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Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (\(\alpha+3\)x^-2-2\alpha x+\(\alpha-2\)=0) में \(\alpha\neq-3\) हो, तो वास्तविक मूलों के लिए \(\alpha\) की शर्त क्या है?

If \(\alpha\neq-3\) in (\(\alpha+3\)x^-2-2\alpha x+\(\alpha-2\)=0), what is the condition on \(\alpha\) for real roots?

Explanation opens after your attempt

Correct Answer

A. \(\alpha\leq3\) और \(\alpha\neq-3\)\(\alpha\leq3\) and \(\alpha\neq-3\)

Step 1

Concept

Here (D=4\alpha^-2-4\(\alpha+3\)\(\alpha-2\)=24-4\alpha). For real roots \(\alpha\leq3\), and for a quadratic \(\alpha\neq-3\).

Step 2

Why this answer is correct

The correct answer is A. \(\alpha\leq3\) और \(\alpha\neq-3\) / \(\alpha\leq3\) and \(\alpha\neq-3\). Here (D=4\alpha^-2-4\(\alpha+3\)\(\alpha-2\)=24-4\alpha). For real roots \(\alpha\leq3\), and for a quadratic \(\alpha\neq-3\).

Step 3

Exam Tip

यहाँ (D=4\alpha^-2-4\(\alpha+3\)\(\alpha-2\)=24-4\alpha) है। वास्तविक मूलों के लिए \(\alpha\leq3\) और द्विघात के लिए \(\alpha\neq-3\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 39

Question Hindi:
यदि ((\alpha+3)x^2-2\alpha x+(\alpha-2)=0) में (\alpha\neq-3) हो, तो वास्तविक मूलों के लिए (\alpha) की शर्त क्या है?

Question English:
If (\alpha\neq-3) in ((\alpha+3)x^2-2\alpha x+(\alpha-2)=0), what is the condition on (\alpha) for real roots?

Options:
A. (\alpha\leq3) और (\alpha\neq-3) / (\alpha\leq3) and (\alpha\neq-3)
B. (\alpha>3)
C. (\alpha=-3)
D. हर (\alpha\neq-3) / Every (\alpha\neq-3)

Correct Answer:
A. (\alpha\leq3) और (\alpha\neq-3) / (\alpha\leq3) and (\alpha\neq-3)

Explanation Hindi:
यहाँ (D=4\alpha^2-4(\alpha+3)(\alpha-2)=24-4\alpha) है। वास्तविक मूलों के लिए (\alpha\leq3) और द्विघात के लिए (\alpha\neq-3)।

Explanation English:
Here (D=4\alpha^2-4(\alpha+3)(\alpha-2)=24-4\alpha). For real roots (\alpha\leq3), and for a quadratic (\alpha\neq-3).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि \(x^2-2\theta x+3\theta=0\) के दो वास्तविक और असमान मूल हों, तो \(\theta\) पर कौन सी शर्त सही है?

If \(x^2-2\theta x+3\theta=0\) has two real and distinct roots, which condition on \(\theta\) is correct?

Explanation opens after your attempt

Correct Answer

A. \(\theta<0\) या \(\theta>3\)\(\theta<0\) or \(\theta>3\)

Step 1

Concept

Here (D=4\theta^-2-12\theta=4\theta\(\theta-3\)). From (D>0), \(\theta<0\) or \(\theta>3\).

Step 2

Why this answer is correct

The correct answer is A. \(\theta<0\) या \(\theta>3\) / \(\theta<0\) or \(\theta>3\). Here (D=4\theta^-2-12\theta=4\theta\(\theta-3\)). From (D>0), \(\theta<0\) or \(\theta>3\).

Step 3

Exam Tip

यहाँ (D=4\theta^-2-12\theta=4\theta\(\theta-3\)) है। (D>0) से \(\theta<0\) या \(\theta>3\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 39

Question Hindi:
यदि (x^2-2\theta x+3\theta=0) के दो वास्तविक और असमान मूल हों, तो (\theta) पर कौन सी शर्त सही है?

Question English:
If (x^2-2\theta x+3\theta=0) has two real and distinct roots, which condition on (\theta) is correct?

Options:
A. (\theta<0) या (\theta>3) / (\theta<0) or (\theta>3)
B. (0<\theta<3)
C. (\theta=0) या (\theta=3) / (\theta=0) or (\theta=3)
D. हर (\theta) / Every (\theta)

Correct Answer:
A. (\theta<0) या (\theta>3) / (\theta<0) or (\theta>3)

Explanation Hindi:
यहाँ (D=4\theta^2-12\theta=4\theta(\theta-3)) है। (D>0) से (\theta<0) या (\theta>3)।

Explanation English:
Here (D=4\theta^2-12\theta=4\theta(\theta-3)). From (D>0), (\theta<0) or (\theta>3).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि ((p-2)x^-2-2(p+2)x+(p+6)=0) में \(p\neq2\) हो, तो वास्तविक मूलों के लिए (p) की शर्त क्या है?

If \(p\neq2\) in ((p-2)x^-2-2(p+2)x+(p+6)=0), what is the condition on (p) for real roots?

Explanation opens after your attempt

Correct Answer

A. \(p\leq5\) और \(p\neq2\)\(p\leq5\) and \(p\neq2\)

Step 1

Concept

Here (D=4(p+2)²-4(p-2)(p+6)=40-8p). For real roots \(p\leq5\), and for a quadratic \(p\neq2\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq5\) और \(p\neq2\) / \(p\leq5\) and \(p\neq2\). Here (D=4(p+2)²-4(p-2)(p+6)=40-8p). For real roots \(p\leq5\), and for a quadratic \(p\neq2\).

Step 3

Exam Tip

यहाँ (D=4(p+2)²-4(p-2)(p+6)=40-8p) है। वास्तविक मूलों के लिए \(p\leq5\) और द्विघात के लिए \(p\neq2\)।

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AI Video Prompt 16:9 + 9:16

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https://muftshiksha.com/question/if-p-neq2-in-p-2-x-2-2-p-2-x-p-6-0-what-is-the-condition-on-p-for-real-roots

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 39

Question Hindi:
यदि ((p-2)x^2-2(p+2)x+(p+6)=0) में (p\neq2) हो, तो वास्तविक मूलों के लिए (p) की शर्त क्या है?

