100 results found for "coefficient-factorisation" 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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कौन सा विकल्प अभाज्य गुणनखंडन नहीं है?
Which option is not a prime factorisation?
#real-numbers
#prime-factorisation
#not-prime-factorisation
#expert
A \(2^2 \times 9 \times 5\)
B \(2^3 \times 3 \times 5\)
C \(3^2 \times 7\)
D \(2 \times 5^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2 \times 9 \times 5\)
Step 1
Concept
In prime factorisation, every base must be prime.
Step 2
Why this answer is correct
(9) is not prime because \(9=3^2\), so the first option is not prime factorisation.
Step 3
Exam Tip
Every base must be prime; writing powers alone is not enough. चरण 1: अभाज्य गुणनखंडन में सभी आधार अभाज्य होने चाहिए। चरण 2: (9) अभाज्य नहीं है क्योंकि \(9=3^2\), इसलिए पहला विकल्प अभाज्य गुणनखंडन नहीं है। चरण 3: हर आधार को अभाज्य होना चाहिए, केवल घात लिखना काफी नहीं।
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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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यदि (2160) और (3780) का अभाज्य गुणनखंडन करके महत्तम समापवर्तक निकाला जाए, तो सही मान क्या होगा?
If the HCF of (2160) and (3780) is found using prime factorisation, what is the correct value?
#hcf
#prime factorisation
#real numbers
A (180)
B (270)
C (540)
D (1080)
Explanation opens after your attempt
Step 1
Concept
\(2160=2^4\times 3^3\times 5\) and \(3780=2^2\times 3^3\times 5\times 7\).
Step 2
Why this answer is correct
For HCF, take the smaller exponents of common prime factors, so \(2^2\times 3^3\times 5=540\).
Step 3
Exam Tip
In such questions, carefully choose the smaller powers. चरण 1: \(2160=2^4\times 3^3\times 5\) और \(3780=2^2\times 3^3\times 5\times 7\)। चरण 2: महत्तम समापवर्तक में समान अभाज्य गुणनखंडों के छोटे घातांक लिए जाते हैं, इसलिए \(2^2\times 3^3\times 5=540\)। चरण 3: ऐसी गणना में छोटे घातांक चुनना न भूलें।
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अभाज्य गुणनखंडन की अद्वितीयता किससे समझी जाती है?
Which idea explains the uniqueness of prime factorisation?
#real-numbers
#fundamental-theorem
#prime-factorisation
A अंकगणित का मूल प्रमेय / Fundamental theorem of arithmetic
B द्विघात सूत्र / Quadratic formula
C शेषफल प्रमेय / Remainder theorem
D त्रिभुज क्षेत्रफल सूत्र / Triangle area formula
Explanation opens after your attempt
Correct Answer
A. अंकगणित का मूल प्रमेय / Fundamental theorem of arithmetic
Step 1
Concept
Every integer greater than (1) can be written as a product of prime factors.
Step 2
Why this answer is correct
This form is unique apart from order, and this comes from the fundamental theorem of arithmetic.
Step 3
Exam Tip
Remember uniqueness of prime factorisation with this theorem. चरण 1: (1) से बड़ी हर पूर्ण संख्या को अभाज्य गुणनखंडों के गुणनफल के रूप में लिखा जा सकता है। चरण 2: यह रूप क्रम को छोड़कर अद्वितीय होता है, और यह बात अंकगणित के मूल प्रमेय से आती है। चरण 3: अभाज्य गुणनखंडन की अद्वितीयता को इसी प्रमेय से याद रखें।
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कौन सा कथन (1) और अभाज्य गुणनखंडन के बारे में सही है?
Which statement about (1) and prime factorisation is correct?
#real-numbers
#number-one
#prime-factorisation
A (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
B (1) सबसे छोटी अभाज्य संख्या है / (1) is the smallest prime number
C (1) हर अभाज्य गुणनखंडन में आधार होता है / (1) is a base in every prime factorisation
D (1) की घात हमेशा (2) होती है / The exponent of (1) is always (2)
Explanation opens after your attempt
Correct Answer
A. (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
Step 1
Concept
A prime number has exactly two positive factors.
Step 2
Why this answer is correct
(1) has only one positive factor, so it is not prime and has no prime factor.
Step 3
Exam Tip
Avoid the common mistake of treating (1) as prime. चरण 1: अभाज्य संख्या के ठीक दो धनात्मक गुणनखंड होते हैं। चरण 2: (1) का केवल एक धनात्मक गुणनखंड है, इसलिए वह अभाज्य नहीं है और उसका कोई अभाज्य गुणनखंड नहीं होता। चरण 3: (1) को अभाज्य मानने की गलती से बचें।
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(343) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (343)?
