100 results found for "function zero count" in Class 10.
कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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माया सभ्यता में लंबी गणना कैलेंडर का उपयोग किसलिए किया जाता था?
What was the Maya Long Count calendar used for?
#world history
#ancient civilizations
#maya
#long count
A लोहे की तलवार बनाने के लिए / To make iron swords
B लंबे ऐतिहासिक समय को दर्ज करने के लिए / To record long historical time
C नदी बांधने के लिए / To dam rivers
D ममी बनाने के लिए / To make mummies
Explanation opens after your attempt
Correct Answer
B. लंबे ऐतिहासिक समय को दर्ज करने के लिए / To record long historical time
Step 1
Concept
The Long Count system helped record long dates and royal events. For exams treat Maya chronology as advanced.
Step 2
Why this answer is correct
The correct answer is B. लंबे ऐतिहासिक समय को दर्ज करने के लिए / To record long historical time. The Long Count system helped record long dates and royal events. For exams treat Maya chronology as advanced.
Step 3
Exam Tip
लंबी गणना प्रणाली लंबी तिथियों और राजकीय घटनाओं को दर्ज करने में सहायक थी। परीक्षा में माया कालगणना को उन्नत मानें।
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माया लांग काउंट कैलेंडर किस प्रकार की बौद्धिक क्षमता का प्रमाण है?
The Maya Long Count calendar is evidence of what intellectual ability?
#world-history
#ancient-civilizations
#maya-long-count
A लंबी अवधि की तिथि गणना और खगोलीय समझ / Long-term date reckoning and astronomical understanding
B रोमन कर संहिता / Roman tax code
C मिस्री राजसूची / Egyptian king list
D फारसी सड़क निर्माण / Persian road construction
Explanation opens after your attempt
Correct Answer
A. लंबी अवधि की तिथि गणना और खगोलीय समझ / Long-term date reckoning and astronomical understanding
Step 1
Concept
The Long Count calendar is famous for long-term date reckoning. Link it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबी अवधि की तिथि गणना और खगोलीय समझ / Long-term date reckoning and astronomical understanding. The Long Count calendar is famous for long-term date reckoning. Link it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना के लिए प्रसिद्ध है। परीक्षा में इसे माया गणित और खगोल से जोड़ें।
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माया लांग काउंट कैलेंडर किस बौद्धिक उपलब्धि का प्रमाण है?
The Maya Long Count calendar is evidence of which intellectual achievement?
#world history
#ancient civilizations
#maya long count
A लंबी अवधि की तिथि गणना / Long-term date reckoning
B रोमन लिखित कानून / Roman written law
C मिस्री ममीकरण / Egyptian mummification
D फारसी सात्रापी / Persian satrapy
Explanation opens after your attempt
Correct Answer
A. लंबी अवधि की तिथि गणना / Long-term date reckoning
Step 1
Concept
The Long Count calendar was useful for long date reckoning. Link it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबी अवधि की तिथि गणना / Long-term date reckoning. The Long Count calendar was useful for long date reckoning. Link it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना में उपयोगी था। परीक्षा में इसे माया गणित और खगोल ज्ञान से जोड़ें।
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माया लांग काउंट कैलेंडर का मुख्य उपयोग क्या था?
What was the main use of the Maya Long Count calendar?
#world history
#ancient civilizations
#maya long count
A लंबे समय की तिथि गणना / Long term date reckoning
B ममी संरक्षण / Mummy preservation
C रोमन चुनाव कराना / Holding Roman elections
D सिंधु ईंट बनाना / Making Indus bricks
Explanation opens after your attempt
Correct Answer
A. लंबे समय की तिथि गणना / Long term date reckoning
Step 1
Concept
The Long Count calendar was useful for recording long periods of dates. Link it with Maya astronomy and calculation.
Step 2
Why this answer is correct
The correct answer is A. लंबे समय की तिथि गणना / Long term date reckoning. The Long Count calendar was useful for recording long periods of dates. Link it with Maya astronomy and calculation.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी अवधि की तिथियों को दर्ज करने के लिए उपयोगी था। परीक्षा में इसे माया खगोल और गणना से जोड़ें।
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माया लांग काउंट कैलेंडर किस उद्देश्य के लिए उपयोगी था?
The Maya Long Count calendar was useful for what purpose?
#world history
#ancient civilizations
#maya long count
A लंबे समय की तिथियों को दर्ज करने के लिए / Recording long periods of dates
B रोमन सैनिक भर्ती / Roman military recruitment
C मिस्री पिरामिड काटने / Cutting Egyptian pyramids
D चीनी रेशम रंगने / Dyeing Chinese silk
Explanation opens after your attempt
Correct Answer
A. लंबे समय की तिथियों को दर्ज करने के लिए / Recording long periods of dates
Step 1
Concept
The Long Count calendar was useful for long date reckoning. Connect it with Maya mathematics and astronomy.
Step 2
Why this answer is correct
The correct answer is A. लंबे समय की तिथियों को दर्ज करने के लिए / Recording long periods of dates. The Long Count calendar was useful for long date reckoning. Connect it with Maya mathematics and astronomy.
Step 3
Exam Tip
लांग काउंट कैलेंडर लंबी तिथि गणना के लिए उपयोगी था। परीक्षा में इसे माया गणना और खगोल ज्ञान से जोड़ें।
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यदि (p(x)=2x-2 +mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=2x-2 +mx+18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A (3)
B -(3)
C (6)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 3
Exam Tip
गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।
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यदि (p(x)=x-2 +3x-18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 +3x-18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A -(6)
B (6)
C -(3)
D (9)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 3
Exam Tip
शून्यकों का गुणनफल (-18) है। एक शून्यक (3) है, इसलिए दूसरा \(-18\div3=-6\) है।
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यदि (p(x)=x-2 -10x+r) का एक शून्यक (4) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -10x+r) is (4), what is the other zero?
#one-zero-given
#sum-zeroes
#quadratic
A (6)
B (4)
C (10)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 3
Exam Tip
शून्यकों का योग (10) है। एक शून्यक (4) है, इसलिए दूसरा (10-4=6) है।
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यदि (p(x)=x-2 -2x-2) का एक शून्यक \(1+\sqrt{3}\) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -2x-2) is \(1+\sqrt{3}\), what is the other zero?
#other-zero
#sum-of-zeroes
#conjugate
A \(1-\sqrt{3}\)
B \(-1+\sqrt{3}\)
C \(1+\sqrt{3}\)
D \(-1-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(1-\sqrt{3}\)
Step 1
Concept
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
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यदि (p(x)=x-2 -13x+k) का एक शून्यक (6) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -13x+k) has one zero (6), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
B दूसरा (-7), कटान ((6,0)), ((-7,0)) / Other (-7), intersections ((6,0)), ((-7,0))
C दूसरा (13), कटान ((6,0)), ((13,0)) / Other (13), intersections ((6,0)), ((13,0))
D दूसरा (0), कटान ((6,0)), ((0,0)) / Other (0), intersections ((6,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=5) है और एक शून्यक (-1) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=5) and one zero is (-1), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (11)
B (9)
C (6)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (11). The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (5) है इसलिए दूसरा शून्यक (11) होगा। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -11x+k) का एक शून्यक (4) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -11x+k) has one zero (4), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
B दूसरा (-7), कटान ((4,0)), ((-7,0)) / Other (-7), intersections ((4,0)), ((-7,0))
C दूसरा (11), कटान ((4,0)), ((11,0)) / Other (11), intersections ((4,0)), ((11,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=-2) है और एक शून्यक (5) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=-2) and one zero is (5), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (-9)
B (-7)
C (9)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-9). The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (-2) है, इसलिए दूसरा शून्यक (-9) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य से जोड़ें।
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यदि (p(x)=x-2 -9x+k) का एक शून्यक (4) है तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -9x+k) has one zero (4), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
B दूसरा (-5), कटान ((4,0)), ((-5,0)) / Other (-5), intersections ((4,0)), ((-5,0))
C दूसरा (9), कटान ((4,0)), ((9,0)) / Other (9), intersections ((4,0)), ((9,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (11) है और सममिति अक्ष (x=3) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (11) and axis of symmetry (x=3). What will be the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-8)
D (8)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (3) है इसलिए दूसरा शून्यक (-5) होगा। टिप: \(\frac{a+b}{2}\) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=4) है और एक शून्यक (-2) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=4) and one zero is (-2). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (10)
B (6)
C (8)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (10). The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दोनों शून्यकों का औसत (4) है इसलिए दूसरा शून्यक (10) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य मान से जोड़ें।
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यदि (p(x)=x-2 -7x+k) का एक शून्यक (3) है, तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -7x+k) has one zero (3), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
B दूसरा (-4), कटान ((3,0)), ((-4,0)) / Other (-4), intersections ((3,0)), ((-4,0))
C दूसरा (7), कटान ((3,0)), ((7,0)) / Other (7), intersections ((3,0)), ((7,0))
D दूसरा (0), कटान ((3,0)), ((0,0)) / Other (0), intersections ((3,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (9) है और सममिति अक्ष (x=2) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (9) and axis of symmetry (x=2). What is the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (2) है, इसलिए दूसरा शून्यक (-5) होगा। टिप: \( \frac{a+b}{2} \) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=1) है और एक शून्यक (-5) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=1) and one zero is (-5). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (5)
B (6)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is C. (7). The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (1) होगा इसलिए दूसरा शून्यक (7) है। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -5x+k) का एक शून्यक (2) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होगा?
