Class 10 real distinct roots MCQ Questions

Question 1/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण ((p+4)x^-2-2(p+1)x+(p-2)=0) के मूलों के बारे में सही कथन क्या है, यदि \(p\neq-4\)?

What is the correct statement about the roots of ((p+4)x^-2-2(p+1)x+(p-2)=0), if \(p\neq-4\)?

Explanation opens after your attempt

Correct Answer

A. हमेशा वास्तविक और भिन्नAlways real and distinct

Step 1

Concept

Here (D=4(p+1)²-4(p+4)(p-2)=36>0). Since \(p\neq-4\), the equation remains quadratic and roots are distinct.

Step 2

Why this answer is correct

The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=4(p+1)²-4(p+4)(p-2)=36>0). Since \(p\neq-4\), the equation remains quadratic and roots are distinct.

Step 3

Exam Tip

यहाँ (D=4(p+1)²-4(p+4)(p-2)=36>0) है। \(p\neq-4\) से समीकरण द्विघात रहता है और मूल भिन्न होते हैं।

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

Question Hindi:
समीकरण ((p+4)x^2-2(p+1)x+(p-2)=0) के मूलों के बारे में सही कथन क्या है, यदि (p\neq-4)?

Question English:
What is the correct statement about the roots of ((p+4)x^2-2(p+1)x+(p-2)=0), if (p\neq-4)?

Options:
A. हमेशा वास्तविक और भिन्न / Always real and distinct
B. हमेशा वास्तविक और समान / Always real and equal
C. वास्तविक मूल नहीं / No real roots
D. केवल (p=2) पर वास्तविक / Real only when (p=2)

Correct Answer:
A. हमेशा वास्तविक और भिन्न / Always real and distinct

Explanation Hindi:
यहाँ (D=4(p+1)^2-4(p+4)(p-2)=36>0) है। (p\neq-4) से समीकरण द्विघात रहता है और मूल भिन्न होते हैं।

Explanation English:
Here (D=4(p+1)^2-4(p+4)(p-2)=36>0). Since (p\neq-4), the equation remains quadratic and roots are distinct.

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1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question 2/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (x^-2-2(a-5)x+a^-2-10a+21=0) के मूलों की प्रकृति क्या है?

What is the nature of roots of (x^-2-2(a-5)x+a^-2-10a+21=0)?

Explanation opens after your attempt

Correct Answer

A. हमेशा वास्तविक और भिन्नAlways real and distinct

Step 1

Concept

Here (D=4(a-5)²-4\(a^2-10a+21\)=16>0). Therefore the roots are real and distinct for every real (a).

Step 2

Why this answer is correct

The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=4(a-5)²-4\(a^2-10a+21\)=16>0). Therefore the roots are real and distinct for every real (a).

Step 3

Exam Tip

यहाँ (D=4(a-5)²-4\(a^2-10a+21\)=16>0) है। इसलिए हर वास्तविक (a) के लिए मूल वास्तविक और भिन्न हैं।

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

Question Hindi:
समीकरण (x^2-2(a-5)x+a^2-10a+21=0) के मूलों की प्रकृति क्या है?

Question English:
What is the nature of roots of (x^2-2(a-5)x+a^2-10a+21=0)?

Options:
A. हमेशा वास्तविक और भिन्न / Always real and distinct
B. हमेशा वास्तविक और समान / Always real and equal
C. वास्तविक मूल नहीं / No real roots
D. प्रकृति (a) पर निर्भर है / Nature depends on (a)

Correct Answer:
A. हमेशा वास्तविक और भिन्न / Always real and distinct

Explanation Hindi:
यहाँ (D=4(a-5)^2-4(a^2-10a+21)=16>0) है। इसलिए हर वास्तविक (a) के लिए मूल वास्तविक और भिन्न हैं।

Explanation English:
Here (D=4(a-5)^2-4(a^2-10a+21)=16>0). Therefore the roots are real and distinct for every real (a).

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Question 3/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि \(a\neq b\), तो (x^-2-2(a+b)x+4ab=0) के मूलों की प्रकृति क्या होगी?

If \(a\neq b\), what will be the nature of roots of (x^-2-2(a+b)x+4ab=0)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Here (D=4(a-b)²). When \(a\neq b\), (D>0), so roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Here (D=4(a-b)²). When \(a\neq b\), (D>0), so roots are real and distinct.