Question English:
If (p\neq2) in ((p-2)x^2-2(p+2)x+(p+6)=0), what is the condition on (p) for real roots?

Options:
A. (p\leq5) और (p\neq2) / (p\leq5) and (p\neq2)
B. (p>5)
C. (p=2)
D. हर (p\neq2) / Every (p\neq2)

Correct Answer:
A. (p\leq5) और (p\neq2) / (p\leq5) and (p\neq2)

Explanation Hindi:
यहाँ (D=4(p+2)^2-4(p-2)(p+6)=40-8p) है। वास्तविक मूलों के लिए (p\leq5) और द्विघात के लिए (p\neq2)।

Explanation English:
Here (D=4(p+2)^2-4(p-2)(p+6)=40-8p). For real roots (p\leq5), and for a quadratic (p\neq2).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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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.
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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (x^-2-2(k+3)x+\(k^2+5k+12\)=0) के वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?

If (x^-2-2(k+3)x+\(k^2+5k+12\)=0) has real roots, which condition on (k) is correct?

Explanation opens after your attempt

Correct Answer

A. \(k\geq3\)

Step 1

Concept

Here (D=4(k+3)²-4\(k^2+5k+12\)=4(k-3)). For real roots \(D\geq0\), so \(k\geq3\).

Step 2

Why this answer is correct

The correct answer is A. \(k\geq3\). Here (D=4(k+3)²-4\(k^2+5k+12\)=4(k-3)). For real roots \(D\geq0\), so \(k\geq3\).

Step 3

Exam Tip

यहाँ (D=4(k+3)²-4\(k^2+5k+12\)=4(k-3)) है। वास्तविक मूलों के लिए \(D\geq0\), इसलिए \(k\geq3\)।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 39

Question Hindi:
यदि (x^2-2(k+3)x+(k^2+5k+12)=0) के वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?

Question English:
If (x^2-2(k+3)x+(k^2+5k+12)=0) has real roots, which condition on (k) is correct?

Options:
A. (k\geq3)
B. (k<3)
C. (k=0)
D. हर वास्तविक (k) / Every real (k)

Correct Answer:
A. (k\geq3)

Explanation Hindi:
यहाँ (D=4(k+3)^2-4(k^2+5k+12)=4(k-3)) है। वास्तविक मूलों के लिए (D\geq0), इसलिए (k\geq3)।

Explanation English:
Here (D=4(k+3)^2-4(k^2+5k+12)=4(k-3)). For real roots (D\geq0), so (k\geq3).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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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.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि (\(\alpha+2\)x^-2-2\alpha x+\(\alpha-1\)=0) में \(\alpha\neq-2\) हो, तो वास्तविक मूलों के लिए \(\alpha\) की शर्त क्या है?

If \(\alpha\neq-2\) in (\(\alpha+2\)x^-2-2\alpha x+\(\alpha-1\)=0), what is the condition on \(\alpha\) for real roots?

Explanation opens after your attempt

Correct Answer

A. \(\alpha\leq2\) और \(\alpha\neq-2\)\(\alpha\leq2\) and \(\alpha\neq-2\)

Step 1

Concept

Here (D=4\alpha^-2-4\(\alpha+2\)\(\alpha-1\)=8-4\alpha). For real roots \(\alpha\leq2\), and for a quadratic \(\alpha\neq-2\).

Step 2

Why this answer is correct

The correct answer is A. \(\alpha\leq2\) और \(\alpha\neq-2\) / \(\alpha\leq2\) and \(\alpha\neq-2\). Here (D=4\alpha^-2-4\(\alpha+2\)\(\alpha-1\)=8-4\alpha). For real roots \(\alpha\leq2\), and for a quadratic \(\alpha\neq-2\).

Step 3

Exam Tip

यहाँ (D=4\alpha^-2-4\(\alpha+2\)\(\alpha-1\)=8-4\alpha) है। वास्तविक मूलों के लिए \(\alpha\leq2\) और द्विघात के लिए \(\alpha\neq-2\)।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 38

Question Hindi:
यदि ((\alpha+2)x^2-2\alpha x+(\alpha-1)=0) में (\alpha\neq-2) हो, तो वास्तविक मूलों के लिए (\alpha) की शर्त क्या है?

Question English:
If (\alpha\neq-2) in ((\alpha+2)x^2-2\alpha x+(\alpha-1)=0), what is the condition on (\alpha) for real roots?

Options:
A. (\alpha\leq2) और (\alpha\neq-2) / (\alpha\leq2) and (\alpha\neq-2)
B. (\alpha>2)
C. (\alpha=-2)
D. हर (\alpha\neq-2) / Every (\alpha\neq-2)

Correct Answer:
A. (\alpha\leq2) और (\alpha\neq-2) / (\alpha\leq2) and (\alpha\neq-2)

Explanation Hindi:
यहाँ (D=4\alpha^2-4(\alpha+2)(\alpha-1)=8-4\alpha) है। वास्तविक मूलों के लिए (\alpha\leq2) और द्विघात के लिए (\alpha\neq-2)।

Explanation English:
Here (D=4\alpha^2-4(\alpha+2)(\alpha-1)=8-4\alpha). For real roots (\alpha\leq2), and for a quadratic (\alpha\neq-2).

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".

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- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि \(x^2-2\mu x+2\mu=0\) के दो वास्तविक और असमान मूल हों, तो \(\mu\) पर कौन सी शर्त सही है?

If \(x^2-2\mu x+2\mu=0\) has two real and distinct roots, which condition on \(\mu\) is correct?

Explanation opens after your attempt

Correct Answer

A. \(\mu<0\) या \(\mu>2\)\(\mu<0\) or \(\mu>2\)

Step 1

Concept

Here (D=4\mu^-2-8\mu=4\mu\(\mu-2\)). From (D>0), \(\mu<0\) or \(\mu>2\).

