QUE 1 HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number.
QUE 2 Find LCM of numbers whose prime factorisation are expressible as 3 × 52 and 32 × 72
QUE 3 Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.
QUE 4 Prove that 2 + 3√5 is an irrational number.
QUE 5 Show that 3√7 is an irrational number.
QUE 6 Explain why (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number?
QUE 7 whether 4n can end with the digit 0 for any natural number n?
QUE 8 Prove that √5 is irrational and hence show that 3 + √5 is also irrational.
QUE 9Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together?
QUE 10 Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times.
QUE 11 There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class.
a) Find the maximum number of parallel rows of each class for the seating arrange¬ment.
(b) Also, find the number of students of class IX and also of class X in a row.
(c) What is the objective of the school administration behind such an arrangement?
QUE 12 Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16 and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together?
QUE 13 If two positive integers x and y are expressible in terms of primes as x = p2q3 and y = p3q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.
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