100 results found for "zero solution" 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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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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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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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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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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शर्करा का जलीय विलयन बल्ब नहीं जलाता, जबकि अम्लीय विलयन जलाता है। सही कारण क्या है?
An aqueous sugar solution does not make a bulb glow, while an acidic solution does. What is the correct reason?
#conductivity
#ions
#sugar-solution
#acid-solution
#class10
A शर्करा विलयन में चलायमान आयन नहीं बनते / Mobile ions are not formed in sugar solution
B शर्करा विलयन हमेशा क्षारीय होता है / Sugar solution is always basic
C अम्लीय विलयन में कोई आयन नहीं होता / Acidic solution has no ions
D बल्ब केवल मीठे पदार्थों में जलता है / A bulb glows only in sweet substances
Explanation opens after your attempt
Correct Answer
A. शर्करा विलयन में चलायमान आयन नहीं बनते / Mobile ions are not formed in sugar solution
Step 1
Concept
Electric current needs mobile ions.
Step 2
Why this answer is correct
Acids form ions in water, but sugar generally does not.
Step 3
Exam Tip
Therefore, acid solution conducts while sugar solution may not. पहला बिंदु: विद्युत धारा के लिए चलायमान आयन चाहिए। दूसरा बिंदु: अम्ल जल में आयन बनाते हैं, पर शर्करा सामान्यतः ऐसे आयन नहीं बनाती। तीसरा बिंदु: इसलिए अम्लीय विलयन चालक और शर्करा विलयन अचालक हो सकता है।
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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)=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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यदि (D=0) और कम से कम एक सहायक सारणिक शून्य नहीं है, तो युग्म की हल-स्थिति क्या होगी?
If (D=0) and at least one auxiliary determinant is non-zero, what is the solution status of the pair?
#class10
#linear-equations
#solvability
A अनंत हल / Infinitely many solutions
B अद्वितीय हल / Unique solution
C कोई हल नहीं / No solution
D सदैव हल / Always solvable
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
(D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. (D=0) with a non-zero auxiliary determinant indicates distinct parallel lines. Hence there is no solution.
Step 3
Exam Tip
(D=0) और असंगत सहायक सारणिक समांतर अलग रेखाओं का संकेत देते हैं। इसलिए कोई हल नहीं होता।
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यदि पीएच सात से कम है पर शून्य के बहुत निकट नहीं है तो विलयन के बारे में सबसे संतुलित निष्कर्ष क्या है?
If pH is less than 7 but not very close to zero, what is the most balanced conclusion about the solution?
#pH scale
#acidic solution
#interpretation
A विलयन अम्लीय है पर आवश्यक नहीं कि अत्यधिक दाहक हो / The solution is acidic but not necessarily highly corrosive
B विलयन हमेशा प्रबल क्षार है / The solution is always a strong base
C विलयन शुद्ध जल है / The solution is pure water
D विलयन में कोई आयन नहीं है / The solution has no ions
Explanation opens after your attempt
Correct Answer
A. विलयन अम्लीय है पर आवश्यक नहीं कि अत्यधिक दाहक हो / The solution is acidic but not necessarily highly corrosive
Step 1
Concept
A pH below 7 means the solution is acidic.
Step 2
Why this answer is correct
Lower pH means higher acidity.
Step 3
Exam Tip
A pH only slightly below 7 may indicate mild acidity. चरण 1: पीएच सात से कम होने पर विलयन अम्लीय होता है। चरण 2: पीएच जितना कम होगा अम्लता उतनी अधिक होगी। चरण 3: सात से थोड़ा कम पीएच हल्की अम्लीयता दिखा सकता है।
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एक अम्लीय विलयन का पीएच दो है और दूसरे अम्लीय विलयन का पीएच पाँच है। पहले विलयन में हाइड्रोजन आयनों की सांद्रता दूसरे की तुलना में कितनी गुना अधिक है?
An acidic solution has pH 2 and another acidic solution has pH 5. How many times higher is the hydrogen ion concentration in the first solution?
#ph-scale
#hydrogen-ion
#acid-strength
#expert
A एक हजार गुना / One thousand times
B तीन गुना / Three times
C सौ गुना / One hundred times
D दस हजार गुना / Ten thousand times
Explanation opens after your attempt
Correct Answer
A. एक हजार गुना / One thousand times
Step 1
Concept
A difference of one pH unit means a tenfold difference in hydrogen ion concentration.
Step 2
Why this answer is correct
The difference between pH 2 and pH 5 is three units.