If (p(x)=x-2 -5x+k) has one zero (2), what will be the other zero and the (x)-axis intersections?
#quadratic
#missing zero
#intercepts
A दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
B दूसरा (-3), कटान ((2,0)), ((-3,0)) / Other (-3), intersections ((2,0)), ((-3,0))
C दूसरा (5), कटान ((2,0)), ((5,0)) / Other (5), intersections ((2,0)), ((5,0))
D दूसरा (0), कटान ((2,0)), ((0,0)) / Other (0), intersections ((2,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (4) है और सममिति अक्ष (x=-1) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (4) and axis of symmetry (x=-1). What will be the other zero?
#axis of symmetry
#missing zero
#parabola
A (-6)
B (-4)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-6). The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (-1) है, इसलिए दूसरा शून्यक (-6) होगा। टिप: औसत को सममिति अक्ष के बराबर रखें।
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यदि (p(-3)=0), तो बहुपद का कौन-सा शून्यक है?
If (p(-3)=0), which value is a zero of the polynomial?
#zero-definition
#function-value
#negative-zero
#easy
A (-3)
B (3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (-3). The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 3
Exam Tip
जिस (x)-मान पर (p(x)=0) हो वही शून्यक होता है। इसलिए (-3) बहुपद का शून्यक है।
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कौन सा बहुपद (x=0) को शून्य बनाता है?
Which polynomial makes (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^2+5\)
B \(3x^3-2x\)
C \(x^4+1\)
D \(2x^2-7x+9\)
Explanation opens after your attempt
Correct Answer
B. \(3x^3-2x\)
Step 1
Concept
Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^3-2x\). Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 3
Exam Tip
(x=0) रखने पर \(3x^3-2x=0\) मिलता है। (x=0) को शून्य बनाने के लिए अचर पद (0) होना चाहिए।
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यदि \(x^2+mx+n\) का एक शून्यक (0) है और दूसरा शून्यक (5) है, तो (m+n) क्या होगा?
If one zero of \(x^2+mx+n\) is (0) and the other zero is (5), what is (m+n)?
#polynomials
#zeroes
#constant_term
#hard
A (-5)
B (5)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 3
Exam Tip
योग (5) है इसलिए (m=-5), और गुणनफल (0) है इसलिए (n=0)। अतः (m+n=-5)।
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कौन सा बहुपद (x=0) को शून्य नहीं बनाता?
Which polynomial does not make (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^3-2x\)
B \(5x^2+x\)
C \(x^4\)
D \(x^2+1\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+1\)
Step 1
Concept
On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 2
Why this answer is correct
The correct answer is D. \(x^2+1\). On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 3
Exam Tip
(x=0) रखने पर \(x^2+1=1\), इसलिए (0) इसका शून्य नहीं है। (x=0) पर अचर पद निर्णायक होता है।
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यदि किसी बहुपद का एक शून्यक \(\sqrt{11}\) है और गुणांक परिमेय हैं, तो कौन सा शून्यक भी होना चाहिए?
If one zero of a polynomial is \(\sqrt{11}\) and the coefficients are rational, which zero should also occur?
#conjugate-zeroes
#polynomials
#irrational-roots
A -\(\sqrt{11}\)
B (11)
C \(\frac{1}{\sqrt{11}}\)
D \(1+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. -\(\sqrt{11}\)
Step 1
Concept
The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 2
Why this answer is correct
The correct answer is A. -\(\sqrt{11}\). The conjugate of \(\sqrt{11}=0+\sqrt{11}\) is \(-\sqrt{11}\). In exams also identify the case (a=0).
Step 3
Exam Tip
\(\sqrt{11}=0+\sqrt{11}\) का संयुग्मी \(-\sqrt{11}\) है। परीक्षा में (a=0) वाला संयुग्मी भी पहचानें।
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यदि \(2+\sqrt{3}\) एक बहुपद \(x^2-4x+1\) का शून्यक है, तो दूसरा शून्यक क्या होगा?
If \(2+\sqrt{3}\) is a zero of the polynomial \(x^2-4x+1\), what is the other zero?
#conjugate roots
#polynomials
#irrational zeroes
A \(2-\sqrt{3}\)
B \(-2+\sqrt{3}\)
C \(-2-\sqrt{3}\)
D \(\sqrt{3}-4\)
Explanation opens after your attempt
Correct Answer
A. \(2-\sqrt{3}\)
Step 1
Concept
For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2-\sqrt{3}\). For a quadratic with rational coefficients, if \(a+\sqrt{b}\) is a zero then \(a-\sqrt{b}\) is also a zero. The conjugate-root rule is useful in exams.
Step 3
Exam Tip
परिमेय गुणांकों वाले द्विघात में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी मूल का नियम उपयोगी है।
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यदि (p(x)=x-2 -2kx+5) का एक शून्यक \(\sqrt{5}\) है, तो दूसरा शून्यक और (k) क्या होंगे?
If one zero of (p(x)=x-2 -2kx+5) is \(\sqrt{5}\), what will be the other zero and (k)?
#parameter
#product-of-zeroes
#irrational
A दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\)
B दूसरा \(-\sqrt{5}\), (k=0) / Other \(-\sqrt{5}\), (k=0)
C दूसरा (5), \(k=\frac{5+\sqrt{5}}{2}\) / Other (5), \(k=\frac{5+\sqrt{5}}{2}\)
D दूसरा (1), \(k=\frac{1+\sqrt{5}}{2}\) / Other (1), \(k=\frac{1+\sqrt{5}}{2}\)
Explanation opens after your attempt
Correct Answer
A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\)
Step 1
Concept
The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. दूसरा \(\sqrt{5}\), \(k=\sqrt{5}\) / Other \(\sqrt{5}\), \(k=\sqrt{5}\). The product is (5), so the other zero is \(\frac{5}{\sqrt{5}}=\sqrt{5}\). The sum is \(2\sqrt{5}=2k\), hence \(k=\sqrt{5}\).
Step 3
Exam Tip
गुणनफल (5) है, इसलिए दूसरा शून्यक \(\frac{5}{\sqrt{5}}=\sqrt{5}\) होगा। योग \(2\sqrt{5}=2k\), अतः \(k=\sqrt{5}\) है।
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किसी परवलय का एक शून्यक (-10) है और दूसरा शून्यक पहले से (18) अधिक है। सममिति अक्ष क्या होगा?
