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D positive MCQ Questions for Class 10

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14 questions tagged with D positive.

Question 1/14 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि \(x^2-2px+p^2-5p=0\) के मूल वास्तविक और भिन्न हैं, तो (p) पर सही शर्त क्या है?

If \(x^2-2px+p^2-5p=0\) has real and distinct roots, what is the correct condition on (p)?

Explanation opens after your attempt
Correct Answer

A. (p>0)

Step 1

Concept

Here (D=4p-2-4\(p^2-5p\)=20p). For real and distinct roots (D>0), hence (p>0).

Step 2

Why this answer is correct

The correct answer is A. (p>0). Here (D=4p-2-4\(p^2-5p\)=20p). For real and distinct roots (D>0), hence (p>0).

Step 3

Exam Tip

यहाँ (D=4p-2-4\(p^2-5p\)=20p) है। वास्तविक और भिन्न मूलों के लिए (D>0), अतः (p>0)।

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Question 2/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

कथन: (D>0) होने पर मूल हमेशा समान होते हैं। सही विकल्प चुनिए।

Statement: When (D>0), roots are always equal. Choose the correct option.

Explanation opens after your attempt
Correct Answer

A. कथन गलत हैThe statement is wrong

Step 1

Concept

When (D>0), roots are real and distinct. Equal roots occur only when (D=0).

Step 2

Why this answer is correct

The correct answer is A. कथन गलत है / The statement is wrong. When (D>0), roots are real and distinct. Equal roots occur only when (D=0).

Step 3

Exam Tip

(D>0) पर मूल वास्तविक और भिन्न होते हैं। समान मूल केवल (D=0) पर होते हैं।

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Question 3/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(3x^2-5x+2=0\) में (D) कितना है?

What is (D) in the equation \(3x^2-5x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

Here (D=(-5)2-4(3)(2)=1). Since (D>0), the roots will be distinct.

Step 2

Why this answer is correct

The correct answer is A. (1). Here (D=(-5)2-4(3)(2)=1). Since (D>0), the roots will be distinct.

Step 3

Exam Tip

यहाँ (D=(-5)2-4(3)(2)=1) है। (D>0) होने से मूल भिन्न होंगे।

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Question 4/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (D>0) और (D) पूर्ण वर्ग नहीं है तो मूल कैसे होंगे?

If (D>0) and (D) is not a perfect square, how will the roots be?

Explanation opens after your attempt
Correct Answer

A. वास्तविक, अपरिमेय और भिन्नReal, irrational and distinct

Step 1

Concept

A positive non-perfect-square (D) gives real, irrational and distinct roots. Only (D>0) tells distinctness.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक, अपरिमेय और भिन्न / Real, irrational and distinct. A positive non-perfect-square (D) gives real, irrational and distinct roots. Only (D>0) tells distinctness.

Step 3

Exam Tip

धनात्मक लेकिन अपूर्ण वर्ग (D) से मूल वास्तविक, अपरिमेय और भिन्न होते हैं। केवल (D>0) से भिन्नता पता चलती है।

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Question 5/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(7x^2-10x+3=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of the equation \(7x^2-10x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Here (D=16>0), so the roots are real and distinct. When (D) is positive, distinct roots are obtained.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Here (D=16>0), so the roots are real and distinct. When (D) is positive, distinct roots are obtained.

Step 3

Exam Tip

इसमें (D=16>0) है इसलिए मूल वास्तविक और भिन्न हैं। (D) धनात्मक हो तो अलग मूल मिलते हैं।

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Question 6/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(7x^2-10x+3=0\) के लिए (D) कितना है?

What is (D) for the equation \(7x^2-10x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. (16)

Step 1

Concept

Here (D=(-10)2-4(7)(3)=16). Since (16>0), the roots will be distinct.

Step 2

Why this answer is correct

The correct answer is A. (16). Here (D=(-10)2-4(7)(3)=16). Since (16>0), the roots will be distinct.

