100 results found for "coefficient-condition" in Class 10.
बहुपद \(2x^4+3x^2-5x+7\) में \(x^3\) के गुणांक और (x) के गुणांक का योग क्या है?
In \(2x^4+3x^2-5x+7\), what is the sum of the coefficient of \(x^3\) and the coefficient of (x)?
#coefficients
#missing-term
#sum
A (-5)
B (0)
C (5)
D (3)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).
Step 3
Exam Tip
\(x^3\) का गुणांक (0) और (x) का गुणांक (-5) है। योग (-5) है।
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समीकरण \(x^2+12x+36=0\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(x^2+12x+36=0\)?
#quadratic equations
#implicit coefficient
#coefficient
A (0)
B (1)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
When no number is written before \(x^2\), its coefficient is (1). This is often asked.
Step 2
Why this answer is correct
The correct answer is B. (1). When no number is written before \(x^2\), its coefficient is (1). This is often asked.
Step 3
Exam Tip
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह अक्सर पूछी जाने वाली बात है।
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(p(x)=4x-6 -5x-4 +2x-2 -11) में \(x^5\) का गुणांक क्या है?
What is the coefficient of \(x^5\) in (p(x)=4x-6 -5x-4 +2x-2 -11)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (4)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 3
Exam Tip
\(x^5\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^5\) मानें।
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((3x-2)\(2x^2+x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((3x-2)\(2x^2+x-5\))?
#multiplication
#coefficient
#expansion
A (-1)
B (1)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-1). ((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), so the coefficient of \(x^2\) is (-1). Combine like terms after expansion.
Step 3
Exam Tip
((3x-2)\(2x^2+x-5\)=6x-3 -x-2 -17x+10), इसलिए \(x^2\) का गुणांक (-1) है। विस्तार के बाद समान पद मिलाएं।
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(p(x)=5x-4 -3x-3 +2x-2 -x+8) और (q(x)=-2x-4 +7x-3 -5x-2 +4x-6) के योग में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in the sum of (p(x)=5x-4 -3x-3 +2x-2 -x+8) and (q(x)=-2x-4 +7x-3 -5x-2 +4x-6)?
#addition
#coefficient
#like terms
A (3)
B (4)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
The coefficients of \(x^3\) are (-3) and (7), so the sum is (4). Add only coefficients of like powers.
Step 2
Why this answer is correct
The correct answer is B. (4). The coefficients of \(x^3\) are (-3) and (7), so the sum is (4). Add only coefficients of like powers.
Step 3
Exam Tip
\(x^3\) के गुणांक (-3) और (7) हैं, इसलिए योग (4) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=3x-5 -2x-4 +7x-6) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in (p(x)=3x-5 -2x-4 +7x-6)?
#missing term
#coefficient
#polynomial
A (0)
B (3)
C (-2)
D (7)
Explanation opens after your attempt
Step 1
Concept
The \(x^3\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^3\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 3
Exam Tip
\(x^3\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^3\) मानें।
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((2x-1)\(x^2-3x+4\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((2x-1)\(x^2-3x+4\))?
#multiplication
#coefficient
#expansion
A (-7)
B (-6)
C (-5)
D (8)
Explanation opens after your attempt
Step 1
Concept
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is A. (-7). ((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), so the coefficient is (-7). Combine like terms after expansion.
Step 3
Exam Tip
((2x-1)\(x^2-3x+4\)=2x-3 -7x-2 +11x-4), इसलिए गुणांक (-7) है। विस्तार के बाद समान पद मिलाएं।
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(p(x)=4x-3 -7x-2 +2x-5) और (q(x)=-x-3 +3x-2 -6x+9) के योग में (x) का गुणांक क्या है?
What is the coefficient of (x) in the sum of (p(x)=4x-3 -7x-2 +2x-5) and (q(x)=-x-3 +3x-2 -6x+9)?
#addition
#coefficient
#like terms
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficients of (x) are (2) and (-6), so the sum is (-4). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is B. (-4). The coefficients of (x) are (2) and (-6), so the sum is (-4). Add coefficients of like powers only.
Step 3
Exam Tip
(x) के गुणांक (2) और (-6) हैं, इसलिए योग (-4) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=2x-4 -3x-3 +5x-9) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=2x-4 -3x-3 +5x-9)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (-3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).
Step 3
Exam Tip
\(x^2\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^2\) मानें।
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((x-2)\(3x^2+4x-5\)) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in ((x-2)\(3x^2+4x-5\))?
#multiplication
#coefficient
#expansion
A (-4)
B (-2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 2
Why this answer is correct
The correct answer is B. (-2). ((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.
Step 3
Exam Tip
((x-2)\(3x^2+4x-5\)=3x-3 -2x-2 -13x+10), इसलिए \(x^2\) का गुणांक (-2) है। विस्तार में समान पद मिलाएं।
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(p(x)=3x-3 -2x-2 +5x-1) और (q(x)=-x-3 +7x-2 -4x+6) के योग में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in the sum of (p(x)=3x-3 -2x-2 +5x-1) and (q(x)=-x-3 +7x-2 -4x+6)?
#addition
#coefficient
#like terms
A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.
Step 2
Why this answer is correct
The correct answer is B. (5). The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.
Step 3
Exam Tip
\(x^2\) के गुणांक (-2) और (7) हैं, जिनका योग (5) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=3x-3 -7x-2 +2x-11) में \(x^2\) के गुणांक और अचर पद का योग क्या है?
In (p(x)=3x-3 -7x-2 +2x-11), what is the sum of the coefficient of \(x^2\) and the constant term?
#coefficient
#constant term
#signs
A (-18)
B (-11)
C (-7)
D (4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.
Step 2
Why this answer is correct
The correct answer is A. (-18). The coefficient of \(x^2\) is (-7) and the constant term is (-11), so the sum is (-18). Do not forget to add with signs.
Step 3
Exam Tip
\(x^2\) का गुणांक (-7) और अचर पद (-11) है, इसलिए योग (-18) है। संकेत सहित जोड़ना न भूलें।
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(p(x)=7x-4 -2x-2 +9) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in (p(x)=7x-4 -2x-2 +9)?
#coefficient
#missing term
#quartic
A (7)
B (-2)
C (0)
D (9)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\)-term, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\)-term, so its coefficient is (0). Treat the missing term as \(0x^3\).
Step 3
Exam Tip
\(x^3\) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^3\) समझें।
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बहुपद (p(x)=5x-3 +0x-2 -4x+12) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 +0x-2 -4x+12)?
#coefficient
#missing term
#polynomial
A (0)
B (5)
C (-4)
D (12)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 3
Exam Tip
\(x^2\) वाला पद \(0x^2\) है इसलिए गुणांक (0) है। अनुपस्थित या शून्य पद का गुणांक (0) माना जाता है।
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(p(x)=8x-4 -5x-3 +2x-6) में \(x^4\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^4\)-term in (p(x)=8x-4 -5x-3 +2x-6)?
