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Mathematics Quiz - Class 10 Mathematics Easy Level 37 Quiz

Question 1/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

द्विघात समीकरण \(ax^2+bx+c=0\) के मूलों की प्रकृति जानने के लिए कौन सा व्यंजक प्रयोग होता है?

Which expression is used to determine the nature of roots of the quadratic equation \(ax^2+bx+c=0\)?

Explanation opens after your attempt

Correct Answer

A. \(b^2-4ac\)

Step 1

Concept

The discriminant is \(D=b^2-4ac\). In exams first identify (a,b,c) correctly.

Step 2

Why this answer is correct

The correct answer is A. \(b^2-4ac\). The discriminant is \(D=b^2-4ac\). In exams first identify (a,b,c) correctly.

Step 3

Exam Tip

विविक्तकर \(D=b^2-4ac\) होता है। परीक्षा में पहले (a,b,c) सही पहचानें।

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Question 2/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि द्विघात समीकरण के लिए (D>0) हो तो मूलों की प्रकृति क्या होगी?

If (D>0) for a quadratic equation, what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

When (D>0), two different real roots are obtained. Check the sign first in exams.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. When (D>0), two different real roots are obtained. Check the sign first in exams.

Step 3

Exam Tip

(D>0) होने पर दो अलग-अलग वास्तविक मूल मिलते हैं। चिन्ह देखकर प्रकृति तुरंत लिखें।

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Question 3/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि द्विघात समीकरण के लिए (D=0) हो तो मूल कैसे होंगे?

If (D=0) for a quadratic equation, how will the roots be?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

When (D=0), both roots are equal. These are also called repeated real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. When (D=0), both roots are equal. These are also called repeated real roots.

Step 3

Exam Tip

(D=0) होने पर दोनों मूल बराबर होते हैं। इसे दोहराए गए वास्तविक मूल भी कहते हैं।

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Question 4/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-5x+6=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of the equation \(x^2-5x+6=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

Here (D=(-5)²-4(1)(6)=1>0). So the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. Here (D=(-5)²-4(1)(6)=1>0). So the roots are real and distinct.

Step 3

Exam Tip

यहां (D=(-5)²-4(1)(6)=1>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 5/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-4x+4=0\) के मूलों की प्रकृति पहचानिए।

Identify the nature of roots of the equation \(x^2-4x+4=0\).

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

Here (D=(-4)²-4(1)(4)=0). (D=0) means equal real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. Here (D=(-4)²-4(1)(4)=0). (D=0) means equal real roots.

Step 3

Exam Tip

यहां (D=(-4)²-4(1)(4)=0) है। (D=0) समान वास्तविक मूल बताता है।

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Question 6/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+2x+5=0\) के मूलों के बारे में सही कथन क्या है?

Which statement is correct about the roots of \(x^2+2x+5=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

Here (D=2²-4(1)(5)=-16<0). So there are no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. Here (D=2²-4(1)(5)=-16<0). So there are no real roots.

Step 3

Exam Tip

यहां (D=2²-4(1)(5)=-16<0) है। इसलिए वास्तविक मूल नहीं हैं।

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Question 7/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2-3x+1=0\) के लिए विविक्तकर का मान क्या है?

What is the value of the discriminant for \(2x^2-3x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

The value is (D=(-3)²-4(2)(1)=1). A positive discriminant gives distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. (1). The value is (D=(-3)²-4(2)(1)=1). A positive discriminant gives distinct real roots.

Step 3

Exam Tip

(D=(-3)²-4(2)(1)=1) है। धनात्मक विविक्तकर असमान वास्तविक मूल देता है।

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Question 8/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(3x^2+6x+3=0\) के मूल किस प्रकार के होंगे?

What type of roots will the equation \(3x^2+6x+3=0\) have?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

(D=6²-4(3)(3)=0). Hence both roots will be equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. (D=6²-4(3)(3)=0). Hence both roots will be equal and real.

Step 3

Exam Tip

(D=6²-4(3)(3)=0) है। इसलिए दोनों मूल समान वास्तविक होंगे।

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Question 9/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(5x^2+x+1=0\) के लिए मूलों की प्रकृति चुनिए।

Choose the nature of roots for \(5x^2+x+1=0\).

