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sign analysis MCQ Questions for Class 10

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9 questions tagged with sign analysis.

Question 1/9 Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (a<0), (c<0) और (b=0), तो \(ax^2+c=0\) के मूलों की प्रकृति क्या होगी?

If (a<0), (c<0), and (b=0), what will be the nature of roots of \(ax^2+c=0\)?

Explanation opens after your attempt
Correct Answer

A. कोई वास्तविक मूल नहींNo real roots

Step 1

Concept

Here (ac>0), so \(D=0^2-4ac<0\). Therefore real roots will not exist.

Step 2

Why this answer is correct

The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. Here (ac>0), so \(D=0^2-4ac<0\). Therefore real roots will not exist.

Step 3

Exam Tip

यहाँ (ac>0), इसलिए \(D=0^2-4ac<0\) है। इसलिए वास्तविक मूल नहीं होंगे।

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Question 2/9 Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

यदि (a<0), (c>0) और (b) कोई वास्तविक संख्या हो, तो \(ax^2+bx+c=0\) के मूलों की प्रकृति क्या होगी?

If (a<0), (c>0), and (b) is any real number, what will be the nature of roots of \(ax^2+bx+c=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक और असमानTwo real and distinct

Step 1

Concept

Here (ac<0), so (-4ac>0) and \(D=b^2-4ac>0\). Hence there will be two distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / Two real and distinct. Here (ac<0), so (-4ac>0) and \(D=b^2-4ac>0\). Hence there will be two distinct real roots.

Step 3

Exam Tip

यहाँ (ac<0), इसलिए (-4ac>0) और \(D=b^2-4ac>0\) है। अतः दो असमान वास्तविक मूल होंगे।

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Question 3/9 Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

यदि (a>0), (c<0) और (b) कोई वास्तविक संख्या हो, तो \(ax^2+bx+c=0\) के मूलों की प्रकृति क्या होगी?

If (a>0), (c<0), and (b) is any real number, what will be the nature of roots of \(ax^2+bx+c=0\)?

Explanation opens after your attempt
Correct Answer

A. दो वास्तविक और असमानTwo real and distinct

Step 1

Concept

Here (ac<0), so (-4ac>0) and \(D=b^2-4ac>0\). Hence there will be two distinct real roots.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और असमान / Two real and distinct. Here (ac<0), so (-4ac>0) and \(D=b^2-4ac>0\). Hence there will be two distinct real roots.

Step 3

Exam Tip

यहाँ (ac<0), इसलिए (-4ac>0) और \(D=b^2-4ac>0\) है। अतः दो असमान वास्तविक मूल होंगे।

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Question 4/9 Expert Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

यदि (a>0) और (c>0) हो तथा (b=0), तो \(ax^2+c=0\) के मूलों की प्रकृति क्या होगी?

If (a>0), (c>0), and (b=0), what will be the nature of roots of \(ax^2+c=0\)?

Explanation opens after your attempt
Correct Answer

A. कोई वास्तविक मूल नहींNo real roots

Step 1

Concept

Here \(D=0^2-4ac=-4ac<0\). Therefore real roots will not exist.

Step 2

Why this answer is correct

The correct answer is A. कोई वास्तविक मूल नहीं / No real roots. Here \(D=0^2-4ac=-4ac<0\). Therefore real roots will not exist.

Step 3

Exam Tip

यहाँ \(D=0^2-4ac=-4ac<0\) है। इसलिए वास्तविक मूल नहीं होंगे।

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Question 5/9 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-4)(x-9)(x-15)) है, तो (4<x<9) में ग्राफ कहाँ होगा?

If (p(x)=(x-4)(x-9)(x-15)), where will the graph be for (4<x<9)?

Explanation opens after your attempt
Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 3

Exam Tip

इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।

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Question 6/9 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x-3)(x-6)(x-11)) है, तो (3<x<6) में ग्राफ कहाँ होगा?

If (p(x)=(x-3)(x-6)(x-11)), where will the graph be for (3<x<6)?

Explanation opens after your attempt
Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 3

Exam Tip

इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।

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Question 7/9 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x-2)(x-5)(x-9)) है तो (2<x<5) में ग्राफ कहाँ होगा?

If (p(x)=(x-2)(x-5)(x-9)), where will the graph be for (2<x<5)?

Explanation opens after your attempt
Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.

Step 3

Exam Tip

इस अंतराल में चिह्न (+), (-), (-) हैं इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।

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Question 8/9 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-1)(x-3)(x-5)) है, तो (1<x<3) में ग्राफ कहाँ होगा?

If (p(x)=(x-1)(x-3)(x-5)), where will the graph be for (1<x<3)?

Explanation opens after your attempt
Correct Answer

A. (x)-अक्ष के ऊपरAbove the (x)-axis

Step 1

Concept

In this interval the signs are (+), (-), (-), so the product is positive. Tip: an odd number of negative factors gives a negative value.

Step 2

Why this answer is correct

The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: an odd number of negative factors gives a negative value.

Step 3

Exam Tip

इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: विषम संख्या ऋणात्मक कारकों से मान ऋणात्मक होता है।

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Question 9/9 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=-(x-1)(x-5)) है, तो (1<x<5) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-1)(x-5)), on which side of the (x)-axis will the graph lie for (1<x<5)?

Explanation opens after your attempt
Correct Answer

A. ऊपरAbove

Step 1

Concept

Between them ((x-1)) is positive and ((x-5)) is negative, and the outside negative makes the value positive. Tip: graph position is decided by the sign of (p(x)).

Step 2

Why this answer is correct

The correct answer is A. ऊपर / Above. Between them ((x-1)) is positive and ((x-5)) is negative, and the outside negative makes the value positive. Tip: graph position is decided by the sign of (p(x)).

Step 3

Exam Tip

बीच में ((x-1)) धनात्मक और ((x-5)) ऋणात्मक है, बाहर का ऋण चिन्ह मान को धनात्मक बनाता है। टिप: ग्राफ की स्थिति (p(x)) के चिह्न से तय करें।

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