#coefficient
#quartic term
#polynomial
A (8)
B (-5)
C (2)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (8). The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 3
Exam Tip
\(x^4\) वाले पद \(8x^4\) का गुणांक (8) है। घात और गुणांक को अलग पहचानें।
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बहुपद (p(z)=-6z-5 +4z-4 -z+8) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(z)=-6z-5 +4z-4 -z+8)?
#leading coefficient
#degree
#polynomial
A (-6)
B (4)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-6). The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 3
Exam Tip
सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है।
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यदि (p(x)=9x-2 +cx-5) में (x) का गुणांक (-4) है, तो (c) क्या है?
If the coefficient of (x) in (p(x)=9x-2 +cx-5) is (-4), what is (c)?
#coefficient
#parameter
#polynomial
A (-9)
B (-5)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 2
Why this answer is correct
The correct answer is C. (-4). In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 3
Exam Tip
(cx) में (x) का गुणांक (c) है। दिया है कि (c=-4)।
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(p(x)=5x-3 -8x-2 +13x-21) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 -8x-2 +13x-21)?
#coefficient
#sign
#polynomial
A (5)
B (-8)
C (13)
D (-21)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is B. (-8). The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 3
Exam Tip
\(x^2\) वाले पद \(-8x^2\) का गुणांक (-8) है। संकेत सहित गुणांक लिखना जरूरी है।
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निम्न में से किस बहुपद में प्रमुख गुणांक (1) नहीं है?
Which of the following polynomials does not have leading coefficient (1)?
#leading-coefficient
#monic-polynomial
#classification
A \(x^3+2x+5\)
B \(x^2-4\)
C \(3x^2+x+1\)
D \(x^5-x\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+x+1\)
Step 1
Concept
The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 2
Why this answer is correct
The correct answer is C. \(3x^2+x+1\). The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 3
Exam Tip
\(3x^2+x+1\) का प्रमुख पद \(3x^2\) है। इसका प्रमुख गुणांक (3) है, (1) नहीं।
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यदि \(x^3+2x^2+cx+5\) में (x) का गुणांक (6) है, तो (c+5) क्या होगा?
If the coefficient of (x) in \(x^3+2x^2+cx+5\) is (6), what will be (c+5)?
#coefficient
#parameter
#evaluation
A (6)
B (9)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 2
Why this answer is correct
The correct answer is C. (11). The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 3
Exam Tip
(x) का गुणांक (c=6) है। इसलिए (c+5=11) होगा।
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बहुपद \(3x^4-5x^2+2x-8\) का प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^4-5x^2+2x-8\)?
#leading-coefficient
#degree-four
#polynomial
A (3)
B (-5)
C (2)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 3
Exam Tip
प्रमुख पद \(3x^4\) है। इसलिए प्रमुख गुणांक (3) है।
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निम्न में से किस बहुपद में (x) का गुणांक (0) है?
In which of the following polynomials is the coefficient of (x) equal to (0)?
#coefficient
#missing-x-term
#polynomial
A \(x^2+5x+6\)
B \(3x^2-4\)
C \(2x^3+x-1\)
D (7x-9)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-4\)
Step 1
Concept
In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-4\). In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 3
Exam Tip
\(3x^2-4\) में (x) का पद नहीं है। इसलिए (x) का गुणांक (0) है।
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बहुपद \(7x^5-3x^4+x^2-11\) में अनुपस्थित \(x^3\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^3\) term in \(7x^5-3x^4+x^2-11\)?
#missing-term
#coefficient
#degree
A (7)
B (-3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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यदि (p(x)=2x-3 +mx-2 -x+4) में \(x^2\) का गुणांक (-5) है, तो (m) क्या है?
If the coefficient of \(x^2\) in (p(x)=2x-3 +mx-2 -x+4) is (-5), what is (m)?
#coefficient
#parameter
#polynomial
A (5)
B (-5)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 2
Why this answer is correct
The correct answer is B. (-5). The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणक (m) है। दिया है (m=-5), इसलिए उत्तर (-5) है।
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बहुपद \(4x^3-2x^2+7x-9\) में \(x^2\) के गुणांक और नियत पद का योग क्या है?
In the polynomial \(4x^3-2x^2+7x-9\), what is the sum of the coefficient of \(x^2\) and the constant term?
#coefficient
#constant-term
#polynomial
A (-11)
B (-7)
C (7)
D (11)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(x^2\) is (-2) and the constant term is (-9). Their sum is (-11).
Step 2
Why this answer is correct
The correct answer is A. (-11). The coefficient of \(x^2\) is (-2) and the constant term is (-9). Their sum is (-11).
Step 3
Exam Tip
\(x^2\) का गुणांक (-2) और नियत पद (-9) है। उनका योग (-11) है।
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निम्न में से किस बहुपद का प्रमुख गुणांक (-2) है?
Which polynomial has leading coefficient (-2)?
#leading-coefficient
#cubic-polynomial
#easy
A \(5x^2-2x+1\)
B \(-2x^3+4x+7\)
C \(x^2-2\)
D (3x-2)
Explanation opens after your attempt
Correct Answer
B. \(-2x^3+4x+7\)
Step 1
Concept
The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 2
Why this answer is correct
The correct answer is B. \(-2x^3+4x+7\). The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 3
Exam Tip
\(-2x^3+4x+7\) का प्रमुख पद \(-2x^3\) है। इसलिए प्रमुख गुणांक (-2) है।
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\(5x^3+2x^2-x+8\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in \(5x^3+2x^2-x+8\)?
#coefficient
#cubic-term
#polynomial
A (5)
B (2)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 2
Why this answer is correct
The correct answer is A. (5). The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 3
Exam Tip
\(x^3\) के साथ लगा गुणक (5) है। गुणांक हमेशा संबंधित पद से पहचाना जाता है।
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(p(x)=2x-3 +3x-2 -5) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-3 +3x-2 -5)?
#coefficient
#missing term
#cubic
A (2)
B (3)
C (0)
D (-5)
Explanation opens after your attempt
Step 1
Concept
There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 3
Exam Tip
इसमें (x) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को (0x) समझें।
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बहुपद (p(x)=2x-2 +0x+3) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-2 +0x+3)?
#coefficient
#missing term
#polynomial
A (0)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The (x)-term is (0x), so the coefficient of (x) is (0). Treat a missing term as having coefficient (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The (x)-term is (0x), so the coefficient of (x) is (0). Treat a missing term as having coefficient (0).
Step 3
Exam Tip
(x) वाला पद (0x) है इसलिए (x) का गुणांक (0) है। अनुपस्थित पद का गुणांक (0) मानें।
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(p(x)=4x-3 -2x-2 +7x-1) में \(x^3\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^3\) term in (p(x)=4x-3 -2x-2 +7x-1)?