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=1²-4(5)(1)=-19<0). Therefore the equation has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=1²-4(5)(1)=-19<0). Therefore the equation has no real roots.

Step 3

Exam Tip

(D=1²-4(5)(1)=-19<0) है। इसलिए कोई वास्तविक मूल नहीं है।

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Question 10/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+6x+k=0\) के समान वास्तविक मूल होने के लिए (k) का मान क्या होगा?

For \(x^2+6x+k=0\) to have equal real roots, what should be the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.

Step 2

Why this answer is correct

The correct answer is A. (9). For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.

Step 3

Exam Tip

समान मूलों के लिए (D=0), इसलिए \(6^2-4k=0\) से (k=9)। ऐसे प्रश्न में (D=0) लगाएं।

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Question 11/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-8x+m=0\) में समान वास्तविक मूलों के लिए (m) क्या होगा?

In \(x^2-8x+m=0\), what is (m) for equal real roots?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

(D=(-8)²-4m=0) gives (m=16). Keep the discriminant zero for equal roots.

Step 2

Why this answer is correct

The correct answer is A. (16). (D=(-8)²-4m=0) gives (m=16). Keep the discriminant zero for equal roots.

Step 3

Exam Tip

(D=(-8)²-4m=0) से (m=16) मिलता है। बराबर मूलों के लिए विविक्तकर शून्य रखें।

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Question 12/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+kx+16=0\) के समान वास्तविक मूल होने के लिए (k) का कौन सा मान सही हो सकता है?

Which value of (k) can make \(x^2+kx+16=0\) have equal real roots?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.

Step 2

Why this answer is correct

The correct answer is A. (8). For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.

Step 3

Exam Tip

समान मूलों के लिए \(k^2-64=0\) होता है, इसलिए (k=8) या (k=-8)। दिए विकल्पों में (8) सही है।

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Question 13/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के दो वास्तविक और असमान मूल होंगे?

Which equation will have two real and distinct roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2-7x+10=0\)

Step 1

Concept

For the first equation, (D=(-7)²-4(1)(10)=9>0). Hence its roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7x+10=0\). For the first equation, (D=(-7)²-4(1)(10)=9>0). Hence its roots are real and distinct.

Step 3

Exam Tip

पहले समीकरण में (D=(-7)²-4(1)(10)=9>0) है। इसलिए उसके मूल वास्तविक और असमान हैं।

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Question 14/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के दो वास्तविक और समान मूल होंगे?

Which equation will have two real and equal roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2+10x+25=0\)

Step 1

Concept

In the first equation, (D=10²-4(1)(25)=0). A perfect square form often gives equal roots.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+10x+25=0\). In the first equation, (D=10²-4(1)(25)=0). A perfect square form often gives equal roots.

Step 3

Exam Tip

पहले समीकरण में (D=10²-4(1)(25)=0) है। पूर्ण वर्ग रूप अक्सर समान मूल देता है।

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Question 15/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

किस समीकरण के वास्तविक मूल नहीं होंगे?

Which equation will have no real roots?

Explanation opens after your attempt

Correct Answer

A. \(x^2+3x+5=0\)

Step 1

Concept

For the first equation, (D=3²-4(1)(5)=-11<0). A negative discriminant gives no real roots.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x+5=0\). For the first equation, (D=3²-4(1)(5)=-11<0). A negative discriminant gives no real roots.

Step 3

Exam Tip

पहले समीकरण में (D=3²-4(1)(5)=-11<0) है। ऋणात्मक विविक्तकर वास्तविक मूल नहीं देता।

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Question 16/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?

By observing \(4x^2-12x+9=0\), what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

\(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. \(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 3

Exam Tip

\(4x^2-12x+9\) एक पूर्ण वर्ग ((2x-3)²) है। इसलिए मूल समान वास्तविक हैं।

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Question 17/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=25) हो तो द्विघात समीकरण के मूलों के बारे में सही बात क्या है?

If (D=25), which statement about the roots of a quadratic equation is correct?

