Mathematics Class 10 Real Number MCQ Test Paper -

Q 1 – ( n² – 1 ) is divisible by 8, if n is.

(A) an integer.

(B) a natural number.

(C) an odd integer.

(D) an even integer.

Ans. Option (C) is correct.

Q 2 – The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is:

(A) 13

(B) 65

(C) 875

(D) 1,750

Ans. Option (A) is correct.

Q 3 – If two positive integers a and b are written as a = x³y² and b = xy³; x, y are prime numbers, then HCF (a, b) is:

(A) xy.

(B)xy²

(C) x³y³

(D) X²y²

Ans. Option (B) is correct.

Q 4 – If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is

(A) 4.

(B) 2.

(C) 1.

(D) 3.

Ans. Option (B) is correct.

Q 5 – If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is

(A) ab.

(B) a²b².

(C) a³b².

(D) a³b³.

Ans. Option (C) is correct

Q 6 – The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(A) 10.

(B) 100.

(C) 504.

(D) 2,520

Ans. Option (D) is correct.

Q 7 – The product of a non-zero rational and an irrational number is :

(A) always irrational

(B) always rational

(C) rational or irrational

(D) one

Ans. Option (A) is correct.

Q 8 – The decimal expansion of the rational number

$\frac{14587}{1250}$ will terminate after :

(A) one decimal place

(B) two decimal places

(C) three decimal places

(D) four decimal places

Ans. Option (D) is correct

Q 9 – $\frac{1}{\sqrt{2}}$ is a/an :

(A) fraction

(B) rational number

(C) irrational number

(D) none of these

Ans. Option (C) is correct.

Q 10 – ( 3 +√ 5) is:

(A) An integer

(B) A rational number

(C) An irrational number

(D) None of these

Ans. Option (C) s Correct.

Q 11 – The number 1.732 is:

(A) an irrational number

(B) a rational number

(C) an integer

(D) a whole number

Ans. Option (B) is correct.

Q 12 – 2.13113111311113……..is

(A) an integer

(B) a rational number

(C) an irrational number

(D) none of these.

Ans. Option (C) is correct

Q 13 – Which of the Following rational numbers is expressible as a terminating decimal?

(A) $\frac{2027}{625}$

(B) $\frac{1625}{462}$

(C) $\frac{131}{35}$

(D) $\frac{124}{165}$

Ans. Option (A) is Correct.

Q 14 – The decimal expansion of the sum of rational numbers $\frac{15}{4}$ and $\frac{5}{40}$ wll terminate after.

(A) one decimal place

(B) two decimal places

(C) three decimal places

(D) four decimal places

Ans. Option (C) is correct

Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Q 15 – Assertion (A): If HCF (336, 54) = 6, then LCM (336,54) = 3000.

Reason (R): The sum of exponents of prime factors in the prime factorisation of 196 is 4.

Ans. Option (D) is correct.

Q 16 – Assertion (A): The product of two consecutive positive integers is divisible by 2.

Reason (R): 13233343563715 is a composite number.

Ans. Option (B) is correct.

Q 17 – Assertion(A):THE decimal expansion of $\frac{15}{16000}$ is 0.09375.

Reason (R) Reason: The decimal expansion $\frac{23}{2353}$ is 0.115

Ans. option (D) is Correct.

Q 18 – What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

(A) 144

(B) 128

(C) 288

(D) 272

Ans. Option (C) is correct.

Q 19 – IF the positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is

(A) 2

(B) 4

(C) 6

(D) 8

Ans. Option (B) is correct.

Q 20 – 36 can be expressed as a product of its primes as

(A) 2² x 3²

(B) 2¹ x 3³

(C) 23x 31

(D) 2^° x 3^°

Ans. Option (A) is correct.

Q 21 – 7x 11 x 13 x 15+ 15 is

(A) a number

(B) Composite number

(C) Neither prime nor composite

(D) None of the above

Ans. Option (B) is correct

Q 22 – If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then the LCM (p, q) is

(A) ab

(B) a²b²

(C) a³b²

(D) a³b³

Ans. Option (B) is correct

Q 23 – In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

(A) 14

(B) 12

(C) 16

(D) 18

Ans. Option (B) is correct.

Q 24 – What is the minimum number of rooms required during the event?

(A) 11

(B) 31

(C) 41

(D) 21

Ans. Option (D) is correct.

Q 25 – The LCM of 60, 84 and 108 is

(A) 3780

(B) 3680

(C) 4780

(D) 4680

Ans. Option (A) is correct

Q 26 – The product of HCF and LCM of 60,84 and 108 is

(A) 55360

(B) 35360

(C) 45500

(D) 45360

Ans. Option (D) is correct.

Q 27 – 108 can be expressed as a product of its primes as

(A) 2³ x 3²

(B) 2³ x 3³

(C) 2² x 3²

(D) 2² x 3³

Ans. Option (D) is correct

Q 28 – What is the maximum number of columns in which they can be planted ?

(A) 45

(B) 40

(C) 15

(13) 35

Ans. Option (A) is correct

Q 29 – Find the total number of plants

(A) 135

(B) 225

(C) 360

(D) 45

Ans. Option (C) is correct

Q 30 – Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.

(A) 5

(B) 3

(C) 4

(D) 6

Ans. Option (B) is correct.

Q 31 – What is total numbers of row in which they can be planted

(A) 3

(B) 5

(C) 8

(D) 15

Ans. Option (C) is correct.

Q 32 – Find the sum of exponents of the prime factors of total number of plants.

(A) 2

(B) 3

(C) 5

(D) 6

Ans. Option (D) is correct

Q 33 – What will be the value of x?

(A) 15005

(B) 13915

(C) 56920

(D) 17429

Ans. Option (B) is correct.

Q 34 – What will be the value of y?

(A) 23

(B) 22

(C) 11

(D) 19

Ans. Option (C) is correct

Q 35 – What will be the value of z?

(A) 22

(B) 23

(C) 17

(D) 19

Ans. Option (B) is correct

Q 36 – According to Fundamental Theorem of Arithmetic 13915 is a

(A) Composite number

(B) Prime number

(C) Neither prime nor composite

(D) Even number

Ans. Option (A) is correct.

Q 37 – The prime factorisation of 13915 is

(A) 5x 11³ x 13²

(B) 5x 11³ x 23²

(C) 5x 11² x 23

(D) 5x 11² x 23²

Ans. Option (C) is correct.

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