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.

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

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

3. 36 can be expressed as a product of its primes as

a) 2² x 3²

b) 2¹ x 3³

c) 2³ x 3¹

d) 2⁰ x 3⁰ 

4. 7 x 11 x 13 x 15 + 15 is a

a) Prime number

b) Composite number

c) Neither prime nor composite

d) None of the above

5. 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) a² b²

c) a³ b²

d) a³ b³

Answer 1

1. c) 288

Minimum number of books will be the

LCM of 32 and 36

2. b) 4

Given that 

Product of two numbers = HCF x LCM

Putting two numbers as 32 , 36 and their LCM as 288

3. a) 2² x 3²

Prime Factorisation of 36

4. b) composite number

7 x 11 x 13 x 15 + 15

Since the number is divisible by a number other than itself and 1

It is a composite number.

5. b) a² b²

LCM of ab² and a²b

Answer 2

1. c) 288

2. b) 4

3. a) 2² x 3²

4. b) composite number

5. b) a² b²