Step 3

Exam Tip

यहाँ (D=4(a-b)²) है। \(a\neq b\) होने पर (D>0), इसलिए मूल वास्तविक और भिन्न होंगे।

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

Question Hindi:
यदि (a\neq b), तो (x^2-2(a+b)x+4ab=0) के मूलों की प्रकृति क्या होगी?

Question English:
If (a\neq b), what will be the nature of roots of (x^2-2(a+b)x+4ab=0)?

Options:
A. वास्तविक और भिन्न / Real and distinct
B. वास्तविक और समान / Real and equal
C. वास्तविक नहीं / Not real
D. सदैव अपरिमेय / Always irrational

Correct Answer:
A. वास्तविक और भिन्न / Real and distinct

Explanation Hindi:
यहाँ (D=4(a-b)^2) है। (a\neq b) होने पर (D>0), इसलिए मूल वास्तविक और भिन्न होंगे।

Explanation English:
Here (D=4(a-b)^2). When (a\neq b), (D>0), so roots are real and distinct.

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Question 4/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण (x^-2-2(m^-4)x+m^-2-16=0) के मूल वास्तविक और भिन्न कब होंगे?

When will the roots of (x^-2-2(m^-4)x+m^-2-16=0) be real and distinct?

Explanation opens after your attempt

Correct Answer

A. (m<4)

Step 1

Concept

Here (D=32(4-m)). For real and distinct roots (D>0), so (m<4).

Step 2

Why this answer is correct

The correct answer is A. (m<4). Here (D=32(4-m)). For real and distinct roots (D>0), so (m<4).

Step 3

Exam Tip

यहाँ (D=32(4-m)) है। वास्तविक और भिन्न मूलों के लिए (D>0), इसलिए (m<4)।

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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: Hard
Level: 38

Question Hindi:
समीकरण (x^2-2(m-4)x+m^2-16=0) के मूल वास्तविक और भिन्न कब होंगे?

Question English:
When will the roots of (x^2-2(m-4)x+m^2-16=0) be real and distinct?

Options:
A. (m<4)
B. (m>4)
C. (m=4)
D. (m\le -4)

Correct Answer:
A. (m<4)

Explanation Hindi:
यहाँ (D=32(4-m)) है। वास्तविक और भिन्न मूलों के लिए (D>0), इसलिए (m<4)।

Explanation English:
Here (D=32(4-m)). For real and distinct roots (D>0), so (m<4).

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5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question 5/16 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

निम्न में से किस समीकरण के दो वास्तविक और असमान मूल हैं?

Which of the following equations has two real and distinct roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2-11x+18=0\)

Step 1

Concept

In option (A), (D=(-11)²-4(1)(18)=49). When (D>0), two distinct real roots exist.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-11x+18=0\). In option (A), (D=(-11)²-4(1)(18)=49). When (D>0), two distinct real roots exist.

Step 3

Exam Tip

विकल्प (A) में (D=(-11)²-4(1)(18)=49) है। (D>0) होने पर दो असमान वास्तविक मूल मिलते हैं।

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

Question Hindi:
निम्न में से किस समीकरण के दो वास्तविक और असमान मूल हैं?

Question English:
Which of the following equations has two real and distinct roots?

Options:
A. (x^2-11x+18=0)
B. (x^2+4x+4=0)
C. (x^2+2x+6=0)
D. (x^2-8x+16=0)

Correct Answer:
A. (x^2-11x+18=0)

Explanation Hindi:
विकल्प (A) में (D=(-11)^2-4(1)(18)=49) है। (D>0) होने पर दो असमान वास्तविक मूल मिलते हैं।

Explanation English:
In option (A), (D=(-11)^2-4(1)(18)=49). When (D>0), two distinct real roots exist.

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Question 6/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-2mx+3m=0\) के वास्तविक और भिन्न मूलों के लिए (m) पर क्या शर्त है?

What condition on (m) gives real and distinct roots for \(x^2-2mx+3m=0\)?

Explanation opens after your attempt

Correct Answer

A. (m<0) या (m>3)(m<0) or (m>3)

Step 1

Concept

Here (D=4m(m^-3)). From (D>0), (m<0) or (m>3).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

यहाँ (D=4m(m^-3)) है। (D>0) से (m<0) या (m>3) मिलता है।

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

Question Hindi:
समीकरण (x^2-2mx+3m=0) के वास्तविक और भिन्न मूलों के लिए (m) पर क्या शर्त है?

Question English:
What condition on (m) gives real and distinct roots for (x^2-2mx+3m=0)?

