English Medium Class 10 - CBSE Question Bank Solutions

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?

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

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?

The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.

Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.