#coefficient
#cubic term
#polynomial
A (4)
B (-2)
C (7)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (4). The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 3
Exam Tip
\(x^3\) के साथ गुणांक (4) जुड़ा है। घात और गुणांक को अलग अलग पहचानें।
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बहुपद (p(y)=9y-4 -y-2 +5y-6) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(y)=9y-4 -y-2 +5y-6)?
#leading coefficient
#degree
#polynomial
A (9)
B (-1)
C (5)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (9). The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 3
Exam Tip
सबसे बड़ी घात \(y^4\) के पद का गुणांक (9) है। अग्र गुणांक वही होता है।
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(p(x)=2x-2 +kx+8) में (x) का गुणांक (5) हो तो (k) क्या है?
If the coefficient of (x) in (p(x)=2x-2 +kx+8) is (5), what is (k)?
#coefficient
#parameter
#polynomial
A (2)
B (5)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
In (kx), the coefficient of (x) is (k). It is given that (k=5).
Step 2
Why this answer is correct
The correct answer is B. (5). In (kx), the coefficient of (x) is (k). It is given that (k=5).
Step 3
Exam Tip
(kx) में (x) का गुणांक (k) है। दिया है (k=5)।
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व्यंजक \(7x^3+2x^2-x+6\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(7x^3+2x^2-x+6\)?
#coefficient
#term
#polynomial
A (7)
B (2)
C (-1)
D (6)
Explanation opens after your attempt
Step 1
Concept
The numerical factor attached to \(x^2\) is (2). When coefficient is asked, identify the exact term.
Step 2
Why this answer is correct
The correct answer is B. (2). The numerical factor attached to \(x^2\) is (2). When coefficient is asked, identify the exact term.
Step 3
Exam Tip
\(x^2\) के साथ लगा संख्या गुणक (2) है। गुणांक पूछने पर उसी पद को पहचानें।
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बहुपद \(6x^2-x+13\) में (x) के गुणांक का सही मान कौन सा है?
Which is the correct coefficient of (x) in \(6x^2-x+13\)?
#coefficient
#negative-one
A (6)
B (-1)
C (1)
D (13)
Explanation opens after your attempt
Step 1
Concept
(-x) means (-1x), so the coefficient is (-1). Identify the hidden (1) with its sign.
Step 2
Why this answer is correct
The correct answer is B. (-1). (-x) means (-1x), so the coefficient is (-1). Identify the hidden (1) with its sign.
Step 3
Exam Tip
(-x) का अर्थ (-1x) है इसलिए गुणांक (-1) है। छिपे हुए (1) को चिह्न सहित पहचानें।
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बहुपद \(x^3+4x^2-5\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(x^3+4x^2-5\)?
#coefficient
#missing-term
A (1)
B (4)
C (0)
D (-5)
Explanation opens after your attempt
Step 1
Concept
It has no (x)-term, so the coefficient of (x) is (0). It is important to identify missing terms quickly.
Step 2
Why this answer is correct
The correct answer is C. (0). It has no (x)-term, so the coefficient of (x) is (0). It is important to identify missing terms quickly.
Step 3
Exam Tip
इसमें (x) का पद नहीं है इसलिए (x) का गुणांक (0) है। अनुपस्थित पद को तुरंत पहचानना जरूरी है।
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बहुपद \(10x^3-6x^2+2x-1\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(10x^3-6x^2+2x-1\)?
#coefficient
#x-term
A (10)
B (-6)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the (x)-term (2x) is (2). Look only at the term containing \(x^1\).
Step 2
Why this answer is correct
The correct answer is C. (2). The coefficient of the (x)-term (2x) is (2). Look only at the term containing \(x^1\).
Step 3
Exam Tip
(x) वाले पद (2x) का गुणांक (2) है। केवल उसी पद को देखें जिसमें \(x^1\) हो।
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\(2x^3-7\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(2x^3-7\)?
#coefficient
#missing-power
A (2)
B (0)
C (-7)
D (3)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\) term, so the coefficient is (0). A missing power can be treated as a term with zero coefficient.
Step 2
Why this answer is correct
The correct answer is B. (0). There is no \(x^2\) term, so the coefficient is (0). A missing power can be treated as a term with zero coefficient.
Step 3
Exam Tip
\(x^2\) का कोई पद नहीं है इसलिए गुणांक (0) है। अनुपस्थित घात को शून्य गुणांक वाला पद माना जा सकता 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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\(3x^2-5x+7\) में प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^2-5x+7\)?
#leading-coefficient
#polynomial
A (3)
B (-5)
C (7)
D (2)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^2\), so the leading coefficient is (3). The coefficient of the highest degree term is the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^2\), so the leading coefficient is (3). The coefficient of the highest degree term is the leading coefficient.
Step 3
Exam Tip
प्रमुख पद \(3x^2\) है इसलिए प्रमुख गुणांक (3) है। सबसे बड़ी घात वाले पद का गुणांक प्रमुख गुणांक कहलाता है।
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बहुपद \(8x^5-3x^2+4\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in \(8x^5-3x^2+4\)?
#missing-term
#coefficient
A (8)
B (-3)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^3\) term, so its coefficient is (0). The coefficient of a missing term is taken as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no \(x^3\) term, so its coefficient is (0). The coefficient of a missing term is taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) का पद नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक (0) माना जाता है।
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\(x^2-7x\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(x^2-7x\)?
#coefficient
#sign-error
A (1)
B (-7)
C (7)
D (0)
Explanation opens after your attempt
Step 1
Concept
The multiplier of (x) is (-7). Treat the negative sign as part of the coefficient.
Step 2
Why this answer is correct
The correct answer is B. (-7). The multiplier of (x) is (-7). Treat the negative sign as part of the coefficient.
Step 3
Exam Tip
(x) के साथ लगा गुणक (-7) है। ऋण चिह्न को गुणांक का भाग मानें।
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बहुपद \(5x^2-8x+6\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(5x^2-8x+6\)?
#coefficient
#polynomial-terms
#easy
A (5)
B (-8)
C (6)
D (2)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^2\) is (5). Identify the coefficient separately from the variable part.
Step 2
Why this answer is correct
The correct answer is A. (5). The multiplier of \(x^2\) is (5). Identify the coefficient separately from the variable part.
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणक (5) है। पद के गुणांक को उसके चर भाग से अलग पहचानें।
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यदि (p(x)=2x-3 -5x+9) है, तो इसमें \(x^2\) का गुणांक क्या है?
If (p(x)=2x-3 -5x+9), what is the coefficient of \(x^2\)?
#polynomials
#one-variable
#coefficient
#missing-term
A (2)
B (-5)
C (9)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक हमेशा (0) माना जाता है।
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बहुपद \(2x^2+3x+4\) में (x) का गुणांक और नियत पद क्रमशः क्या हैं?
In \(2x^2+3x+4\), what are the coefficient of (x) and the constant term respectively?
