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concept test MCQ Questions for Class 12

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Question 1/2 Medium Mathematics Relations and Functions One-one function Class 12 Level 23

यदि किसी फलन (f) के लिए (f(3)=8) और (f(5)=8), तो कौन-सा निष्कर्ष निश्चित है?

If for a function (f), (f(3)=8) and (f(5)=8), which conclusion is certain?

Explanation opens after your attempt
Correct Answer

B. (f) एकैकी नहीं है(f) is not one-one

Step 1

Concept

(3) and (5) are different inputs.

Step 2

Why this answer is correct

Both have image (8).

Step 3

Exam Tip

The same image for different inputs is direct proof against one-one nature. चरण 1: (3) और (5) अलग-अलग आगत हैं। चरण 2: दोनों की छवि (8) है। चरण 3: अलग आगतों की समान छवि एकैकीता के विरुद्ध सीधा प्रमाण है।

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Question 2/2 Medium Mathematics Relations and Functions Symmetric relation Class 12 Level 10

यदि किसी संबंध (R) का प्रतिलोम \(R^{-1}\) उसी संबंध के बराबर है, तो (R) के बारे में सही निष्कर्ष क्या है?

If the inverse \(R^{-1}\) of a relation (R) is equal to the relation itself, what is the correct conclusion about (R)?

Explanation opens after your attempt
Correct Answer

A. (R) सममित है(R) is symmetric

Step 1

Concept

In \(R^{-1}\), every ordered pair is reversed.

Step 2

Why this answer is correct

If \(R^{-1}=R\), then every reverse pair already belongs to (R).

Step 3

Exam Tip

Treat equality with the inverse as a quick test for symmetry. चरण 1: \(R^{-1}\) में हर युग्म उलट जाता है। चरण 2: यदि \(R^{-1}=R\), तो हर उलटा युग्म पहले से (R) में है। चरण 3: प्रतिलोम बराबरी को सममितता की तेज पहचान मानें।

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