One zero of a parabola is (-10), and the other zero is (18) more than the first. What is the axis of symmetry?
#axis symmetry
#word problem
#zeroes
A (x=-1)
B (x=1)
C (x=8)
D (x=-8)
Explanation opens after your attempt
Step 1
Concept
The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-1). The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (8) है और औसत \(\frac{-10+8}{2}=-1\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
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किसी परवलय का एक शून्यक (-8) है और दूसरा शून्यक पहले से (12) अधिक है। सममिति अक्ष क्या होगा?
One zero of a parabola is (-8), and the other zero is (12) more than the first. What is the axis of symmetry?
#axis symmetry
#word problem
#zeroes
A (x=-2)
B (x=2)
C (x=4)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-2). The other zero is (4), and the average is \(\frac{-8+4}{2}=-2\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (4) है और औसत \(\frac{-8+4}{2}=-2\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
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किसी परवलय का सममिति अक्ष (x=2) है और एक शून्यक (-3) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=2) and one zero is (-3). What will be the other zero?
#parabola
#axis of symmetry
#zeroes
A (7)
B (5)
C (3)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (7). The average of the two zeroes is (2), so the other zero is (7). Tip: in a parabola the axis of symmetry passes through the midpoint of the zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (2) होगा, इसलिए दूसरा शून्यक (7) है। टिप: परवलय में सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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किसी बहुपद के ग्राफ पर शून्यक पहचानने के लिए कौन-सा मान शून्य होना चाहिए?
Which value must be zero to identify a zero on the graph of a polynomial?
#polynomials
#zeroes
#graph
#value-test
A बहुपद का मान / Value of the polynomial
B चर का गुणांक / Coefficient of the variable
C घात का मान / Value of the degree
D स्थिर पद / Constant term
Explanation opens after your attempt
Correct Answer
A. बहुपद का मान / Value of the polynomial
Step 1
Concept
At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 2
Why this answer is correct
The correct answer is A. बहुपद का मान / Value of the polynomial. At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। ग्राफ पढ़ते समय (y=0) वाले बिंदु देखें।
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यदि किसी ग्राफ के लिए (p(-3)<0), (p(1)=0), और (p(4)>0) है तो निश्चित शून्यक कौन सा है?
If for a graph (p(-3)<0), (p(1)=0), and (p(4)>0), which zero is certain?
#function-values
#zero-identification
#reasoning
A (1)
B (-3)
C (4)
D (-3) और (4) / (-3) and (4)
Explanation opens after your attempt
Step 1
Concept
Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is A. (1). Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 3
Exam Tip
केवल (p(1)=0) सीधे शून्यक बताता है। धनात्मक या ऋणात्मक मान शून्यक नहीं होते।
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किस स्थिति में (x=3) बहुपद (p(x)) का शून्यक कहलाएगा?
In which situation will (x=3) be called a zero of polynomial (p(x))?
#definition
#zero
#function-value
A जब (p(3)=0) / When (p(3)=0)
B जब (p(0)=3) / When (p(0)=3)
C जब ग्राफ ((0,3)) से गुजरे / When the graph passes through ((0,3))
D जब (p(3)=3) / When (p(3)=3)
Explanation opens after your attempt
Correct Answer
A. जब (p(3)=0) / When (p(3)=0)
Step 1
Concept
A zero is the (x)-value at which the polynomial value is zero. In exams check (p(a)=0).
Step 2
Why this answer is correct
The correct answer is A. जब (p(3)=0) / When (p(3)=0). A zero is the (x)-value at which the polynomial value is zero. In exams check (p(a)=0).
Step 3
Exam Tip
शून्यक वही (x)-मान है जिस पर बहुपद का मान शून्य हो। परीक्षा में (p(a)=0) जांचें।
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यदि (p(-1)<0), (p(0)<0) और (p(2)=0), तो दिए गए मानों में कौन सा शून्यक निश्चित है?
If (p(-1)<0), (p(0)<0) and (p(2)=0), which zero is definite among the given values?
#definite zero
#function value
#graph
A (-1)
B (0)
C (2)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Only (p(2)=0) directly shows a zero. Tip: positive or negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is C. (2). Only (p(2)=0) directly shows a zero. Tip: positive or negative values are not zeroes.
Step 3
Exam Tip
केवल (p(2)=0) सीधे शून्यक बताता है। टिप: धनात्मक या ऋणात्मक मान शून्यक नहीं होते।
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विश्व बैंक और आई एम एफ को संयुक्त राष्ट्र के छह प्रमुख अंगों में गिनना क्यों गलत है?
Why is it wrong to count the World Bank and IMF among the six principal organs of the UN?
#world bank
#imf
#principal organs
A वे संबद्ध आर्थिक संस्थाएं हैं मुख्य चार्टर अंग नहीं / They are affiliated economic institutions not principal Charter organs
B वे सुरक्षा परिषद के न्यायाधीश हैं / They are judges of the Security Council
C वे महासभा की भाषाएं हैं / They are languages of the General Assembly
D वे यूनेस्को की शांति सेना हैं / They are UNESCO peace forces
Explanation opens after your attempt
Correct Answer
A. वे संबद्ध आर्थिक संस्थाएं हैं मुख्य चार्टर अंग नहीं / They are affiliated economic institutions not principal Charter organs
Step 1
Concept
The World Bank and IMF are economic institutions linked with the UN system but not principal organs. Exam tip: remember institution types.
Step 2
Why this answer is correct
The correct answer is A. वे संबद्ध आर्थिक संस्थाएं हैं मुख्य चार्टर अंग नहीं / They are affiliated economic institutions not principal Charter organs. The World Bank and IMF are economic institutions linked with the UN system but not principal organs. Exam tip: remember institution types.
Step 3
Exam Tip
विश्व बैंक और आई एम एफ संयुक्त राष्ट्र प्रणाली से जुड़े आर्थिक संस्थान हैं पर छह प्रमुख अंग नहीं हैं। परीक्षा में संस्था प्रकार याद रखें।
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एक परीक्षा में (x) विद्यार्थी हैं और प्रत्येक को (x-18) प्रश्न दिए गए। कुल प्रश्न गिनती (1600) है। विद्यार्थियों की संख्या क्या है?
In an exam, there are (x) students and each is given (x-18) questions. The total question count is (1600). What is the number of students?
#quadratic equations
#exam arrangement
#application
A (40)
B (48)
C (50)
D (64)
Explanation opens after your attempt
Step 1
Concept
The total count is (x(x-18)=1600). This gives (x=50).
Step 2
Why this answer is correct
The correct answer is C. (50). The total count is (x(x-18)=1600). This gives (x=50).
Step 3
Exam Tip
कुल गिनती (x(x-18)=1600) है। इससे (x=50) मिलता है।
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एक परीक्षा में (x) विद्यार्थी हैं और प्रत्येक को (x-11) प्रश्न दिए गए। कुल प्रश्न गिनती (1050) है। विद्यार्थियों की संख्या क्या है?
In an exam, there are (x) students and each is given (x-11) questions. The total question count is (1050). What is the number of students?
#quadratic equations
#exam arrangement
#application
A (30)
B (35)
C (39)
D (42)
Explanation opens after your attempt
Step 1
Concept
The total count is (x(x-11)=1050). This gives (x=42).
Step 2
Why this answer is correct
The correct answer is D. (42). The total count is (x(x-11)=1050). This gives (x=42).
Step 3
Exam Tip
कुल गिनती (x(x-11)=1050) है। इससे (x=42) मिलता है।
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एक परीक्षा में (x) विद्यार्थी हैं और प्रत्येक को (x-7) प्रश्न दिए गए। कुल प्रश्न गिनती (725) है। विद्यार्थियों की संख्या क्या है?
In an exam, there are (x) students and each is given (x-7) questions. The total question count is (725). What is the number of students?