#polynomials
#coefficient
#constant-term
#easy
A (3,4)
B (2,3)
C (4,3)
D (2,4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (3), and the constant term is (4). Keep the asked order in mind.
Step 2
Why this answer is correct
The correct answer is A. (3,4). The coefficient of (x) is (3), and the constant term is (4). Keep the asked order in mind.
Step 3
Exam Tip
(x) का गुणांक (3) और नियत पद (4) है। क्रमशः पूछे गए क्रम का ध्यान रखें।
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\(4x^3+x+2\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(4x^3+x+2\)?
#polynomials
#missing-term
#easy
#coefficient
A (4)
B (1)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\)-term, so its coefficient is (0). The coefficient of a missing term is taken as zero.
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\)-term, so its coefficient is (0). The coefficient of a missing term is taken as zero.
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक शून्य माना जाता है।
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बहुपद \(2x^2-7x+1\) में अग्र गुणांक क्या है?
What is the leading coefficient of \(2x^2-7x+1\)?
#polynomials
#leading-coefficient
#easy
A (2)
B (-7)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest-degree term \(2x^2\) is (2). This is called the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). The coefficient of the highest-degree term \(2x^2\) is (2). This is called the leading coefficient.
Step 3
Exam Tip
सबसे बड़ी घात वाले पद \(2x^2\) का गुणांक (2) है। इसी को अग्र गुणांक कहते हैं।
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\(8x^3-5x^2+4\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(8x^3-5x^2+4\)?
#polynomials
#coefficient
#easy
#sign
A (8)
B (-5)
C (4)
D (2)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is \(-5x^2\), so the coefficient is (-5). Write the sign with the coefficient.
Step 2
Why this answer is correct
The correct answer is B. (-5). The \(x^2\)-term is \(-5x^2\), so the coefficient is (-5). Write the sign with the coefficient.
Step 3
Exam Tip
\(x^2\) वाला पद \(-5x^2\) है, इसलिए गुणांक (-5) है। चिह्न को गुणांक के साथ लिखें।
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बहुपद \(4x^2+0x+6\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(4x^2+0x+6\)?
#polynomials
#coefficient
#easy
#level48
A (4)
B (0)
C (6)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-term is (0x), so its coefficient is (0). Notice hidden zero terms.
Step 2
Why this answer is correct
The correct answer is B. (0). The (x)-term is (0x), so its coefficient is (0). Notice hidden zero terms.
Step 3
Exam Tip
(x) वाला पद (0x) है इसलिए गुणांक (0) है। छिपे हुए शून्य पदों पर ध्यान दें।
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बहुपद (p(x)=2x-4 -5x-3 +x-8) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=2x-4 -5x-3 +x-8)?
#coefficient
#missing_term
#degree_four
A (2)
B \(-5\)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\) term in this polynomial. Therefore the coefficient of \(x^2\) is (0).
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\) term in this polynomial. Therefore the coefficient of \(x^2\) is (0).
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है। इसलिए \(x^2\) का गुणांक (0) है।
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यदि (p(x)=2x-2 +kx+3) में (x) का गुणांक (5) है, तो (k) का मान क्या है?
If the coefficient of (x) in (p(x)=2x-2 +kx+3) is (5), what is the value of (k)?
#coefficient
#parameter
#polynomials
A (2)
B (3)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
In (kx), the coefficient of (x) is (k). Therefore (k=5).
Step 2
Why this answer is correct
The correct answer is C. (5). In (kx), the coefficient of (x) is (k). Therefore (k=5).
Step 3
Exam Tip
(kx) में (x) का गुणांक (k) है। इसलिए (k=5) होगा।
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बहुपद \(2x^2-9\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(2x^2-9\)?
#coefficient
#missing_term
#polynomials
A (2)
B \(-9\)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no (x)-term, so its coefficient is (0). In exams, treat the coefficient of a missing term as (0).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). In exams, treat the coefficient of a missing term as (0).
Step 3
Exam Tip
इसमें (x) वाला पद लिखा नहीं है इसलिए उसका गुणांक (0) है। परीक्षा में लुप्त पद का गुणांक (0) मानें।
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बहुपद \(x^5-4x^2+10\) में लुप्त \(x^4\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^4\) term in \(x^5-4x^2+10\)?
#missing_term
#coefficient
#polynomials
A (1)
B \(-4\)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
Step 2
Why this answer is correct
The correct answer is C. (0). A missing term is treated as having coefficient (0). So the coefficient of \(x^4\) is (0).
Step 3
Exam Tip
जो पद लिखा नहीं है उसका गुणांक (0) माना जाता है। इसलिए \(x^4\) का गुणांक (0) है।
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बहुपद \(9x^4-2x^3+7\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in \(9x^4-2x^3+7\)?
#coefficient
#terms
#polynomials
A (9)
B \(-2\)
C (7)
D (3)
Explanation opens after your attempt
Step 1
Concept
The number attached to \(x^3\) is (-2). So the coefficient of \(x^3\) is (-2).
Step 2
Why this answer is correct
The correct answer is B. \(-2\). The number attached to \(x^3\) is (-2). So the coefficient of \(x^3\) is (-2).
Step 3
Exam Tip
\(x^3\) के साथ (-2) लगा है। इसलिए \(x^3\) का गुणांक (-2) है।
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बहुपद \(5x^4-3x^2+x-6\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(5x^4-3x^2+x-6\)?
#coefficient
#polynomials
#terms
A (5)
B \(-3\)
C (1)
D \(-6\)
Explanation opens after your attempt
Step 1
Concept
The number attached to \(x^2\) is (-3). In exams, include the sign of the term in the coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(-3\). The number attached to \(x^2\) is (-3). In exams, include the sign of the term in the coefficient.
Step 3
Exam Tip
\(x^2\) के साथ लगा संख्या गुणांक (-3) है। परीक्षा में पद का चिह्न भी गुणांक में शामिल करें।
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यदि किसी द्विघात समीकरण की जड़ें (3) और (-2) हैं और \(x^2\) का गुणांक (2) है, तो समीकरण कौन-सा है?
If the roots of a quadratic equation are (3) and (-2), and the coefficient of \(x^2\) is (2), which is the equation?
#quadratic-roots
#forming-equation
#leading-coefficient
A \(2x^2-2x-12=0\)
B \(2x^2+2x-12=0\)
C \(2x^2-2x+12=0\)
D \(x^2-x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-2x-12=0\)
Step 1
Concept
The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-2x-12=0\). The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 3
Exam Tip
मॉनिक समीकरण \(x^2-x-6=0\) है। \(x^2\) का गुणांक (2) चाहिए, इसलिए पूरे समीकरण को (2) से गुणा करें।
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मानक रूप \(ax^2+bx+c=0\) में \(x^2\) का गुणांक किससे दर्शाया जाता है?
