Class 11 Mathematics - Relations and Functions - Real valued functions, domain and range of these functions Easy Quiz

Mathematics Relations and Functions Real valued functions, domain and range of these functions Easy Class 11 Level 35

Level 35 • 4/50 questions • 60 seconds per question.

Level readiness 4/50 Questions

Time Left 04:00 60 sec/question

RewardsCoins + XP

ModeClassic Quiz

This level needs 46 more active questions. Admin panel me same class, subject, difficulty aur level_no 35 par question add karein.

Question 1 / 4 0 score

Answered 0/4 Correct 0 Time 04:00

Question 1/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 35

फलन \(f(x)=\operatorname{sgn}(x)\) का परिसर क्या है?

What is the range of the function \(f(x)=\operatorname{sgn}(x)\)?

Explanation opens after your attempt

Correct Answer

A. \(\{-1,0,1\}\)

Explanation

Simple Explanation

साइनम फलन में \(x<0\) के लिए \(\operatorname{sgn}(x)=-1\), \(x=0\) के लिए \(\operatorname{sgn}(x)=0\), तथा \(x>0\) के लिए \(\operatorname{sgn}(x)=1\) होता है। अतः फलन केवल \(-1,0,1\) तीन मान लेता है, इसलिए इसका परिसर \(\{-1,0,1\}\) है। विकल्प D में ऋणात्मक \(x\) के लिए मिलने वाला मान \(-1\) नहीं है। परीक्षा-युक्ति: साइनम फलन के प्रश्न में \(x<0\), \(x=0\) और \(x>0\) के तीनों मामलों को अलग-अलग जाँचें। / For the signum function, \(\operatorname{sgn}(x)=-1\) for \(x<0\), \(\operatorname{sgn}(x)=0\) for \(x=0\), and \(\operatorname{sgn}(x)=1\) for \(x>0\). Hence, the function takes only the three values \(-1,0,1\), so its range is \(\{-1,0,1\}\). Option D omits \(-1\), which occurs for negative values of \(x\). Exam tip: evaluate the three cases \(x<0\), \(x=0\), and \(x>0\) for every signum-function question.

Open Question Page

Question 2/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 35

फलन (f(x)=\sqrt{x+2}) का डोमेन क्या है?

What is the domain of (f(x)=\sqrt{x+2})?

Explanation opens after your attempt

Correct Answer

A. \(x\ge -2\)

Explanation

Simple Explanation

वास्तविक वर्गमूल के अंदर का व्यंजक ऋणात्मक नहीं हो सकता, इसलिए \(x+2\ge 0\) होना आवश्यक है। इससे \(x\ge -2\) प्राप्त होता है, अतः डोमेन \([-2,\infty)\) है। विकल्प B में \(x\ge 2\) लेना अनावश्यक रूप से अधिक प्रतिबंध लगाता है। परीक्षा-युक्ति: वर्गमूल वाले फलन के डोमेन के लिए radicand को \(\ge 0\) रखें। / The expression inside a real square root cannot be negative, so \(x+2\ge 0\) is required. Therefore, \(x\ge -2\), and the domain is \([-2,\infty)\). Option B incorrectly imposes the stronger condition \(x\ge 2\). Exam tip: For a square-root function, set the radicand greater than or equal to zero to find the domain.

Open Question Page

Question 3/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 35

फलन \(f(x)=\sqrt{x}+4\), जहाँ \(x\ge 0\), का न्यूनतम मान क्या है?

What is the minimum value of the function \(f(x)=\sqrt{x}+4\), where \(x\ge 0\)?

Explanation opens after your attempt

Correct Answer

C. 4

Explanation

Simple Explanation

वर्गमूल का मान सदैव गैर-ऋणात्मक होता है, इसलिए \(\sqrt{x}\ge 0\)। अतः \(f(x)=\sqrt{x}+4\ge 4\)। जब \(x=0\), तब \(f(0)=4\), इसलिए न्यूनतम मान 4 है। विकल्प 0 केवल \(\sqrt{x}\) का न्यूनतम मान है, पूरे फलन का नहीं। परीक्षा-युक्ति: वर्गमूल वाले फलन में पहले \(\sqrt{x}\ge 0\) का उपयोग करें। / A square root is always non-negative, so \(\sqrt{x}\ge 0\). Therefore, \(f(x)=\sqrt{x}+4\ge 4\). At \(x=0\), \(f(0)=4\), so the minimum value is 4. The value 0 is the minimum of \(\sqrt{x}\) alone, not of the whole function. Exam tip: For a square-root function, first use the fact that the square-root term is at least zero.

Open Question Page

Question 4/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 35

फलन \(f(x)=\frac{1}{x-2}\) किस \(x\)-मान पर परिभाषित नहीं है?

For which value of \(x\) is the function \(f(x)=\frac{1}{x-2}\) not defined?

Explanation opens after your attempt

Correct Answer

C. \(x=2\)

Explanation

Simple Explanation

भिन्न के हर का मान शून्य नहीं हो सकता, क्योंकि शून्य से भाग देना परिभाषित नहीं होता। यहाँ हर \(x-2\) है। \(x-2=0\) रखने पर \(x=2\) मिलता है, इसलिए फलन \(x=2\) पर परिभाषित नहीं है। परीक्षा-युक्ति: किसी परिमेय फलन का डोमेन निकालते समय उसके हर को शून्य के बराबर करके निषिद्ध मान ज्ञात करें। / The denominator of a fraction cannot be zero because division by zero is undefined. Here the denominator is \(x-2\). Setting \(x-2=0\) gives \(x=2\), so the function is not defined at \(x=2\). Exam tip: For a rational function, set its denominator equal to zero to find the excluded value from the domain.

Open Question Page

Mathematics Quiz Navigation

FAQs

Class 11 Mathematics Quiz FAQs

How many questions are in this quiz?

This level is designed for 50 active questions. Currently 4 questions are available for the selected class and difficulty.

Is there a timer in this quiz?

Yes, the timer uses 60 seconds per question for Easy difficulty and shows the total remaining time on the page.

Can I open each question separately?

Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.

Class 11 Mathematics - Relations and Functions - Real valued functions, domain and range of these functions Easy Quiz

फलन \(f(x)=\operatorname{sgn}(x)\) का परिसर क्या है?

Simple Explanation

फलन (f(x)=\sqrt{x+2}) का डोमेन क्या है?

Simple Explanation

फलन \(f(x)=\sqrt{x}+4\), जहाँ \(x\ge 0\), का न्यूनतम मान क्या है?

Simple Explanation

फलन \(f(x)=\frac{1}{x-2}\) किस \(x\)-मान पर परिभाषित नहीं है?

Simple Explanation

Your Score: 0 / 4

Mathematics Quiz Navigation

Mathematics Subject

Real valued functions, domain and range of these functions Topic

Relations and Functions Chapter

Search Mathematics

All Subjects

Class 11 Mathematics Quiz FAQs

Login to view answers

फलन (f(x)=\sqrt{x+2}) का डोमेन क्या है?