#quadratic equations
#exam arrangement
#application
A (25)
B (29)
C (32)
D (36)
Explanation opens after your attempt
Step 1
Concept
The total count is (x(x-7)=725). This gives (x=29).
Step 2
Why this answer is correct
The correct answer is B. (29). The total count is (x(x-7)=725). This gives (x=29).
Step 3
Exam Tip
कुल गिनती (x(x-7)=725) है। इससे (x=29) मिलता है।
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एक परीक्षा में (x) विद्यार्थी हैं और प्रत्येक को (x-5) प्रश्न दिए गए। कुल प्रश्न गिनती (414) है। विद्यार्थियों की संख्या क्या है?
In an exam, there are (x) students and each is given (x-5) questions. The total question count is (414). What is the number of students?
#quadratic equations
#exam arrangement
#application
A (18)
B (23)
C (27)
D (31)
Explanation opens after your attempt
Step 1
Concept
The total count is (x(x-5)=414). This gives (x=23).
Step 2
Why this answer is correct
The correct answer is B. (23). The total count is (x(x-5)=414). This gives (x=23).
Step 3
Exam Tip
कुल गिनती (x(x-5)=414) है। इससे (x=23) मिलता है।
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प्लेटलेट्स की संख्या बहुत कम होने पर छोटी चोट भी गंभीर क्यों हो सकती है?
Why can even a small injury become serious when platelet count is very low?
#platelets
#clotting
#injury
A रक्त का थक्का बनने में कठिनाई होगी / Blood clotting will be difficult
B ऑक्सीजन बहुत अधिक बनेगी / Too much oxygen will form
C भोजन नली बंद हो जाएगी / Food pipe will close
D गुर्दे ग्लूकोज बनाएंगे / Kidneys will make glucose
Explanation opens after your attempt
Correct Answer
A. रक्त का थक्का बनने में कठिनाई होगी / Blood clotting will be difficult
Step 1
Concept
Platelets help form clots.
Step 2
Why this answer is correct
Clots stop bleeding.
Step 3
Exam Tip
Low platelets increase the risk of excessive blood loss. चरण 1: प्लेटलेट्स थक्का बनाने में सहायता करते हैं। चरण 2: थक्का रक्त बहना रोकता है। चरण 3: प्लेटलेट्स कम होने पर अधिक रक्त हानि का खतरा बढ़ जाता है।
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काउंट कावूर की कूटनीति मैजिनी की राष्ट्रवादी कल्पना से किस प्रकार अलग थी?
How was Count Cavour's diplomacy different from Mazzini's nationalist vision?
#cavour
#mazzini
#diplomacy
#comparison
A कावूर ने राज्य शक्ति और विदेशी सहयोग का प्रयोग किया / Cavour used state power and foreign alliances
B कावूर ने केवल गुप्त युवा संगठन बनाए / Cavour only formed secret youth organisations
C मैजिनी ने फ्रांस से सैन्य संधि की / Mazzini made a military alliance with France
D दोनों ने जर्मन साम्राज्य बनाया / Both created the German Empire
Explanation opens after your attempt
Correct Answer
A. कावूर ने राज्य शक्ति और विदेशी सहयोग का प्रयोग किया / Cavour used state power and foreign alliances
Step 1
Concept
Mazzini was linked with ideas and inspiration.
Step 2
Why this answer is correct
Cavour used the government, army, and diplomacy of Sardinia-Piedmont.
Step 3
Exam Tip
Their methods were different but the goal was national unity. चरण 1: मैजिनी विचार और प्रेरणा से जुड़े थे। चरण 2: कावूर ने सार्डिनिया पीडमोंट की सरकार, सेना और कूटनीति का उपयोग किया। चरण 3: इसलिए दोनों की विधियां अलग थीं पर लक्ष्य राष्ट्रीय एकता था।
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काउंट कावूर ने इटली के एकीकरण में मुख्य रूप से किस साधन का उपयोग किया?
What method did Count Cavour mainly use in Italian unification?
#cavour
#diplomacy
#italy
A कूटनीति और युद्ध / Diplomacy and war
B केवल कविता / Only poetry
C केवल खेती / Only farming
D केवल धर्म प्रचार / Only religious preaching
Explanation opens after your attempt
Correct Answer
A. कूटनीति और युद्ध / Diplomacy and war
Step 1
Concept
Cavour was a practical leader.
Step 2
Why this answer is correct
He used foreign support and war to strengthen Sardinia-Piedmont.
Step 3
Exam Tip
Connect Cavour's role with diplomacy. चरण 1: कावूर व्यावहारिक नेता थे। चरण 2: उन्होंने विदेशी सहायता और युद्ध का उपयोग कर सार्डिनिया पीडमोंट को मजबूत किया। चरण 3: कावूर की भूमिका को कूटनीति से जोड़ें।
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यदि (p(2)=0), (p(5)=0) और (p(9)=0), तो ग्राफ पर (x)-अक्ष कटान कितने अलग होंगे?
If (p(2)=0), (p(5)=0) and (p(9)=0), how many distinct (x)-axis intersections will be on the graph?
#function zero count
A एक / One
B दो / Two
C तीन / Three
D नौ / Nine
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).
Step 3
Exam Tip
तीन अलग (x)-मान तीन अलग (x)-अक्ष बिंदु देते हैं। टिप: (p(a)=0) से ((a,0)) मिलता है।
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माया सभ्यता में शून्य के उपयोग का महत्व किस क्षेत्र से सबसे अधिक जुड़ा था?
The importance of the use of zero in Maya civilization was most connected with which field?
#world history
#ancient civilizations
#maya
#zero
A गणना और कैलेंडर / Calculation and calendar
B घुड़सवारी / Horse riding
C लोहे की तलवार / Iron sword
D मुद्रण मशीन / Printing machine
Explanation opens after your attempt
Correct Answer
A. गणना और कैलेंडर / Calculation and calendar
Step 1
Concept
The Maya used zero in calculation and timekeeping. For exams connect the Maya with mathematical achievement.
Step 2
Why this answer is correct
The correct answer is A. गणना और कैलेंडर / Calculation and calendar. The Maya used zero in calculation and timekeeping. For exams connect the Maya with mathematical achievement.
Step 3
Exam Tip
माया गणना और समय मापन में शून्य का उपयोग करते थे। परीक्षा में माया को गणितीय उपलब्धि से जोड़ें।
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किस प्राचीन सभ्यता में शून्य की अवधारणा का उन्नत उपयोग माया कैलेंडर में दिखता है?
In which ancient civilization is an advanced use of zero seen in the Maya calendar?
#world history
#ancient civilizations
#maya zero
A माया / Maya
B रोमन / Roman
C मिस्री / Egyptian
D फोनीशियन / Phoenician
Explanation opens after your attempt
Correct Answer
A. माया / Maya
Step 1
Concept
Maya civilization had an advanced counting and calendar system. Link it with astronomical knowledge in exams.
Step 2
Why this answer is correct
The correct answer is A. माया / Maya. Maya civilization had an advanced counting and calendar system. Link it with astronomical knowledge in exams.
Step 3
Exam Tip
माया सभ्यता में गणना और कैलेंडर प्रणाली उन्नत थी। परीक्षा में इसे खगोल ज्ञान से जोड़ें।
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ब्रह्मगुप्त का शून्य संबंधी नियम किस क्षेत्र की उपलब्धि है?
Brahmagupta's rules related to zero are achievements of which field?
#ancient-history
#brahmagupta
#zero
A गणित / Mathematics
B मूर्तिकला / Sculpture
C राजस्व प्रशासन / Revenue administration
D संगम कविता / Sangam poetry
Explanation opens after your attempt
Correct Answer
A. गणित / Mathematics
Step 1
Concept
Brahmagupta gave important mathematical rules on zero and numbers. For exams, connect zero with a major achievement of Indian mathematics.