Step 3
Exam Tip
Therefore the concentration differs by 10 × 10 × 10 = 1000 times. चरण 1: पीएच में एक इकाई का अंतर हाइड्रोजन आयन सांद्रता में दस गुना अंतर दिखाता है। चरण 2: पीएच दो और पाँच में तीन इकाई का अंतर है। चरण 3: इसलिए अंतर दस गुणा दस गुणा दस यानी एक हजार गुना है।
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चीनी का जलीय विलयन विद्युत नहीं चलाता जबकि नमक का विलयन चलाता है। मुख्य कारण क्या है?
Aqueous sugar solution does not conduct electricity while salt solution does. What is the main reason?
#conductivity
#ions
#sugar solution
A चीनी जल में आयन नहीं बनाती पर नमक आयन बनाता है / Sugar does not form ions in water but salt does
B चीनी अम्ल है और नमक क्षार है / Sugar is acid and salt is base
C चीनी में जल नहीं घुलता / Water does not dissolve sugar
D नमक में कोई आयन नहीं होते / Salt has no ions
Explanation opens after your attempt
Correct Answer
A. चीनी जल में आयन नहीं बनाती पर नमक आयन बनाता है / Sugar does not form ions in water but salt does
Step 1
Concept
Electrical conduction needs mobile ions.
Step 2
Why this answer is correct
Sugar remains as molecules in water and does not give ions.
Step 3
Exam Tip
Salt gives ions, so its solution conducts. चरण 1: विद्युत चालकता के लिए चलायमान आयन चाहिए। चरण 2: चीनी जल में अणु रूप में रहती है और आयन नहीं देती। चरण 3: नमक जल में आयन देता है इसलिए उसका विलयन चालक होता है।
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पीएच नौ वाला विलयन किस प्रकार का माना जाएगा?
A solution with pH 9 will be considered what type of solution?
#pH
#basic solution
#alkali
A अम्लीय / Acidic
B क्षारीय / Basic
C उदासीन / Neutral
D वाष्पशील / Volatile
Explanation opens after your attempt
Correct Answer
B. क्षारीय / Basic
Step 1
Concept
A solution is basic when pH is greater than 7.
Step 2
Why this answer is correct
9 is greater than 7.
Step 3
Exam Tip
Therefore a solution with pH 9 is basic. चरण 1: पीएच सात से अधिक होने पर विलयन क्षारीय होता है। चरण 2: नौ सात से अधिक है। चरण 3: इसलिए पीएच नौ वाला विलयन क्षारीय है।
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पीएच पाँच वाला विलयन किस प्रकार का माना जाएगा?
A solution with pH 5 will be considered what type of solution?
#pH
#acidic solution
#indicator
A अम्लीय / Acidic
B क्षारीय / Basic
C उदासीन / Neutral
D लवणहीन / Salt-free
Explanation opens after your attempt
Correct Answer
A. अम्लीय / Acidic
Step 1
Concept
A solution is acidic when pH is less than 7.
Step 2
Why this answer is correct
5 is less than 7.
Step 3
Exam Tip
Therefore a solution with pH 5 is acidic. चरण 1: पीएच सात से कम होने पर विलयन अम्लीय होता है। चरण 2: पाँच सात से कम है। चरण 3: इसलिए पीएच पाँच वाला विलयन अम्लीय माना जाएगा।
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एक विलयन में पीएच सात है और वह विद्युत चलाता है। यह कौन सा विलयन हो सकता है?
A solution has pH 7 and conducts electricity. Which solution could it be?
#sodium chloride
#conductivity
#neutral solution
A सोडियम क्लोराइड का जलीय विलयन / Aqueous sodium chloride solution
B चीनी का जलीय विलयन / Aqueous sugar solution
C अल्कोहल का जलीय विलयन / Aqueous alcohol solution
D शुद्ध आसुत जल ही / Pure distilled water only
Explanation opens after your attempt
Correct Answer
A. सोडियम क्लोराइड का जलीय विलयन / Aqueous sodium chloride solution
Step 1
Concept
pH 7 shows neutrality.
Step 2
Why this answer is correct
Sodium chloride gives ions in water and conducts electricity.
Step 3
Exam Tip
Therefore this solution can be neutral yet conducting. चरण 1: पीएच सात उदासीनता दिखाता है। चरण 2: सोडियम क्लोराइड जल में आयन देता है इसलिए चालक होता है। चरण 3: इसलिए यह विलयन उदासीन होते हुए भी बिजली चला सकता है।
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यदि पीएच दो वाला विलयन पीएच पाँच वाले विलयन से तुलना किया जाए तो पहला विलयन कितना अधिक अम्लीय है?
