The decimal expansion of the rational number  $\frac{43}{2^45^3}$  will terminate after how many places of decimals?

If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.

Find LCM of numbers whose prime factorisation are expressible as 3 × 52 and 32 × 72. (2014)

Find the HCF (865, 255) using Euclid’s division lemma. (2013)

Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively. (2015)

Complete the following factor tree and find the composite number x and y respectively. (2014)

Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together? (2013)

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. (2012)

The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly. (2015)

In a school, there are two Sections A and B of class X. There are 48 students in Section A and 60 students in Section B. Determine the least number of books required for the library of the school so that the books can be distributed equally among all students of each Section. (2017 OD)

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. (2013)

(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.

If two positive integers x and y are expressible in terms of primes as x = $p^2q^3$  and y =  $p^3q$ , find their LCM and HCF. Is LCM a multiple of HCF? Explain. (2014)

Dudhnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled. (2014)

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? (2013)