Step 2
Why this answer is correct
The correct answer is A. गणित / Mathematics. Brahmagupta gave important mathematical rules on zero and numbers. For exams, connect zero with a major achievement of Indian mathematics.
Step 3
Exam Tip
ब्रह्मगुप्त ने शून्य और संख्याओं पर महत्वपूर्ण गणितीय नियम दिए। परीक्षा में शून्य को भारतीय गणित की प्रमुख उपलब्धि से जोड़ें।
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संख्या रेखा पर (r(x)=4x+6) का शून्यक किस अंतराल में होगा?
In which interval will the zero of (r(x)=4x+6) lie on the number line?
#polynomials
#number-line
#linear-zero
#medium
A (-2) और (-1) / (-2) and (-1)
B (-1) और (0) / (-1) and (0)
C (1) और (2) / (1) and (2)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) / (-2) and (-1)
Step 1
Concept
From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) / (-2) and (-1). From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
Step 3
Exam Tip
(4x+6=0) से \(x=-\frac{3}{2}\), जो (-2) और (-1) के बीच है। परीक्षा में ऋणात्मक भिन्न का अंतराल सावधानी से पहचानें।
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बहुपद (q(x)=3x-7) का शून्यक संख्या रेखा पर किस दो पूर्णांकों के बीच होगा?
Between which two integers will the zero of (q(x)=3x-7) lie on the number line?
#polynomials
#number-line
#zero-location
#medium
A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (-3) और (-2) / (-3) and (-2)
Explanation opens after your attempt
Correct Answer
B. (2) और (3) / (2) and (3)
Step 1
Concept
From (3x-7=0), \(x=\frac{7}{3}\), which lies between (2) and (3). In exams, first find the zero and then locate it.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). From (3x-7=0), \(x=\frac{7}{3}\), which lies between (2) and (3). In exams, first find the zero and then locate it.
Step 3
Exam Tip
(3x-7=0) से \(x=\frac{7}{3}\), जो (2) और (3) के बीच है। परीक्षा में पहले शून्यक निकालें फिर स्थान तय करें।
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संख्या रेखा पर (p(x)=2x+5) का शून्यक किस बिंदु पर होगा?
At which point will the zero of (p(x)=2x+5) lie on the number line?
#polynomials
#number-line
#linear-polynomial-zero
#medium
A (2.5)
B (-2.5)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
From (2x+5=0), we get \(x=-\frac{5}{2}=-2.5\). In exams, find the zero and place it like a real number.
Step 2
Why this answer is correct
The correct answer is B. (-2.5). From (2x+5=0), we get \(x=-\frac{5}{2}=-2.5\). In exams, find the zero and place it like a real number.
Step 3
Exam Tip
(2x+5=0) से \(x=-\frac{5}{2}=-2.5\) मिलता है। परीक्षा में शून्यक निकालकर उसे वास्तविक संख्या की तरह रखें।
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संख्या रेखा पर (u(x)=6x-18) का शून्यक किस बिंदु पर होगा?
At which point will the zero of (u(x)=6x-18) lie on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A (2)
B (3)
C (6)
D (18)
Explanation opens after your attempt
Step 1
Concept
From (6x-18=0), we get (x=3). In exams, find the zero first and then place it correctly on the number line.
Step 2
Why this answer is correct
The correct answer is B. (3). From (6x-18=0), we get (x=3). In exams, find the zero first and then place it correctly on the number line.
Step 3
Exam Tip
(6x-18=0) से (x=3) मिलता है। परीक्षा में शून्यक निकालकर उसे संख्या रेखा पर सही बिंदु पर रखें।
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संख्या रेखा पर (p(x)=x) का शून्यक कौन सा है?
What is the zero of (p(x)=x) on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A \(-1\)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
For (p(x)=x), putting (x=0) gives (p(x)=0). In exams, a zero is the value where the polynomial becomes (0).
Step 2
Why this answer is correct
The correct answer is B. (0). For (p(x)=x), putting (x=0) gives (p(x)=0). In exams, a zero is the value where the polynomial becomes (0).
Step 3
Exam Tip
(p(x)=x) में (x=0) रखने पर (p(x)=0) होता है। परीक्षा में शून्यक वह मान है जहां बहुपद का मान (0) हो।
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यदि बहुपद का शून्यक (-5) है, तो संख्या रेखा पर वह किस दिशा में होगा?
If the zero of a polynomial is (-5), in which direction will it lie on the number line?
#polynomials
#number-line
#zero-direction
#class-10
A (0) के दाईं ओर / To the right of (0)
B (0) के बाईं ओर / To the left of (0)
C ठीक (0) पर / Exactly at (0)
D (5) और (6) के बीच / Between (5) and (6)
Explanation opens after your attempt
Correct Answer
B. (0) के बाईं ओर / To the left of (0)
Step 1
Concept
The zero (-5) is negative, so it lies to the left of (0). In exams, the sign of the zero tells its direction.
Step 2
Why this answer is correct
The correct answer is B. (0) के बाईं ओर / To the left of (0). The zero (-5) is negative, so it lies to the left of (0). In exams, the sign of the zero tells its direction.
Step 3
Exam Tip
शून्यक (-5) ऋणात्मक है इसलिए वह (0) के बाईं ओर होगा। परीक्षा में शून्यक का चिह्न उसकी दिशा बताता है।
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बहुपद (q(x)=x-8) का शून्यक संख्या रेखा पर किस बिंदु पर होगा?
At which point will the zero of the polynomial (q(x)=x-8) lie on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A \(-8\)
B (0)
C (8)
D (1)
Explanation opens after your attempt
Step 1
Concept
From (x-8=0), we get (x=8). In exams, the zero of (x-a) is (a).
Step 2
Why this answer is correct
The correct answer is C. (8). From (x-8=0), we get (x=8). In exams, the zero of (x-a) is (a).
Step 3
Exam Tip
(x-8=0) से (x=8) मिलता है। परीक्षा में (x-a) का शून्यक (a) होता है।
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संख्या रेखा पर (p(x)=x+3) के शून्यक को कहां दर्शाया जाएगा?
Where will the zero of (p(x)=x+3) be represented on the number line?
#polynomials
#number-line
#zero-of-polynomial
#class-10
A (3) पर / At (3)
B (-3) पर / At (-3)
C (0) पर / At (0)
D (1) पर / At (1)
Explanation opens after your attempt
Correct Answer
B. (-3) पर / At (-3)
Step 1
Concept
From (x+3=0), we get (x=-3). In exams, find the zero and show it as a point on the number line.
Step 2
Why this answer is correct
The correct answer is B. (-3) पर / At (-3). From (x+3=0), we get (x=-3). In exams, find the zero and show it as a point on the number line.
Step 3
Exam Tip
(x+3=0) से (x=-3) मिलता है। परीक्षा में शून्यक निकालकर उसे संख्या रेखा पर बिंदु की तरह दिखाएं।
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यदि (p(x)=x-3 -2x-2 -13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -2x-2 -13x-10), which of the following is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (5)
B (2)
C -(1)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 2
Why this answer is correct
The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 3
Exam Tip
(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।
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(p(x)=16x-2 -24x+9) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=16x-2 -24x+9)?
#zero
#fraction
#quadratic
A \(\frac{3}{4}\)
B \(-\frac{3}{4}\)
C \(\frac{4}{3}\)
D \(-\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{4}\)
Step 1
Concept
(16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{4}\). (16x-2 -24x+9=(4x-3)2 ), so the zero is \(x=\frac{3}{4}\). Recognize the perfect square.
Step 3
Exam Tip
(16x-2 -24x+9=(4x-3)2 ), इसलिए शून्य \(x=\frac{3}{4}\) है। पूर्ण वर्ग पहचानें।
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यदि (x=-3), बहुपद (p(x)=x-2 +kx-18) का शून्य है, तो (k) क्या है?
If (x=-3) is a zero of (p(x)=x-2 +kx-18), what is (k)?