#real-numbers
#prime-factorisation
#343
A \(7^2\)
B \(7^3\)
C \(3 \times 7^2\)
D \(49 \times 7\)
Explanation opens after your attempt
Correct Answer
B. \(7^3\)
Step 1
Concept
Write (343) as \(7 \times 49\).
Step 2
Why this answer is correct
Since \(49=7^2\), \(343=7^3\).
Step 3
Exam Tip
\(49 \times 7\) gives the value, but it is not final prime factorisation. चरण 1: (343) को \(7 \times 49\) लिखें। चरण 2: \(49=7^2\), इसलिए \(343=7^3\)। चरण 3: \(49 \times 7\) मान देता है, पर अंतिम अभाज्य गुणनखंडन नहीं है।
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(1024) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (1024)?
#real-numbers
#prime-factorisation
#1024
A \(2^8\)
B \(2^9\)
C \(2^{10}\)
D \(4^5\)
Explanation opens after your attempt
Correct Answer
C. \(2^{10}\)
Step 1
Concept
Recognise (1024) as a power of (2).
Step 2
Why this answer is correct
\(1024=2^{10}\).
Step 3
Exam Tip
\(4^5\) gives the value, but prime factorisation must use base (2). चरण 1: (1024) को (2) की घात के रूप में पहचानें। चरण 2: \(1024=2^{10}\) होता है। चरण 3: \(4^5\) मान के लिए सही है, पर अभाज्य गुणनखंडन में आधार (2) होना चाहिए।
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(1250) का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of (1250)?
#real-numbers
#prime-factorisation
#1250
A \(2 \times 5^4\)
B \(2^2 \times 5^3\)
C \(2 \times 5^3\)
D \(10 \times 5^3\)
Explanation opens after your attempt
Correct Answer
A. \(2 \times 5^4\)
Step 1
Concept
Write (1250) as \(125 \times 10\).
Step 2
Why this answer is correct
\(125=5^3\) and \(10=2 \times 5\), so \(1250=2 \times 5^4\).
Step 3
Exam Tip
Do not keep (10) in the final form because it is not prime. चरण 1: (1250) को \(125 \times 10\) लिखें। चरण 2: \(125=5^3\) और \(10=2 \times 5\), इसलिए \(1250=2 \times 5^4\)। चरण 3: (10) को अंतिम रूप में न रखें क्योंकि वह अभाज्य नहीं है।
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^4 \times 3^3\) है, तो वह किससे अवश्य विभाज्य होगी?
If a number has prime factorisation \(2^4 \times 3^3\), by which number must it be divisible?
#real-numbers
#divisibility
#prime-factorisation
A 72
B 96
C 108
D 144
Explanation opens after your attempt
Step 1
Concept
A divisor's prime exponents must not exceed the given number's exponents.
Step 2
Why this answer is correct
\(144=2^4 \times 3^2\), which is fully contained in \(2^4 \times 3^3\).
Step 3
Exam Tip
For divisibility, match each prime exponent separately. चरण 1: भाजक की अभाज्य घातें दी गई संख्या की घातों से अधिक नहीं होनी चाहिए। चरण 2: \(144=2^4 \times 3^2\), जो \(2^4 \times 3^3\) में पूरा मौजूद है। चरण 3: विभाज्यता में हर अभाज्य की घात अलग-अलग मिलाएं।
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कौन सा विकल्प अभाज्य गुणनखंडन नहीं है?
Which option is not a prime factorisation?
#real-numbers
#not-prime-factorisation
#concept-check
A \(2^2 \times 3 \times 13\)
B \(3^2 \times 5 \times 7\)
C \(2 \times 21 \times 5\)
D \(5^2 \times 17\)
Explanation opens after your attempt
Correct Answer
C. \(2 \times 21 \times 5\)
Step 1
Concept
In prime factorisation, every base must be prime.
Step 2
Why this answer is correct
(21) is not prime because \(21=3 \times 7\), so the third option is not prime factorisation.
Step 3
Exam Tip
Always identify hidden composite numbers in options. चरण 1: अभाज्य गुणनखंडन में हर आधार अभाज्य होना चाहिए। चरण 2: (21) अभाज्य नहीं है क्योंकि \(21=3 \times 7\), इसलिए तीसरा विकल्प अभाज्य गुणनखंडन नहीं है। चरण 3: विकल्पों में छिपी संयुक्त संख्याएं जरूर पहचानें।
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(729) के अभाज्य गुणनखंडन में (3) की घात कितनी है?
What is the exponent of (3) in the prime factorisation of (729)?