In the standard form \(ax^2+bx+c=0\), which symbol denotes the coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#coefficient-a
A (b)
B (a)
C (c)
D (x)
Explanation opens after your attempt
Step 1
Concept
In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 2
Why this answer is correct
The correct answer is B. (a). In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 3
Exam Tip
मानक रूप में \(x^2\) का गुणांक (a) होता है। यही गुणांक (0) नहीं होना चाहिए।
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समीकरण \(2x^2-x+8=0\) में (x) का गुणांक क्या है?
What is the coefficient of (x) in \(2x^2-x+8=0\)?
#quadratic-equations
#coefficient-b
#signs
A (-1)
B (1)
C (2)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-1). The coefficient of (-x) is (-1). It is necessary to write the coefficient with its sign.
Step 3
Exam Tip
(-x) का गुणांक (-1) होता है। चिन्ह सहित गुणांक लिखना जरूरी है।
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समीकरण \(5x^2-2x+1=0\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(5x^2-2x+1=0\)?
#quadratic-equations
#coefficient-a
#easy
A (5)
B (2)
C (1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^2\) is (5). While writing a coefficient, take the numerical part attached to the term.
Step 2
Why this answer is correct
The correct answer is A. (5). The coefficient attached to \(x^2\) is (5). While writing a coefficient, take the numerical part attached to the term.
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणांक (5) है। गुणांक लिखते समय केवल पद के साथ लगा संख्यात्मक भाग लें।
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यदि \(x^2+kx+12=0\) एक द्विघात समीकरण है तो (k) किस पद का गुणांक है?
If \(x^2+kx+12=0\) is a quadratic equation, then (k) is the coefficient of which term?
#quadratic equations
#coefficient
#standard form
A \(x^2\) पद / \(x^2\) term
B (x) पद / (x) term
C स्थिर पद (12) / Constant term (12)
D शून्य पद (0) / Zero term (0)
Explanation opens after your attempt
Correct Answer
B. (x) पद / (x) term
Step 1
Concept
In \(ax^2+bx+c=0\), (b) is the coefficient of (x). Here in (kx), (k) is the coefficient of (x).
Step 2
Why this answer is correct
The correct answer is B. (x) पद / (x) term. In \(ax^2+bx+c=0\), (b) is the coefficient of (x). Here in (kx), (k) is the coefficient of (x).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में (x) का गुणांक (b) होता है। यहां (kx) में (k) (x) का गुणांक है।
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समीकरण \(x^2+8x+16=0\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(x^2+8x+16=0\)?
#quadratic equations
#coefficient
#implicit one
A (0)
B (1)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
When no number is written before \(x^2\), its coefficient is (1). This is a common exam mistake.
Step 2
Why this answer is correct
The correct answer is B. (1). When no number is written before \(x^2\), its coefficient is (1). This is a common exam mistake.
Step 3
Exam Tip
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह सामान्य परीक्षा गलती है।
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मैग्नीशियम के जलने की अभिक्रिया में ऑक्सीजन अणु के आगे गुणांक एक है। संतुलित समीकरण में मैग्नीशियम के आगे कौन सा गुणांक होगा?
In the burning reaction of magnesium the coefficient before oxygen molecule is one. What coefficient will be before magnesium in the balanced equation?
#science
#class10
#hard
#magnesium-oxide
#balancing
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
One oxygen molecule has two oxygen atoms.
Step 2
Why this answer is correct
In magnesium oxide one magnesium combines with one oxygen.
Step 3
Exam Tip
Therefore two magnesium atoms are required. चरण 1: एक ऑक्सीजन अणु में दो ऑक्सीजन परमाणु होते हैं। चरण 2: मैग्नीशियम ऑक्साइड में एक मैग्नीशियम के साथ एक ऑक्सीजन जुड़ती है। चरण 3: इसलिए दो मैग्नीशियम परमाणुओं की जरूरत होगी।
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किस शर्त पर \(px^2+qx+r=0\) द्विघात समीकरण होगा?
Under which condition will \(px^2+qx+r=0\) be a quadratic equation?
#quadratic equations
#condition
#leading coefficient
A (p=0)
B \(p\neq0\)
C (q=0)
D (r=0)
Explanation opens after your attempt
Correct Answer
B. \(p\neq0\)
Step 1
Concept
The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 2
Why this answer is correct
The correct answer is B. \(p\neq0\). The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 3
Exam Tip
द्विघात पद \(px^2\) बना रहे इसलिए \(p\neq0\) होना चाहिए। यदि (p=0) हो तो घात (2) नहीं रहेगी।
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समीकरण \(kx^2-6x+k=0\) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?
What is the correct condition for real and distinct roots of \(kx^2-6x+k=0\)?
#quadratic equations
#real distinct roots
#leading coefficient
A \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\)
B \(k^2>9\)
C \(k^2=9\)
D (k=0)
Explanation opens after your attempt
Correct Answer
A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\)
Step 1
Concept
Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 2
Why this answer is correct
The correct answer is A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\). Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 3
Exam Tip
यहाँ \(D=36-4k^2\) है। वास्तविक और भिन्न मूलों के लिए (D>0) और \(k\neq0\), अतः \(k^2<9\)।
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समीकरण ((k-1)x-2 +3x+2=0) द्विघात रहे इसके लिए कौन सी शर्त सही है?
Which condition is correct for ((k-1)x-2 +3x+2=0) to remain quadratic?
#quadratic equations
#parameter
#leading coefficient
A (k=1)
B \(k\neq1\)
C (k=0)
D (k=-1)
Explanation opens after your attempt
Correct Answer
B. \(k\neq1\)
Step 1
Concept
The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq1\). The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 3
Exam Tip
द्विघात पद का गुणांक ((k-1)) है जो (0) नहीं होना चाहिए। इसलिए \(k\neq1\) होना जरूरी है।
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यदि किसी युग्म में गुणांक अनुपात समान है और स्थिर पद का अनुपात अलग है, तो हल-स्थिति क्या होगी?
If coefficient ratios are equal and the constant ratio is different in a pair, what is the solution status?
#class10
#linear-equations
#solvability
A अद्वितीय हल / Unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D सदैव दो हल / Always two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. This condition forms distinct parallel lines. Therefore, the pair is inconsistent.
Step 3
Exam Tip
यह स्थिति अलग-अलग समांतर रेखाएँ बनाती है। इसलिए युग्म असंगत होता है।
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किस युग्म की रेखाएं अलग गुणांक अनुपातों के कारण एक अद्वितीय समाधान देंगी?
Which pair will give a unique solution because of different coefficient ratios?
#graphical method
#unique solution
#intersecting lines
#ratio test
A (4x+8y=16), (x+2y=5)
B (5x-2y=11), (x+y=7)
C (6x-3y=9), (2x-y=3)
D (7x+14y=28), (x+2y=4)
Explanation opens after your attempt
Correct Answer
B. (5x-2y=11), (x+y=7)
Step 1
Concept
For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 2
Why this answer is correct
The correct answer is B. (5x-2y=11), (x+y=7). For (5x-2y=11) and (x+y=7), \(\frac{5}{1}\neq\frac{-2}{1}\), so the lines intersect. Different coefficient ratios give a unique solution.
