Class X Maths | Chapter 1 Real Numbers | Five Interesting Questions

Following Questions are discussed:

Question 1 : If the product of two co-prime numbers is 1260 , then their HCF and LCM are: (A) 1, 1260 (B) 1260, 1 (C) 7, 780 (D) 780, 7

Question 2: If ' 𝑝 ' and ' 𝑞 ' are natural numbers and ' 𝑝 ' is the multiple of ' 𝑞 ', then what is the HCF and LCM of ' 𝑝 ' and ' 𝑞 '?(a) 1, pq (b) p, q (c) q, 𝑝 (d) p+q, p−q

Question 3 : A number 𝑞 is prime factorized as 3^2×7^2×𝑏, where 𝑏 is a prime number other than 3 and 7.
Assertion (A): 𝑞 is definitely an odd number.Reason (𝑅):3^2×7^2 is an odd number.
(a) Both (A) and (R) are true and (R) is the correct explanation for (A).(b) Both (A) and (R) are true but (R) is not the correct explanation for (A).(c) (A) is true but (R) is false.(d) (A) is false but (R) is true.
Question 4: Check whether the statement below is true or false."The square root of every composite number is rational"Justify your answer by proving rationality or irrationality as applicable.

Question 5: Prime factorization of three numbers A,B and C is given below:
A=(2^𝑟×3^𝑝×5^𝑞 , B=2^𝑝×3^𝑟×5^𝑝 , C=(2^𝑞×3^𝑞×5^𝑝 )
such that, 𝑝 is less tan 𝑞 and q is less than r and 𝑝, 𝑞, & 𝑟 are natural numbers.

The largest number that divides A,B and C without leaving a remainder is 30.
The smallest number that leaves a remainder of 2 when divided by each of A, B and C is 5402 . Find A, B and C.