Step 2

Why this answer is correct

The correct answer is A. \(\mu<0\) या \(\mu>2\) / \(\mu<0\) or \(\mu>2\). Here (D=4\mu^-2-8\mu=4\mu\(\mu-2\)). From (D>0), \(\mu<0\) or \(\mu>2\).

Step 3

Exam Tip

यहाँ (D=4\mu^-2-8\mu=4\mu\(\mu-2\)) है। (D>0) से \(\mu<0\) या \(\mu>2\)।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 38

Question Hindi:
यदि (x^2-2\mu x+2\mu=0) के दो वास्तविक और असमान मूल हों, तो (\mu) पर कौन सी शर्त सही है?

Question English:
If (x^2-2\mu x+2\mu=0) has two real and distinct roots, which condition on (\mu) is correct?

Options:
A. (\mu<0) या (\mu>2) / (\mu<0) or (\mu>2)
B. (0<\mu<2)
C. (\mu=0) या (\mu=2) / (\mu=0) or (\mu=2)
D. हर (\mu) / Every (\mu)

Correct Answer:
A. (\mu<0) या (\mu>2) / (\mu<0) or (\mu>2)

Explanation Hindi:
यहाँ (D=4\mu^2-8\mu=4\mu(\mu-2)) है। (D>0) से (\mu<0) या (\mu>2)।

Explanation English:
Here (D=4\mu^2-8\mu=4\mu(\mu-2)). From (D>0), (\mu<0) or (\mu>2).

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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".

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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि ((p-1)x^-2-2(p+1)x+(p+3)=0) में \(p\neq1\) हो, तो वास्तविक मूलों के लिए (p) की शर्त क्या है?

If \(p\neq1\) in ((p-1)x^-2-2(p+1)x+(p+3)=0), what is the condition on (p) for real roots?

Explanation opens after your attempt

Correct Answer

A. \(p\leq2\) और \(p\neq1\)\(p\leq2\) and \(p\neq1\)

Step 1

Concept

Here (D=4(p+1)²-4(p-1)(p+3)=16-4p). For real roots \(p\leq2\), and for a quadratic \(p\neq1\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq2\) और \(p\neq1\) / \(p\leq2\) and \(p\neq1\). Here (D=4(p+1)²-4(p-1)(p+3)=16-4p). For real roots \(p\leq2\), and for a quadratic \(p\neq1\).

Step 3

Exam Tip

यहाँ (D=4(p+1)²-4(p-1)(p+3)=16-4p) है। वास्तविक मूलों के लिए \(p\leq2\) और द्विघात के लिए \(p\neq1\)।

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https://muftshiksha.com/question/if-p-neq1-in-p-1-x-2-2-p-1-x-p-3-0-what-is-the-condition-on-p-for-real-roots

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 38

Question Hindi:
यदि ((p-1)x^2-2(p+1)x+(p+3)=0) में (p\neq1) हो, तो वास्तविक मूलों के लिए (p) की शर्त क्या है?

Question English:
If (p\neq1) in ((p-1)x^2-2(p+1)x+(p+3)=0), what is the condition on (p) for real roots?

Options:
A. (p\leq2) और (p\neq1) / (p\leq2) and (p\neq1)
B. (p>2)
C. (p=1)
D. हर (p\neq1) / Every (p\neq1)

Correct Answer:
A. (p\leq2) और (p\neq1) / (p\leq2) and (p\neq1)

Explanation Hindi:
यहाँ (D=4(p+1)^2-4(p-1)(p+3)=16-4p) है। वास्तविक मूलों के लिए (p\leq2) और द्विघात के लिए (p\neq1)।

Explanation English:
Here (D=4(p+1)^2-4(p-1)(p+3)=16-4p). For real roots (p\leq2), and for a quadratic (p\neq1).

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".

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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि (x^-2-2(k+2)x+\(k^2+3k+7\)=0) के वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?

If (x^-2-2(k+2)x+\(k^2+3k+7\)=0) has real roots, which condition on (k) is correct?

Explanation opens after your attempt

Correct Answer

A. \(k\geq3\)

Step 1

Concept

Here (D=4(k+2)²-4\(k^2+3k+7\)=4(k-3)). For real roots \(D\geq0\), so \(k\geq3\).

Step 2

Why this answer is correct

The correct answer is A. \(k\geq3\). Here (D=4(k+2)²-4\(k^2+3k+7\)=4(k-3)). For real roots \(D\geq0\), so \(k\geq3\).

Step 3

Exam Tip

यहाँ (D=4(k+2)²-4\(k^2+3k+7\)=4(k-3)) है। वास्तविक मूलों के लिए \(D\geq0\), इसलिए \(k\geq3\)।

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AI Video Prompt 16:9 + 9:16

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https://muftshiksha.com/question/if-x-2-2-k-2-x-k-2-3k-7-0-has-real-roots-which-condition-on-k-is-correct

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 38

Question Hindi:
यदि (x^2-2(k+2)x+(k^2+3k+7)=0) के वास्तविक मूल हों, तो (k) पर कौन सी शर्त सही है?

Question English:
If (x^2-2(k+2)x+(k^2+3k+7)=0) has real roots, which condition on (k) is correct?

Options:
A. (k\geq3)
B. (k<3)
C. (k=0)
D. हर वास्तविक (k) / Every real (k)

Correct Answer:
A. (k\geq3)

Explanation Hindi:
यहाँ (D=4(k+2)^2-4(k^2+3k+7)=4(k-3)) है। वास्तविक मूलों के लिए (D\geq0), इसलिए (k\geq3)।

Explanation English:
Here (D=4(k+2)^2-4(k^2+3k+7)=4(k-3)). For real roots (D\geq0), so (k\geq3).

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".

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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (\(\alpha+1\)x^-2-2\alpha x+\alpha=0) में \(\alpha\neq-1\) हो, तो वास्तविक मूलों के लिए \(\alpha\) की शर्त क्या है?

If \(\alpha\neq-1\) in (\(\alpha+1\)x^-2-2\alpha x+\alpha=0), what is the condition on \(\alpha\) for real roots?

Explanation opens after your attempt

Correct Answer

A. \(\alpha\leq0\)

Step 1

Concept

Here (D=4\alpha^-2-4\alpha\(\alpha+1\)=-4\alpha). For real roots \(\alpha\leq0\) is needed.