Explanation opens after your attempt

Correct Answer

A. मूल वास्तविक और असमान होंगेroots will be real and distinct

Step 1

Concept

(25>0), so the roots will be real and distinct. The sign of (D) is enough for nature.

Step 2

Why this answer is correct

The correct answer is A. मूल वास्तविक और असमान होंगे / roots will be real and distinct. (25>0), so the roots will be real and distinct. The sign of (D) is enough for nature.

Step 3

Exam Tip

(25>0) है, इसलिए मूल वास्तविक और असमान होंगे। (D) का केवल चिन्ह प्रकृति बताने के लिए काफी है।

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Question 18/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=-7) हो तो मूलों की प्रकृति क्या होगी?

If (D=-7), what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(-7<0), so there will be no real roots. Never treat negative (D) as equal roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (-7<0), so there will be no real roots. Never treat negative (D) as equal roots.

Step 3

Exam Tip

(-7<0) है, इसलिए वास्तविक मूल नहीं होंगे। ऋणात्मक (D) को कभी समान मूल न मानें।

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Question 19/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?

If (D=0) and \(a\neq0\), how many distinct real roots will the quadratic equation have?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.

Step 2

Why this answer is correct

The correct answer is A. (1). At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.

Step 3

Exam Tip

(D=0) पर दोनों मूल समान होते हैं, इसलिए अलग-अलग वास्तविक मूलों की संख्या (1) है। ध्यान रखें मूल दो बार दोहरता है।

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Question 20/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2+5x+2=0\) के लिए सही प्रकृति चुनिए।

Choose the correct nature for \(2x^2+5x+2=0\).

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

(D=5²-4(2)(2)=9>0). Hence the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=5²-4(2)(2)=9>0). Hence the roots are real and distinct.

Step 3

Exam Tip

(D=5²-4(2)(2)=9>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 21/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(9x^2-6x+1=0\) में मूलों की प्रकृति क्या है?

What is the nature of roots in \(9x^2-6x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

(D=(-6)²-4(9)(1)=0). Therefore this is a case of equal real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. (D=(-6)²-4(9)(1)=0). Therefore this is a case of equal real roots.

Step 3

Exam Tip

(D=(-6)²-4(9)(1)=0) है। इसलिए यह समान वास्तविक मूलों का मामला है।

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Question 22/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

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

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

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=1²-4(1)(3)=-11<0). Hence real roots will not be obtained.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=1²-4(1)(3)=-11<0). Hence real roots will not be obtained.

Step 3

Exam Tip

(D=1²-4(1)(3)=-11<0) है। इसलिए वास्तविक मूल नहीं मिलेंगे।

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Question 23/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(6x^2-5x+1=0\) का विविक्तकर क्या है?

What is the discriminant of \(6x^2-5x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(D=(-5)²-4(6)(1)=1). This gives two real and distinct roots.

Step 2

Why this answer is correct

The correct answer is A. (1). (D=(-5)²-4(6)(1)=1). This gives two real and distinct roots.

Step 3

Exam Tip

(D=(-5)²-4(6)(1)=1) है। इससे दो वास्तविक और असमान मूल होंगे।

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Question 24/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(7x^2+2x+3=0\) के लिए सही निष्कर्ष क्या है?

What is the correct conclusion for \(7x^2+2x+3=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=2²-4(7)(3)=-80<0). So this equation has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=2²-4(7)(3)=-80<0). So this equation has no real roots.

Step 3

Exam Tip

(D=2²-4(7)(3)=-80<0) है। इसलिए यह समीकरण वास्तविक मूल नहीं रखता।

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Question 25/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-2x+n=0\) के दो वास्तविक और असमान मूल होने के लिए कौन सी शर्त सही है?

For \(x^2-2x+n=0\) to have two real and distinct roots, which condition is correct?

Explanation opens after your attempt

Correct Answer

A. (n<1)

Step 1

Concept

For distinct real roots (D>0), so ((-2)²-4n>0) gives (n<1). Use a strict inequality for distinct roots.

Step 2

Why this answer is correct

The correct answer is A. (n<1). For distinct real roots (D>0), so ((-2)²-4n>0) gives (n<1). Use a strict inequality for distinct roots.