Step 3

Exam Tip

यहाँ (D=(-10)2-4(7)(3)=16) है। (16>0) होने से मूल भिन्न होंगे।

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Question 7/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(2x^2-7x+3=0\) में मूलों की प्रकृति क्या है?

What is the nature of roots in the equation \(2x^2-7x+3=0\)?

Explanation opens after your attempt
Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Here (D=(-7)2-4(2)(3)=25>0). Hence the roots will be real and distinct.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Here (D=(-7)2-4(2)(3)=25>0). Hence the roots will be real and distinct.

Step 3

Exam Tip

यहाँ (D=(-7)2-4(2)(3)=25>0) है। अतः मूल वास्तविक और भिन्न होंगे।

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Question 8/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

कौन सा समीकरण वास्तविक और भिन्न मूल रखता है?

Which equation has real and distinct roots?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x+2=0\)

Step 1

Concept

In the first equation (D=(-3)2-4(1)(2)=1>0). Hence its roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x+2=0\). In the first equation (D=(-3)2-4(1)(2)=1>0). Hence its roots are real and distinct.

Step 3

Exam Tip

पहले समीकरण में (D=(-3)2-4(1)(2)=1>0) है। इसलिए उसके मूल वास्तविक और भिन्न हैं।

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Question 9/14 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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Question 10/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(2x^2+5x+2=0\) के मूलों की प्रकृति बताइए।

State the nature of roots of the equation \(2x^2+5x+2=0\).

Explanation opens after your attempt
Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Here (D=9>0), so there will be two real and distinct roots. Finding (D) first is the safest method.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Here (D=9>0), so there will be two real and distinct roots. Finding (D) first is the safest method.

Step 3

Exam Tip

इसमें (D=9>0) है इसलिए दो वास्तविक और भिन्न मूल होंगे। पहले (D) निकालना सबसे सुरक्षित तरीका है।

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Question 11/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(2x^2+5x+2=0\) के लिए (D) क्या होगा?

What will be (D) for the equation \(2x^2+5x+2=0\)?

Explanation opens after your attempt
Correct Answer

A. (9)

Step 1

Concept

Here (D=(5)2-4(2)(2)=9). Since (9>0), the roots will be distinct.

Step 2

Why this answer is correct

The correct answer is A. (9). Here (D=(5)2-4(2)(2)=9). Since (9>0), the roots will be distinct.

Step 3

Exam Tip

यहाँ (D=(5)2-4(2)(2)=9) है। (9>0) इसलिए मूल भिन्न होंगे।

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Question 12/14 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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Question 13/14 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(2x^2-3x+1=0\) के मूल कैसे होंगे?

What will be the roots of the equation \(2x^2-3x+1=0\)?

Explanation opens after your attempt
Correct Answer

A. वास्तविक और भिन्नReal and distinct

Step 1

Concept

Here (D=1>0), so the roots will be two real and distinct. Apply this rule when (D) is positive.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और भिन्न / Real and distinct. Here (D=1>0), so the roots will be two real and distinct. Apply this rule when (D) is positive.

Step 3

Exam Tip

इसमें (D=1>0) है इसलिए दो वास्तविक और भिन्न मूल होंगे। (D) धनात्मक हो तो यही नियम लगाएँ।

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

यदि (D>0) हो तो \(ax^2+bx+c=0\) के मूल कैसे होंगे?

If (D>0), what will be the roots of \(ax^2+bx+c=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक और भिन्नTwo real and distinct

Step 1

Concept

When (D>0), two different real roots are obtained. Watch the sign (>) carefully.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और भिन्न / Two real and distinct. When (D>0), two different real roots are obtained. Watch the sign (>) carefully.

Step 3

Exam Tip

जब (D>0) होता है तो दो अलग वास्तविक मूल मिलते हैं। संकेत (>) को ध्यान से देखें।

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