CBSE Class 10 Mathematics Real Numbers MCQs Set 02

Question. Which of the following statements is true? 

Answer: A

Question. If 3/7 + x+(-8/21) + 5/22 = -125/462 , then x is
(A) 125/462
(B) -124/462
(C) -125/462
(D) 124/462

Answer: C

Question. Consider the following statements 

(A) 1 alone is correct
(B) 2 alone is correct
(C) both 1 and 2 are false
(D) both 1 and 2 are correct

Answer: D

Question. The value of x for which the two rational numbers 3/7,x/42 are equivalent is
(A) 18
(B) 15
(C) 12
(D) 10

Answer: A

Question.

(A) 133/99
(B) 371/90
(C) 5169/990
(D) 5411/990

Answer: D

Question. To satisfy the equation a+b/a = b/a+b , a and b must be
(A) both rational
(B) both real, but not rational
(C) one real, other non real
(D) either one ral or both non-real

Answer: D

Question. Match the following:
1. Natural numbers (p) 0, 1, 2, 3, 4, 5 ...etc
2. Whole numbers (q) 1, 2, 3, 4, 5,....etc.
3. Integers (r) 3/-5 , -7/9 , 13/9 , -11/36 etc.
4. Rational numbers (s) ....., – 4, –3, –2, –1, 0, 1, 2
(A) 1q, 2p, 3s, 4r
(B) 1p, 2q, 3r, 4s
(C) 1p, 2s, 3q, 4r
(D) 1q, 2p, 3r, 4s

Answer: A

Question. What is the value of 1+√2/1-√2 + 1-√2/1+√2 ?
(A) – 6
(B) √2
(C) √2/2
(D) 4

Answer: A

Question. 

Answer: D

Question. If x = -1/3 and y = 2/7 , then | x + y | is
(A) ≥ | x | + | y |
(B) = | x | + | y |
(C) ≤ | x | + | y |
(D) = x + y

Answer: C

Question. The set of positive real numbers does not satisfy the property of
(A) Multiplicative inverse
(B) Additive inverse
(C) Multiplicative identity
(D) None of these

Answer: D

Question. What is the value of the fraction, 

(A) 1.5
(B) 2.25
(C) 2.5
(D) 2.6

Answer: B

Question. 

Answer: D

Question. The expresion 1= 1/1+√3 + 1/1-√3 is equal to
(A) 1 – √3
(B) 1
(C) – √3
(D) √3

Answer: A

Question. The value of expression 2/3 + 5/11 + -1/3 + -3/11 is equal to
(A) 1/33
(B) 2/33
(C) 10/33
(D) 17/33

Answer: D

Question. What is the value of 

(A) 1/4
(B) 11/31
(C) 22/31
(D) 1/2

Answer: C

Question. Which of the following expressions is not equal to the others? 

Answer: C

Question. If x = -2/7 , then | – x | is equal to
(A) | x |
(B) x
(C) 0
(D) 1

Answer: A 

Question. The rational number which is not lying between 5/16 and 1/2 is
(A) 3/8
(B) 7/16
(C) 1/4
(D) 13/32

Answer: C

Question. Which property is used in the identity given below
x + y = y + x
(A) Associative property of addition
(B) Commutative property of addition
(C) Distributive property
(D) Reflexive property

Answer: B

Question. Which of the following illustrates the inverse property of addition?
(A) 3 – 3 = 0
(B) 3 + 3 = 6
(C) 3 + 0 = 0
(D) 3 – 0 = 3

Answer: A

Question. 

(A) 28.5
(B) 27.5
(C) 30.5
(D) 29.5

Answer: D

Question. The difference between the largest and the smallest of the fractions 5/8 , 7/12 , 1/3 , 2/5 is
(A) 1/4
(B) 5/24
(C) 7/24
(D) 13/21

Answer: C

Question. Which of the following statements is false?
(A) π is an irrational number
(B) The set of real numbers is closed for addition
(C) The set of irrational numbers is closed for multiplication
(D) The set of a real numbers is closed for multiplication

Answer: C

Question. Which of the following is an irrational number?
(A) 4/3
(B) √24 
(C) √81 
(D) – 4.07

Answer: B

Question. Additive inverse of 3/-4 is
(A) 3/4
(B) 1/4
(C) 3
(D) 0

Answer: A

Question. 