Step 3

Exam Tip

असमान वास्तविक मूलों के लिए (D>0), इसलिए ((-2)²-4n>0) से (n<1)। असमान के लिए कड़ाई वाली असमता लगती है।

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Question 26/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+4x+p=0\) के वास्तविक मूल न होने के लिए कौन सी शर्त सही है?

For \(x^2+4x+p=0\) to have no real roots, which condition is correct?

Explanation opens after your attempt

Correct Answer

A. (p>4)

Step 1

Concept

For no real roots (D<0), so (16-4p<0) gives (p>4). A negative discriminant gives no real roots.

Step 2

Why this answer is correct

The correct answer is A. (p>4). For no real roots (D<0), so (16-4p<0) gives (p>4). A negative discriminant gives no real roots.

Step 3

Exam Tip

वास्तविक मूल न होने के लिए (D<0), इसलिए (16-4p<0) से (p>4)। ऋणात्मक विविक्तकर पर वास्तविक मूल नहीं होते।

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Question 27/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-10x+r=0\) में समान वास्तविक मूलों के लिए (r) का मान चुनिए।

Choose the value of (r) for equal real roots in \(x^2-10x+r=0\).

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

(D=(-10)²-4r=0) gives (r=25). Equal roots have zero discriminant.

Step 2

Why this answer is correct

The correct answer is A. (25). (D=(-10)²-4r=0) gives (r=25). Equal roots have zero discriminant.

Step 3

Exam Tip

(D=(-10)²-4r=0) से (r=25) मिलता है। समान मूलों में विविक्तकर शून्य होता है।

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Question 28/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(3x^2+kx+12=0\) में समान वास्तविक मूलों के लिए (k) का कौन सा मान सही हो सकता है?

Which value of (k) can give equal real roots in \(3x^2+kx+12=0\)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

For equal roots (k^-2-4(3)(12)=0), so (k=12) or (k=-12). Among the options, (12) is correct.

Step 2

Why this answer is correct

The correct answer is A. (12). For equal roots (k^-2-4(3)(12)=0), so (k=12) or (k=-12). Among the options, (12) is correct.

Step 3

Exam Tip

समान मूलों के लिए (k^-2-4(3)(12)=0), इसलिए (k=12) या (k=-12)। दिए विकल्पों में (12) सही है।

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Question 29/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2+3x+\lambda=0\) के वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?

For \(2x^2+3x+\lambda=0\) to have real and distinct roots, which condition is correct?

Explanation opens after your attempt

Correct Answer

A. \(\lambda<\frac{9}{8}\)

Step 1

Concept

(D=3²-4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).

Step 2

Why this answer is correct

The correct answer is A. \(\lambda<\frac{9}{8}\). (D=3²-4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).

Step 3

Exam Tip

(D=3²-4(2)\lambda=9-8\lambda) है। (D>0) से \(\lambda<\frac{9}{8}\) मिलता है।

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Question 30/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+12x+36=0\) के बारे में सही कथन कौन सा है?

Which statement is correct about \(x^2+12x+36=0\)?

Explanation opens after your attempt

Correct Answer

A. यह समान वास्तविक मूल रखता हैit has equal real roots

Step 1

Concept

(x^-2+12x+36=(x+6)²). Being a perfect square, it has equal real roots.

Step 2

Why this answer is correct

The correct answer is A. यह समान वास्तविक मूल रखता है / it has equal real roots. (x^-2+12x+36=(x+6)²). Being a perfect square, it has equal real roots.

Step 3

Exam Tip

(x^-2+12x+36=(x+6)²) है। पूर्ण वर्ग होने से मूल समान वास्तविक हैं।

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Question 31/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-9=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-9=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

Here (D=0²-4(1)(-9)=36>0). So the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. Here (D=0²-4(1)(-9)=36>0). So the roots are real and distinct.

Step 3

Exam Tip

यहां (D=0²-4(1)(-9)=36>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 32/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+9=0\) के लिए सही विकल्प चुनिए।

Choose the correct option for \(x^2+9=0\).

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

Here (D=0²-4(1)(9)=-36<0). Therefore there are no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. Here (D=0²-4(1)(9)=-36<0). Therefore there are no real roots.

