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quadratic-vertex MCQ Questions for Class 12

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2 questions tagged with quadratic-vertex.

Question 1/2 Medium Mathematics Relations and Functions Onto function Class 12 Level 27

फलन \(f:\mathbb{R}\to \mathbb{R}\), (f(x)=x^-2-x) के लिए कौन सा निष्कर्ष सही है?

Which conclusion is correct for \(f:\mathbb{R}\to \mathbb{R}\), (f(x)=x^-2-x)?

Explanation opens after your attempt

Correct Answer

B. आच्छादक नहीं हैNot onto

Step 1

Concept

(x^-2-x=\left\(x-\frac{1}{2}\right\)²-\frac{1}{4}).

Step 2

Why this answer is correct

The minimum value is \(-\frac{1}{4}\), so smaller values are not obtained.

Step 3

Exam Tip

For quadratics, use the vertex form to find the range. चरण 1: (x^-2-x=\left\(x-\frac{1}{2}\right\)²-\frac{1}{4})। चरण 2: न्यूनतम मान \(-\frac{1}{4}\) है इसलिए इससे छोटी संख्याएँ नहीं मिलतीं। चरण 3: द्विघात फलन में शीर्ष बिंदु से परास निकालना आसान होता है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Onto function
Difficulty: Medium
Level: 27

Question Hindi:
फलन (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^2-x) के लिए कौन सा निष्कर्ष सही है?

Question English:
Which conclusion is correct for (f:\mathbb{R}\to \mathbb{R}), (f(x)=x^2-x)?

Options:
A. आच्छादक है / Onto
B. आच्छादक नहीं है / Not onto
C. परास (\mathbb{R}) है / Range is (\mathbb{R})
D. केवल ऋणात्मक मान देता है / Gives only negative values

Correct Answer:
B. आच्छादक नहीं है / Not onto

Explanation Hindi:
चरण 1: (x^2-x=\left(x-\frac{1}{2}\right)^2-\frac{1}{4})। चरण 2: न्यूनतम मान (-\frac{1}{4}) है इसलिए इससे छोटी संख्याएँ नहीं मिलतीं। चरण 3: द्विघात फलन में शीर्ष बिंदु से परास निकालना आसान होता है।

Explanation English:
Step 1: (x^2-x=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}). Step 2: The minimum value is (-\frac{1}{4}), so smaller values are not obtained. Step 3: For quadratics, use the vertex form to find the range.

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Question 2/2 Medium Mathematics Relations and Functions Onto function Class 12 Level 26

यदि \(f:\mathbb{R}\to[3,\infty\)), (f(x)=(x-2)²+3) है, तो सही विकल्प चुनिए।

If \(f:\mathbb{R}\to[3,\infty\)), (f(x)=(x-2)²+3), choose the correct option.

Explanation opens after your attempt

Correct Answer

A. आच्छादी लेकिन एकैकी नहींOnto but not one-one

Step 1

Concept

((x-2)²\ge 0), so the minimum value is (3).

Step 2

Why this answer is correct

The range is \([3,\infty\)), equal to the codomain. Hence the function is onto. But (x=1) and (x=3) give the same value, so it is not one-one.

Step 3

Exam Tip

The vertex of a quadratic tells the range. चरण 1: ((x-2)²\ge 0), इसलिए न्यूनतम मान (3) है। चरण 2: परास \([3,\infty\)) है, जो सहप्रांत के बराबर है। इसलिए फलन आच्छादी है। लेकिन (x=1) और (x=3) पर मान समान है, इसलिए एकैकी नहीं है। चरण 3: द्विघात फलन का शीर्ष परास बताता है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Onto function
Difficulty: Medium
Level: 26

Question Hindi:
यदि (f:\mathbb{R}\to[3,\infty)), (f(x)=(x-2)^2+3) है, तो सही विकल्प चुनिए।

Question English:
If (f:\mathbb{R}\to[3,\infty)), (f(x)=(x-2)^2+3), choose the correct option.

Options:
A. आच्छादी लेकिन एकैकी नहीं / Onto but not one-one
B. एकैकी लेकिन आच्छादी नहीं / One-one but not onto
C. आच्छादी और एकैकी / Onto and one-one
D. न आच्छादी न एकैकी / Neither onto nor one-one

Correct Answer:
A. आच्छादी लेकिन एकैकी नहीं / Onto but not one-one

Explanation Hindi:
चरण 1: ((x-2)^2\ge 0), इसलिए न्यूनतम मान (3) है। चरण 2: परास ([3,\infty)) है, जो सहप्रांत के बराबर है। इसलिए फलन आच्छादी है। लेकिन (x=1) और (x=3) पर मान समान है, इसलिए एकैकी नहीं है। चरण 3: द्विघात फलन का शीर्ष परास बताता है।

Explanation English:
Step 1: ((x-2)^2\ge 0), so the minimum value is (3). Step 2: The range is ([3,\infty)), equal to the codomain. Hence the function is onto. But (x=1) and (x=3) give the same value, so it is not one-one. Step 3: The vertex of a quadratic tells the range.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
- Scene-by-scene visual direction.
- Text overlays for 16:9 and 9:16.
- Thumbnail idea.
- Hashtags: #MuftShiksha #FreeEducation #MCQ #Quiz #Class12 #Study

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quadratic-vertex MCQ Questions for Class 12

Practice Questions

फलन \(f:\mathbb{R}\to \mathbb{R}\), (f(x)=x^-2-x) के लिए कौन सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:\mathbb{R}\to[3,\infty\)), (f(x)=(x-2)²+3) है, तो सही विकल्प चुनिए।

Concept

Why this answer is correct

Exam Tip

quadratic-vertex Revision Links

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quadratic-vertex MCQ Questions for Class 12

Practice Questions

फलन \(f:\mathbb{R}\to \mathbb{R}\), (f(x)=x-2-x) के लिए कौन सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(f:\mathbb{R}\to[3,\infty\)), (f(x)=(x-2)2+3) है, तो सही विकल्प चुनिए।

Concept

Why this answer is correct

Exam Tip

quadratic-vertex Revision Links

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फलन \(f:\mathbb{R}\to \mathbb{R}\), (f(x)=x^-2-x) के लिए कौन सा निष्कर्ष सही है?

यदि \(f:\mathbb{R}\to[3,\infty\)), (f(x)=(x-2)²+3) है, तो सही विकल्प चुनिए।