#real-numbers
#exponent-of-3
#prime-factorisation
A 4
B 5
C 6
D 7
Explanation opens after your attempt
Step 1
Concept
\(729=27 \times 27\).
Step 2
Why this answer is correct
Since \(27=3^3\), \(729=3^3 \times 3^3=3^6\).
Step 3
Exam Tip
For larger powers, split the number into familiar cubes. चरण 1: \(729=27 \times 27\) है। चरण 2: \(27=3^3\), इसलिए \(729=3^3 \times 3^3=3^6\)। चरण 3: बड़ी घातों के लिए संख्या को पहचाने हुए घनों में तोड़ें।
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कौन सा अभाज्य गुणनखंडन सम संख्या को दर्शाता है?
Which prime factorisation represents an even number?
#real-numbers
#even-number
#prime-factorisation
A \(3^2 \times 5\)
B \(5 \times 11\)
C \(7^2 \times 13\)
D \(2 \times 3 \times 13\)
Explanation opens after your attempt
Correct Answer
D. \(2 \times 3 \times 13\)
Step 1
Concept
An even number must contain (2) in its prime factorisation.
Step 2
Why this answer is correct
Only the fourth option contains (2), so it represents an even number.
Step 3
Exam Tip
You do not need to calculate the whole number to check evenness. चरण 1: सम संख्या के अभाज्य गुणनखंडन में (2) अवश्य होता है। चरण 2: केवल चौथे विकल्प में (2) है, इसलिए वही सम संख्या दर्शाता है। चरण 3: समता जांचने के लिए पूरी संख्या निकालने की जरूरत नहीं होती।
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कौन सा अभाज्य गुणनखंडन विषम संख्या को दर्शाता है?
Which prime factorisation represents an odd number?
#real-numbers
#odd-number
#prime-factorisation
A \(2^2 \times 3 \times 5\)
B \(3^3 \times 5\)
C \(2 \times 7^2\)
D \(2^3 \times 11\)
Explanation opens after your attempt
Correct Answer
B. \(3^3 \times 5\)
Step 1
Concept
An odd number does not contain (2) as a prime factor.
Step 2
Why this answer is correct
The second option has (3) and (5), but no (2), so it is odd.
Step 3
Exam Tip
The presence of (2) makes the number even. चरण 1: विषम संख्या में (2) अभाज्य गुणनखंड नहीं होता। चरण 2: दूसरे विकल्प में (3) और (5) हैं, लेकिन (2) नहीं है, इसलिए वह विषम संख्या है। चरण 3: (2) की उपस्थिति संख्या को सम बना देती है।
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(245) का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of (245)?
#real-numbers
#prime-factorisation
#245
A \(5 \times 7^2\)
B \(5^2 \times 7\)
C \(7^3\)
D \(3 \times 5 \times 7\)
Explanation opens after your attempt
Correct Answer
A. \(5 \times 7^2\)
Step 1
Concept
Write (245) as \(5 \times 49\).
Step 2
Why this answer is correct
Since \(49=7^2\), \(245=5 \times 7^2\).
Step 3
Exam Tip
Do not leave (49) in the final answer because it is not prime. चरण 1: (245) को \(5 \times 49\) लिखें। चरण 2: \(49=7^2\), इसलिए \(245=5 \times 7^2\)। चरण 3: (49) को अंतिम उत्तर में न रखें क्योंकि वह अभाज्य नहीं है।
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किस संख्या का अभाज्य गुणनखंडन \(2^2 \times 3^2 \times 11\) है?
Which number has prime factorisation \(2^2 \times 3^2 \times 11\)?
#real-numbers
#prime-factorisation
#value-practice
A 198
B 297
C 396
D 594
Explanation opens after your attempt
Step 1
Concept
\(2^2=4\) and \(3^2=9\).
Step 2
Why this answer is correct
\(4 \times 9 \times 11=36 \times 11=396\).
Step 3
Exam Tip
Evaluating powers first makes the calculation simple. चरण 1: \(2^2=4\) और \(3^2=9\) है। चरण 2: \(4 \times 9 \times 11=36 \times 11=396\)। चरण 3: पहले घातों को हल करना गणना को सरल बनाता है।
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(324) के अभाज्य गुणनखंडन में (3) की घात कितनी है?
What is the exponent of (3) in the prime factorisation of (324)?
#real-numbers
#exponent-of-3
#prime-factorisation
A 2
B 3
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
Write (324) as \(4 \times 81\).
Step 2
Why this answer is correct
\(4=2^2\) and \(81=3^4\), so \(324=2^2 \times 3^4\).
