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multiplicity MCQ Questions for Class 10

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17 questions tagged with multiplicity.

Question 1/17 Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 48

यदि (p(x)=x-3-6x-2+12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?

If (p(x)=x-3-6x-2+12x-8), what is the zero of (p(x)) with its multiplicity?

Explanation opens after your attempt
Correct Answer

A. (2) गुणनता (3)(2) with multiplicity (3)

Step 1

Concept

This is (p(x)=(x-2)3), so (2) is a zero three times. Recognizing cube identities is useful.

Step 2

Why this answer is correct

The correct answer is A. (2) गुणनता (3) / (2) with multiplicity (3). This is (p(x)=(x-2)3), so (2) is a zero three times. Recognizing cube identities is useful.

Step 3

Exam Tip

यह (p(x)=(x-2)3) है, इसलिए (2) तीन बार शून्यक है। घन पूर्ण पहचान को पहचानना उपयोगी है।

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Question 2/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=11(x+5)2(x-14)) है, तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?

If (p(x)=11(x+5)2(x-14)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?

Explanation opens after your attempt
Correct Answer

A. दो बिंदु, (x=-5) पर स्पर्शTwo points, touching at (x=-5)

Step 1

Concept

The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो बिंदु, (x=-5) पर स्पर्श / Two points, touching at (x=-5). The zeroes are (-5) and (14), and ((x+5)2) causes touching at (-5). Tip: the outside (11) does not change the zeroes.

Step 3

Exam Tip

शून्यक (-5) और (14) हैं तथा ((x+5)2) के कारण (-5) पर स्पर्श है। टिप: बाहरी (11) शून्यक नहीं बदलता।

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Question 3/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x(x+6)4(x-3)5) है, तो (x=3) पर ग्राफ का व्यवहार क्या होगा?

If (p(x)=x(x+6)4(x-3)5), what will be the graph behavior at (x=3)?

Explanation opens after your attempt
Correct Answer

A. ग्राफ (x)-अक्ष को काटेगाThe graph will cross the (x)-axis

Step 1

Concept

((x-3)5) is an odd-power factor, so the graph crosses at (x=3). Tip: at an odd power the graph usually crosses the axis.

Step 2

Why this answer is correct

The correct answer is A. ग्राफ (x)-अक्ष को काटेगा / The graph will cross the (x)-axis. ((x-3)5) is an odd-power factor, so the graph crosses at (x=3). Tip: at an odd power the graph usually crosses the axis.

Step 3

Exam Tip

((x-3)5) विषम घात का कारक है, इसलिए (x=3) पर कटान होगा। टिप: विषम घात में ग्राफ सामान्यतः अक्ष पार करता है।

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Question 4/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-c)5(x+d)2), जहाँ \(c\neq -d\), तो अलग शून्यक कौन से हैं?

If (p(x)=(x-c)5(x+d)2), where \(c\neq -d\), what are the distinct zeroes?

Explanation opens after your attempt
Correct Answer

A. (c) और (-d)(c) and (-d)

Step 1

Concept

From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (c) और (-d) / (c) and (-d). From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.

Step 3

Exam Tip

(x-c=0) से (c) और (x+d=0) से (-d) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।

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Question 5/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-4)4(x+3)3) है, तो ग्राफ कहाँ स्पर्श करेगा और कहाँ काटेगा?

If (p(x)=(x-4)4(x+3)3), where will the graph touch and where will it cross?

Explanation opens after your attempt
Correct Answer

A. (x=4) पर स्पर्श और (x=-3) पर कटानTouches at (x=4) and crosses at (x=-3)

Step 1

Concept

An even-power zero gives touching and an odd-power zero gives crossing. Tip: identify graph behavior from the power of the factor.

Step 2

Why this answer is correct

The correct answer is A. (x=4) पर स्पर्श और (x=-3) पर कटान / Touches at (x=4) and crosses at (x=-3). An even-power zero gives touching and an odd-power zero gives crossing. Tip: identify graph behavior from the power of the factor.

Step 3

Exam Tip

सम घात वाला शून्यक स्पर्श और विषम घात वाला शून्यक कटान देता है। टिप: कारक की घात से ग्राफ का व्यवहार पहचानें।

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Question 6/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=9(x+4)2(x-12)) है, तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?

If (p(x)=9(x+4)2(x-12)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?

Explanation opens after your attempt
Correct Answer

A. दो बिंदु, (x=-4) पर स्पर्शTwo points, touching at (x=-4)

Step 1

Concept

The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो बिंदु, (x=-4) पर स्पर्श / Two points, touching at (x=-4). The zeroes are (-4) and (12), and ((x+4)2) causes touching at (-4). Tip: the outside (9) does not change the zeroes.