#zero
#parameter
#quadratic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(-3)=9-3k-18=0), so (-3k=9) and (k=-3). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-3)=9-3k-18=0), इसलिए (-3k=9) और (k=-3)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (x=0), (p(x)=7x-3 -2x) का शून्यक है, तो कारण क्या है?
If (x=0) is a zero of (p(x)=7x-3 -2x), what is the reason?
#zero-at-origin
#factor
#polynomial
A हर पद में (x) गुणनखंड है / Every term has factor (x)
B स्थिर पद (7) है / Constant term is (7)
C घात (3) है / Degree is (3)
D गुणांक ऋणात्मक है / A coefficient is negative
Explanation opens after your attempt
Correct Answer
A. हर पद में (x) गुणनखंड है / Every term has factor (x)
Step 1
Concept
(p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 2
Why this answer is correct
The correct answer is A. हर पद में (x) गुणनखंड है / Every term has factor (x). (p(x)=x\(7x^2-2\)), so at (x=0) the value is (0). If every term has (x), then (0) is a zero.
Step 3
Exam Tip
(p(x)=x\(7x^2-2\)), इसलिए (x=0) पर मान (0) होता है। यदि हर पद में (x) हो, तो (0) शून्यक होता है।
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यदि (p(x)=4x-12), तो इसका शून्यक क्या है?
If (p(x)=4x-12), what is its zero?
#linear-polynomial
#zero
#evaluation
A (3)
B -(3)
C (4)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (4x-12=0), we get (x=3). A zero is the value where the polynomial becomes (0).
Step 2
Why this answer is correct
The correct answer is A. (3). From (4x-12=0), we get (x=3). A zero is the value where the polynomial becomes (0).
Step 3
Exam Tip
(4x-12=0) से (x=3) मिलता है। शून्यक वह मान है जहाँ बहुपद का मान (0) हो।
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यदि (p(x)=ax+b) और \(a\neq0\), तो इसका शून्यक क्या है?
If (p(x)=ax+b) and \(a\neq0\), what is its zero?
#linear-zero
#general-form
#polynomial
A -\(\frac{b}{a}\)
B \(\frac{b}{a}\)
C -\(\frac{a}{b}\)
D \(\frac{a}{b}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{b}{a}\)
Step 1
Concept
Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{b}{a}\). Putting (ax+b=0) gives \(x=-\frac{b}{a}\). A linear polynomial has exactly one zero.
Step 3
Exam Tip
(ax+b=0) रखने पर \(x=-\frac{b}{a}\) मिलता है। रेखीय बहुपद में केवल एक शून्यक होता है।
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कौन-सा कथन सही है: (p(x)=0) जहाँ (p(x)) शून्य बहुपद है?
Which statement is correct for (p(x)=0), where (p(x)) is the zero polynomial?
#zero-polynomial
#degree
#concept
A इसकी घात परिभाषित नहीं होती / Its degree is not defined
B इसकी घात (0) होती है / Its degree is (0)
C इसकी घात (1) होती है / Its degree is (1)
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
A. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is A. इसकी घात परिभाषित नहीं होती / Its degree is not defined. The zero polynomial has no non-zero term, so its degree is not defined. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
शून्य बहुपद में कोई अशून्य पद नहीं होता, इसलिए उसकी घात परिभाषित नहीं होती। स्थिर अशून्य बहुपद की घात (0) होती है।
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यदि (p(x)=x-3 -4x-2 +x+6), तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -4x-2 +x+6), which of these is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (2)
B (1)
C (-1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 3
Exam Tip
(p(2)=8-16+2+6=0), इसलिए (2) शून्यक है। विकल्पों में छोटे पूर्णांकों को पहले जाँचें।
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(p(x)=9x-2 +12x+4) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=9x-2 +12x+4)?
#zero
#fraction
#quadratic
A \(-\frac{2}{3}\)
B \(\frac{2}{3}\)
C \(-\frac{3}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{2}{3}\)
Step 1
Concept
(9x-2 +12x+4=(3x+2)2 ), so the zero is \(x=-\frac{2}{3}\). Recognize the perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{2}{3}\). (9x-2 +12x+4=(3x+2)2 ), so the zero is \(x=-\frac{2}{3}\). Recognize the perfect square.
Step 3
Exam Tip
(9x-2 +12x+4=(3x+2)2 ), इसलिए शून्य \(x=-\frac{2}{3}\) है। पूर्ण वर्ग पहचानें।
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यदि (x=-2), बहुपद (p(x)=x-2 +kx-8) का शून्य है, तो (k) क्या है?
If (x=-2) is a zero of (p(x)=x-2 +kx-8), what is (k)?
#zero
#parameter
#quadratic
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-2). (p(-2)=4-2k-8=0), so (-2k=4) and (k=-2). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(-2)=4-2k-8=0), इसलिए (-2k=4) और (k=-2)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=kx-2 -5x+6) का एक शून्यक (2) है, तो (k) का मान क्या होगा?
If (2) is a zero of (p(x)=kx-2 -5x+6), what is the value of (k)?
#polynomials
#zero
#value
#hard
A (1)
B (2)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 3
Exam Tip
(p(2)=0) रखने पर (4k-10+6=0) से (k=1) मिलता है। शून्यक के लिए (p\(\alpha\)=0) लगाएं।
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(p(x)=4x-2 -12x+9) में कौन सा मान शून्य है?
Which value is a zero of (p(x)=4x-2 -12x+9)?
#zero
#fraction
#quadratic
A \(\frac{1}{2}\)
B \(\frac{3}{2}\)
C (2)
D (3)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{2}\)
Step 1
Concept
(p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{2}\). (p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.
Step 3
Exam Tip
(p\left\(\frac{3}{2}\right\)=9-18+9=0)। भिन्न मान रखते समय वर्ग और गुणा सही करें।
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यदि (x=3), बहुपद (p(x)=x-2 -kx+12) का शून्य है, तो (k) क्या है?
If (x=3) is a zero of (p(x)=x-2 -kx+12), what is (k)?
#zero
#parameter
#quadratic
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is C. (7). (p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(3)=9-3k+12=0), इसलिए (21=3k) और (k=7)। शून्य की शर्त में बहुपद का मान (0) रखें।
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यदि (p(x)=ax-2 +4x-12) और (x=2) इसका शून्य है, तो (a) क्या होगा?
If (p(x)=ax-2 +4x-12) and (x=2) is its zero, what is (a)?
#zero condition
#parameter
#quadratic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(2)=4a+8-12=0), इसलिए (4a=4) और (a=1)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=cx+d) और \(c\ne0\), तो इसका शून्य क्या होगा?
If (p(x)=cx+d) and \(c\ne0\), what will be its zero?
#linear zero
#general form
#formula
A \(\frac{d}{c}\)
B \(-\frac{d}{c}\)
C (cd)
D (c-d)
Explanation opens after your attempt
Correct Answer
B. \(-\frac{d}{c}\)
Step 1
Concept
From (cx+d=0), we get \(x=-\frac{d}{c}\). Remember the negative sign in the formula.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{d}{c}\). From (cx+d=0), we get \(x=-\frac{d}{c}\). Remember the negative sign in the formula.
Step 3
Exam Tip
(cx+d=0) से \(x=-\frac{d}{c}\) मिलता है। सूत्र में ऋण चिह्न ध्यान रखें।
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(p(x)=4x+20) का शून्य कौन सा है?
Which is the zero of (p(x)=4x+20)?
#linear polynomial
#zero
#solution
A (5)
B (-5)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
From (4x+20=0), we get (x=-5). A zero is the value that makes the polynomial equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-5). From (4x+20=0), we get (x=-5). A zero is the value that makes the polynomial equal to (0).
Step 3
Exam Tip
(4x+20=0) से (x=-5) मिलता है। शून्य वह मान है जिससे बहुपद (0) हो जाए।
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(p(x)=9x-27) का शून्य क्या है?