If a solution of pH 2 is compared with a solution of pH 5, how much more acidic is the first solution?
#pH
#acidity
#logarithmic scale
A दस गुना / Ten times
B सौ गुना / Hundred times
C हजार गुना / Thousand times
D तीन गुना / Three times
Explanation opens after your attempt
Correct Answer
C. हजार गुना / Thousand times
Step 1
Concept
A difference of one pH unit means a tenfold difference in acidity.
Step 2
Why this answer is correct
pH 2 and pH 5 differ by three units.
Step 3
Exam Tip
Therefore the pH 2 solution is a thousand times more acidic. चरण 1: पीएच में एक इकाई का अंतर अम्लीयता में दस गुना अंतर देता है। चरण 2: दो और पाँच में तीन इकाई का अंतर है। चरण 3: इसलिए पीएच दो वाला विलयन हजार गुना अधिक अम्लीय है।
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किसी विलयन में लाल लिटमस नीला हो जाता है, पर नीले लिटमस में कोई परिवर्तन नहीं होता। विलयन किस प्रकार का है?
In a solution, red litmus turns blue, but blue litmus shows no change. What type of solution is it?
#litmus
#basic-solution
#indicator
#class10
A अम्लीय / Acidic
B उदासीन / Neutral
C लवणीय पर अम्लीय / Salty but acidic
D क्षारीय / Basic
Explanation opens after your attempt
Correct Answer
D. क्षारीय / Basic
Step 1
Concept
Bases turn red litmus blue.
Step 2
Why this answer is correct
Blue litmus remains blue in a base.
Step 3
Exam Tip
Both observations indicate a basic solution. पहला बिंदु: क्षार लाल लिटमस को नीला करते हैं। दूसरा बिंदु: नीला लिटमस क्षार में नीला ही रहता है। तीसरा बिंदु: दोनों अवलोकन क्षारीय विलयन को दर्शाते हैं।
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किसी विलयन का पीएच मान चार है। उसी विलयन में जल मिलाने पर पीएच मान किस दिशा में बदलने की संभावना है?
A solution has pH 4. When water is added to the same solution, in which direction is its pH likely to change?
#ph
#dilution
#acidic-solution
#class10
A सात के पास / Towards 7
B शून्य के पास / Towards 0
C चौदह के पास तुरंत / Immediately towards 14
D कोई परिवर्तन नहीं / No change
Explanation opens after your attempt
Correct Answer
A. सात के पास / Towards 7
Step 1
Concept
A solution with pH 4 is acidic.
Step 2
Why this answer is correct
Adding water dilutes the acid and decreases its acidity.
Step 3
Exam Tip
On dilution, the pH of an acidic solution moves towards 7 but usually does not become greater than 7. पहला बिंदु: पीएच चार वाला विलयन अम्लीय होता है। दूसरा बिंदु: जल मिलाने पर अम्ल तनु हो जाता है और अम्लीयता घटती है। तीसरा बिंदु: अम्लीय विलयन के तनुकरण पर पीएच सात के पास जाता है, पर सामान्यतः सात से अधिक नहीं होता।
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टमाटर के रस, साबुन के विलयन, शुद्ध जल और बेकिंग सोडा विलयन में उदासीन पदार्थ कौन सा होगा?
Among tomato juice, soap solution, pure water and baking soda solution, which substance will be neutral?
#neutral-solution
#pure-water
#ph
#household-substances
#class10
A टमाटर का रस / Tomato juice
B शुद्ध जल / Pure water
C साबुन का विलयन / Soap solution
D बेकिंग सोडा का विलयन / Baking soda solution
Explanation opens after your attempt
Correct Answer
B. शुद्ध जल / Pure water
Step 1
Concept
A neutral substance has a pH of about 7.
Step 2
Why this answer is correct
Pure water is generally considered neutral.
Step 3
Exam Tip
Tomato juice is acidic, while soap and baking soda solutions are basic. पहला बिंदु: उदासीन पदार्थ का पीएच लगभग सात होता है। दूसरा बिंदु: शुद्ध जल सामान्यतः उदासीन माना जाता है। तीसरा बिंदु: टमाटर अम्लीय तथा साबुन और बेकिंग सोडा क्षारीय होते हैं।
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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)=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)=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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शून्य गुणनफल नियम से ((x-7)(x+1)=0) के मूल क्या हैं?
Using zero product rule, what are the roots of ((x-7)(x+1)=0)?