Step 3

Exam Tip

शून्यक (-4) और (12) हैं तथा ((x+4)2) के कारण (-4) पर स्पर्श है। टिप: बाहरी (9) शून्यक नहीं बदलता।

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Question 7/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x(x-7)4(x+2)3) है, तो (x=7) पर ग्राफ का व्यवहार क्या होगा?

If (p(x)=x(x-7)4(x+2)3), what will be the graph behavior at (x=7)?

Explanation opens after your attempt
Correct Answer

B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis

Step 1

Concept

((x-7)4) is an even-power factor, so the graph touches at (x=7). Tip: at an even power the graph usually turns back.

Step 2

Why this answer is correct

The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x-7)4) is an even-power factor, so the graph touches at (x=7). Tip: at an even power the graph usually turns back.

Step 3

Exam Tip

((x-7)4) सम घात का कारक है, इसलिए (x=7) पर स्पर्श होगा। टिप: सम घात में ग्राफ आमतौर पर लौटता है।

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Question 8/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x+a)3(x-b)2), जहाँ \(a\neq -b\), तो अलग शून्यक कौन से हैं?

If (p(x)=(x+a)3(x-b)2), where \(a\neq -b\), what are the distinct zeroes?

Explanation opens after your attempt
Correct Answer

A. (-a) और (b)(-a) and (b)

Step 1

Concept

From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.

Step 2

Why this answer is correct

The correct answer is A. (-a) और (b) / (-a) and (b). From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.

Step 3

Exam Tip

(x+a=0) से (-a) और (x-b=0) से (b) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।

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Question 9/17 Expert Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=(x+5)3(x-2)2) है, तो ग्राफ कहाँ काटेगा और कहाँ स्पर्श करेगा?

If (p(x)=(x+5)3(x-2)2), where will the graph cross and where will it touch?

Explanation opens after your attempt
Correct Answer

A. (x=-5) पर काटेगा और (x=2) पर स्पर्श करेगाIt crosses at (x=-5) and touches at (x=2)

Step 1

Concept

An odd-power zero gives crossing and an even-power zero gives touching. Tip: identify graph behavior from the power of the factor.

Step 2

Why this answer is correct

The correct answer is A. (x=-5) पर काटेगा और (x=2) पर स्पर्श करेगा / It crosses at (x=-5) and touches at (x=2). An odd-power zero gives crossing and an even-power zero gives touching. Tip: identify graph behavior from the power of the factor.

Step 3

Exam Tip

विषम घात वाला शून्यक कटान और सम घात वाला शून्यक स्पर्श देता है। टिप: कारक की घात से ग्राफ का व्यवहार पहचानें।

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Question 10/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=7(x+3)2(x-10)) है तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?

If (p(x)=7(x+3)2(x-10)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?

Explanation opens after your attempt
Correct Answer

A. दो बिंदु, (x=-3) पर स्पर्शTwo points, touching at (x=-3)

Step 1

Concept

The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो बिंदु, (x=-3) पर स्पर्श / Two points, touching at (x=-3). The zeroes are (-3) and (10), and ((x+3)2) causes touching at (-3). Tip: the outside (7) does not change the zeroes.

Step 3

Exam Tip

शून्यक (-3) और (10) हैं तथा ((x+3)2) के कारण (-3) पर स्पर्श है। टिप: बाहरी (7) शून्यक नहीं बदलता।

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Question 11/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=x(x+4)2(x-6)) है तो (x=-4) पर ग्राफ का व्यवहार क्या होगा?

If (p(x)=x(x+4)2(x-6)), what will be the graph behavior at (x=-4)?

Explanation opens after your attempt
Correct Answer

B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis

Step 1

Concept

((x+4)2) is an even-power factor, so the graph touches at (x=-4). Tip: power (2) shows a repeated zero.

Step 2

Why this answer is correct

The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x+4)2) is an even-power factor, so the graph touches at (x=-4). Tip: power (2) shows a repeated zero.

Step 3

Exam Tip

((x+4)2) सम घात का कारक है इसलिए (x=-4) पर स्पर्श होगा। टिप: घात (2) दोहराया शून्यक दिखाती है।

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Question 12/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

यदि (p(x)=(x+6)2(x-2)) है तो ग्राफ कहाँ स्पर्श करेगा और कहाँ काटेगा?

If (p(x)=(x+6)2(x-2)), where will the graph touch and where will it cross?

Explanation opens after your attempt
Correct Answer

B. (x=-6) पर स्पर्श और (x=2) पर कटानTouches at (x=-6) and crosses at (x=2)

Step 1

Concept

The even-power factor ((x+6)2) gives touching and the single factor (x-2) gives crossing. Tip: identify graph behavior from the power of the factor.

Step 2

Why this answer is correct

The correct answer is B. (x=-6) पर स्पर्श और (x=2) पर कटान / Touches at (x=-6) and crosses at (x=2). The even-power factor ((x+6)2) gives touching and the single factor (x-2) gives crossing. Tip: identify graph behavior from the power of the factor.