Step 3
Exam Tip
(5x-2y=11) और (x+y=7) में \(\frac{5}{1}\neq\frac{-2}{1}\), इसलिए रेखाएं प्रतिच्छेदी हैं। अलग गुणांक अनुपात अद्वितीय समाधान देता है।
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बहुपद \(6x^5+x^2-4\) का अग्र गुणांक क्या है?
What is the leading coefficient of \(6x^5+x^2-4\)?
#leading_coefficient
#polynomials
#degree
A (6)
B (1)
C \(-4\)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term with the highest power is \(6x^5\). So the leading coefficient is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The term with the highest power is \(6x^5\). So the leading coefficient is (6).
Step 3
Exam Tip
सबसे बड़ी घात वाला पद \(6x^5\) है। इसलिए अग्र गुणांक (6) है।
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यदि (x=3) और (x=8) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=3) and (x=8) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-11)
B (11)
C (24)
D (-24)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (3+8=11). In a monic equation the coefficient of (x) is (-(\)sum\()=-11).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-11). The sum of roots is (3+8=11). In a monic equation the coefficient of (x) is (-(\)sum\()=-11).\)
Step 3
Exam Tip
मूलों का योग (3+8=11) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-11) होता है\)।
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यदि (x=2) और (x=7) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=2) and (x=7) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-9)
B (9)
C (14)
D (-14)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (2+7=9). In a monic equation the coefficient of (x) is (-(\)sum\()=-9).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-9). The sum of roots is (2+7=9). In a monic equation the coefficient of (x) is (-(\)sum\()=-9).\)
Step 3
Exam Tip
मूलों का योग (2+7=9) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-9) होता है\)।
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यदि (x=1) और (x=4) किसी मोनिक द्विघात समीकरण के मूल हैं तो (x) का गुणांक क्या होगा?
If (x=1) and (x=4) are roots of a monic quadratic equation, what will be the coefficient of (x)?
#roots
#coefficient_from_roots
#monic
A (-5)
B (5)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
\(The sum of roots is (1+4=5). In a monic equation the coefficient of (x) is (-(\)sum\()=-5).\)
Step 2
Why this answer is correct
\(The correct answer is A. (-5). The sum of roots is (1+4=5). In a monic equation the coefficient of (x) is (-(\)sum\()=-5).\)
Step 3
Exam Tip
मूलों का योग (1+4=5) है। मोनिक समीकरण में (x) का गुणांक (-(योग\()=-5) होता है\)।
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समीकरण \(8x-x^2=15\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(8x-x^2=15\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#transposition
#medium
A \(x^2-8x+15=0\)
B \(x^2+8x-15=0\)
C \(x^2-8x-15=0\)
D \(x^2+8x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+15=0\)
Step 1
Concept
Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+15=0\). Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 3
Exam Tip
सभी पद एक ओर लाने पर \(-x^2+8x-15=0\) मिलता है। (-1) से गुणा करने पर \(x^2-8x+15=0\) मिलता है।
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समीकरण \(5x-2x^2=9\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(5x-2x^2=9\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#signs
#medium
A \(2x^2-5x+9=0\)
B \(2x^2+5x-9=0\)
C \(2x^2-5x-9=0\)
D \(2x^2+5x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+9=0\)
Step 1
Concept
Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+9=0\). Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 3
Exam Tip
सभी पद एक ओर लाकर \(-2x^2+5x-9=0\) मिलता है और (-1) से गुणा करने पर \(2x^2-5x+9=0\) मिलता है। मानक रूप में चिन्ह सावधानी से बदलें।
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यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?
If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?
#radical-simplification
#monic-polynomial
#coefficient
A \(-3\sqrt{3}\)
B \(-\sqrt{15}\)
C \(3\sqrt{3}\)
D \(-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
Step 2
Why this answer is correct
The correct answer is A. \(-3\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है।
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यदि \(2+\sqrt{13}\) परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक है, तो उस बहुपद में (x) का गुणांक किस रूप में हो सकता है?
If \(2+\sqrt{13}\) is one zero of a quadratic polynomial with rational coefficients, what can the coefficient of (x) be?
#rational-coefficients
#conjugate-root
#coefficient
A (-4)
B (4)
C \(-2-\sqrt{13}\)
D \(\sqrt{13}\)
Explanation opens after your attempt
Step 1
Concept
The other zero will be \(2-\sqrt{13}\), so the sum is (4). In a monic polynomial, the coefficient of (x) will be (-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). The other zero will be \(2-\sqrt{13}\), so the sum is (4). In a monic polynomial, the coefficient of (x) will be (-4).
Step 3
Exam Tip
दूसरा शून्यक \(2-\sqrt{13}\) होगा, इसलिए योग (4) है। एकक बहुपद में (x) का गुणांक (-4) होगा।
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मैग्नीशियम के जलने की अभिक्रिया को संतुलित करते समय मैग्नीशियम ऑक्साइड के आगे कौन सा गुणांक लगाया जाता है?
While balancing the burning reaction of magnesium what coefficient is placed before magnesium oxide?
#science
#class10
#balancing
#magnesium-oxide
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Magnesium combines with oxygen to form magnesium oxide.
Step 2
Why this answer is correct
To balance oxygen atoms coefficient two is placed before magnesium oxide.
Step 3
Exam Tip
Then magnesium is also made two to balance the equation. चरण 1: मैग्नीशियम ऑक्सीजन से मिलकर मैग्नीशियम ऑक्साइड बनाता है। चरण 2: ऑक्सीजन परमाणुओं को बराबर करने के लिए मैग्नीशियम ऑक्साइड के आगे दो लगाया जाता है। चरण 3: फिर मैग्नीशियम के आगे भी दो लगाकर समीकरण संतुलित होता है।
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संतुलित समीकरण में हाइड्रोजन और ऑक्सीजन से जल बनने पर जल के आगे कौन सा गुणांक लगता है?
In the balanced equation for formation of water from hydrogen and oxygen what coefficient is placed before water?
#science
#class10
#balanced-equation
#water
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
In water formation atoms must be equal on both sides.
Step 2
Why this answer is correct
In the balanced form coefficient two is placed before water.
Step 3
Exam Tip
Count atoms first in small equations. चरण 1: हाइड्रोजन और ऑक्सीजन से जल बनने में दोनों ओर परमाणु बराबर करने होते हैं। चरण 2: संतुलित रूप में जल के आगे दो लगाया जाता है। चरण 3: छोटे समीकरणों में पहले परमाणुओं की गिनती करें।
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विश्व धरोहर स्थल के लिए अखंडता की शर्त किस बात से संबंधित है?
The condition of integrity for a World Heritage Site is related to what?