Options:
A. (m<0) या (m>3) / (m<0) or (m>3)
B. (0<m<3)
C. (m=0) या (m=3) / (m=0) or (m=3)
D. (m>0)

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

Explanation Hindi:
यहाँ (D=4m(m-3)) है। (D>0) से (m<0) या (m>3) मिलता है।

Explanation English:
Here (D=4m(m-3)). From (D>0), (m<0) or (m>3).

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Question 7/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (x^-2-2\(\alpha+2\)x+\alpha^-2=0) के मूल वास्तविक और भिन्न हैं, तो \(\alpha\) पर शर्त क्या है?

If (x^-2-2\(\alpha+2\)x+\alpha^-2=0) has real and distinct roots, what is the condition on \(\alpha\)?

Explanation opens after your attempt

Correct Answer

A. \(\alpha>-1\)

Step 1

Concept

(D=4\(\alpha+2\)²-4\alpha^-2=16\(\alpha+1\)). From (D>0), \(\alpha>-1\).

Step 2

Why this answer is correct

The correct answer is A. \(\alpha>-1\). (D=4\(\alpha+2\)²-4\alpha^-2=16\(\alpha+1\)). From (D>0), \(\alpha>-1\).

Step 3

Exam Tip

(D=4\(\alpha+2\)²-4\alpha^-2=16\(\alpha+1\)) है। (D>0) से \(\alpha>-1\) मिलता है।

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

Question Hindi:
यदि (x^2-2(\alpha+2)x+\alpha^2=0) के मूल वास्तविक और भिन्न हैं, तो (\alpha) पर शर्त क्या है?

Question English:
If (x^2-2(\alpha+2)x+\alpha^2=0) has real and distinct roots, what is the condition on (\alpha)?

Options:
A. (\alpha>-1)
B. (\alpha<-1)
C. (\alpha=-1)
D. (\alpha>2) केवल / (\alpha>2) only

Correct Answer:
A. (\alpha>-1)

Explanation Hindi:
(D=4(\alpha+2)^2-4\alpha^2=16(\alpha+1)) है। (D>0) से (\alpha>-1) मिलता है।

Explanation English:
(D=4(\alpha+2)^2-4\alpha^2=16(\alpha+1)). From (D>0), (\alpha>-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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Question 8/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस शर्त पर \(x^2-2sx+s+2=0\) के मूल वास्तविक और भिन्न होंगे?

Under which condition will \(x^2-2sx+s+2=0\) have real and distinct roots?

Explanation opens after your attempt

Correct Answer

A. (s<-1) या (s>2)(s<-1) or (s>2)

Step 1

Concept

Here (D=4s^-2-4(s+2)=4(s^-2)(s+1)). From (D>0), (s<-1) or (s>2).

Step 2

Why this answer is correct

The correct answer is A. (s<-1) या (s>2) / (s<-1) or (s>2). Here (D=4s^-2-4(s+2)=4(s^-2)(s+1)). From (D>0), (s<-1) or (s>2).

Step 3

Exam Tip

यहाँ (D=4s^-2-4(s+2)=4(s^-2)(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है।

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

Question Hindi:
किस शर्त पर (x^2-2sx+s+2=0) के मूल वास्तविक और भिन्न होंगे?

Question English:
Under which condition will (x^2-2sx+s+2=0) have real and distinct roots?

Options:
A. (s<-1) या (s>2) / (s<-1) or (s>2)
B. (-1<s<2)
C. (s=-1) या (s=2) / (s=-1) or (s=2)
D. (0<s<1)

Correct Answer:
A. (s<-1) या (s>2) / (s<-1) or (s>2)

Explanation Hindi:
यहाँ (D=4s^2-4(s+2)=4(s-2)(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है।

Explanation English:
Here (D=4s^2-4(s+2)=4(s-2)(s+1)). From (D>0), (s<-1) or (s>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 9/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(kx^2-6x+k=0\) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?

What is the correct condition for real and distinct roots of \(kx^2-6x+k=0\)?

Explanation opens after your attempt

Correct Answer

A. \(k^2<9\) और \(k\neq0\)\(k^2<9\) and \(k\neq0\)

Step 1

Concept

Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).

Step 2

Why this answer is correct

The correct answer is A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\). Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).

Step 3

Exam Tip

यहाँ \(D=36-4k^2\) है। वास्तविक और भिन्न मूलों के लिए (D>0) और \(k\neq0\), अतः \(k^2<9\)।

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

Question Hindi:
समीकरण (kx^2-6x+k=0) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?

Question English:
What is the correct condition for real and distinct roots of (kx^2-6x+k=0)?

