HCF AND LCM OF NUMBERS AND POLYNOMIALS (CDS)

Total Questions: 31

11. Solve the following equation [2017 (I) Morning Shift ]

Correct Answer: (a)
Solution:We have,

12. The HCF of two expressions p and q is 1. What is the reciprocal of their LCM? [2017 (I) Morning Shift ]

Correct Answer: (d) (pq)⁻¹
Solution:We have,

13. A is a set of those positive integers such that when these are divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A? [2016 (II) Evening Shift ]

Correct Answer: (b) One
Solution:Let p = 2 q = 3 r = 4 s = 5 andt = 6 and remainders a = 1, b = 2, c = 3, e = 5, d = 4

14. There are two numbers p and q such that their HCF is 1. Which of the following statements are correct? [2016 (II) Evening Shift ]

I. Both p and q may be prime.
II. One number may be prime and the other composite.
III. Both the numbers may be composite.

Select the correct answer using the code given below.

Correct Answer: (d) I, II and III
Solution:Let two prime numbers 2 and 3, then their HCF = 1.

15. Consider the following in respect of natural numbers a, b and c [2016 (I) Morning Shift ]

1. LCM (ab, ac) = a LCM (b, c)
2. HCF (ab, ac) = a HCF (b, c)
3. HCF (a, b) < LCM (a, b)
4. HCF (a, b) divides LCM (a, b).

Which of the above are correct?

Correct Answer: (d) 1, 2, 3 and 4
Solution:Given, a, b and c are natural numbers.

16. What is the sum of digits of the least multiple of 13, which when divided by 6 and 12 leaves 5 and 11, respectively, as the remainders? [2015 (II) Evening Shift ]

Correct Answer: (d) 8
Solution:Here, 6 - 5 = 1 and 12 - 11 = 1

17. If (x + l) is the HCF of Ax² + Bx + C and Bx² + Ax + C where A ≠ B then the value of C is [2015 (II) Evening Shift ]

Correct Answer: (d) 0
Solution:Since x + 1 is the HCF

18. The LCM of two numbers is 12 times their HCF. The sum of HCF and LCM is 403. If one of the numbers is 93, then the other number is [2015 (II) Evening Shift ]

Correct Answer: (a) 124
Solution:Let other number be b and HCF be x

19. The HCF and LCM of two polynomials are (x + y) and [2015 (I) Morning Shift ]


Correct Answer: (c)
Solution:Given, HCF = (x + y) and LCM


20. What is the lowest common multiple of ab(x² + 1) + x(a² + b²) and ab(x² - 1) + x(a² - b²) ? [2014 (II) Evening Shift ]

Correct Answer: (a)
Solution:We have,