Step 3

Exam Tip

यहां (D=0²-4(1)(9)=-36<0) है। इसलिए वास्तविक मूल नहीं हैं।

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Question 33/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2-1=0\) के मूल कैसे होंगे?

How will the roots of \(4x^2-1=0\) be?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

(D=0²-4(4)(-1)=16>0). Hence two distinct real roots will be obtained.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=0²-4(4)(-1)=16>0). Hence two distinct real roots will be obtained.

Step 3

Exam Tip

(D=0²-4(4)(-1)=16>0) है। इसलिए दो असमान वास्तविक मूल मिलेंगे।

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Question 34/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2+8=0\) के मूलों की प्रकृति क्या होगी?

What will be the nature of roots of \(2x^2+8=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=0²-4(2)(8)=-64<0). Therefore the equation will have no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=0²-4(2)(8)=-64<0). Therefore the equation will have no real roots.

Step 3

Exam Tip

(D=0²-4(2)(8)=-64<0) है। इसलिए समीकरण के वास्तविक मूल नहीं होंगे।

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Question 35/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि किसी द्विघात समीकरण के दो समान वास्तविक मूल हैं, तो (D) का मान क्या होगा?

If a quadratic equation has two equal real roots, what will be the value of (D)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For equal real roots, (D=0) is necessary. This is the main rule for nature questions.

Step 2

Why this answer is correct

The correct answer is A. (0). For equal real roots, (D=0) is necessary. This is the main rule for nature questions.

Step 3

Exam Tip

समान वास्तविक मूलों के लिए (D=0) अनिवार्य है। प्रकृति वाले प्रश्नों में यही मुख्य नियम है।

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Question 36/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि किसी द्विघात समीकरण के दो असमान वास्तविक मूल हैं, तो (D) कैसा होगा?

If a quadratic equation has two distinct real roots, how will (D) be?

Explanation opens after your attempt

Correct Answer

A. (D>0)

Step 1

Concept

For distinct real roots, (D>0). Do not add the equality sign by mistake.

Step 2

Why this answer is correct

The correct answer is A. (D>0). For distinct real roots, (D>0). Do not add the equality sign by mistake.

Step 3

Exam Tip

असमान वास्तविक मूलों के लिए (D>0) होता है। बराबर का चिन्ह गलती से न लगाएं।

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Question 37/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि किसी द्विघात समीकरण के वास्तविक मूल नहीं हैं, तो (D) के लिए सही शर्त क्या है?

If a quadratic equation has no real roots, what is the correct condition for (D)?

Explanation opens after your attempt

Correct Answer

A. (D<0)

Step 1

Concept

When there are no real roots, (D<0). The condition \(D\geq0\) indicates real roots.

Step 2

Why this answer is correct

The correct answer is A. (D<0). When there are no real roots, (D<0). The condition \(D\geq0\) indicates real roots.

Step 3

Exam Tip

वास्तविक मूल न होने पर (D<0) होता है। \(D\geq0\) वास्तविक मूलों की स्थिति बताता है।

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Question 38/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-6x+9=0\) के लिए कौन सा कथन सही है?

Which statement is correct for \(x^2-6x+9=0\)?

Explanation opens after your attempt

Correct Answer

A. दो समान वास्तविक मूल हैंit has two equal real roots

Step 1

Concept

(D=(-6)²-4(1)(9)=0). Therefore it has two equal real roots.

Step 2

Why this answer is correct

The correct answer is A. दो समान वास्तविक मूल हैं / it has two equal real roots. (D=(-6)²-4(1)(9)=0). Therefore it has two equal real roots.

Step 3

Exam Tip

(D=(-6)²-4(1)(9)=0) है। इसलिए दो समान वास्तविक मूल हैं।

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Question 39/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

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

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

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

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

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=(-7)²-4(2)(3)=25>0). Hence the roots are real and distinct.

Step 3

Exam Tip

(D=(-7)²-4(2)(3)=25>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Question 40/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2+4x+5=0\) के लिए सही प्रकृति कौन सी है?

