#ncertnotes

शीत युद्ध (Cold War) का अंत 1991 में सोवियत संघ (USSR) के विघटन के साथ हुआ। इसके बाद विश्व राजनीति में कई बड़े बदलाव आए:

1️⃣ अमेरिका का उदय – सोवियत संघ के टूटने के बाद अमेरिका (USA) एकमात्र महाशक्ति (Superpower) बनकर उभरा।

2️⃣ संयुक्त राष्ट्र की भूमिका – शांति स्थापना, मानवीय सहायता और संघर्ष समाधान में UN की भूमिका बढ़ी।

3️⃣ वैश्वीकरण (Globalisation) – दुनिया आपस में जुड़ने लगी, व्यापार, तकनीक और सूचना क्रांति तेज़ हुई।4️⃣ आतंकवाद और नए खतरे – 9/11 जैसी घटनाओं ने सुरक्षा चिंताओं को नया रूप दिया।

5️⃣ भारत की भूमिका – भारत ने उदारीकरण (1991) शुरू किया और वैश्विक मंच पर अपनी जगह मजबूत की।👉 शीत युद्ध के बाद की राजनीति ने दुनिया को एकध्रुवीय (Unipolar World) बनाया, जहाँ अमेरिका प्रमुख शक्ति रहा, लेकिन आज चीन, रूस, यूरोपीय संघ और भारत जैसे देश भी महत्वपूर्ण भूमिका निभा रहे हैं।

Relations and Functions Class 12 Notes PDF

In class 12, students study Relations and Functions, which is a crucial topic in mathematics. Mathematics is a subject that involves a lot of concepts, theories, and formulas. Keeping in mind all those things for a longer period of time could be a challenge; however, Relations and Functions Class 12 Notes PDF helps in retaining those things for a certain period of time. 

The Sets Relations and Functions class 12 notes can be prepared by students or they can refer to the revision note that is prepared by Selfstudys subject experts. The Relations and Functions class 12 notes prepared by subject experts are easy to comprehend and information is distributed among the PDF in chunk size.

Thus, in this blog, I will guide you on how to download the Relations and Functions class 12 notes pdf and what are its uses? Along with that, you can get a brief idea about the topic relations and functions.

What are Relations?

A relation is a set of ordered pairs (x, y) where x is called the independent variable and y is called the dependent variable. The relation between x and y is defined by a rule that assigns a unique value of y for each value of x. Sets Relations and Functions class 12 notes contain this definition along with some examples.

What are Functions?

A function is a special type of relation in which each value of x corresponds to exactly one value of y. The relation between x and y is defined by a rule or formula, and the dependent variable y is said to be a function of x.

Notation:

The function is denoted by f(x), where x is the independent variable and f(x) is the dependent variable.

Types of Functions:

One-to-One (Injective) Function: A function is said to be one-to-one if no two different values of x correspond to the same value of y.

Onto (Surjective) Function: A function is said to be onto if for every value of y, there exists at least one value of x that corresponds to it.

One-to-One Correspondence (Bijective) Function: A function is said to be a one-to-one correspondence if it is both one-to-one and onto.

Where To Download Class 12 Maths Relations and Functions Notes?

You can find Relations and Functions notes for class 12 anywhere on the internet, but there is no guarantee you will get accurate and authentic revision notes for Relations and Functions. I will advise you to visit the Selfstudys website which has over 6 million monthly visitors and many subject matter experts. 

If you are looking for very short, precise and accurate Relations and Functions class 12 notes pdf then you should use Selfstudys website.

What Are The Uses of Class 12 Maths Relations and Functions Notes?

Relations and Functions note class 12 can be used in various ways, especially while preparing for the board examination. Below, I have listed where you can use the Class 12 Maths Relations and Functions Notes to your advantage.

Refer to the Relations and Functions class 12 notes pdf when you know you are missing some topics while solving questions of Relations and Functions.

While doing the last-minute exam preparation.