Concept-wise Practice

direct proof MCQ Questions for Class 12

direct proof se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

All Tags Search Similar

Practice Questions

3 questions tagged with direct proof.

Question 1/3 Expert Mathematics Relations and Functions One-one function Class 12 Level 24

फलन \(f:\mathbb{Z}\to\mathbb{Z}\), (f(n)=2n+3) के लिए (f(a)=f(b)) से क्या निष्कर्ष निकलेगा?

For \(f:\mathbb{Z}\to\mathbb{Z}\), (f(n)=2n+3), what conclusion follows from (f(a)=f(b))?

Explanation opens after your attempt
Correct Answer

A. \(a=b\)

Step 1

Concept

Put (f(a)=f(b)), giving (2a+3=2b+3).

Step 2

Why this answer is correct

This gives (2a=2b), hence (a=b).

Step 3

Exam Tip

(f(a)=f(b)\Rightarrow a=b) is a direct proof of one-one nature. चरण 1: (f(a)=f(b)) रखने पर (2a+3=2b+3) मिलता है। चरण 2: इससे (2a=2b), अतः (a=b)। चरण 3: (f(a)=f(b)\Rightarrow a=b) एकैकी फलन का सीधा प्रमाण है।

Open Question Page
Ask Friends
Question 2/3 Expert Mathematics Relations and Functions One-one function Class 12 Level 23

फलन \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x-3) के लिए सही कथन क्या है?

What is the correct statement for \(f:\mathbb{R}\to\mathbb{R}\), (f(x)=x-3)?

Explanation opens after your attempt
Correct Answer

A. यह एकैकी हैIt is one-one

Step 1

Concept

Assume (f(a)=f(b)).

Step 2

Why this answer is correct

\(a^3=b^3\) gives (a=b), because the cube function preserves order on real numbers.

Step 3

Exam Tip

Simple odd-power functions are often one-one on the whole real domain. चरण 1: (f(a)=f(b)) मानें। चरण 2: \(a^3=b^3\) से (a=b) मिलता है, क्योंकि वास्तविक संख्याओं में घन फलन क्रम बनाए रखता है। चरण 3: विषम घात वाले सरल घात फलन अक्सर पूरे वास्तविक प्रांत पर एकैकी होते हैं।

Open Question Page
Ask Friends
Question 3/3 Expert Mathematics Relations and Functions One-one function Class 12 Level 23

फलन (f:\(0,\infty\)\to\(0,\infty\)), (f(x)=\frac{1}{x}) के बारे में कौन-सा कथन सही है?

Which statement is correct about (f:\(0,\infty\)\to\(0,\infty\)), (f(x)=\frac{1}{x})?

Explanation opens after your attempt
Correct Answer

A. यह एकैकी हैIt is one-one

Step 1

Concept

Assume (f(a)=f(b)).

Step 2

Why this answer is correct

\(\frac{1}{a}=\frac{1}{b}\) gives (a=b), since (a,b>0).

Step 3

Exam Tip

For reciprocal-type functions, direct proof using equal images is very effective. चरण 1: (f(a)=f(b)) मान लें। चरण 2: \(\frac{1}{a}=\frac{1}{b}\) से (a=b) मिलता है, क्योंकि (a,b>0)। चरण 3: व्युत्क्रम प्रकार के फलनों में समान मान रखकर सीधा प्रमाण अच्छा रहता है।

Open Question Page
Ask Friends

direct proof Revision Links

All MCQ Tags

Browse concept directory

All Subjects

Subject-wise practice

Search direct proof

More keyword results
Student Class Required

Select your class first

Quiz questions, daily challenge and practice pages will open according to your selected class. Class 11/12 ke liye stream bhi select karein.