Step 3
Exam Tip
Identify the required exponent separately in the final answer. चरण 1: (324) को \(4 \times 81\) लिखें। चरण 2: \(4=2^2\) और \(81=3^4\), इसलिए \(324=2^2 \times 3^4\)। चरण 3: मांगी गई घात को अंतिम उत्तर में अलग से पहचानें।
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कौन सा विकल्प (675) का सही अभाज्य गुणनखंडन है?
Which option is the correct prime factorisation of (675)?
#real-numbers
#prime-factorisation
#675
A \(3^2 \times 5^2\)
B \(3^3 \times 5^2\)
C \(3^2 \times 5^3\)
D \(3^3 \times 5\)
Explanation opens after your attempt
Correct Answer
B. \(3^3 \times 5^2\)
Step 1
Concept
Write (675) as \(27 \times 25\).
Step 2
Why this answer is correct
\(27=3^3\) and \(25=5^2\), so \(675=3^3 \times 5^2\).
Step 3
Exam Tip
Splitting a number into familiar squares and cubes is a good method. चरण 1: (675) को \(27 \times 25\) लिखें। चरण 2: \(27=3^3\) और \(25=5^2\), इसलिए \(675=3^3 \times 5^2\)। चरण 3: संख्या को आसान वर्ग और घन में तोड़ना अच्छा तरीका है।
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(384) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (384)?
#real-numbers
#prime-factorisation
#384
A \(2^6 \times 3\)
B \(2^7 \times 3\)
C \(2^8 \times 3\)
D \(2^5 \times 3^2\)
Explanation opens after your attempt
Correct Answer
B. \(2^7 \times 3\)
Step 1
Concept
Write (384) as \(128 \times 3\).
Step 2
Why this answer is correct
\(128=2^7\), so \(384=2^7 \times 3\).
Step 3
Exam Tip
Remembering powers of (2) saves time in such questions. चरण 1: (384) को \(128 \times 3\) लिखें। चरण 2: \(128=2^7\), इसलिए \(384=2^7 \times 3\)। चरण 3: (2) की बड़ी घातों को याद रखना ऐसे प्रश्नों में समय बचाता है।
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(275) का अभाज्य गुणनखंडन कौन सा है?
What is the prime factorisation of (275)?
#real-numbers
#prime-factorisation
#275
A \(5 \times 11^2\)
B \(5^2 \times 11\)
C \(25 \times 11\)
D \(5^3 \times 11\)
Explanation opens after your attempt
Correct Answer
B. \(5^2 \times 11\)
Step 1
Concept
Write (275) as \(25 \times 11\).
Step 2
Why this answer is correct
Since \(25=5^2\), \(275=5^2 \times 11\).
Step 3
Exam Tip
Do not leave (25) in the final form because it is not prime. चरण 1: (275) को \(25 \times 11\) लिखें। चरण 2: \(25=5^2\), इसलिए \(275=5^2 \times 11\)। चरण 3: (25) को अंतिम रूप में न छोड़ें क्योंकि वह अभाज्य नहीं है।
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(224) के अभाज्य गुणनखंडन में (2) की घात कितनी है?
What is the exponent of (2) in the prime factorisation of (224)?
#real-numbers
#exponent
#prime-factorisation
A 4
B 5
C 6
D 7
Explanation opens after your attempt
Step 1
Concept
Write (224) as \(32 \times 7\).
Step 2
Why this answer is correct
\(32=2^5\), so \(224=2^5 \times 7\).
Step 3
Exam Tip
Repeated division by the same prime helps find its exponent. चरण 1: (224) को \(32 \times 7\) लिखें। चरण 2: \(32=2^5\), इसलिए \(224=2^5 \times 7\)। चरण 3: किसी अभाज्य की घात जानने के लिए उसी अभाज्य से बार-बार भाग देना उपयोगी है।
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(132) का सही अभाज्य गुणनखंडन कौन सा है?
Which is the correct prime factorisation of (132)?
#real-numbers
#prime-factorisation
#class-10
A \(2^2 \times 3 \times 11\)
B \(2 \times 3^2 \times 11\)
C \(2^2 \times 3^2 \times 5\)
D \(2^3 \times 3 \times 11\)
Explanation opens after your attempt
Correct Answer
A. \(2^2 \times 3 \times 11\)
Step 1
Concept
Write (132) as \(12 \times 11\).
Step 2
Why this answer is correct
\(12=2^2 \times 3\), so \(132=2^2 \times 3 \times 11\).