Step 2

Why this answer is correct

The correct answer is A. \(\alpha\leq0\). Here (D=4\alpha^-2-4\alpha\(\alpha+1\)=-4\alpha). For real roots \(\alpha\leq0\) is needed.

Step 3

Exam Tip

यहाँ (D=4\alpha^-2-4\alpha\(\alpha+1\)=-4\alpha) है। वास्तविक मूलों के लिए \(\alpha\leq0\) चाहिए।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/if-alpha-neq-1-in-alpha-1-x-2-2-alpha-x-alpha-0-what-is-the-condition-on-alpha-for-real-ro

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 37

Question Hindi:
यदि ((\alpha+1)x^2-2\alpha x+\alpha=0) में (\alpha\neq-1) हो, तो वास्तविक मूलों के लिए (\alpha) की शर्त क्या है?

Question English:
If (\alpha\neq-1) in ((\alpha+1)x^2-2\alpha x+\alpha=0), what is the condition on (\alpha) for real roots?

Options:
A. (\alpha\leq0)
B. (\alpha>0)
C. (\alpha=1)
D. हर (\alpha\neq-1) / Every (\alpha\neq-1)

Correct Answer:
A. (\alpha\leq0)

Explanation Hindi:
यहाँ (D=4\alpha^2-4\alpha(\alpha+1)=-4\alpha) है। वास्तविक मूलों के लिए (\alpha\leq0) चाहिए।

Explanation English:
Here (D=4\alpha^2-4\alpha(\alpha+1)=-4\alpha). For real roots (\alpha\leq0) is needed.

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".

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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि \(x^2-2\lambda x+\lambda=0\) के दो वास्तविक और असमान मूल हों, तो \(\lambda\) पर कौन सी शर्त सही है?

If \(x^2-2\lambda x+\lambda=0\) has two real and distinct roots, which condition on \(\lambda\) is correct?

Explanation opens after your attempt

Correct Answer

A. \(\lambda<0\) या \(\lambda>1\)\(\lambda<0\) or \(\lambda>1\)

Step 1

Concept

Here (D=4\lambda^-2-4\lambda=4\lambda\(\lambda-1\)). For distinct real roots (D>0), so \(\lambda<0\) or \(\lambda>1\).

Step 2

Why this answer is correct

The correct answer is A. \(\lambda<0\) या \(\lambda>1\) / \(\lambda<0\) or \(\lambda>1\). Here (D=4\lambda^-2-4\lambda=4\lambda\(\lambda-1\)). For distinct real roots (D>0), so \(\lambda<0\) or \(\lambda>1\).

Step 3

Exam Tip

यहाँ (D=4\lambda^-2-4\lambda=4\lambda\(\lambda-1\)) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए \(\lambda<0\) या \(\lambda>1\)।

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AI Video Prompt 16:9 + 9:16

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 37

Question Hindi:
यदि (x^2-2\lambda x+\lambda=0) के दो वास्तविक और असमान मूल हों, तो (\lambda) पर कौन सी शर्त सही है?

Question English:
If (x^2-2\lambda x+\lambda=0) has two real and distinct roots, which condition on (\lambda) is correct?

Options:
A. (\lambda<0) या (\lambda>1) / (\lambda<0) or (\lambda>1)
B. (0<\lambda<1)
C. (\lambda=0) या (\lambda=1) / (\lambda=0) or (\lambda=1)
D. हर वास्तविक (\lambda) / Every real (\lambda)

Correct Answer:
A. (\lambda<0) या (\lambda>1) / (\lambda<0) or (\lambda>1)

Explanation Hindi:
यहाँ (D=4\lambda^2-4\lambda=4\lambda(\lambda-1)) है। असमान वास्तविक मूलों के लिए (D>0), इसलिए (\lambda<0) या (\lambda>1)।

Explanation English:
Here (D=4\lambda^2-4\lambda=4\lambda(\lambda-1)). For distinct real roots (D>0), so (\lambda<0) or (\lambda>1).

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".

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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण ((k-2)x^-2+2kx+(k+3)=0) में \(k\neq2\) हो, तो वास्तविक मूलों के लिए सही शर्त क्या है?

In ((k-2)x^-2+2kx+(k+3)=0), with \(k\neq2\), what is the correct condition for real roots?

Explanation opens after your attempt

Correct Answer

A. \(k\geq\frac{3}{2}\)

Step 1

Concept

Here (D=(2k)²-4(k-2)(k+3)=4(6-k)). For real roots we need \(k\leq6\), so check simplification carefully.

Step 2

Why this answer is correct

The correct answer is A. \(k\geq\frac{3}{2}\). Here (D=(2k)²-4(k-2)(k+3)=4(6-k)). For real roots we need \(k\leq6\), so check simplification carefully.

Step 3

Exam Tip

यहाँ (D=(2k)²-4(k-2)(k+3)=4(6-k)) नहीं, सही सरल रूप (4(6-k)) है। वास्तविक मूलों के लिए \(k\leq6\) चाहिए।

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AI Video Prompt 16:9 + 9:16

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 37

Question Hindi:
समीकरण ((k-2)x^2+2kx+(k+3)=0) में (k\neq2) हो, तो वास्तविक मूलों के लिए सही शर्त क्या है?

Question English:
In ((k-2)x^2+2kx+(k+3)=0), with (k\neq2), what is the correct condition for real roots?

Options:
A. (k\geq\frac{3}{2})
B. (k<\frac{3}{2})
C. (k=2) मात्र / Only (k=2)
D. हर (k\neq2) / Every (k\neq2)

Correct Answer:
A. (k\geq\frac{3}{2})

Explanation Hindi:
यहाँ (D=(2k)^2-4(k-2)(k+3)=4(6-k)) नहीं, सही सरल रूप (4(6-k)) है। वास्तविक मूलों के लिए (k\leq6) चाहिए।

Explanation English:
Here (D=(2k)^2-4(k-2)(k+3)=4(6-k)). For real roots we need (k\leq6), so check simplification carefully.

