English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Mathematics

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

[1] Real Numbers

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Chapter: [1] Real Numbers
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The LCM of smallest 2-digit number and smallest composite number is ______.

[1] Real Numbers

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Chapter: [1] Real Numbers
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The distance between the points (0, 5) and (–3, 1) is ______.

[6] Coordinate Geometry

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Chapter: [6] Coordinate Geometry
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The zeroes of the polynomial 3x² + 11x – 4 are ______.

[2] Polynomials

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

[1] Real Numbers

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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.

[1] Real Numbers

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Chapter: [1] Real Numbers
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Read the following passage:

Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C.

Based on the above information, answer the following questions.

How far is Alia's house from Shagun's house?
How far is the library from Shagun's house?
Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.

[6] Coordinate Geometry

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Chapter: [6] Coordinate Geometry
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Show that Alia's house, Shagun's house and library for an isosceles right triangle.

[6] Coordinate Geometry

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Chapter: [6] Coordinate Geometry
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(HCF × LCM) for the numbers 70 and 40 is ______.

[1] Real Numbers

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Read the following passage:

Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.

Based on the above information, answer the following questions:

Find the coordinates of the point of intersection of diagonals AC and BD.
Find the length of the diagonal AC.
1. Find the area of the campaign Board ABCD.
  OR
2. Find the ratio of the length of side AB to the length of the diagonal AC.

[6] Coordinate Geometry

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Chapter: [6] Coordinate Geometry
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Read the following passage:

Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all.

Based on the above information, answer the following questions:

How many guests Khushi can invite at the most?
How many apples and bananas will each guest get?
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.