

Question. Two ropes of length 28 m and 36 m are to be cut into bits of same length. The greatest possible length of each is
(a) 7
(b) 3
(3) 4
(d) 5

Answer: C

Question. The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54, is
(a) 427
(b) 859
(3) 869
(d) 4320

Answer: B

Question. If a = 2 +√3/ 2−√3 , b = 2−√3/ 2 +√3 , then the value of a + b is
(a) 14
(b) −14
(3) 8 √3
(d) − √3

Answer: A

Question. The least number divisible by 12, 15, 20, and is perfect square is
(a) 900
(b) 400
(3) 36
(d) 256

Answer: A

Question. The product of three consecutive positive integers is always divisible by :
(a) 4
(b) 5
(c) 6
(d) 12

Answer: C

Question. Four bells toll at an interval of 8, 12, 15 and 18 seconds respectively. All the four begin to toll together. The number of times they toll together in one hour excluding the one at the start will be
(a) 5
(b) 8
(c) 10
(d) 12

Answer: C

Question. The HCF of 657and 963 is :
(a) 3
(b) 6
(c) 9
(d) None of the options

Answer: C

Question. If x: Every whole number is a natural number and y: 0 is not a natural number, Then which of the following statement is true?
(a) x is false and y is the correct explanation of x.
(b) x is true and y is the correct explanation of x.
(3) x is true and y is false.
(d) Both x and y are true.

Answer: A

Question. If √3 -1/ √3 + 1 = a + b√3 , then the value of ‘a’ and ‘b’ is
(a) a = 2, b = − 1
(b) a = 2, b = 1
(3) a = − 2, b = 1
(d) a = − 2, b = − 1

Answer: A

Question. The decimal expansions (without actual division) and its nature (terminating or nonterminating) of 987 10500 will be
(a) 0.094 __ , non-terminating
(b) 0.094, terminating
(c) 0.094, non-terminating
(d) 0.049, terminating

Answer: B

Question. The following are the first and last steps in finding the H.C.F. of 408 and 1032 using Euclid’s algorithm.
Step 1: 1032 = 408X2 + 216
Step 2: ___________
Step 3: ___________
Step 4: 192 = 24 X 8+0
Choose the steps 2 and 3.
(i) 408=2161+1921
(ii) 408=216+180+12
(iii) 216 =192 1 + 24
(iv) 192 = 24 8 + 0
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iii)
(d) (iii) and (iv)

Answer: B

Question. For what value of ‘x’ does 6″ end with 5?
(a) 0
(b) 1
(c) 5
(d) Never ends with 5.

Answer: D

Question. An irrational number is
(a) A terminating and nonrepeating decimal
(b) A nonterminating and nonrepeating decimal
(3) A terminating and repeating decimal
(d) A nonterminating and repeating decimal

Answer: B

Question. Which of the following has most number of divisors ?
(a) 99
(b) 101
(3) 176
(d) 182

Answer: C

Question. The smallest number by which 3600 can be divided to make it a perfect cube is
(a) 9
(b) 50
(3) 300
(d) 450

Answer: D

Question. If A =14 + (1x 2 x 3 x 4 x 5 …………….A x 10 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

Question. The sum of LCM and HCF of two numbers is 29610. If their LCM is 140 times v the HCF of the numbers then which among the following can be one of the numbers?
(a) 330
(b) 1470
(c) 525
(d) 462

Answer: B

Question. The H.C.F,. of two numbers is 1/ 5 of their L.C.M. If the product of two number is 720, then the H.C.F. of the numbers is
(a) 13
(b) 12
(3) 14
(d) 18

Answer: B

Question. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8, is
(a) 504
(b) 536
(3) 544
(d) 548

Answer: D

Question. 2ⁿ⁺⁴ −2(b)n/2(2ⁿ⁺³) +2⁻³ is equal to
(a) 2ⁿ⁺¹
(b) −2ⁿ⁺¹ + 1/ 8
(3) 9/8−2ⁿ 
(d) 1

Answer: D

Question. The largest number which divides 615 and 963 leaving remainder 6 in each case is :
(a) 29
(b) 87
(c) 116
(d) None of the options

Answer: B

Question. [HCF × LCM] for the numbers 100 and 190 is
(a) 190
(b) 1900
(c) 19000
(d) None of the options

Answer: C

Question. The remainder when 7⁸⁴ is divided by 3⁴² is
(a) 0
(b) 1
(3) 49
(d) 341

Answer: B

Question. The decimal expansion of the rational number 43/ 2⁴ 5³ will terminate after how many places of decimals?
(a) 2 places
(b) 3 places
(c) 4 places
(d) 5 places

Answer: C

Question. What is the L.C.M. of 6/14 and 2/7 ?
(a) 3/7
(b) 6/7
(c) 4/7
(d) 5/7

Answer: B

Question. The L.C.M. of two numbers is 14 times of their H.C.F. The sum of L.C.M. and H.C.F. is 600. If one of the number is 80, then other is
(a) 280
(b) 218
(3) 25
(d) 45

Answer: A

Question. The H.C.F. of 2² × 3³ × 5⁵, 2³ × 3² × 5² × 7 and 2⁴ × 3⁴ × 5 × 7² × 11 is
(a) 2² × 3² × 5
(b) 2² × 3² × 5 × 7 × 11
(3) 2⁴ × 3⁴ × 5⁵
(d) 2⁴ × 3⁴ × 5⁵ × 7 × 11

Answer: A

Question. For P ∈ N, 3^4P – 2^4P  is always divisible by ____  
(a) 15
(b) 5
(c) 13
(d) Both
(b) and (c)

Answer: D

Question. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is
(a) 74
(b) 94
(3) 184
(d) 364

Answer: D

Question. The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
(a) 1008
(b) 1015
(3) 1022
(d) 1032

Answer: B

Question. (x^a+b)²(x^b+c)²(x^c+a)²/(xa.xb.xc)⁴ 
(a) −1
(b) 0
(3) 1
(d) None of the options

Answer: C

Question. The HCF of the smallest composite number and the smallest prime number is
(a) 1
(b) 2
(c) 3
(d) 5

Answer: B

Question. If a = 1/ 3−2√2 , b = 1/ 3+ 2√2 then the value of a² + b² is
(a) 34
(b) 35
(3) 36
(d) 37

Answer: A

Question. Find the greatest four digit number which when divided by 18 and 12 leaves a remainder of 4 in each case
(a) 9976
(b) 9940
(3) 9904
(d) 9868

Answer: A

Question. Which of the following is true for two coprime numbers?
(a) Their H.C.F. is 1.
(b) TheirL.CM.is1.
(c) Their H.C.F. is equal to their product.
(d) Their L.C.M. is twice their H.C.F.

Answer: A

Question. 0.¯230.¯22 + = ?
(a) 0.45
(b) 0.43
(3) 0.45
(d) 0.45

Answer: A

Question. The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is
(a) 1600
(b) 3600
(3) 6400
(d) 14400

Answer: B

Question. The smallest number, which when increased by 19 is exactly divisible by both 2079 and 1404, is _______
(a) 6200
(b) 625
(c) 6218
(d) 3208

Answer: C

Question. Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.
(a) 3002
(b) 3013
(3) 3024
(d) 3036

Answer: B