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:
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- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
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Open Question

Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण ((p+1)x^-2-2(p+2)x+(p+4)=0) में वास्तविक मूलों के लिए (p) की शर्त क्या है, जबकि \(p\neq-1\)?

What is the condition on (p) for real roots in ((p+1)x^-2-2(p+2)x+(p+4)=0), where \(p\neq-1\)?

Explanation opens after your attempt

Correct Answer

A. \(p\leq0\)

Step 1

Concept

Here (D=4(p+2)²-4(p+1)(p+4)=-4p). For real roots \(-4p\geq0\), so \(p\leq0\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq0\). Here (D=4(p+2)²-4(p+1)(p+4)=-4p). For real roots \(-4p\geq0\), so \(p\leq0\).

Step 3

Exam Tip

यहाँ (D=4(p+2)²-4(p+1)(p+4)=-4p) है। वास्तविक मूलों के लिए \(-4p\geq0\), इसलिए \(p\leq0\)।

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https://muftshiksha.com/question/what-is-the-condition-on-p-for-real-roots-in-p-1-x-2-2-p-2-x-p-4-0-where-p-neq-1

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 37

Question Hindi:
समीकरण ((p+1)x^2-2(p+2)x+(p+4)=0) में वास्तविक मूलों के लिए (p) की शर्त क्या है, जबकि (p\neq-1)?

Question English:
What is the condition on (p) for real roots in ((p+1)x^2-2(p+2)x+(p+4)=0), where (p\neq-1)?

Options:
A. (p\leq0)
B. (p>0)
C. (p=1) मात्र / Only (p=1)
D. हर (p\neq-1) / Every (p\neq-1)

Correct Answer:
A. (p\leq0)

Explanation Hindi:
यहाँ (D=4(p+2)^2-4(p+1)(p+4)=-4p) है। वास्तविक मूलों के लिए (-4p\geq0), इसलिए (p\leq0)।

Explanation English:
Here (D=4(p+2)^2-4(p+1)(p+4)=-4p). For real roots (-4p\geq0), so (p\leq0).

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".

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Question Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (x^-2-2(k+1)x+\(k^2+4\)=0) के मूल वास्तविक हों, तो (k) पर सही शर्त क्या है?

If (x^-2-2(k+1)x+\(k^2+4\)=0) has real roots, what is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. \(k\geq\frac{3}{2}\)

Step 1

Concept

Here (D=4(k+1)²-4\(k^2+4\)=8k-12). For real roots \(D\geq0\), so \(k\geq\frac{3}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(k\geq\frac{3}{2}\). Here (D=4(k+1)²-4\(k^2+4\)=8k-12). For real roots \(D\geq0\), so \(k\geq\frac{3}{2}\).

Step 3

Exam Tip

यहाँ (D=4(k+1)²-4\(k^2+4\)=8k-12) है। वास्तविक मूलों के लिए \(D\geq0\), इसलिए \(k\geq\frac{3}{2}\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Expert
Level: 37

Question Hindi:
यदि (x^2-2(k+1)x+(k^2+4)=0) के मूल वास्तविक हों, तो (k) पर सही शर्त क्या है?

Question English:
If (x^2-2(k+1)x+(k^2+4)=0) has real roots, what is the correct condition on (k)?

Options:
A. (k\geq\frac{3}{2})
B. (k<\frac{3}{2})
C. (k=\frac{3}{2}) मात्र / Only (k=\frac{3}{2})
D. हर वास्तविक (k) / Every real (k)

Correct Answer:
A. (k\geq\frac{3}{2})

Explanation Hindi:
यहाँ (D=4(k+1)^2-4(k^2+4)=8k-12) है। वास्तविक मूलों के लिए (D\geq0), इसलिए (k\geq\frac{3}{2})।

Explanation English:
Here (D=4(k+1)^2-4(k^2+4)=8k-12). For real roots (D\geq0), so (k\geq\frac{3}{2}).

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".

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Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण (x^-2+2(k+1)x+k+5=0) के वास्तविक मूलों के लिए कौन सी शर्त सही है?

Which condition is correct for real roots of (x^-2+2(k+1)x+k+5=0)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq-3\) या \(k\geq1\)\(k\leq-3\) or \(k\geq1\)

Step 1

Concept

Here (D=4(k+1)²-4(k+5)). \(D\geq0\) gives \(k^2+k-4\geq0\), so solve the resulting inequality carefully.

Step 2

Why this answer is correct

The correct answer is A. \(k\leq-3\) या \(k\geq1\) / \(k\leq-3\) or \(k\geq1\). Here (D=4(k+1)²-4(k+5)). \(D\geq0\) gives \(k^2+k-4\geq0\), so solve the resulting inequality carefully.

Step 3

Exam Tip

यहाँ (D=4(k+1)²-4(k+5)) है। \(D\geq0\) से \(k^2+k-4\geq0\) नहीं, सही सरल रूप \(k^2+k-4\geq0\) देता है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 39

Question Hindi:
समीकरण (x^2+2(k+1)x+k+5=0) के वास्तविक मूलों के लिए कौन सी शर्त सही है?

Question English:
Which condition is correct for real roots of (x^2+2(k+1)x+k+5=0)?

Options:
A. (k\leq-3) या (k\geq1) / (k\leq-3) or (k\geq1)
B. (-3<k<1)
C. (k=0) मात्र / Only (k=0)
D. (k=5) मात्र / Only (k=5)

Correct Answer:
A. (k\leq-3) या (k\geq1) / (k\leq-3) or (k\geq1)

Explanation Hindi:
यहाँ (D=4(k+1)^2-4(k+5)) है। (D\geq0) से (k^2+k-4\geq0) नहीं, सही सरल रूप (k^2+k-4\geq0) देता है।

Explanation English:
Here (D=4(k+1)^2-4(k+5)). (D\geq0) gives (k^2+k-4\geq0), so solve the resulting inequality carefully.

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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण (2x^-2+(2k+1)x+5=0) में वास्तविक मूलों के लिए सही शर्त कौन सी है?