Options:
A. (k^2<9) और (k\neq0) / (k^2<9) and (k\neq0)
B. (k^2>9)
C. (k^2=9)
D. (k=0)

Correct Answer:
A. (k^2<9) और (k\neq0) / (k^2<9) and (k\neq0)

Explanation Hindi:
यहाँ (D=36-4k^2) है। वास्तविक और भिन्न मूलों के लिए (D>0) और (k\neq0), अतः (k^2<9)।

Explanation English:
Here (D=36-4k^2). For real and distinct roots (D>0) and (k\neq0), hence (k^2<9).

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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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 10/16 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण (x^-2-2(k+1)x+k^-2=0) के मूल वास्तविक और भिन्न कब होंगे?

When will the roots of (x^-2-2(k+1)x+k^-2=0) be real and distinct?

Explanation opens after your attempt

Correct Answer

A. \(k>-\frac{1}{2}\)

Step 1

Concept

Here (D=4(k+1)²-4k^-2=4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(k>-\frac{1}{2}\). Here (D=4(k+1)²-4k^-2=4(2k+1)). For distinct real roots (D>0), so \(k>-\frac{1}{2}\).

Step 3

Exam Tip

यहाँ (D=4(k+1)²-4k^-2=4(2k+1)) है। भिन्न वास्तविक मूलों के लिए (D>0), इसलिए \(k>-\frac{1}{2}\)।

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

Question Hindi:
समीकरण (x^2-2(k+1)x+k^2=0) के मूल वास्तविक और भिन्न कब होंगे?

Question English:
When will the roots of (x^2-2(k+1)x+k^2=0) be real and distinct?

Options:
A. (k>-\frac{1}{2})
B. (k<-\frac{1}{2})
C. (k=-\frac{1}{2})
D. (k=0)

Correct Answer:
A. (k>-\frac{1}{2})

Explanation Hindi:
यहाँ (D=4(k+1)^2-4k^2=4(2k+1)) है। भिन्न वास्तविक मूलों के लिए (D>0), इसलिए (k>-\frac{1}{2})।

Explanation English:
Here (D=4(k+1)^2-4k^2=4(2k+1)). For distinct real roots (D>0), so (k>-\frac{1}{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.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 11/16 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-2x-3=0\) के मूल कैसे होंगे?

How will the roots of \(x^2-2x-3=0\) be?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमान ((D=16))Two real and distinct ((D=16))

Step 1

Concept

Here (D=(-2)²-4(1)(-3)=16). A positive perfect-square (D) gives two rational distinct roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान ((D=16)) / Two real and distinct ((D=16)). Here (D=(-2)²-4(1)(-3)=16). A positive perfect-square (D) gives two rational distinct roots.

Step 3

Exam Tip

यहाँ (D=(-2)²-4(1)(-3)=16) है। धनात्मक पूर्ण वर्ग (D) से दो परिमेय असमान मूल मिलते हैं।

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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 (x^2-2x-3=0) के मूल कैसे होंगे?

Question English:
How will the roots of (x^2-2x-3=0) be?

Options:
A. दो वास्तविक और असमान ((D=16)) / Two real and distinct ((D=16))
B. दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0))
C. कोई वास्तविक मूल नहीं ((D<0)) / No real roots ((D<0))
D. सिर्फ एक परिमेय मूल ((D=1)) / Only one rational root ((D=1))

Correct Answer:
A. दो वास्तविक और असमान ((D=16)) / Two real and distinct ((D=16))

Explanation Hindi:
यहाँ (D=(-2)^2-4(1)(-3)=16) है। धनात्मक पूर्ण वर्ग (D) से दो परिमेय असमान मूल मिलते हैं।

Explanation English:
Here (D=(-2)^2-4(1)(-3)=16). A positive perfect-square (D) gives two rational distinct roots.

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.
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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 12/16 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि \(x^2+px+6=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए कौन सी शर्त सही है?

If the roots of \(x^2+px+6=0\) are real and distinct, which condition is correct for (p)?

Explanation opens after your attempt

Correct Answer

A. \(p^2>24\)

Step 1

Concept

For real and distinct roots (D>0). So \(p^2-24>0\), that is \(p^2>24\).

Step 2

Why this answer is correct

The correct answer is A. \(p^2>24\). For real and distinct roots (D>0). So \(p^2-24>0\), that is \(p^2>24\).

