Question 1/16
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ का एक भाग (x)-अक्ष के ऊपर और दूसरा भाग नीचे है तथा बीच में ((9,0)) है तो ((9,0)) क्या दर्शाता है?
If one part of a graph is above the (x)-axis and another part is below it with ((9,0)) between them, what does ((9,0)) represent?
#sign-change
#crossing
#zero
A (x=9) शून्यक है / (x=9) is a zero
B (y=9) शून्यक है / (y=9) is a zero
C बहुपद स्थिर है / The polynomial is constant
D शून्यक नहीं है / It is not a zero
Explanation opens after your attempt
Correct Answer
A. (x=9) शून्यक है / (x=9) is a zero
Step 1
Concept
((9,0)) lies on the (x)-axis so (p(9)=0). Moving from above to below also shows crossing.
Step 2
Why this answer is correct
The correct answer is A. (x=9) शून्यक है / (x=9) is a zero. ((9,0)) lies on the (x)-axis so (p(9)=0). Moving from above to below also shows crossing.
Step 3
Exam Tip
((9,0)) (x)-अक्ष पर है इसलिए (p(9)=0) है। ऊपर से नीचे जाना कटान को भी दिखाता है।
Login to save your score, XP, coins and progress.
Question 2/16
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((11,0)) पर छूता है और ((-6,0)) पर काटता है, तो शून्यकों का गुणनफल क्या है?
If a graph touches the (x)-axis at ((11,0)) and crosses it at ((-6,0)), what is the product of the zeroes?
#product of zeroes
#touching
#crossing
A (-66)
B (66)
C (5)
D (-17)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (11) and (-6), so the product is (-66). Tip: a touching point is also a zero.
Step 2
Why this answer is correct
The correct answer is A. (-66). The zeroes are (11) and (-6), so the product is (-66). Tip: a touching point is also a zero.
Step 3
Exam Tip
शून्यक (11) और (-6) हैं, इसलिए गुणनफल (-66) है। टिप: स्पर्श बिंदु भी शून्यक होता है।
Login to save your score, XP, coins and progress.
Question 3/16
Expert Mathematics
Chapter 2: 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)?
#multiplicity
#crossing
#zero
A ग्राफ (x)-अक्ष को काटेगा / The graph will cross the (x)-axis
B ग्राफ (x)-अक्ष को स्पर्श करेगा / The graph will touch the (x)-axis
C ग्राफ (x)-अक्ष से नहीं मिलेगा / The graph will not meet the (x)-axis
D (x=3) शून्यक नहीं है / (x=3) is not a zero
Explanation opens after your attempt
Correct Answer
A. ग्राफ (x)-अक्ष को काटेगा / The 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।
Login to save your score, XP, coins and progress.
Question 4/16
Expert Mathematics
Chapter 2: 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?
#multiplicity
#touching
#crossing
A (x=4) पर स्पर्श और (x=-3) पर कटान / Touches at (x=4) and crosses at (x=-3)
B (x=4) पर कटान और (x=-3) पर स्पर्श / Crosses at (x=4) and touches at (x=-3)
C दोनों पर कटान / Crosses at both
D दोनों पर स्पर्श / Touches at both
Explanation opens after your attempt
Correct Answer
A. (x=4) पर स्पर्श और (x=-3) पर कटान / Touches 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।
Login to save your score, XP, coins and progress.
Question 5/16
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((9,0)) पर छूता है और ((-5,0)) पर काटता है, तो शून्यकों का गुणनफल क्या है?
If a graph touches the (x)-axis at ((9,0)) and crosses it at ((-5,0)), what is the product of the zeroes?
#product of zeroes
#touching
#crossing
A (-45)
B (45)
C (4)
D (-14)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (9) and (-5), so the product is (-45). Tip: a touching point is also a zero.
Step 2
Why this answer is correct
The correct answer is A. (-45). The zeroes are (9) and (-5), so the product is (-45). Tip: a touching point is also a zero.