Which condition is correct for real roots in (2x^-2+(2k+1)x+5=0)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq\frac{-1-2\sqrt{10}}{2}\) या \(k\geq\frac{-1+2\sqrt{10}}{2}\)\(k\leq\frac{-1-2\sqrt{10}}{2}\) or \(k\geq\frac{-1+2\sqrt{10}}{2}\)

Step 1

Concept

For real roots, ((2k+1)²-40\geq0) is needed. Hence \(2k+1\leq-2\sqrt{10}\) or \(2k+1\geq2\sqrt{10}\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq\frac{-1-2\sqrt{10}}{2}\) या \(k\geq\frac{-1+2\sqrt{10}}{2}\) / \(k\leq\frac{-1-2\sqrt{10}}{2}\) or \(k\geq\frac{-1+2\sqrt{10}}{2}\). For real roots, ((2k+1)²-40\geq0) is needed. Hence \(2k+1\leq-2\sqrt{10}\) or \(2k+1\geq2\sqrt{10}\).

Step 3

Exam Tip

वास्तविक मूलों के लिए ((2k+1)²-40\geq0) चाहिए। इसलिए \(2k+1\leq-2\sqrt{10}\) या \(2k+1\geq2\sqrt{10}\)।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 39

Question Hindi:
समीकरण (2x^2+(2k+1)x+5=0) में वास्तविक मूलों के लिए सही शर्त कौन सी है?

Question English:
Which condition is correct for real roots in (2x^2+(2k+1)x+5=0)?

Options:
A. (k\leq\frac{-1-2\sqrt{10}}{2}) या (k\geq\frac{-1+2\sqrt{10}}{2}) / (k\leq\frac{-1-2\sqrt{10}}{2}) or (k\geq\frac{-1+2\sqrt{10}}{2})
B. (\frac{-1-2\sqrt{10}}{2}<k<\frac{-1+2\sqrt{10}}{2})
C. (k=0) मात्र / Only (k=0)
D. (k=-\frac{1}{2}) मात्र / Only (k=-\frac{1}{2})

Correct Answer:
A. (k\leq\frac{-1-2\sqrt{10}}{2}) या (k\geq\frac{-1+2\sqrt{10}}{2}) / (k\leq\frac{-1-2\sqrt{10}}{2}) or (k\geq\frac{-1+2\sqrt{10}}{2})

Explanation Hindi:
वास्तविक मूलों के लिए ((2k+1)^2-40\geq0) चाहिए। इसलिए (2k+1\leq-2\sqrt{10}) या (2k+1\geq2\sqrt{10})।

Explanation English:
For real roots, ((2k+1)^2-40\geq0) is needed. Hence (2k+1\leq-2\sqrt{10}) or (2k+1\geq2\sqrt{10}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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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.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(5x^2+2kx+2=0\) के वास्तविक मूलों के लिए (k) पर कौन सी शर्त सही है?

Which condition on (k) is correct for real roots of \(5x^2+2kx+2=0\)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq-\sqrt{10}\) या \(k\geq\sqrt{10}\)\(k\leq-\sqrt{10}\) or \(k\geq\sqrt{10}\)

Step 1

Concept

Here (D=(2k)²-4(5)(2)=4\(k^2-10\)). From \(D\geq0\), we get \(k^2\geq10\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq-\sqrt{10}\) या \(k\geq\sqrt{10}\) / \(k\leq-\sqrt{10}\) or \(k\geq\sqrt{10}\). Here (D=(2k)²-4(5)(2)=4\(k^2-10\)). From \(D\geq0\), we get \(k^2\geq10\).

Step 3

Exam Tip

यहाँ (D=(2k)²-4(5)(2)=4\(k^2-10\)) है। \(D\geq0\) से \(k^2\geq10\) मिलता है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 39

Question Hindi:
समीकरण (5x^2+2kx+2=0) के वास्तविक मूलों के लिए (k) पर कौन सी शर्त सही है?

Question English:
Which condition on (k) is correct for real roots of (5x^2+2kx+2=0)?

Options:
A. (k\leq-\sqrt{10}) या (k\geq\sqrt{10}) / (k\leq-\sqrt{10}) or (k\geq\sqrt{10})
B. (-\sqrt{10}<k<\sqrt{10})
C. (k=0) मात्र / Only (k=0)
D. (k>0) मात्र / Only (k>0)

Correct Answer:
A. (k\leq-\sqrt{10}) या (k\geq\sqrt{10}) / (k\leq-\sqrt{10}) or (k\geq\sqrt{10})

Explanation Hindi:
यहाँ (D=(2k)^2-4(5)(2)=4(k^2-10)) है। (D\geq0) से (k^2\geq10) मिलता है।

Explanation English:
Here (D=(2k)^2-4(5)(2)=4(k^2-10)). From (D\geq0), we get (k^2\geq10).

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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि \(3x^2-4x+p=0\) के वास्तविक मूल हों, तो (p) पर सही शर्त कौन सी है?

If \(3x^2-4x+p=0\) has real roots, which condition on (p) is correct?

Explanation opens after your attempt

Correct Answer

A. \(p\leq\frac{4}{3}\)

Step 1

Concept

For real roots \(D\geq0\) is needed. Here \(16-12p\geq0\) gives \(p\leq\frac{4}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq\frac{4}{3}\). For real roots \(D\geq0\) is needed. Here \(16-12p\geq0\) gives \(p\leq\frac{4}{3}\).

Step 3

Exam Tip

वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(16-12p\geq0\) से \(p\leq\frac{4}{3}\)।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/if-3x-2-4x-p-0-has-real-roots-which-condition-on-p-is-correct

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 39

Question Hindi:
यदि (3x^2-4x+p=0) के वास्तविक मूल हों, तो (p) पर सही शर्त कौन सी है?

Question English:
If (3x^2-4x+p=0) has real roots, which condition on (p) is correct?

Options:
A. (p\leq\frac{4}{3})
B. (p>\frac{4}{3})
C. (p=\frac{3}{4})
D. (p<0) मात्र / Only (p<0)

Correct Answer:
A. (p\leq\frac{4}{3})

Explanation Hindi:
वास्तविक मूलों के लिए (D\geq0) चाहिए। यहाँ (16-12p\geq0) से (p\leq\frac{4}{3})।

Explanation English:
For real roots (D\geq0) is needed. Here (16-12p\geq0) gives (p\leq\frac{4}{3}).