Which is the correct nature for \(4x^2+4x+5=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=4²-4(4)(5)=-64<0). Therefore it has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=4²-4(4)(5)=-64<0). Therefore it has no real roots.

Step 3

Exam Tip

(D=4²-4(4)(5)=-64<0) है। इसलिए इसके वास्तविक मूल नहीं हैं।

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Question 41/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+5x+6=0\) के लिए विविक्तकर और प्रकृति का सही युग्म कौन सा है?

Which pair of discriminant and nature is correct for \(x^2+5x+6=0\)?

Explanation opens after your attempt

Correct Answer

A. (D=1), दो वास्तविक और असमान(D=1), two real and distinct

Step 1

Concept

(D=5²-4(1)(6)=1). A positive (D) gives real and distinct roots.

Step 2

Why this answer is correct

The correct answer is A. (D=1), दो वास्तविक और असमान / (D=1), two real and distinct. (D=5²-4(1)(6)=1). A positive (D) gives real and distinct roots.

Step 3

Exam Tip

(D=5²-4(1)(6)=1) है। धनात्मक (D) से वास्तविक और असमान मूल होते हैं।

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Question 42/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(3x^2-2x+4=0\) के लिए विविक्तकर का चिन्ह क्या है?

What is the sign of the discriminant for \(3x^2-2x+4=0\)?

Explanation opens after your attempt

Correct Answer

A. ऋणात्मकnegative

Step 1

Concept

(D=(-2)²-4(3)(4)=-44<0). Hence the discriminant is negative.

Step 2

Why this answer is correct

The correct answer is A. ऋणात्मक / negative. (D=(-2)²-4(3)(4)=-44<0). Hence the discriminant is negative.

Step 3

Exam Tip

(D=(-2)²-4(3)(4)=-44<0) है। अतः विविक्तकर ऋणात्मक है।

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Question 43/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(2x^2+4x+2=0\) के लिए विविक्तकर का चिन्ह क्या है?

What is the sign of the discriminant for \(2x^2+4x+2=0\)?

Explanation opens after your attempt

Correct Answer

A. शून्यzero

Step 1

Concept

(D=4²-4(2)(2)=0). So this is the case of equal real roots.

Step 2

Why this answer is correct

The correct answer is A. शून्य / zero. (D=4²-4(2)(2)=0). So this is the case of equal real roots.

Step 3

Exam Tip

(D=4²-4(2)(2)=0) है। इसलिए यह समान वास्तविक मूलों की स्थिति है।

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Question 44/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-11x+30=0\) के लिए मूलों की प्रकृति क्या होगी?

What will be the nature of roots for \(x^2-11x+30=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

(D=(-11)²-4(1)(30)=1>0). Therefore the roots will be real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=(-11)²-4(1)(30)=1>0). Therefore the roots will be real and distinct.

Step 3

Exam Tip

(D=(-11)²-4(1)(30)=1>0) है। इसलिए मूल वास्तविक और असमान होंगे।

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Question 45/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+14x+49=0\) के लिए सही उत्तर चुनिए।

Choose the correct answer for \(x^2+14x+49=0\).

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

(D=14²-4(1)(49)=0). Hence the roots are equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. (D=14²-4(1)(49)=0). Hence the roots are equal and real.

Step 3

Exam Tip

(D=14²-4(1)(49)=0) है। अतः मूल समान वास्तविक हैं।

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Question 46/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-4x+8=0\) के मूलों की प्रकृति बताइए।

State the nature of roots of \(x^2-4x+8=0\).

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहींno real roots

Step 1

Concept

(D=(-4)²-4(1)(8)=-16<0). So there are no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=(-4)²-4(1)(8)=-16<0). So there are no real roots.

Step 3

Exam Tip

(D=(-4)²-4(1)(8)=-16<0) है। इसलिए कोई वास्तविक मूल नहीं है।

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Question 47/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-3x+s=0\) के समान वास्तविक मूलों के लिए (s) का मान क्या होगा?

