Question

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

To enhance the reading skills of grade - Teachoo.jpg

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Question 1


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

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Question 2

If the product of two 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

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Question 3


36 can be expressed as a product of it’s primes as
(a) 2 2   × 3 2  
(b) 2 1 × 3 3   
(c) 2 3 × 3 1  
(d) 2 0 × 3 0

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Question 4


7 × 11 × 13 × 15 + 15 is a
(a) Prime number 
(b) Composite Number 
(c) Neither prime nor composite 
(d) None of the above

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Question 5


If p and q are positive integers such that p = ab 2 and q = a 2 b, where a, b are prime numbers, then the LCM (p, q) is
(a) ab  (b) a 2 b 2 (c) a 3 b 2 (d) a 3 b 3

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Transcript

Question To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.Question 1 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 Minimum Number of books will be the LCM of 32 and 36 LCM = 2 . 2 . 2 . 2 . 2 . 3. 3 = 288 So, correct answer is (C) Question 2 If the product of two 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 Given that Product of two numbers = HCF × LCM Putting two numbers as 32, 36 and their LCM as 288 32 × 36 = HCF × 288 (32 × 36)/288 = HCF HCF = (32 × 36)/288 HCF = 36/9 = 4 So, correct answer is (B) Question 3 36 can be expressed as a product of it’s primes as (a) 2^2 × 3^2 (b) 2^1 × 3^3 (c) 2^3 × 3^1 (d) 2^0 × 3^0 Doing Prime Factorisation of 36 36 = 2 . 2 . 3 . 3 = 22 × 32 So, correct answer is (A) Question 4 7 × 11 × 13 × 15 + 15 is a (a) Prime number (b) Composite Number (c) Neither prime nor composite (d) None of the above 7 × 11 × 13 × 15 + 15 = 15 × (7 × 11 × 13 + 1) Since the number is divisible by a number other than itself and 1 It is a composite number So, correct answer is (B) Question 5 If p and q are positive integers such that 〖𝑝=𝑎𝑏〗^2 and 𝑞=𝑎^2 𝑏, where a, b are prime numbers, then the LCM (p, q) is (a) ab (b) 𝑎^2 𝑏^2 (c) 𝑎^3 𝑏^2 (d) 𝑎^3 𝑏^3 Finding LCM of ab2 and a2b LCM = a . a . b . b = a2b2 So, correct answer is (A)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.