What is the zero of (p(x)=9x-27)?
#linear zero
#equation
#polynomial
A (2)
B (3)
C (9)
D (27)
Explanation opens after your attempt
Step 1
Concept
From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 2
Why this answer is correct
The correct answer is B. (3). From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 3
Exam Tip
(9x-27=0) से (x=3) मिलता है। रैखिक बहुपद का शून्य समीकरण हल करके निकालें।
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किस मान के लिए \(x^2-6x+m\) में (x=2) शून्य होगा?
For what value of (m) will (x=2) be a zero of \(x^2-6x+m\)?
#zero
#parameter
#quadratic
A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (8). (4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(4-12+m=0), इसलिए (m=8)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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(x=-3) किस बहुपद का शून्य है?
For which polynomial is (x=-3) a zero?
#zero
#linear polynomial
#evaluation
A (p(x)=x+3)
B (p(x)=x-3)
C (p(x)=3x+1)
D (p(x)=x-2 +3)
Explanation opens after your attempt
Correct Answer
A. (p(x)=x+3)
Step 1
Concept
(p(-3)=-3+3=0), so (x=-3) is its zero. To test a zero, substitute the value and check for (0).
Step 2
Why this answer is correct
The correct answer is A. (p(x)=x+3). (p(-3)=-3+3=0), so (x=-3) is its zero. To test a zero, substitute the value and check for (0).
Step 3
Exam Tip
(p(-3)=-3+3=0), इसलिए (x=-3) इसका शून्य है। शून्य जांचने के लिए मान रखकर परिणाम (0) देखें।
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निम्न में से कौन सा कथन शून्य बहुपद के लिए सही है?
Which statement is correct for the zero polynomial?
#zero-polynomial
#degree
#concept
A इसकी घात (0) होती है / Its degree is (0)
B इसकी घात (1) होती है / Its degree is (1)
C इसकी घात परिभाषित नहीं होती / Its degree is not defined
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is C. इसकी घात परिभाषित नहीं होती / Its degree is not defined. The degree of the zero polynomial is not defined. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। गैर-शून्य नियत बहुपद की घात (0) होती है।
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यदि (p(x)=x-2 +px+16) और (4) इसका शून्य है, तो (p) का मान क्या है?
If (4) is a zero of (p(x)=x-2 +px+16), what is the value of (p)?
#zero
#parameter
#quadratic
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). \(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 3
Exam Tip
\(4^2+4p+16=0\) से (32+4p=0) मिलता है। इसलिए (p=-8) है।
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यदि (p(x)=x-2 -9), तो कौन सी संख्या (p(x)) का शून्य नहीं है?
If (p(x)=x-2 -9), which number is not a zero of (p(x))?
#zero-of-polynomial
#quadratic
#checking
A (3)
B (-3)
C (0)
D इनमें से कोई नहीं / None of these
Explanation opens after your attempt
Step 1
Concept
(p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is C. (0). (p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
Step 3
Exam Tip
(p(0)=02 -9=-9) है जो (0) नहीं है। इसलिए (0) शून्य नहीं है।
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यदि (p(x)=kx+12) का शून्य (3) है, तो (k) का मान क्या है?
If (3) is a zero of (p(x)=kx+12), what is the value of (k)?
#linear-polynomial
#zero
#parameter
A (4)
B (-4)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 3
Exam Tip
(p(3)=0) से (3k+12=0) मिलता है। इसलिए (k=-4) है।
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यदि (f(x)=x-2 +2x-8), तो निम्न में से कौन (f(x)) का शून्य है?
If (f(x)=x-2 +2x-8), which of the following is a zero of (f(x))?
#zero-of-polynomial
#substitution
#quadratic
A (4)
B (2)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
(f(2)=4+4-8=0). Therefore (2) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is B. (2). (f(2)=4+4-8=0). Therefore (2) is a zero of this polynomial.
Step 3
Exam Tip
(f(2)=4+4-8=0) है। इसलिए (2) इस बहुपद का शून्य है।
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यदि (p(x)=3x-2 +bx-10) में (x=2) एक शून्य है, तो (b) का मान क्या होगा?
If (x=2) is a zero of (p(x)=3x-2 +bx-10), what will be the value of (b)?
#zero
#parameter
#quadratic polynomial
A (-1)
B (-2)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(2)=12+2b-10=0), so (2b=-2) and (b=-1). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(2)=12+2b-10=0), so (2b=-2) and (b=-1). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(2)=12+2b-10=0), इसलिए (2b=-2) और (b=-1)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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(p(x)=x+9) का शून्य क्या है?
What is the zero of (p(x)=x+9)?
#linear-polynomial
#zero
#easy
A (9)
B (-9)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Setting (x+9=0) gives (x=-9). The zero of (x+a) is (-a).
Step 2
Why this answer is correct
The correct answer is B. (-9). Setting (x+9=0) gives (x=-9). The zero of (x+a) is (-a).
Step 3
Exam Tip
(x+9=0) करने पर (x=-9) मिलता है। (x+a) का शून्य (-a) होता है।
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यदि (p(x)=ax+b) और \(a\ne0\), तो इसका शून्य क्या होगा?
If (p(x)=ax+b) and \(a\ne0\), what will be its zero?
#linear zero
#general form
#formula
A \(\frac{b}{a}\)
B \(-\frac{b}{a}\)
C (ab)
D (a+b)
Explanation opens after your attempt
Correct Answer
B. \(-\frac{b}{a}\)
Step 1
Concept
From (ax+b=0), we get \(x=-\frac{b}{a}\). Remember the general formula but do not miss the sign.
Step 2
Why this answer is correct
The correct answer is B. \(-\frac{b}{a}\). From (ax+b=0), we get \(x=-\frac{b}{a}\). Remember the general formula but do not miss the sign.
Step 3
Exam Tip
(ax+b=0) से \(x=-\frac{b}{a}\) मिलता है। सामान्य सूत्र याद रखें लेकिन संकेत न भूलें।
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(p(x)=3x+12) का शून्य कौन सा है?
Which is the zero of (p(x)=3x+12)?
#linear polynomial
#zero
#solution
A (4)
B (-4)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
From (3x+12=0), we get (x=-4). A zero is the value that makes the polynomial equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (-4). From (3x+12=0), we get (x=-4). A zero is the value that makes the polynomial equal to (0).
Step 3
Exam Tip
(3x+12=0) से (x=-4) मिलता है। शून्य वह मान है जिससे बहुपद (0) हो जाए।
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(p(x)=7x-14) का शून्य क्या है?
What is the zero of (p(x)=7x-14)?
#linear zero
#equation
#polynomial
A (1)
B (2)
C (7)
D (14)
Explanation opens after your attempt
Step 1
Concept
From (7x-14=0), we get (x=2). Solve the equation to find the zero of a linear polynomial.
Step 2
Why this answer is correct
The correct answer is B. (2). From (7x-14=0), we get (x=2). Solve the equation to find the zero of a linear polynomial.
Step 3
Exam Tip
(7x-14=0) से (x=2) मिलता है। रैखिक बहुपद का शून्य जल्दी निकालने के लिए समीकरण हल करें।
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किस मान के लिए \(x^2-4x+m\) में (x=1) शून्य होगा?
For what value of (m) will (x=1) be a zero of \(x^2-4x+m\)?
#zero
#parameter
#quadratic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(1-4+m=0), so (m=3). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is C. (3). (1-4+m=0), so (m=3). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(1-4+m=0), इसलिए (m=3)। शून्य मिलने पर बहुपद का मान (0) रखें।
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(x=2) किस बहुपद का शून्य है?
For which polynomial is (x=2) a zero?
#zero
#linear polynomial
#evaluation
A (p(x)=x-2)
B (p(x)=x+2)
C (p(x)=2x+1)
D (p(x)=x-2 +2)
Explanation opens after your attempt
Correct Answer
A. (p(x)=x-2)
Step 1
Concept
(p(2)=2-2=0), so (x=2) is its zero. To test a zero, substitute and check for (0).
