HCF AND LCM OF NUMBERS AND POLYNOMIALS (CDS)

Total Questions: 31

21. The LCM of two integers is 1237. What is their HCF? [2014 (II) Evening Shift ]

Correct Answer: (c) 1
Solution:Given, LCM of two integers is 1237, which is a prime number. So, their HCF is 1.

22. There are 48 cricket balls, 72 hockey balls and 84 tennis balls and they have to be arranged in several rows in such a way that every row contains the same number of balls of one type. What is the minimum number of rows required for this to happen? [2014 (II) Evening Shift ]

Correct Answer: (c) 17
Solution:Given number of cricket balls = 48 = 2⁴ × 3

23. The HCF of two natural numbers m and n is 24 and their product is 552. How many sets of values of m and n are possible? [2014 (II) Evening Shift ]

Correct Answer: (d) No set of m and n is possible satisfying the given conditions
Solution:Given HCF of two natural numbers m and n = 24

24. What is the highest common factor of 2x³ + x² - x - 2 and 3x³ - 2x² + x - 2 ? [2014 (II) Evening Shift ]

Correct Answer: (a) x - 1
Solution:Let f(x) = 2x³ + x² - x - 2

25. The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456. If one of the numbers is 160, then what is the other number? [2014 (II) Evening Shift ]

Correct Answer: (c) 144
Solution:Let the HCF of two numbers be x.

26. What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65? [2014 (I) Morning Shift ]

Correct Answer: (c) Less than 65
Solution:∵ HCF (a, b) = 5

27. If a and b are positive integers, then what is HCF [2014 (I) Morning Shift ]

Correct Answer: (c)
Solution:


28. For any integers ‘a’ and ‘b’ with HCF(a, b) = 1, what is HCF (a + b, a - b) equal to? [2014 (I) Morning Shift ]

Correct Answer: (c) Either 1 or 2
Solution:HCF (a + b, a - b) is either 1 or 2

29. For any integer n, what is HCF (22n + 7, 33n + 10) equal to? [2014 (I) Morning Shift ]

Correct Answer: (b) 1
Solution:Apply Euclidean algorithm on (22n + 7, 33n + 10),

30. In a fire range, 4 shooters are firing at their respective targets. The first, the second, the third and the fourth shooters hit the target once in every 5 s, 6 s, 7 s and 8 s, respectively. If all of them hit their target at 9 : 00 am, when will they hit their target together again? [2014 (I) Morning Shift ]

Correct Answer: (c) 9 : 14 am
Solution:Time after which they will hit the target again together