What are real numbers?

Real numbers include both rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi). Any number that can be placed on a number line is a real number.

What is the Fundamental Theorem of Arithmetic?

The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of prime numbers, and this factorisation is unique, apart from the order in which the prime factors occur.

What is the relationship between HCF and LCM of two numbers?

For any two positive integers a and b, the product of their HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is equal to the product of the two numbers. That is, HCF(a, b) × LCM(a, b) = a × b.

How do we identify an irrational number?

An irrational number cannot be expressed as a simple fraction (p/q). In decimal form, it is non-terminating and non-repeating. Examples include square roots of non-perfect squares.

How to find if a rational number has a terminating decimal expansion?

A rational number in its simplest form (p/q) has a terminating decimal expansion if the prime factorisation of its denominator (q) is of the form 2^n × 5^m, where n and m are non-negative integers.

What are real numbers?

Real numbers include both rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or pi). Any number that can be placed on a number line is a real number.

What is the Fundamental Theorem of Arithmetic?

The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of prime numbers, and this factorisation is unique, apart from the order in which the prime factors occur.

What is the relationship between HCF and LCM of two numbers?

For any two positive integers a and b, the product of their HCF (Highest Common Factor) and LCM (Lowest Common Multiple) is equal to the product of the two numbers. That is, HCF(a, b) × LCM(a, b) = a × b.

How do we identify an irrational number?

An irrational number cannot be expressed as a simple fraction (p/q). In decimal form, it is non-terminating and non-repeating. Examples include square roots of non-perfect squares.

How to find if a rational number has a terminating decimal expansion?

A rational number in its simplest form (p/q) has a terminating decimal expansion if the prime factorisation of its denominator (q) is of the form 2^n × 5^m, where n and m are non-negative integers.

The National Cadet Corps (NCC) is the youth wing of the Indian Armed Forces with its headquarters in New Delhi, open to school and college students on voluntary basis.

What are the benefits of an NCC certificate?

NCC certificate holders receive preference in armed forces recruitment, paramilitary forces, state police, and various government jobs.

What is the motto of NCC?

The motto of NCC is 'Unity and Discipline' (Ekta aur Anushasan).

What are the different certificates in NCC?

There are three types of certificates in NCC: 'A' certificate for school students, and 'B' and 'C' certificates for college students.

What is reflection of light?

The phenomenon of bouncing back of light rays into the same medium when they fall on a polished or smooth surface is called the reflection of light.

What are the laws of reflection of light?

The laws of reflection state that: (1) The angle of incidence is equal to the angle of reflection. (2) The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.

What is the nature of the image formed by a plane mirror?

The image formed by a plane mirror is always virtual, erect, of the same size as the object, and laterally inverted.

What is the relation between the angle of incidence and deviation for a plane mirror?

For a plane mirror, the angle of deviation (δ) is given by δ = 180° - 2i, where i is the angle of incidence.

What is reflection of light?

The phenomenon of bouncing back of light rays into the same medium when they fall on a polished or smooth surface is called the reflection of light.

What are the laws of reflection of light?

The laws of reflection state that: (1) The angle of incidence is equal to the angle of reflection. (2) The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.

What is the nature of the image formed by a plane mirror?

The image formed by a plane mirror is always virtual, erect, of the same size as the object, and laterally inverted.

What is the relation between the angle of incidence and deviation for a plane mirror?

For a plane mirror, the angle of deviation (δ) is given by δ = 180° - 2i, where i is the angle of incidence.

What is a chemical reaction?

A chemical reaction is a process in which atoms of reactants are rearranged to form new substances called products. It involves breaking of bonds in reactants and formation of new bonds in products.

What is a balanced chemical equation?

A balanced chemical equation is one in which the number of atoms of each element is equal on both the reactant and product sides, satisfying the law of conservation of mass.

What are the types of chemical reactions?

The main types of chemical reactions are: combination reactions, decomposition reactions, displacement reactions, double displacement reactions, and oxidation-reduction (redox) reactions.

What is the law of conservation of mass?

The law of conservation of mass states that mass can neither be created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

What is a decomposition reaction?

A decomposition reaction is one in which a single compound breaks down into two or more simpler substances, usually when energy (heat, light, or electricity) is supplied.

What is a chemical reaction?

A chemical reaction is a process in which atoms of reactants are rearranged to form new substances called products. It involves breaking of bonds in reactants and formation of new bonds in products.

What is a balanced chemical equation?

A balanced chemical equation is one in which the number of atoms of each element is equal on both the reactant and product sides, satisfying the law of conservation of mass.

What are the types of chemical reactions?

The main types of chemical reactions are: combination reactions, decomposition reactions, displacement reactions, double displacement reactions, and oxidation-reduction (redox) reactions.

What is the law of conservation of mass?

The law of conservation of mass states that mass can neither be created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

What is a decomposition reaction?

A decomposition reaction is one in which a single compound breaks down into two or more simpler substances, usually when energy (heat, light, or electricity) is supplied.

What is a chemical reaction?

A chemical reaction is a process in which atoms of reactants are rearranged to form new substances called products. It involves breaking of bonds in reactants and formation of new bonds in products.

What is a balanced chemical equation?

A balanced chemical equation is one in which the number of atoms of each element is equal on both the reactant and product sides, satisfying the law of conservation of mass.

What are the types of chemical reactions?

The main types of chemical reactions are: combination reactions, decomposition reactions, displacement reactions, double displacement reactions, and oxidation-reduction (redox) reactions.

What is the law of conservation of mass?

The law of conservation of mass states that mass can neither be created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

What is a decomposition reaction?

A decomposition reaction is one in which a single compound breaks down into two or more simpler substances, usually when energy (heat, light, or electricity) is supplied.

What is a chemical reaction?

A chemical reaction is a process in which atoms of reactants are rearranged to form new substances called products. It involves breaking of bonds in reactants and formation of new bonds in products.

What is a balanced chemical equation?

A balanced chemical equation is one in which the number of atoms of each element is equal on both the reactant and product sides, satisfying the law of conservation of mass.

What are the types of chemical reactions?

The main types of chemical reactions are: combination reactions, decomposition reactions, displacement reactions, double displacement reactions, and oxidation-reduction (redox) reactions.

What is the law of conservation of mass?

The law of conservation of mass states that mass can neither be created nor destroyed in a chemical reaction. The total mass of reactants equals the total mass of products.

What is a decomposition reaction?

A decomposition reaction is one in which a single compound breaks down into two or more simpler substances, usually when energy (heat, light, or electricity) is supplied.

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