Step 3
Exam Tip
Always check that all bases in the final answer are prime. चरण 1: (132) को \(12 \times 11\) लिखें। चरण 2: \(12=2^2 \times 3\), इसलिए \(132=2^2 \times 3 \times 11\)। चरण 3: अंतिम उत्तर में सभी आधार अभाज्य हैं या नहीं, यह जरूर जांचें।
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अभाज्य गुणनखंडन की अद्वितीयता किससे समझी जाती है?
Which idea explains the uniqueness of prime factorisation?
#real-numbers
#fundamental-theorem
#prime-factorisation
A अंकगणित का मूल प्रमेय / Fundamental theorem of arithmetic
B द्विघात सूत्र / Quadratic formula
C शेषफल प्रमेय / Remainder theorem
D क्षेत्रफल सूत्र / Area formula
Explanation opens after your attempt
Correct Answer
A. अंकगणित का मूल प्रमेय / Fundamental theorem of arithmetic
Step 1
Concept
Every integer greater than (1) can be written as a product of prime factors.
Step 2
Why this answer is correct
This form is unique apart from order, and this comes from the fundamental theorem of arithmetic.
Step 3
Exam Tip
Remember uniqueness of prime factorisation with this theorem. चरण 1: (1) से बड़ी हर पूर्ण संख्या को अभाज्य गुणनखंडों के गुणनफल के रूप में लिखा जा सकता है। चरण 2: यह रूप क्रम को छोड़कर अद्वितीय होता है, और यह बात अंकगणित के मूल प्रमेय से आती है। चरण 3: अभाज्य गुणनखंडन की अद्वितीयता को इसी प्रमेय से जोड़कर याद रखें।
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कौन सा कथन (1) और अभाज्य गुणनखंडन के बारे में सही है?
Which statement about (1) and prime factorisation is correct?
#real-numbers
#number-one
#prime-factorisation
A (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
B (1) सबसे छोटी अभाज्य संख्या है / (1) is the smallest prime number
C (1) हर अभाज्य गुणनखंडन में लिखा जाता है / (1) is written in every prime factorisation
D (1) की दो अभाज्य घातें होती हैं / (1) has two prime exponents
Explanation opens after your attempt
Correct Answer
A. (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
Step 1
Concept
A prime number has exactly two positive factors.
Step 2
Why this answer is correct
(1) has only one positive factor, so it is not prime and has no prime factor.
Step 3
Exam Tip
Avoid the common mistake of treating (1) as prime. चरण 1: अभाज्य संख्या के ठीक दो धनात्मक गुणनखंड होते हैं। चरण 2: (1) का केवल एक धनात्मक गुणनखंड है, इसलिए वह अभाज्य नहीं है और उसका कोई अभाज्य गुणनखंड नहीं होता। चरण 3: (1) को अभाज्य मानने की गलती से बचें।
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(81) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (81)?
#real-numbers
#prime-factorisation
#81
A \(3^2\)
B \(3^3\)
C \(3^4\)
D \(9^2\)
Explanation opens after your attempt
Correct Answer
C. \(3^4\)
Step 1
Concept
\(81=9 \times 9\).
Step 2
Why this answer is correct
Since \(9=3^2\), \(81=3^2 \times 3^2=3^4\).
Step 3
Exam Tip
\(9^2\) is not final prime factorisation because (9) is not prime. चरण 1: \(81=9 \times 9\) है। चरण 2: \(9=3^2\), इसलिए \(81=3^2 \times 3^2=3^4\)। चरण 3: \(9^2\) अंतिम अभाज्य गुणनखंडन नहीं है क्योंकि (9) अभाज्य नहीं है।
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(512) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (512)?
#real-numbers
#prime-factorisation
#512
A \(2^7\)
B \(2^8\)
C \(2^9\)
D \(8^3\)
Explanation opens after your attempt
Correct Answer
C. \(2^9\)
Step 1
Concept
Write (512) as \(64 \times 8\).
Step 2
Why this answer is correct
\(64=2^6\) and \(8=2^3\), so \(512=2^9\).
Step 3
Exam Tip
\(8^3\) may give the value, but prime factorisation must use base (2). चरण 1: (512) को \(64 \times 8\) लिखें। चरण 2: \(64=2^6\) और \(8=2^3\), इसलिए \(512=2^9\)। चरण 3: \(8^3\) मान के लिए सही हो सकता है, पर अभाज्य गुणनखंडन में आधार (2) होना चाहिए।
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(1000) का अभाज्य गुणनखंडन कौन सा है?
Which is the prime factorisation of (1000)?
#real-numbers
#prime-factorisation
#1000
A \(2^3 \times 5^3\)
B \(2^2 \times 5^3\)
C \(2^3 \times 5^2\)
D \(10^3\)
Explanation opens after your attempt
Correct Answer
A. \(2^3 \times 5^3\)
Step 1
Concept
\(1000=10^3\).