#integrity
#heritage-condition
#site-management
A स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
B केवल टिकट खिड़की की संख्या / Only number of ticket counters
C केवल स्थानीय भोजन सूची / Only local food list
D स्थल के नाम की लंबाई / Length of the site's name
Explanation opens after your attempt
Correct Answer
A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
Step 1
Concept
Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 2
Why this answer is correct
The correct answer is A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value. Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 3
Exam Tip
अखंडता बताती है कि स्थल का मूल्य सुरक्षित और पर्याप्त रूप से प्रतिनिधित है या नहीं। परीक्षा में अखंडता और प्रामाणिकता अलग रखें।
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यदि (5x+8y=37) और (15x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (5x+8y=37) and (15x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#expert
#inconsistent
#condition
A (m=111)
B \(m\ne111\)
C (m=37)
D (m=74)
Explanation opens after your attempt
Correct Answer
B. \(m\ne111\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 2
Why this answer is correct
The correct answer is B. \(m\ne111\). The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए।
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यदि (7x+3y=25) और (14x+6y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (7x+3y=25) and (14x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=50)
B \(m \ne 50\)
C (m=25)
D (m=75)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 50\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 50\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(m \ne 50\)।
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यदि (3x+8y=25) और (9x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (3x+8y=25) and (9x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=75)
B \(m \ne 75\)
C (m=25)
D (m=50)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 75\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 75\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 75\) सही है।
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यदि (2x+5y=17) और (4x+10y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (2x+5y=17) and (4x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=34)
B \(m \ne 34\)
C (m=17)
D (m=68)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 34\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 34\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 34\) होगा।
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यदि (5x+2y=13) और (10x+4y=m) असंगत युग्म हैं तो (m) के लिए सही शर्त क्या है?
If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=26)
B (m=13)
C \(m \ne 26\)
D (m=39)
Explanation opens after your attempt
Correct Answer
C. \(m \ne 26\)
Step 1
Concept
The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 2
Why this answer is correct
The correct answer is C. \(m \ne 26\). The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 26\)।
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यदि (4x+5y=16) और (8x+10y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (4x+5y=16) and (8x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=32)
B \(m \ne 32\)
C (m=16)
D (m=24)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 32\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 32\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 32\)।
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यदि (2x+3y=7) और (4x+6y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent pair
#condition
A (m=14)
B \(m \ne 14\)
C (m=7)
D (m=21)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 14\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 14\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 14\)।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और आश्रित कहलाता है?
In which condition is a pair of two linear equations called consistent and dependent?
#linear equations
#consistent dependent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
C जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
D जब रेखाएं कटती हों / When lines intersect
Explanation opens after your attempt
Correct Answer
A. जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
Step 1
Concept
If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. जब \(a_1 / a_2=b_1 / b_2=c_1 / c_2\) हो / When \(a_1 / c_2\). If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और स्वतंत्र कहलाता है?
In which condition is a pair of two linear equations called consistent and independent?
#linear equations
#consistent independent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
C जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
D जब कोई हल न हो / When there is no solution
Explanation opens after your attempt
Correct Answer
C. जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
Step 1
Concept
A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 2
Why this answer is correct
The correct answer is C. जब \(a_1 / a_2 \ne b_1 / b_2\) हो / When \(a_1 / b_2\). A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 3
Exam Tip
संगत और स्वतंत्र युग्म में एक अद्वितीय हल होता है। इसके लिए (a) और (b) के अनुपात अलग होने चाहिए।
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यदि \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) के ग्राफ प्रतिच्छेदी हैं, तो कौन सी शर्त सही है?
If the graphs of \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) are intersecting, which condition is correct?
#linear equations
#graphical method
#intersecting lines
#ratio condition
A \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{c_1}{c_2}=0\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
Step 1
Concept
For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 3
Exam Tip
प्रतिच्छेदी रेखाओं के लिए (x) और (y) के गुणांक अनुपात बराबर नहीं होते। यही अद्वितीय समाधान की शर्त है।
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किस स्थिति में दो रेखाओं का ग्राफ अनंत समाधान दिखाता है?
In which condition does the graph of two lines show infinitely many solutions?
#linear equations
#graphical method
#ratio condition
#infinite solutions
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{a_1}{a_2}=0\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Step 1
Concept
Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 3
Exam Tip
अनंत समाधान तब होते हैं जब दोनों रेखाएं एक ही रेखा हों। इसके लिए तीनों अनुपात बराबर होते हैं।
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समीकरण (x-2 +2(k+1)x+k-2 +6k+9=0) के वास्तविक मूल न होने के लिए (k) पर क्या शर्त है?
What condition on (k) is needed for (x-2 +2(k+1)x+k-2 +6k+9=0) to have no real roots?
#quadratic equations
#no real roots
#parameter condition
A (k>-2)
B (k<-2)
C (k=-2)
D सभी वास्तविक (k) / All real (k)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 2
Why this answer is correct
The correct answer is A. (k>-2). For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=-16(k+2)), इसलिए (k>-2)।
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यदि \(x^2+2gx+g^2-6g+11=0\) के वास्तविक मूल हैं, तो (g) पर क्या शर्त है?
If \(x^2+2gx+g^2-6g+11=0\) has real roots, what condition on (g) is required?
#quadratic equations
#real roots
#fraction condition
A \(g\ge\frac{11}{6}\)
B \(g<\frac{11}{6}\)
C (g=0)
D सभी वास्तविक (g) / All real (g)
Explanation opens after your attempt
Correct Answer
A. \(g\ge\frac{11}{6}\)
Step 1
Concept
Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(g\ge\frac{11}{6}\). Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 3
Exam Tip
यहाँ (D=4g-2 -4\(g^2-6g+11\)=24g-44) है। \(D\ge0\) से \(g\ge\frac{11}{6}\) मिलता है।
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यदि \(x^2+2px+2p+9=0\) के मूल वास्तविक हैं, तो (p) पर सही शर्त कौन सी है?
If \(x^2+2px+2p+9=0\) has real roots, which condition on (p) is correct?
#quadratic equations
#real roots
#interval condition
A \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
B \(-2<p<\frac{9}{2}\)
C (p=-2) केवल / (p=-2) only
D \(p=\frac{9}{2}\) केवल / \(p=\frac{9}{2}\) only
Explanation opens after your attempt
Correct Answer
A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\). For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। यहाँ (D=4(p+2)(2p-9)), इसलिए \(p\le -2\) या \(p\ge \frac{9}{2}\)।
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यदि \(x^2+2kx+k^2-4k+8=0\) के वास्तविक मूल हैं, तो (k) पर क्या शर्त है?
If \(x^2+2kx+k^2-4k+8=0\) has real roots, what is the condition on (k)?