Answer: D

Question. The standard form of 192/-168 is
(A) -2/3
(B) -8/7
(C) -1/7
(D) -6/7

Answer: B

Question. The number which is subtracted from 27/13 to get -3/7 is
(A) 228/91
(B) 1/91
(C) 200/91
(D) 198/91

Answer: A

Question. √2-1/√2+1 = ......
(A) 3 – 2√2
(B) 3 + 3√2
(C) 1/√2
(D) 1.632

Answer: A

Question. -24/36 is a rational number with denominator is
(A) 3
(B) 4
(C) 1
(D) 2

Answer: A

Question. √5-√3/√5+√3 is equal to
(A) 4 + √15
(B) 4 – √15
(C) 1/2
(D) 1

Answer: B

Question. The unit digit in the product (327)¹⁷³ is
(A) 9
(B) 7
(C) 1
(D) 3

Answer: B

Question. The unit digit in the product (7⁷¹ × 6⁵⁹ × 3⁶⁵) as:
(A) 6
(B) 2
(C) 4
(D) 1

Answer: C

Question. The unit digit in (7²⁷ – 3¹⁴) is
(A) 0
(B) 7
(C) 4
(D) 6

Answer: C

Question. If -1≤ x ≤ 3 and 1≤ y ≤ 3, then the maximum value of (3y – 4x) is
(A) 18
(B) 13
(C) 5
(D) –6

Answer: B

Question. If x is negative
(A) | x | = x
(B) | x | = x
(C) | x |= 1/x
(D) | x|= -1/x

Answer: B

Question. 235.235235235... is a/an:
(A) integer
(B) whole number
(C) rational number
(D) irrational number

Answer: C

Question. Find the value of ‘a’ and ‘b’ if 

(A) 2, 11
(B) 11, 2
(C) 1, 1
(D) 2, 1

Answer: B

Question. If √[0.04x 0.4x x] = 0.4x 0.04x√y then the value of x/y is:
(A) 0.0016
(B) 0.16
(C) 0.016
(D) None of these

Answer: C

Question. The unit in the product (281 × 15 × 16 × 18) is:
(A) 6
(B) 0
(C) 5
(D) 8

Answer: B

Question. The unit digit in the product (127)¹⁷⁰ is
(A) 3
(B) 9
(C) 7
(D) 3

Answer: B

Question. If x/y = 3/5 , then the value of x-y/x+y is
(A) -1/4
(B) 1/4
(C) 1/6
(D) – 6

Answer: A

Question. The LCM of two numbers is 198 and their product is 1188. Find their HCF
a. 18
b. 6
c. 66
d. None of above

Answer : B

Question. Two natural numbers whose sum is 85 and the least common multiple is 102 are:
(a) 30 and 55
(b) 17 and 68
(c) 35 and 55
(d) 51 and 34

Answer : D

Question. The values of x and y in the given figure are:
(a) x = 10; y = 14
(b) x = 21; y = 84
(c) x = 21; y = 25
(d) x = 10; y = 40

Answer : B

Question. What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact number of minutes?
(a) 17 m/min
(b) 7 m/min
(c) 13 m/min
(d) 26 m/min

Answer : C

Question. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2 the quotient is 33. The other number is:
(a) 66
(b) 130
(c) 132
(d) 196

Answer : C

Question. Pairs of natural numbers whose least common multiple is 78 and the greatest common divisor is 13 are:
(a) 58 and 13 or 16 and 29
(b) 68 and 23 or 36 and 49
(c) 18 and 73 or 56 and 93
(d) 78 and 13 or 26 and 39

Answer : D

Question. What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?
(a) 5
(b) 6
(c) 7
(d) none of these

Answer : C

Question. If two positive integers and are expressible in terms of primes as a = p⁶ q³ and b = p⁴ q⁸, then which of the following is true?
a. HCF = p⁵q² × LCM
b. LCM = p²q⁵ × HCF
c. LCM = p⁵q² × HCF
d. HCF = p²q⁵ × LCM

Answer : B

Question. If A = 2n + 13, B = n + 7, where n is a natural number then HCF of A and B is:
(a) 2
(b) 1
(c) 3
(d) 4

Answer : B

Question. 4 Bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?
(a) 3
(b) 4
(c) 5
(d) 6

Answer : C

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

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 and b are two positive integers, then H.C.F. × L.C.M. = a × b.
Answer : D

Question. Assertion: For any two positive integers p and q, HCF (p, q) × LCM (p, q) = p × q
Reason: If the HCF of two numbers is 5 and their product is 150, then their LCM is 4
Answer : C

Question. Assertion: A number N when divided by 15 gives the remainder 2. Then the remainder is same when N is divided by 5.
Reason: √3 is an irrational number.
Answer : B

Question. Assertion: 2 is an example of a rational number.
Reason: The square roots of all positive integers are irrational numbers.
Answer : C

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