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.
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Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2-2kx+9=0\) के वास्तविक मूलों के लिए (k) पर कौन सी शर्त सही है?

Which condition on (k) is correct for real roots of \(x^2-2kx+9=0\)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq-3\) या \(k\geq3\)\(k\leq-3\) or \(k\geq3\)

Step 1

Concept

For real roots, \(D\geq0\) is needed. Here \(4k^2-36\geq0\) gives \(k\leq-3\) or \(k\geq3\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq-3\) या \(k\geq3\) / \(k\leq-3\) or \(k\geq3\). For real roots, \(D\geq0\) is needed. Here \(4k^2-36\geq0\) gives \(k\leq-3\) or \(k\geq3\).

Step 3

Exam Tip

वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(4k^2-36\geq0\) से \(k\leq-3\) या \(k\geq3\) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 38

Question Hindi:
समीकरण (x^2-2kx+9=0) के वास्तविक मूलों के लिए (k) पर कौन सी शर्त सही है?

Question English:
Which condition on (k) is correct for real roots of (x^2-2kx+9=0)?

Options:
A. (k\leq-3) या (k\geq3) / (k\leq-3) or (k\geq3)
B. (-3<k<3)
C. (k=0) मात्र / Only (k=0)
D. (k=3) मात्र / Only (k=3)

Correct Answer:
A. (k\leq-3) या (k\geq3) / (k\leq-3) or (k\geq3)

Explanation Hindi:
वास्तविक मूलों के लिए (D\geq0) चाहिए। यहाँ (4k^2-36\geq0) से (k\leq-3) या (k\geq3) मिलता है।

Explanation English:
For real roots, (D\geq0) is needed. Here (4k^2-36\geq0) gives (k\leq-3) or (k\geq3).

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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (x^-2+2(k-1)x+k+2=0) के वास्तविक मूलों के लिए कौन सी शर्त सही है?

Which condition is correct for real roots of (x^-2+2(k-1)x+k+2=0)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq-1\) या \(k\geq4\)\(k\leq-1\) or \(k\geq4\)

Step 1

Concept

Here (D=4(k-1)²-4(k+2)). From \(D\geq0\), \(k^2-3k-4\geq0\), so \(k\leq-1\) or \(k\geq4\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq-1\) या \(k\geq4\) / \(k\leq-1\) or \(k\geq4\). Here (D=4(k-1)²-4(k+2)). From \(D\geq0\), \(k^2-3k-4\geq0\), so \(k\leq-1\) or \(k\geq4\).

Step 3

Exam Tip

यहाँ (D=4(k-1)²-4(k+2)) है। \(D\geq0\) से \(k^2-3k-4\geq0\), इसलिए \(k\leq-1\) या \(k\geq4\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 38

Question Hindi:
समीकरण (x^2+2(k-1)x+k+2=0) के वास्तविक मूलों के लिए कौन सी शर्त सही है?

Question English:
Which condition is correct for real roots of (x^2+2(k-1)x+k+2=0)?

Options:
A. (k\leq-1) या (k\geq4) / (k\leq-1) or (k\geq4)
B. (-1<k<4)
C. (k=1) मात्र / Only (k=1)
D. (k=2) मात्र / Only (k=2)

Correct Answer:
A. (k\leq-1) या (k\geq4) / (k\leq-1) or (k\geq4)

Explanation Hindi:
यहाँ (D=4(k-1)^2-4(k+2)) है। (D\geq0) से (k^2-3k-4\geq0), इसलिए (k\leq-1) या (k\geq4)।

Explanation English:
Here (D=4(k-1)^2-4(k+2)). From (D\geq0), (k^2-3k-4\geq0), so (k\leq-1) or (k\geq4).

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".

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- Make 9:16 version for Shorts/Reels.
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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (3x^-2+(2k-1)x+1=0) में वास्तविक मूलों के लिए सही शर्त कौन सी है?

Which condition is correct for real roots in (3x^-2+(2k-1)x+1=0)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq\frac{1-2\sqrt{3}}{2}\) या \(k\geq\frac{1+2\sqrt{3}}{2}\)\(k\leq\frac{1-2\sqrt{3}}{2}\) or \(k\geq\frac{1+2\sqrt{3}}{2}\)

Step 1

Concept

For real roots, ((2k-1)²-12\geq0) is needed. Hence \(2k-1\leq-2\sqrt{3}\) or \(2k-1\geq2\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq\frac{1-2\sqrt{3}}{2}\) या \(k\geq\frac{1+2\sqrt{3}}{2}\) / \(k\leq\frac{1-2\sqrt{3}}{2}\) or \(k\geq\frac{1+2\sqrt{3}}{2}\). For real roots, ((2k-1)²-12\geq0) is needed. Hence \(2k-1\leq-2\sqrt{3}\) or \(2k-1\geq2\sqrt{3}\).

Step 3

Exam Tip

वास्तविक मूलों के लिए ((2k-1)²-12\geq0) चाहिए। इसलिए \(2k-1\leq-2\sqrt{3}\) या \(2k-1\geq2\sqrt{3}\)।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 38

Question Hindi:
समीकरण (3x^2+(2k-1)x+1=0) में वास्तविक मूलों के लिए सही शर्त कौन सी है?

Question English:
Which condition is correct for real roots in (3x^2+(2k-1)x+1=0)?

Options:
A. (k\leq\frac{1-2\sqrt{3}}{2}) या (k\geq\frac{1+2\sqrt{3}}{2}) / (k\leq\frac{1-2\sqrt{3}}{2}) or (k\geq\frac{1+2\sqrt{3}}{2})
B. (\frac{1-2\sqrt{3}}{2}<k<\frac{1+2\sqrt{3}}{2})
C. (k=0) मात्र / Only (k=0)
D. (k=\frac{1}{2}) मात्र / Only (k=\frac{1}{2})

Correct Answer:
A. (k\leq\frac{1-2\sqrt{3}}{2}) या (k\geq\frac{1+2\sqrt{3}}{2}) / (k\leq\frac{1-2\sqrt{3}}{2}) or (k\geq\frac{1+2\sqrt{3}}{2})

Explanation Hindi:
वास्तविक मूलों के लिए ((2k-1)^2-12\geq0) चाहिए। इसलिए (2k-1\leq-2\sqrt{3}) या (2k-1\geq2\sqrt{3})।

Explanation English:
For real roots, ((2k-1)^2-12\geq0) is needed. Hence (2k-1\leq-2\sqrt{3}) or (2k-1\geq2\sqrt{3}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(4x^2+4kx+9=0\) के वास्तविक मूलों के लिए (k) पर सही शर्त चुनिए।

Choose the correct condition on (k) for real roots of \(4x^2+4kx+9=0\).

