English Medium Class 10 - CBSE Question Bank Solutions

Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF (a, b) = p^mqⁿ and LCM (a, b) = p^rq^s, then (m + n)(r + s) = ______.

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.

Find the HCF and LCM of 26, 65 and 117, using prime factorisation.

The LCM of smallest 2-digit number and smallest composite number is ______.

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.

Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.

(HCF × LCM) for the numbers 70 and 40 is ______.

Read the following passage:

Based on the above information, answer the following questions:

1. How many guests Khushi can invite at the most?
2. How many apples and bananas will each guest get?
3. 1. If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
      OR
   2. If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
      

(HCF × LCM) for the numbers 30 and 70 is ______.

If HCF (72, 120) = 24, then LCM (72, 120) is ______.

The prime factorisation of the number 2304 is ______.

If n is a natural number, then 8ⁿ cannot end with digit

The HCF of the smallest 2-digit number and the smallest composite number is ______.

The mean of first ten natural numbers is ______.

The prime factorisation of the number 5488 is ______.

If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.

National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?

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