Step 3

Exam Tip

वास्तविक और भिन्न मूलों के लिए (D>0) होता है। इसलिए \(p^2-24>0\), अर्थात \(p^2>24\)।

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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: Easy
Level: 39

Question Hindi:
यदि (x^2+px+6=0) के मूल वास्तविक और भिन्न हैं तो (p) के लिए कौन सी शर्त सही है?

Question English:
If the roots of (x^2+px+6=0) are real and distinct, which condition is correct for (p)?

Options:
A. (p^2>24)
B. (p^2=24)
C. (p^2<24)
D. (p^2=6)

Correct Answer:
A. (p^2>24)

Explanation Hindi:
वास्तविक और भिन्न मूलों के लिए (D>0) होता है। इसलिए (p^2-24>0), अर्थात (p^2>24)।

Explanation English:
For real and distinct roots (D>0). So (p^2-24>0), that is (p^2>24).

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 13/16 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि \(x^2+px+4=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए सही शर्त क्या है?

If the roots of \(x^2+px+4=0\) are real and distinct, what is the correct condition for (p)?

Explanation opens after your attempt

Correct Answer

A. \(p^2>16\)

Step 1

Concept

For real and distinct roots (D>0), so \(p^2-16>0\). Therefore \(p^2>16\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(p^2>16\). For real and distinct roots (D>0), so \(p^2-16>0\). Therefore \(p^2>16\) is correct.

Step 3

Exam Tip

वास्तविक और भिन्न मूलों के लिए (D>0) होता है इसलिए \(p^2-16>0\)। अतः \(p^2>16\) सही है।

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

Question Hindi:
यदि (x^2+px+4=0) के मूल वास्तविक और भिन्न हैं तो (p) के लिए सही शर्त क्या है?

Question English:
If the roots of (x^2+px+4=0) are real and distinct, what is the correct condition for (p)?

Options:
A. (p^2>16)
B. (p^2=16)
C. (p^2<16)
D. (p^2=4)

Correct Answer:
A. (p^2>16)

Explanation Hindi:
वास्तविक और भिन्न मूलों के लिए (D>0) होता है इसलिए (p^2-16>0)। अतः (p^2>16) सही है।

Explanation English:
For real and distinct roots (D>0), so (p^2-16>0). Therefore (p^2>16) is correct.

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Question 14/16 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2+7x+10=0\) की प्रकृति क्या होगी?

What will be the nature of the equation \(x^2+7x+10=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और भिन्न मूलTwo real and distinct roots

Step 1

Concept

Since (D=9>0), two real and distinct roots are obtained. (D>0) means two different real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और भिन्न मूल / Two real and distinct roots. Since (D=9>0), two real and distinct roots are obtained. (D>0) means two different real roots.

Step 3

Exam Tip

(D=9>0) होने से दो वास्तविक और भिन्न मूल मिलेंगे। (D>0) का अर्थ दो अलग वास्तविक मूल है।

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

Question Hindi:
समीकरण (x^2+7x+10=0) की प्रकृति क्या होगी?

Question English:
What will be the nature of the equation (x^2+7x+10=0)?

Options:
A. दो वास्तविक और भिन्न मूल / Two real and distinct roots
B. दो वास्तविक और समान मूल / Two real and equal roots
C. कोई वास्तविक मूल नहीं / No real roots
D. केवल एक काल्पनिक मूल / Only one imaginary root

Correct Answer:
A. दो वास्तविक और भिन्न मूल / Two real and distinct roots

Explanation Hindi:
(D=9>0) होने से दो वास्तविक और भिन्न मूल मिलेंगे। (D>0) का अर्थ दो अलग वास्तविक मूल है।

Explanation English:
Since (D=9>0), two real and distinct roots are obtained. (D>0) means two different real roots.

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Question 15/16 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(x^2-2x-3=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of the equation \(x^2-2x-3=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Since (D=16>0), the roots are real and distinct. Positive (D) always gives distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Since (D=16>0), the roots are real and distinct. Positive (D) always gives distinct real roots.

Step 3

Exam Tip

(D=16>0) है इसलिए मूल वास्तविक और भिन्न हैं। धनात्मक (D) हमेशा भिन्न वास्तविक मूल देता है।

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

Question Hindi:
समीकरण (x^2-2x-3=0) के मूलों की प्रकृति क्या है?

Question English:
What is the nature of roots of the equation (x^2-2x-3=0)?