Step 2
Why this answer is correct
Since \(10=2 \times 5\), (103 =\(2 \times 5\)3 =23 \times 53 ).
Step 3
Exam Tip
\(10^3\) is not final prime factorisation because (10) is not prime. चरण 1: \(1000=10^3\) है। चरण 2: \(10=2 \times 5\), इसलिए (103 =\(2 \times 5\)3 =23 \times 53 )। चरण 3: \(10^3\) अंतिम अभाज्य गुणनखंडन नहीं है क्योंकि (10) अभाज्य नहीं है।
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यदि किसी संख्या का अभाज्य गुणनखंडन \(2^3 \times 3^2\) है, तो वह किससे अवश्य विभाज्य होगी?
If a number has prime factorisation \(2^3 \times 3^2\), by which number must it be divisible?
#real-numbers
#divisibility
#prime-factorisation
A 54
B 72
C 96
D 108
Explanation opens after your attempt
Step 1
Concept
For a divisor, its prime exponents must not exceed the available exponents.
Step 2
Why this answer is correct
\(72=2^3 \times 3^2\), which is fully present in the given number.
Step 3
Exam Tip
To test divisibility, match each prime exponent separately. चरण 1: किसी भाजक के लिए उसकी अभाज्य घातें उपलब्ध घातों से अधिक नहीं होनी चाहिए। चरण 2: \(72=2^3 \times 3^2\), जो पूरी तरह दी गई संख्या में मौजूद है। चरण 3: विभाज्यता जांचने में हर अभाज्य की घात अलग से मिलाएं।
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कौन सा विकल्प अभाज्य गुणनखंडन नहीं है?
Which option is not a prime factorisation?
#real-numbers
#not-prime-factorisation
#concept-check
A \(2^3 \times 3 \times 7\)
B \(3^2 \times 5\)
C \(2 \times 15 \times 7\)
D \(5^2 \times 11\)
Explanation opens after your attempt
Correct Answer
C. \(2 \times 15 \times 7\)
Step 1
Concept
In prime factorisation, every base must be prime.
Step 2
Why this answer is correct
(15) is not prime because \(15=3 \times 5\), so the third option is not prime factorisation.
Step 3
Exam Tip
Identify hidden composite numbers in the options. चरण 1: अभाज्य गुणनखंडन में हर आधार अभाज्य होना चाहिए। चरण 2: (15) अभाज्य नहीं है क्योंकि \(15=3 \times 5\), इसलिए तीसरा विकल्प अभाज्य गुणनखंडन नहीं है। चरण 3: विकल्प में छिपी संयुक्त संख्याओं को पहचानें।
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(625) के अभाज्य गुणनखंडन में (5) की घात कितनी है?
What is the exponent of (5) in the prime factorisation of (625)?
#real-numbers
#exponent-of-5
#prime-factorisation
A 2
B 3
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
\(625=25 \times 25\).
Step 2
Why this answer is correct
Since \(25=5^2\), \(625=5^2 \times 5^2=5^4\).
Step 3
Exam Tip
You can also divide repeatedly by (5) to find the exponent. चरण 1: \(625=25 \times 25\) है। चरण 2: \(25=5^2\), इसलिए \(625=5^2 \times 5^2=5^4\)। चरण 3: (5) की घात जानने के लिए (5) से बार-बार भाग भी कर सकते हैं।
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कौन सा अभाज्य गुणनखंडन सम संख्या को दर्शाता है?
Which prime factorisation represents an even number?
#real-numbers
#even-number
#prime-factorisation
A \(3 \times 5^2\)
B \(5 \times 7\)
C \(2^2 \times 3 \times 5\)
D \(3^3 \times 11\)
Explanation opens after your attempt
Correct Answer
C. \(2^2 \times 3 \times 5\)
Step 1
Concept
An even number must have (2) as a prime factor.
Step 2
Why this answer is correct
Only the third option contains (2), so it represents an even number.
Step 3
Exam Tip
To check evenness, calculating the whole number is not necessary. चरण 1: सम संख्या में (2) अभाज्य गुणनखंड अवश्य होता है। चरण 2: केवल तीसरे विकल्प में (2) मौजूद है, इसलिए वही सम संख्या को दर्शाता है। चरण 3: समता जांचने के लिए पूरी संख्या निकालने की जरूरत नहीं है।
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कौन सा अभाज्य गुणनखंडन विषम संख्या को दर्शाता है?
Which prime factorisation represents an odd number?