What is the value of (s) for equal real roots of \(x^2-3x+s=0\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{9}{4}\)

Step 1

Concept

For equal roots (D=0), so ((-3)²-4s=0) gives \(s=\frac{9}{4}\). Do not fear fractional answers.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{9}{4}\). For equal roots (D=0), so ((-3)²-4s=0) gives \(s=\frac{9}{4}\). Do not fear fractional answers.

Step 3

Exam Tip

समान मूलों के लिए (D=0), इसलिए ((-3)²-4s=0) से \(s=\frac{9}{4}\)। भिन्न उत्तर से न डरें।

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Question 48/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(5x^2-4x+t=0\) के वास्तविक और समान मूलों के लिए (t) क्या होगा?

What is (t) for real and equal roots of \(5x^2-4x+t=0\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{4}{5}\)

Step 1

Concept

(D=(-4)²-4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{4}{5}\). (D=(-4)²-4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.

Step 3

Exam Tip

(D=(-4)²-4(5)t=0) से \(t=\frac{4}{5}\) मिलता है। समान मूलों के लिए हमेशा (D=0) रखें।

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Question 49/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

कथन पढ़िए: \(x^2+1=0\) के वास्तविक मूल नहीं हैं क्योंकि (D<0)। यह कथन कैसा है?

Read the statement: \(x^2+1=0\) has no real roots because (D<0). How is this statement?

Explanation opens after your attempt

Correct Answer

A. सहीcorrect

Step 1

Concept

(D=0²-4(1)(1)=-4<0). Hence the statement is correct and there are no real roots.

Step 2

Why this answer is correct

The correct answer is A. सही / correct. (D=0²-4(1)(1)=-4<0). Hence the statement is correct and there are no real roots.

Step 3

Exam Tip

(D=0²-4(1)(1)=-4<0) है। इसलिए कथन सही है और वास्तविक मूल नहीं हैं।

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Question 50/50 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

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

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

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और असमानtwo real and distinct

Step 1

Concept

(D=10²-4(3)(3)=64>0). Therefore the roots are real and distinct.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=10²-4(3)(3)=64>0). Therefore the roots are real and distinct.

Step 3

Exam Tip

(D=10²-4(3)(3)=64>0) है। इसलिए मूल वास्तविक और असमान हैं।

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Class 10 Mathematics Easy Quiz

द्विघात समीकरण \(ax^2+bx+c=0\) के मूलों की प्रकृति जानने के लिए कौन सा व्यंजक प्रयोग होता है?

Concept

Why this answer is correct

Exam Tip

यदि द्विघात समीकरण के लिए (D>0) हो तो मूलों की प्रकृति क्या होगी?

Concept

Why this answer is correct

Exam Tip

यदि द्विघात समीकरण के लिए (D=0) हो तो मूल कैसे होंगे?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-5x+6=0\) के मूलों की प्रकृति क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-4x+4=0\) के मूलों की प्रकृति पहचानिए।

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+2x+5=0\) के मूलों के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(2x^2-3x+1=0\) के लिए विविक्तकर का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(3x^2+6x+3=0\) के मूल किस प्रकार के होंगे?

Concept

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समीकरण \(5x^2+x+1=0\) के लिए मूलों की प्रकृति चुनिए।

Concept

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समीकरण \(x^2+6x+k=0\) के समान वास्तविक मूल होने के लिए (k) का मान क्या होगा?

Concept

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समीकरण \(x^2-8x+m=0\) में समान वास्तविक मूलों के लिए (m) क्या होगा?

Concept

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समीकरण \(x^2+kx+16=0\) के समान वास्तविक मूल होने के लिए (k) का कौन सा मान सही हो सकता है?

Concept

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किस समीकरण के दो वास्तविक और असमान मूल होंगे?

Concept

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Exam Tip

किस समीकरण के दो वास्तविक और समान मूल होंगे?

Concept

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किस समीकरण के वास्तविक मूल नहीं होंगे?

Concept

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समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?

Concept

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यदि (D=25) हो तो द्विघात समीकरण के मूलों के बारे में सही बात क्या है?

Concept

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यदि (D=-7) हो तो मूलों की प्रकृति क्या होगी?

Concept

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यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?

Concept

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समीकरण \(2x^2+5x+2=0\) के लिए सही प्रकृति चुनिए।

Concept

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