Explanation opens after your attempt

Correct Answer

A. \(k\leq-\frac{3}{2}\) या \(k\geq\frac{3}{2}\)\(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\)

Step 1

Concept

Here (D=(4k)²-4(4)(9)=16\(k^2-9\)). For real roots \(k^2\geq9\), so \(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq-\frac{3}{2}\) या \(k\geq\frac{3}{2}\) / \(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\). Here (D=(4k)²-4(4)(9)=16\(k^2-9\)). For real roots \(k^2\geq9\), so \(k\leq-\frac{3}{2}\) or \(k\geq\frac{3}{2}\).

Step 3

Exam Tip

यहाँ (D=(4k)²-4(4)(9)=16\(k^2-9\)) है। वास्तविक मूलों के लिए \(k^2\geq9\) यानी \(k\leq-\frac{3}{2}\) या \(k\geq\frac{3}{2}\)।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 38

Question Hindi:
समीकरण (4x^2+4kx+9=0) के वास्तविक मूलों के लिए (k) पर सही शर्त चुनिए।

Question English:
Choose the correct condition on (k) for real roots of (4x^2+4kx+9=0).

Options:
A. (k\leq-\frac{3}{2}) या (k\geq\frac{3}{2}) / (k\leq-\frac{3}{2}) or (k\geq\frac{3}{2})
B. (-\frac{3}{2}<k<\frac{3}{2})
C. (k=0) मात्र / Only (k=0)
D. (k>0) मात्र / Only (k>0)

Correct Answer:
A. (k\leq-\frac{3}{2}) या (k\geq\frac{3}{2}) / (k\leq-\frac{3}{2}) or (k\geq\frac{3}{2})

Explanation Hindi:
यहाँ (D=(4k)^2-4(4)(9)=16(k^2-9)) है। वास्तविक मूलों के लिए (k^2\geq9) यानी (k\leq-\frac{3}{2}) या (k\geq\frac{3}{2})।

Explanation English:
Here (D=(4k)^2-4(4)(9)=16(k^2-9)). For real roots (k^2\geq9), so (k\leq-\frac{3}{2}) or (k\geq\frac{3}{2}).

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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि \(2x^2-3x+p=0\) के मूल वास्तविक हों, तो (p) पर कौन सी शर्त सही है?

If \(2x^2-3x+p=0\) has real roots, which condition on (p) is correct?

Explanation opens after your attempt

Correct Answer

A. \(p\leq\frac{9}{8}\)

Step 1

Concept

For real roots we need \(D\geq0\). Here \(9-8p\geq0\) gives \(p\leq\frac{9}{8}\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq\frac{9}{8}\). For real roots we need \(D\geq0\). Here \(9-8p\geq0\) gives \(p\leq\frac{9}{8}\).

Step 3

Exam Tip

वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(9-8p\geq0\) से \(p\leq\frac{9}{8}\)।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 38

Question Hindi:
यदि (2x^2-3x+p=0) के मूल वास्तविक हों, तो (p) पर कौन सी शर्त सही है?

Question English:
If (2x^2-3x+p=0) has real roots, which condition on (p) is correct?

Options:
A. (p\leq\frac{9}{8})
B. (p>\frac{9}{8})
C. (p=\frac{8}{9})
D. (p<0) मात्र / Only (p<0)

Correct Answer:
A. (p\leq\frac{9}{8})

Explanation Hindi:
वास्तविक मूलों के लिए (D\geq0) चाहिए। यहाँ (9-8p\geq0) से (p\leq\frac{9}{8})।

Explanation English:
For real roots we need (D\geq0). Here (9-8p\geq0) gives (p\leq\frac{9}{8}).

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".

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Open Question

Question Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(3x^2+2kx+k=0\) के वास्तविक मूलों के लिए (k) की सही शर्त कौन सी है?

Which condition on (k) is correct for real roots of \(3x^2+2kx+k=0\)?

Explanation opens after your attempt

Correct Answer

A. \(k\leq0\) या \(k\geq3\)\(k\leq0\) or \(k\geq3\)

Step 1

Concept

Here (D=(2k)²-4(3)(k)=4k(k-3)). For real roots use \(D\geq0\).

Step 2

Why this answer is correct

The correct answer is A. \(k\leq0\) या \(k\geq3\) / \(k\leq0\) or \(k\geq3\). Here (D=(2k)²-4(3)(k)=4k(k-3)). For real roots use \(D\geq0\).

Step 3

Exam Tip

यहाँ (D=(2k)²-4(3)(k)=4k(k-3)) है। वास्तविक मूलों के लिए \(D\geq0\) लें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Quadratic Equations
Topic: Nature of Roots
Difficulty: Medium
Level: 37

Question Hindi:
समीकरण (3x^2+2kx+k=0) के वास्तविक मूलों के लिए (k) की सही शर्त कौन सी है?

Question English:
Which condition on (k) is correct for real roots of (3x^2+2kx+k=0)?

Options:
A. (k\leq0) या (k\geq3) / (k\leq0) or (k\geq3)
B. (0<k<3)
C. (k=1) मात्र / Only (k=1)
D. (k>0) मात्र / Only (k>0)

Correct Answer:
A. (k\leq0) या (k\geq3) / (k\leq0) or (k\geq3)

Explanation Hindi:
यहाँ (D=(2k)^2-4(3)(k)=4k(k-3)) है। वास्तविक मूलों के लिए (D\geq0) लें।

Explanation English:
Here (D=(2k)^2-4(3)(k)=4k(k-3)). For real roots use (D\geq0).

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