Step 3
Exam Tip
शून्यक (9) और (-5) हैं, इसलिए गुणनफल (-45) है। टिप: स्पर्श बिंदु भी शून्यक होता है।
Login to save your score, XP, coins and progress.
Question 6/16
Expert Mathematics
Chapter 2: 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?
#multiplicity
#crossing
#touching
A (x=-5) पर काटेगा और (x=2) पर स्पर्श करेगा / It crosses at (x=-5) and touches at (x=2)
B (x=-5) पर स्पर्श करेगा और (x=2) पर काटेगा / It touches at (x=-5) and crosses at (x=2)
C दोनों पर काटेगा / It crosses at both
D दोनों पर स्पर्श करेगा / It touches at both
Explanation opens after your attempt
Correct Answer
A. (x=-5) पर काटेगा और (x=2) पर स्पर्श करेगा / It 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।
Login to save your score, XP, coins and progress.
Question 7/16
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि ग्राफ (x)-अक्ष को ((7,0)) पर छूता है और ((-4,0)) पर काटता है तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((7,0)) and crosses it at ((-4,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (3)
B (11)
C (-11)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (3). The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (7) और (-4) हैं इसलिए योग (3) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
Login to save your score, XP, coins and progress.
Question 8/16
Hard Mathematics
Chapter 2: 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?
#multiplicity
#touching
#crossing
A (x=6) पर स्पर्श और (x=-2) पर कटान / Touches at (x=6) and crosses at (x=-2)
B (x=-6) पर स्पर्श और (x=2) पर कटान / Touches at (x=-6) and crosses at (x=2)
C दोनों पर कटान / Crosses at both
D दोनों पर स्पर्श / Touches at both
Explanation opens after your attempt
Correct Answer
B. (x=-6) पर स्पर्श और (x=2) पर कटान / Touches 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।
Login to save your score, XP, coins and progress.
Question 9/16
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((5,0)) पर छूता है और ((-3,0)) पर काटता है, तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((5,0)) and crosses it at ((-3,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (2)
B (8)
C (-8)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (2). The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (5) और (-3) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
Login to save your score, XP, coins and progress.
Question 10/16
Hard Mathematics
Chapter 2: 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?
#multiplicity
#touching
#crossing
A (x=3) पर स्पर्श और (x=-4) पर कटान / Touches at (x=3) and crosses at (x=-4)
B (x=-3) पर स्पर्श और (x=4) पर कटान / Touches at (x=-3) and crosses at (x=4)
C दोनों पर स्पर्श / Touches at both
D दोनों पर कटान / Crosses at both
Explanation opens after your attempt
Correct Answer
A. (x=3) पर स्पर्श और (x=-4) पर कटान / Touches 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।
Login to save your score, XP, coins and progress.
Question 11/16
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी ग्राफ का (x)-अक्ष से एक स्पर्श ((4,0)) पर है और एक कटान ((-2,0)) पर है, तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((4,0)) and crosses it at ((-2,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (2)
B (6)
C (-6)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (2). The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (4) और (-2) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
Login to save your score, XP, coins and progress.
Question 12/16
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद का ग्राफ (x=-3) पर (x)-अक्ष को काटता है और (x=2) पर केवल छूता है, तो कौन सा कथन सही है?
If a polynomial graph crosses the (x)-axis at (x=-3) and only touches it at (x=2), which statement is correct?
#crossing
#touching
#concept
A दोनों वास्तविक शून्यक हैं / Both are real zeroes
B केवल (-3) शून्यक है / Only (-3) is a zero
C केवल (2) शून्यक है / Only (2) is a zero
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
A. दोनों वास्तविक शून्यक हैं / Both are real zeroes
Step 1
Concept
In both crossing and touching, (p(x)=0). Tip: crossing is not necessary for a zero.
Step 2
Why this answer is correct
The correct answer is A. दोनों वास्तविक शून्यक हैं / Both are real zeroes. In both crossing and touching, (p(x)=0). Tip: crossing is not necessary for a zero.