Options:
A. वास्तविक और भिन्न / Real and distinct
B. वास्तविक और समान / Real and equal
C. वास्तविक नहीं / Not real
D. दो समान ऋणात्मक / Two equal negative

Correct Answer:
A. वास्तविक और भिन्न / Real and distinct

Explanation Hindi:
(D=16>0) है इसलिए मूल वास्तविक और भिन्न हैं। धनात्मक (D) हमेशा भिन्न वास्तविक मूल देता है।

Explanation English:
Since (D=16>0), the roots are real and distinct. Positive (D) always gives distinct real roots.

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Question 16/16 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि किसी द्विघात समीकरण में \(b^2-4ac=9\) है तो मूलों की प्रकृति क्या होगी?

If \(b^2-4ac=9\) in a quadratic equation, what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Since (9>0), we have (D>0). Therefore the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Since (9>0), we have (D>0). Therefore the roots are real and distinct.

Step 3

Exam Tip

क्योंकि (9>0) है इसलिए (D>0) होगा। अतः मूल वास्तविक और भिन्न होंगे।

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

Question Hindi:
यदि किसी द्विघात समीकरण में (b^2-4ac=9) है तो मूलों की प्रकृति क्या होगी?

Question English:
If (b^2-4ac=9) in a quadratic equation, what will be the nature of roots?

Options:
A. वास्तविक और भिन्न / Real and distinct
B. वास्तविक और समान / Real and equal
C. वास्तविक नहीं / Not real
D. एक मूल शून्य / One root zero

Correct Answer:
A. वास्तविक और भिन्न / Real and distinct

Explanation Hindi:
क्योंकि (9>0) है इसलिए (D>0) होगा। अतः मूल वास्तविक और भिन्न होंगे।

Explanation English:
Since (9>0), we have (D>0). Therefore the roots are real and distinct.

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2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
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real distinct roots MCQ Questions for Class 10

Practice Questions

समीकरण ((p+4)x-2-2(p+1)x+(p-2)=0) के मूलों के बारे में सही कथन क्या है, यदि \(p\neq-4\)?

Concept

Why this answer is correct

Exam Tip

समीकरण (x-2-2(a-5)x+a-2-10a+21=0) के मूलों की प्रकृति क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a\neq b\), तो (x-2-2(a+b)x+4ab=0) के मूलों की प्रकृति क्या होगी?

Concept

Why this answer is correct

Exam Tip

समीकरण (x-2-2(m-4)x+m-2-16=0) के मूल वास्तविक और भिन्न कब होंगे?

Concept

Why this answer is correct

Exam Tip

निम्न में से किस समीकरण के दो वास्तविक और असमान मूल हैं?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-2mx+3m=0\) के वास्तविक और भिन्न मूलों के लिए (m) पर क्या शर्त है?

Concept

Why this answer is correct

Exam Tip

यदि (x-2-2\(\alpha+2\)x+\alpha-2=0) के मूल वास्तविक और भिन्न हैं, तो \(\alpha\) पर शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

किस शर्त पर \(x^2-2sx+s+2=0\) के मूल वास्तविक और भिन्न होंगे?

Concept

Why this answer is correct

Exam Tip

समीकरण \(kx^2-6x+k=0\) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण (x-2-2(k+1)x+k-2=0) के मूल वास्तविक और भिन्न कब होंगे?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-2x-3=0\) के मूल कैसे होंगे?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+px+6=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए कौन सी शर्त सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+px+4=0\) के मूल वास्तविक और भिन्न हैं तो (p) के लिए सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+7x+10=0\) की प्रकृति क्या होगी?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-2x-3=0\) के मूलों की प्रकृति क्या है?

Concept

Why this answer is correct

Exam Tip

यदि किसी द्विघात समीकरण में \(b^2-4ac=9\) है तो मूलों की प्रकृति क्या होगी?

Concept

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Exam Tip

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समीकरण ((p+4)x^-2-2(p+1)x+(p-2)=0) के मूलों के बारे में सही कथन क्या है, यदि \(p\neq-4\)?

समीकरण (x^-2-2(a-5)x+a^-2-10a+21=0) के मूलों की प्रकृति क्या है?

यदि \(a\neq b\), तो (x^-2-2(a+b)x+4ab=0) के मूलों की प्रकृति क्या होगी?

समीकरण (x^-2-2(m^-4)x+m^-2-16=0) के मूल वास्तविक और भिन्न कब होंगे?

यदि (x^-2-2\(\alpha+2\)x+\alpha^-2=0) के मूल वास्तविक और भिन्न हैं, तो \(\alpha\) पर शर्त क्या है?

समीकरण (x^-2-2(k+1)x+k^-2=0) के मूल वास्तविक और भिन्न कब होंगे?