#real-numbers
#odd-number
#prime-factorisation
A \(2 \times 5^2\)
B \(3^2 \times 7\)
C \(2^3 \times 3\)
D \(2^2 \times 11\)
Explanation opens after your attempt
Correct Answer
B. \(3^2 \times 7\)
Step 1
Concept
An odd number does not contain (2) in its prime factorisation.
Step 2
Why this answer is correct
The second option has (3) and (7) but no (2), so it is odd.
Step 3
Exam Tip
The presence of (2) makes a number even. चरण 1: विषम संख्या के अभाज्य गुणनखंडन में (2) नहीं होता। चरण 2: दूसरे विकल्प में (3) और (7) हैं लेकिन (2) नहीं है, इसलिए वह विषम संख्या है। चरण 3: (2) की उपस्थिति संख्या को सम बना देती है।
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(175) का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of (175)?
#real-numbers
#prime-factorisation
#175
A \(5^2 \times 7\)
B \(5 \times 7^2\)
C \(3 \times 5^2\)
D \(25 \times 7\)
Explanation opens after your attempt
Correct Answer
A. \(5^2 \times 7\)
Step 1
Concept
Write (175) as \(25 \times 7\).
Step 2
Why this answer is correct
Since \(25=5^2\), \(175=5^2 \times 7\).
Step 3
Exam Tip
\(25 \times 7\) gives the value, but it is not final prime factorisation. चरण 1: (175) को \(25 \times 7\) लिखें। चरण 2: \(25=5^2\), इसलिए \(175=5^2 \times 7\)। चरण 3: \(25 \times 7\) मान देता है, पर अंतिम अभाज्य गुणनखंडन नहीं है।
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किस संख्या का अभाज्य गुणनखंडन \(2^4 \times 3 \times 5\) है?
Which number has prime factorisation \(2^4 \times 3 \times 5\)?
#real-numbers
#prime-factorisation
#value-practice
A 120
B 180
C 240
D 480
Explanation opens after your attempt
Step 1
Concept
\(2^4=16\).
Step 2
Why this answer is correct
\(16 \times 3 \times 5=16 \times 15=240\).
Step 3
Exam Tip
Calculate the number yourself before checking the options. चरण 1: \(2^4=16\) होता है। चरण 2: \(16 \times 3 \times 5=16 \times 15=240\)। चरण 3: विकल्पों में जाने से पहले स्वयं संख्या निकालें।
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(288) के अभाज्य गुणनखंडन में (3) की घात कितनी है?
What is the exponent of (3) in the prime factorisation of (288)?
#real-numbers
#exponent-of-3
#prime-factorisation
A 1
B 2
C 3
D 4
Explanation opens after your attempt
Step 1
Concept
Write (288) as \(32 \times 9\).
Step 2
Why this answer is correct
\(32=2^5\) and \(9=3^2\), so \(288=2^5 \times 3^2\).
Step 3
Exam Tip
Clearly identify the required exponent in the final answer. चरण 1: (288) को \(32 \times 9\) लिखें। चरण 2: \(32=2^5\) और \(9=3^2\), इसलिए \(288=2^5 \times 3^2\)। चरण 3: मांगी गई घात को अंतिम उत्तर में साफ पहचानें।
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कौन सा विकल्प (432) का सही अभाज्य गुणनखंडन है?
Which option is the correct prime factorisation of (432)?
#real-numbers
#prime-factorisation
#432
A \(2^3 \times 3^3\)
B \(2^4 \times 3^3\)
C \(2^3 \times 3^4\)
D \(2^4 \times 3^2\)
Explanation opens after your attempt
Correct Answer
B. \(2^4 \times 3^3\)
Step 1
Concept
Write (432) as \(16 \times 27\).
Step 2
Why this answer is correct
\(16=2^4\) and \(27=3^3\), so \(432=2^4 \times 3^3\).
Step 3
Exam Tip
Recognising squares and cubes makes factorisation faster. चरण 1: (432) को \(16 \times 27\) लिखें। चरण 2: \(16=2^4\) और \(27=3^3\), इसलिए \(432=2^4 \times 3^3\)। चरण 3: वर्ग और घन संख्याएं पहचानना अभाज्य गुणनखंडन को तेज बनाता है।
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(320) का अभाज्य गुणनखंडन क्या है?
What is the prime factorisation of (320)?
#real-numbers
#prime-factorisation
#320
A \(2^5 \times 5\)
B \(2^6 \times 5\)
C \(2^4 \times 5^2\)
D \(2^5 \times 10\)
Explanation opens after your attempt
Correct Answer
B. \(2^6 \times 5\)
Step 1
Concept
Write (320) as \(32 \times 10\).