Step 3
Exam Tip
कटान और स्पर्श दोनों स्थितियों में (p(x)=0) होता है। टिप: शून्यक के लिए पार करना जरूरी नहीं है।
Login to save your score, XP, coins and progress.
Question 13/16
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ पर (x=-2) पर कटान, (x=1) पर स्पर्श और (x=5) पर कटान है, तो अलग वास्तविक शून्यक कितने हैं?
If a polynomial graph crosses at (x=-2), touches at (x=1), and crosses at (x=5), how many distinct real zeroes are there?
#touching
#crossing
#distinct zeroes
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The graph meets the (x)-axis at three distinct (x)-values. Tip: both touching and crossing give zeroes.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The graph meets the (x)-axis at three distinct (x)-values. Tip: both touching and crossing give zeroes.
Step 3
Exam Tip
तीनों अलग (x)-मानों पर ग्राफ (x)-अक्ष से मिलता है। टिप: स्पर्श और कटान दोनों शून्यक देते हैं।
Login to save your score, XP, coins and progress.
Question 14/16
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद के ग्राफ में (x=4) पर (x)-अक्ष से स्पर्श है और (x=-6) पर कटान है। कौन सा कथन सही है?
In a polynomial graph, there is a touch with the (x)-axis at (x=4) and a crossing at (x=-6). Which statement is correct?
#touching
#crossing
#zeroes
A केवल (4) शून्यक है / Only (4) is a zero
B केवल (-6) शून्यक है / Only (-6) is a zero
C (4) और (-6) दोनों शून्यक हैं / Both (4) and (-6) are zeroes
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
C. (4) और (-6) दोनों शून्यक हैं / Both (4) and (-6) are zeroes
Step 1
Concept
In both touching and crossing, the graph meets the (x)-axis. Tip: for a zero, meeting the axis is enough, crossing is not necessary.
Step 2
Why this answer is correct
The correct answer is C. (4) और (-6) दोनों शून्यक हैं / Both (4) and (-6) are zeroes. In both touching and crossing, the graph meets the (x)-axis. Tip: for a zero, meeting the axis is enough, crossing is not necessary.
Step 3
Exam Tip
स्पर्श और कटान दोनों स्थितियों में ग्राफ (x)-अक्ष से मिलता है। टिप: शून्यक पहचानते समय मिलना देखें, पार करना जरूरी नहीं।
Login to save your score, XP, coins and progress.
Question 15/16
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)) का ग्राफ (x)-अक्ष को ((2,0)) पर काटता है और ((-1,0)) पर स्पर्श करता है, तो अलग वास्तविक शून्यक कितने हैं?
If the graph of (p(x)) cuts the (x)-axis at ((2,0)) and touches it at ((-1,0)), how many distinct real zeroes are there?
#distinct zeroes
#touching
#crossing
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Both cutting and touching give zeroes (2) and (-1). Tip: count distinct (x)-values.
Step 3
Exam Tip
कटान और स्पर्श दोनों से (x)-मान (2) और (-1) शून्यक हैं। टिप: अलग (x)-मानों की गिनती करें।
Login to save your score, XP, coins and progress.
Question 16/16
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x=-2) पर (x)-अक्ष को पार करता है और (x=3) पर केवल छूता है, तो अलग वास्तविक शून्यक कौन से हैं?
If a graph crosses the (x)-axis at (x=-2) and only touches it at (x=3), what are the distinct real zeroes?
#crossing
#touching
#distinct zeroes
A केवल (-2) / Only (-2)
B केवल (3) / Only (3)
C (-2) और (3) / (-2) and (3)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
C. (-2) और (3) / (-2) and (3)
Step 1
Concept
Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.
Step 2
Why this answer is correct
The correct answer is C. (-2) और (3) / (-2) and (3). Both crossing and touching give (p(x)=0). Tip: write both (x)-values as distinct zeroes.
Step 3
Exam Tip
पार करना और छूना दोनों (p(x)=0) देते हैं। टिप: अलग शून्यक में दोनों (x)-मान लिखें।
Login to save your score, XP, coins and progress.