Step 3

Exam Tip

सम घात वाला कारक ((x+6)2) स्पर्श देता है और एकल कारक (x-2) कटान देता है। टिप: कारक की घात से ग्राफ का व्यवहार पहचानें।

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Question 13/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=5(x+2)2(x-7)) है, तो ग्राफ कितने अलग बिंदुओं पर (x)-अक्ष से मिलेगा और कौन सा बिंदु स्पर्श होगा?

If (p(x)=5(x+2)2(x-7)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?

Explanation opens after your attempt
Correct Answer

A. दो बिंदु, (x=-2) पर स्पर्शTwo points, touching at (x=-2)

Step 1

Concept

The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो बिंदु, (x=-2) पर स्पर्श / Two points, touching at (x=-2). The zeroes are (-2) and (7), and ((x+2)2) causes touching at (-2). Tip: the outside (5) does not change the zeroes.

Step 3

Exam Tip

शून्यक (-2) और (7) हैं, तथा ((x+2)2) के कारण (-2) पर स्पर्श है। टिप: बाहरी (5) शून्यक नहीं बदलता।

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Question 14/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=x(x-3)2(x+5)) है, तो (x=3) पर ग्राफ का व्यवहार क्या होगा?

If (p(x)=x(x-3)2(x+5)), what will be the graph behavior at (x=3)?

Explanation opens after your attempt
Correct Answer

B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis

Step 1

Concept

((x-3)2) is an even-power factor, so the graph touches at (x=3). Tip: power (2) shows a repeated zero.

Step 2

Why this answer is correct

The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x-3)2) is an even-power factor, so the graph touches at (x=3). Tip: power (2) shows a repeated zero.

Step 3

Exam Tip

((x-3)2) सम घात का कारक है, इसलिए (x=3) पर स्पर्श होगा। टिप: घात (2) दोहराया शून्यक दिखाती है।

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Question 15/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

यदि (p(x)=(x-3)2(x+4)) है, तो ग्राफ कहाँ स्पर्श करेगा और कहाँ काटेगा?

If (p(x)=(x-3)2(x+4)), where will the graph touch and where will it cross?

Explanation opens after your attempt
Correct Answer

A. (x=3) पर स्पर्श और (x=-4) पर कटानTouches at (x=3) and crosses at (x=-4)

Step 1

Concept

The even-power factor ((x-3)2) gives touching and the single factor (x+4) gives crossing. Tip: identify behavior from factor power.

Step 2

Why this answer is correct

The correct answer is A. (x=3) पर स्पर्श और (x=-4) पर कटान / Touches at (x=3) and crosses at (x=-4). The even-power factor ((x-3)2) gives touching and the single factor (x+4) gives crossing. Tip: identify behavior from factor power.

Step 3

Exam Tip

सम घात वाला कारक ((x-3)2) स्पर्श देता है और एकल कारक (x+4) कटान देता है। टिप: गुणनखंड की घात से व्यवहार पहचानें।

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Question 16/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=3(x-2)2(x+1)) है, तो ग्राफ (x)-अक्ष से कितने अलग बिंदुओं पर मिलेगा और कौन सा बिंदु स्पर्श होगा?

If (p(x)=3(x-2)2(x+1)), at how many distinct points will the graph meet the (x)-axis and which point will be a touching point?

Explanation opens after your attempt
Correct Answer

A. दो बिंदु, (x=2) पर स्पर्शTwo points, touching at (x=2)

Step 1

Concept

The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.

Step 2

Why this answer is correct

The correct answer is A. दो बिंदु, (x=2) पर स्पर्श / Two points, touching at (x=2). The zeroes are (2) and (-1), and ((x-2)2) causes touching at (x=2). Tip: the outside (3) does not change the zeroes.

Step 3

Exam Tip

शून्यक (2) और (-1) हैं, तथा ((x-2)2) के कारण (x=2) पर स्पर्श है। टिप: बाहरी (3) शून्यक नहीं बदलता।

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Question 17/17 Hard Mathematics Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x(x-2)2(x+3)) है, तो (x=2) पर ग्राफ का व्यवहार क्या होगा?

If (p(x)=x(x-2)2(x+3)), what will be the graph behavior at (x=2)?

Explanation opens after your attempt
Correct Answer

B. ग्राफ (x)-अक्ष को स्पर्श करेगाThe graph will touch the (x)-axis

Step 1

Concept

((x-2)2) is an even-power factor, so the graph touches at (x=2). Tip: power (2) shows a repeated zero.

Step 2

Why this answer is correct

The correct answer is B. ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis. ((x-2)2) is an even-power factor, so the graph touches at (x=2). Tip: power (2) shows a repeated zero.

Step 3

Exam Tip

((x-2)2) सम घात का कारक है, इसलिए (x=2) पर स्पर्श होगा। टिप: घात (2) दोहराया शून्यक दिखाती है।

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