Step 2
Why this answer is correct
\(32=2^5\) and \(10=2 \times 5\), so \(320=2^6 \times 5\).
Step 3
Exam Tip
Do not keep (10) in the final form because it is not prime. चरण 1: (320) को \(32 \times 10\) लिखें। चरण 2: \(32=2^5\) और \(10=2 \times 5\), इसलिए \(320=2^6 \times 5\)। चरण 3: (10) को अंतिम रूप में न रखें क्योंकि वह अभाज्य नहीं है।
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(196) का अभाज्य गुणनखंडन कौन सा है?
What is the prime factorisation of (196)?
#real-numbers
#prime-factorisation
#196
A \(2^2 \times 7^2\)
B \(2 \times 7^2\)
C \(2^2 \times 7\)
D \(4 \times 7^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2 \times 7^2\)
Step 1
Concept
Write (196) as \(14 \times 14\).
Step 2
Why this answer is correct
Since \(14=2 \times 7\), \(196=2^2 \times 7^2\).
Step 3
Exam Tip
Do not leave composite bases like (4) or (14) in the final answer. चरण 1: (196) को \(14 \times 14\) लिखें। चरण 2: \(14=2 \times 7\), इसलिए \(196=2^2 \times 7^2\)। चरण 3: अंतिम उत्तर में (4) या (14) जैसे संयुक्त आधार न छोड़ें।
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(168) के अभाज्य गुणनखंडन में (2) की घात कितनी है?
What is the exponent of (2) in the prime factorisation of (168)?
#real-numbers
#exponent
#prime-factorisation
A 2
B 3
C 4
D 5
Explanation opens after your attempt
Step 1
Concept
Write (168) as \(8 \times 21\).
Step 2
Why this answer is correct
\(8=2^3\) and \(21=3 \times 7\), so \(168=2^3 \times 3 \times 7\).
Step 3
Exam Tip
To find the required exponent, you do not need to calculate any extra value. चरण 1: (168) को \(8 \times 21\) के रूप में लिखें। चरण 2: \(8=2^3\) और \(21=3 \times 7\), इसलिए \(168=2^3 \times 3 \times 7\)। चरण 3: मांगी गई घात के लिए पूरी संख्या का मान निकालना जरूरी नहीं होता।
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(210) का सही अभाज्य गुणनखंडन कौन सा है?
Which is the correct prime factorisation of (210)?
#real-numbers
#prime-factorisation
#class-10
A \(2 \times 3 \times 5 \times 7\)
B \(2^2 \times 3 \times 5\)
C \(3^2 \times 5 \times 7\)
D \(2 \times 3 \times 7^2\)
Explanation opens after your attempt
Correct Answer
A. \(2 \times 3 \times 5 \times 7\)
Step 1
Concept
Write (210) as \(21 \times 10\).
Step 2
Why this answer is correct
\(21=3 \times 7\) and \(10=2 \times 5\), so \(210=2 \times 3 \times 5 \times 7\).
Step 3
Exam Tip
After factorisation, check that every base is prime. चरण 1: (210) को \(21 \times 10\) लिखें। चरण 2: \(21=3 \times 7\) और \(10=2 \times 5\), इसलिए \(210=2 \times 3 \times 5 \times 7\)। चरण 3: गुणनखंडन के बाद सभी आधार अभाज्य हैं या नहीं यह जरूर जांचें।
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(1) के अभाज्य गुणनखंडन के बारे में कौन सा कथन सही है?
Which statement about the prime factorisation of (1) is correct?
#real-numbers
#number-one
#prime-factorisation
A (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
B (1) एक अभाज्य संख्या है / (1) is a prime number
C \(1=1 \times 1\) अभाज्य गुणनखंडन है / \(1=1 \times 1\) is prime factorisation
D (1) हर संख्या का सबसे बड़ा अभाज्य गुणनखंड है / (1) is the greatest prime factor of every number
Explanation opens after your attempt
Correct Answer
A. (1) का कोई अभाज्य गुणनखंड नहीं होता / (1) has no prime factor
Step 1
Concept
A prime number has exactly two positive factors.
Step 2
Why this answer is correct
(1) has only one positive factor, so it is not prime and has no prime factor.
Step 3
Exam Tip
Do not make the mistake of treating (1) as prime. चरण 1: अभाज्य संख्या के ठीक दो धनात्मक गुणनखंड होते हैं। चरण 2: (1) का केवल एक धनात्मक गुणनखंड है, इसलिए (1) अभाज्य नहीं है और उसका कोई अभाज्य गुणनखंड नहीं होता। चरण 3: (1) को अभाज्य मानने की गलती न करें।
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