#quadratic equations
#real roots
#parameter condition
A \(k\ge2\)
B \(k\le2\)
C (k>4)
D (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\ge2\)
Step 1
Concept
Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 2
Why this answer is correct
The correct answer is A. \(k\ge2\). Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 3
Exam Tip
यहाँ (D=4k-2 -4\(k^2-4k+8\)=16(k-2)) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(k\ge2\)।
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किस शर्त पर \(x^2-2sx+s+2=0\) के मूल वास्तविक और भिन्न होंगे?
Under which condition will \(x^2-2sx+s+2=0\) have real and distinct roots?
#quadratic equations
#interval condition
#real distinct roots
A (s<-1) या (s>2) / (s<-1) or (s>2)
B (-1<s<2)
C (s=-1) या (s=2) / (s=-1) or (s=2)
D (0<s<1)
Explanation opens after your attempt
Correct Answer
A. (s<-1) या (s>2) / (s<-1) or (s>2)
Step 1
Concept
Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 2
Why this answer is correct
The correct answer is A. (s<-1) या (s>2) / (s<-1) or (s>2). Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 3
Exam Tip
यहाँ (D=4s-2 -4(s+2)=4(s-2 )(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है।
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समीकरण (x-2 +2(m-1 )x+(m+5)=0) के वास्तविक मूल न होने की शर्त क्या है?
What is the condition for (x-2 +2(m-1 )x+(m+5)=0) to have no real roots?
#quadratic equations
#no real roots
#parameter condition
A \(m^2-3m-4<0\)
B \(m^2-3m-4>0\)
C \(m^2-3m-4=0\)
D \(m^2+3m+4<0\)
Explanation opens after your attempt
Correct Answer
A. \(m^2-3m-4<0\)
Step 1
Concept
For no real roots, (D<0) is needed. Here (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)).
Step 2
Why this answer is correct
The correct answer is A. \(m^2-3m-4<0\). For no real roots, (D<0) is needed. Here (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)) है।
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यदि \(x^2-6x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?
If both roots of \(x^2-6x+c=0\) are real and positive, what is the correct condition on (c)?
#quadratic-roots
#positive-roots
#condition
A \(0<c\le9\)
B (c>9)
C (c<0)
D (c=0)
Explanation opens after your attempt
Correct Answer
A. \(0<c\le9\)
Step 1
Concept
The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, \(36-4c\ge0\), so \(0<c\le9\).
Step 2
Why this answer is correct
The correct answer is A. \(0<c\le9\). The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, \(36-4c\ge0\), so \(0<c\le9\).
Step 3
Exam Tip
योग (6) धनात्मक है और दोनों धनात्मक जड़ों के लिए (c>0) चाहिए। वास्तविक जड़ों के लिए \(36-4c\ge0\), इसलिए \(0<c\le9\)।
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(9x-2 -6(a-1)x+a-2 -4a-5=0) की जड़ें वास्तविक हों, तो सही शर्त क्या है?
What is the correct condition for (9x-2 -6(a-1)x+a-2 -4a-5=0) to have real roots?
#quadratic-roots
#real-roots
#parameter-condition
A \(a\ge-3\)
B \(a\le-3\)
C (a>3)
D (a< -3)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-3\)
Step 1
Concept
Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-3\). Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 3
Exam Tip
यहाँ (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)) है। वास्तविक जड़ों के लिए \(D\ge0\), इसलिए \(a\ge-3\)।
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यदि ((m-1 )x-2 +2(m+1)x+(m-1 )=0) की जड़ें वास्तविक और व्युत्क्रम हों, तो (m) पर सही शर्त क्या है?
If ((m-1 )x-2 +2(m+1)x+(m-1 )=0) has real reciprocal roots, what is the correct condition on (m)?
#quadratic-roots
#reciprocal-roots
#parameter-condition
A \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
B (m<0)
C (m=1)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
Step 1
Concept
The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 2
Why this answer is correct
The correct answer is A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\). The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 3
Exam Tip
जड़ों का गुणनफल \(\frac{m-1}{m-1}=1\) है, इसलिए \(m\neq1\) चाहिए। वास्तविक जड़ों के लिए \(D=16m\ge0\), अतः \(m\ge0\) और \(m\neq1\)।
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यदि (x-2 -2mx+\(m^2-m\)=0) की जड़ें वास्तविक हों, तो (m) पर सही शर्त क्या है?
If (x-2 -2mx+\(m^2-m\)=0) has real roots, what is the correct condition on (m)?
#quadratic-roots
#real-roots
#parameter-condition
A (m>0)
B (m<0)
C \(m\ge0\)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
C. \(m\ge0\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 2
Why this answer is correct
The correct answer is C. \(m\ge0\). For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=4m), इसलिए \(m\ge0\)।
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यदि \(x^2-sx+1=0\) की जड़ें \(\tan\theta\) और \(\cot\theta\) हो सकती हैं, तो वास्तविक \(\theta\) के लिए (s) पर सही शर्त क्या है?
If the roots of \(x^2-sx+1=0\) can be \(\tan\theta\) and \(\cot\theta\), what is the correct condition on (s) for real \(\theta\)?
#quadratic-roots
#trigonometric-roots
#condition
A (-2<s<2)
B (s=0)
C \(s^2\ge4\)
D \(s^2<4\)
Explanation opens after your attempt
Correct Answer
C. \(s^2\ge4\)
Step 1
Concept
We have \(\tan\theta\cdot\cot\theta=1\) and \(\tan\theta+\cot\theta=s\). For real values, \(s^2-4\ge0\), so \(s^2\ge4\).
Step 2
Why this answer is correct
The correct answer is C. \(s^2\ge4\). We have \(\tan\theta\cdot\cot\theta=1\) and \(\tan\theta+\cot\theta=s\). For real values, \(s^2-4\ge0\), so \(s^2\ge4\).
Step 3
Exam Tip
\(\tan\theta\cdot\cot\theta=1\) और \(\tan\theta+\cot\theta=s\) है। वास्तविक मानों के लिए \(s^2-4\ge0\), इसलिए \(s^2\ge4\)।
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यदि \(x^2-5x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?
If both roots of \(x^2-5x+c=0\) are real and positive, what is the correct condition on (c)?
#quadratic-roots
#positive-roots
#condition
A (c<0)
B \(0<c\le\frac{25}{4}\)
C \(c>\frac{25}{4}\)
D (c=0)
Explanation opens after your attempt
Correct Answer
B. \(0<c\le\frac{25}{4}\)
Step 1
Concept
The sum (5) is positive and product (c>0) is needed for both roots. For real roots, \(25-4c\ge0\), so \(0<c\le\frac{25}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(0<c\le\frac{25}{4}\). The sum (5) is positive and product (c>0) is needed for both roots. For real roots, \(25-4c\ge0\), so \(0<c\le\frac{25}{4}\).
Step 3
Exam Tip
योग (5) धनात्मक है और दोनों जड़ों के लिए गुणनफल (c>0) चाहिए। वास्तविक जड़ों के लिए \(25-4c\ge0\), इसलिए \(0<c\le\frac{25}{4}\)।
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