#quadratic
#zero-product-rule
#roots
A (x=7,-1)
B (x=-7,1)
C (x=7,1)
D (x=-7,-1)
Explanation opens after your attempt
Correct Answer
A. (x=7,-1)
Step 1
Concept
((x-7)=0) or ((x+1)=0), so (x=7) or (x=-1). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=7,-1). ((x-7)=0) or ((x+1)=0), so (x=7) or (x=-1). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
((x-7)=0) या ((x+1)=0), इसलिए (x=7) या (x=-1) है। परीक्षा में हर गुणनखंड को अलग से शून्य रखें।
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शून्य गुणनफल नियम से (x(x-4)=0) के हल क्या हैं?
Using zero product rule, what are the solutions of (x(x-4)=0)?
#quadratic
#zero-product-rule
#factorisation
A (x=0,4)
B (x=0,-4)
C (x=4,8)
D (x=1,4)
Explanation opens after your attempt
Correct Answer
A. (x=0,4)
Step 1
Concept
If (x(x-4)=0), then (x=0) or (x-4=0). In exams, set each factor equal to zero separately.
Step 2
Why this answer is correct
The correct answer is A. (x=0,4). If (x(x-4)=0), then (x=0) or (x-4=0). In exams, set each factor equal to zero separately.
Step 3
Exam Tip
यदि (x(x-4)=0), तो (x=0) या (x-4=0) होगा। परीक्षा में हर गुणनखंड को अलग-अलग शून्य के बराबर रखें।
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यदि \(5+\sqrt{21}\) किसी परिमेय गुणांक वाले द्विघात बहुपद का शून्यक है, तो उस बहुपद का एक संभव रूप कौन सा है?
If \(5+\sqrt{21}\) is a zero of a quadratic polynomial with rational coefficients, which is one possible form of that polynomial?
#polynomial-from-zero
#conjugate-roots
#irrational-numbers
A \(x^2-10x+4\)
B \(x^2+10x+4\)
C \(x^2-5x+21\)
D \(x^2-10x+46\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+4\)
Step 1
Concept
The other zero will be \(5-\sqrt{21}\). Sum (10) and product (25-21=4) give the polynomial \(x^2-10x+4\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+4\). The other zero will be \(5-\sqrt{21}\). Sum (10) and product (25-21=4) give the polynomial \(x^2-10x+4\).
Step 3
Exam Tip
दूसरा शून्यक \(5-\sqrt{21}\) होगा। योग (10) और गुणनफल (25-21=4) से बहुपद \(x^2-10x+4\) बनता है।
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यदि \(x=3+\sqrt{8}\), तो (x) किस द्विघात बहुपद का शून्यक हो सकता है?
If \(x=3+\sqrt{8}\), which quadratic polynomial can have (x) as a zero?
#polynomial-from-zero
#conjugates
#irrational-roots
A \(x^2-6x+1\)
B \(x^2+6x+1\)
C \(x^2-3x+8\)
D \(x^2-6x+17\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x+1\)
Step 1
Concept
The companion zero is \(3-\sqrt{8}\). Sum (6) and product (9-8=1) form \(x^2-6x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x+1\). The companion zero is \(3-\sqrt{8}\). Sum (6) and product (9-8=1) form \(x^2-6x+1\).
Step 3
Exam Tip
साथी शून्यक \(3-\sqrt{8}\) है। योग (6) और गुणनफल (9-8=1) से बहुपद \(x^2-6x+1\) बनता है।
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यदि परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक \(4+\sqrt{11}\) है, तो दूसरा शून्यक कौन सा होगा?
If one zero of a quadratic polynomial with rational coefficients is \(4+\sqrt{11}\), what will be the other zero?
#conjugate-zeroes
#polynomials
#irrational-roots
A \(4-\sqrt{11}\)
B \(-4+\sqrt{11}\)
C \(\sqrt{11}-4\)
D \(4+\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(4-\sqrt{11}\)
Step 1
Concept
With rational coefficients \(a+\sqrt{b}\) is accompanied by \(a-\sqrt{b}\). In exams identify conjugate zeroes quickly.
Step 2
Why this answer is correct
The correct answer is A. \(4-\sqrt{11}\). With rational coefficients \(a+\sqrt{b}\) is accompanied by \(a-\sqrt{b}\). In exams identify conjugate zeroes quickly.
Step 3
Exam Tip
परिमेय गुणांकों में \(a+\sqrt{b}\) के साथ \(a-\sqrt{b}\) भी शून्यक होता है। परीक्षा में संयुग्मी शून्यक तुरंत पहचानें।
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