Step 2
Why this answer is correct
The correct answer is A. (p(x)=x-2). (p(2)=2-2=0), so (x=2) is its zero. To test a zero, substitute and check for (0).
Step 3
Exam Tip
(p(2)=2-2=0), इसलिए (x=2) इसका शून्य है। शून्य जांचने के लिए मान रखकर (0) देखें।
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(p(x)=x-6) का शून्य क्या है?
What is the zero of (p(x)=x-6)?
#zero
#linear-polynomial
A (6)
B (-6)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Setting (x-6=0) gives (x=6). The zero of (x-a) is (a).
Step 2
Why this answer is correct
The correct answer is A. (6). Setting (x-6=0) gives (x=6). The zero of (x-a) is (a).
Step 3
Exam Tip
(x-6=0) करने पर (x=6) आता है। (x-a) का शून्य (a) होता है।
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\(4x^2+0x+9\) में कितने शून्य गुणांक वाले पद को स्पष्ट लिखा गया है?
How many terms with zero coefficient are explicitly written in \(4x^2+0x+9\)?
#zero-coefficient
#terms
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(0x) is one term whose coefficient is (0). A zero-coefficient term does not change the value.
Step 2
Why this answer is correct
The correct answer is B. (1). (0x) is one term whose coefficient is (0). A zero-coefficient term does not change the value.
Step 3
Exam Tip
(0x) एक ऐसा पद है जिसका गुणांक (0) है। शून्य गुणांक वाला पद लिखने पर भी मान नहीं बदलता।
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शून्य बहुपद (0) की घात के बारे में सही कथन कौन सा है?
Which statement about the degree of the zero polynomial (0) is correct?
#zero-polynomial
#degree
A घात (0) है / Degree is (0)
B घात (1) है / Degree is (1)
C घात परिभाषित नहीं है / Degree is not defined
D घात (2) है / Degree is (2)
Explanation opens after your attempt
Correct Answer
C. घात परिभाषित नहीं है / Degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. घात परिभाषित नहीं है / Degree is not defined. The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। इसे गैर-शून्य नियत बहुपद से अलग याद रखें।
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बहुपद \(x^2-9\) का कौन सा मान शून्यक है?
Which value is a zero of the polynomial \(x^2-9\)?
#polynomials
#zero
#quadratic
#easy
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
Step 2
Why this answer is correct
The correct answer is B. (3). \(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
Step 3
Exam Tip
\(3^2-9=0\), इसलिए (3) शून्यक है। विकल्पों को रखकर जांचना आसान तरीका है।
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(p(x)=5x+10) का शून्यक कौन सा है?
Which is the zero of (p(x)=5x+10)?
#polynomials
#zero
#linear
#easy
A (2)
B (-2)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
From (5x+10=0), we get (x=-2). Do not forget the sign change.
Step 2
Why this answer is correct
The correct answer is B. (-2). From (5x+10=0), we get (x=-2). Do not forget the sign change.
Step 3
Exam Tip
(5x+10=0) से (x=-2) मिलता है। चिह्न बदलना न भूलें।
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यदि (p(x)=3x-12) है, तो इसका शून्यक क्या है?
If (p(x)=3x-12), what is its zero?
#polynomials
#zero
#linear
#easy
A (3)
B (4)
C (-4)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
Step 2
Why this answer is correct
The correct answer is B. (4). From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
Step 3
Exam Tip
(3x-12=0) से (x=4) मिलता है। रैखिक बहुपद में सीधे समीकरण बनाएं।
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कौन सा मान (p(x)=x+4) का शून्यक है?
Which value is a zero of (p(x)=x+4)?
#polynomials
#zero
#linear
#easy
A (4)
B (-4)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
(p(-4)=-4+4=0), so (-4) is the zero. For (x+a), the zero is (-a).
Step 2
Why this answer is correct
The correct answer is B. (-4). (p(-4)=-4+4=0), so (-4) is the zero. For (x+a), the zero is (-a).
Step 3
Exam Tip
(p(-4)=-4+4=0), इसलिए (-4) शून्यक है। रैखिक बहुपद (x+a) का शून्यक (-a) होता है।
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निम्न में से कौन सा शून्य बहुपद है?
Which of the following is the zero polynomial?
#polynomials
#zero-polynomial
#easy
#level48
A (0)
B (1)
C (x)
D \(x^0\)
Explanation opens after your attempt
Step 1
Concept
(0) is the zero polynomial because every coefficient is zero. Do not apply the usual degree rule to it.
Step 2
Why this answer is correct
The correct answer is A. (0). (0) is the zero polynomial because every coefficient is zero. Do not apply the usual degree rule to it.
Step 3
Exam Tip
(0) को शून्य बहुपद कहते हैं क्योंकि इसका हर गुणांक शून्य होता है। इसकी घात पर सामान्य घात नियम न लगाएं।
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यदि ((x-6)(x-13)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-6)(x-13)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=6,13)
B (x=-6,-13)
C (x=0,19)
D (x=1,78)
Explanation opens after your attempt
Correct Answer
A. (x=6,13)
Step 1
Concept
((x-6)=0) or ((x-13)=0), so (x=6) or (x=13). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=6,13). ((x-6)=0) or ((x-13)=0), so (x=6) or (x=13). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-6)=0) या ((x-13)=0), इसलिए (x=6) या (x=13) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि ((x-5)(x-11)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-5)(x-11)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=5,11)
B (x=-5,-11)
C (x=0,16)
D (x=1,55)
Explanation opens after your attempt
Correct Answer
A. (x=5,11)
Step 1
Concept
((x-5)=0) or ((x-11)=0), so (x=5) or (x=11). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=5,11). ((x-5)=0) or ((x-11)=0), so (x=5) or (x=11). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-5)=0) या ((x-11)=0), इसलिए (x=5) या (x=11) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि ((x-4)(x-9)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-4)(x-9)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=4,9)
B (x=-4,-9)
C (x=0,13)
D (x=1,36)
Explanation opens after your attempt
Correct Answer
A. (x=4,9)
Step 1
Concept
((x-4)=0) or ((x-9)=0), so (x=4) or (x=9). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=4,9). ((x-4)=0) or ((x-9)=0), so (x=4) or (x=9). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-4)=0) या ((x-9)=0), इसलिए (x=4) या (x=9) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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यदि ((x-3)(x-7)=0), तो शून्य गुणनफल नियम से हल क्या होंगे?
If ((x-3)(x-7)=0), what are the solutions by zero product rule?
#quadratic
#zero-product
#method
A (x=3,7)
B (x=-3,-7)
C (x=0,10)
D (x=1,21)
Explanation opens after your attempt
Correct Answer
A. (x=3,7)
Step 1
Concept
((x-3)=0) or ((x-7)=0), so (x=3) or (x=7). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=3,7). ((x-3)=0) or ((x-7)=0), so (x=3) or (x=7). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-3)=0) या ((x-7)=0), इसलिए (x=3) या (x=7) है। परीक्षा में हर गुणनखंड को अलग शून्य रखें।
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शून्य गुणनफल नियम से ((x-9)(x+2)=0) के मूल क्या हैं?
Using zero product rule, what are the roots of ((x-9)(x+2)=0)?
#quadratic
#zero-product-rule
#roots
A (x=9,-2)
B (x=-9,2)
C (x=9,2)
D (x=-9,-2)
Explanation opens after your attempt
Correct Answer
A. (x=9,-2)
Step 1
Concept
((x-9)=0) or ((x+2)=0), so (x=9) or (x=-2). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=9,-2). ((x-9)=0) or ((x+2)=0), so (x=9) or (x=-2). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-9)=0) या ((x+2)=0), इसलिए (x=9) या (x=-2) है। परीक्षा में हर गुणनखंड को अलग-अलग शून्य रखें।
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