100 results found for "constant-domain" in Class 10.
यदि (p(x)=x-2 +ax+4) का स्थिर पद (4) है, तो स्थिर पद कौन-सा है?
If the constant term of (p(x)=x-2 +ax+4) is (4), which term is the constant term?
#constant_term
#parameter
#polynomials
A \(x^2\)
B (ax)
C (4)
D (a)
Explanation opens after your attempt
Step 1
Concept
The constant term does not contain (x). So (4) is the constant term.
Step 2
Why this answer is correct
The correct answer is C. (4). The constant term does not contain (x). So (4) is the constant term.
Step 3
Exam Tip
स्थिर पद में (x) नहीं होता। इसलिए (4) स्थिर पद है।
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किस मान के लिए ((r+4)x-3 +(r-1)x-2 +9) अचर बहुपद बन सकता है?
For what value of (r) can ((r+4)x-3 +(r-1)x-2 +9) become a constant polynomial?
#constant polynomial
#parameter
#condition
A (r=-4)
B (r=1)
C (r=0)
D ऐसा कोई मान नहीं / No such value
Explanation opens after your attempt
Correct Answer
D. ऐसा कोई मान नहीं / No such value
Step 1
Concept
For a constant polynomial, both (r+4=0) and (r-1=0) are needed, which is impossible together. All variable terms must vanish.
Step 2
Why this answer is correct
The correct answer is D. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (r+4=0) and (r-1=0) are needed, which is impossible together. All variable terms must vanish.
Step 3
Exam Tip
अचर बहुपद के लिए (r+4=0) और (r-1=0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।
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((4x+3)\(x^2-2x+5\)) में अचर पद क्या है?
What is the constant term in ((4x+3)\(x^2-2x+5\))?
#constant term
#multiplication
#polynomial
A (3)
B (5)
C (8)
D (15)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is D. (15). The constant term comes only from \(3\cdot5=15\). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल \(3\cdot5=15\) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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निम्न में से कौन-सा स्थिर बहुपद है?
Which of the following is a constant polynomial?
#constant-polynomial
#degree
#basic-concept
A (7)
B (7x)
C (x+7)
D \(x^2+7\)
Explanation opens after your attempt
Step 1
Concept
A constant polynomial has no variable term, so (7) is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is A. (7). A constant polynomial has no variable term, so (7) is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
स्थिर बहुपद में चर का पद नहीं होता, इसलिए (7) स्थिर बहुपद है। अशून्य स्थिर बहुपद की घात (0) होती है।
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किस मान के लिए ((n-2)x-2 +(n+1)x+5) अचर बहुपद बन सकता है?
For what value of (n) can ((n-2)x-2 +(n+1)x+5) become a constant polynomial?
#constant polynomial
#parameter
#condition
A (n=2)
B (n=-1)
C (n=1)
D ऐसा कोई मान नहीं / No such value
Explanation opens after your attempt
Correct Answer
D. ऐसा कोई मान नहीं / No such value
Step 1
Concept
For a constant polynomial, both (n-2=0) and (n+1=0) are needed, which is impossible together. All variable terms must vanish.
Step 2
Why this answer is correct
The correct answer is D. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (n-2=0) and (n+1=0) are needed, which is impossible together. All variable terms must vanish.
Step 3
Exam Tip
अचर बहुपद के लिए (n-2=0) और (n+1=0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।
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((3x-2)\(x^2+5x-1\)) में अचर पद क्या है?
What is the constant term in ((3x-2)\(x^2+5x-1\))?
#constant term
#multiplication
#polynomial
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is C. (2). The constant term comes only from ((-2)(-1)=2). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल ((-2)(-1)=2) से आता है। अचर पद के लिए अचर भागों का गुणन देखें।
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किस मान के लिए ((m+1)x-2 +(m-2 )x+7) अचर बहुपद बन सकता है?
For what value of (m) can ((m+1)x-2 +(m-2 )x+7) become a constant polynomial?
#constant polynomial
#parameter
#condition
A (m=-1)
B (m=2)
C ऐसा कोई मान नहीं / No such value
D (m=1)
Explanation opens after your attempt
Correct Answer
C. ऐसा कोई मान नहीं / No such value
Step 1
Concept
For a constant polynomial, both (m+1=0) and (m-2 =0) are needed, which is impossible together. All variable terms must vanish.
Step 2
Why this answer is correct
The correct answer is C. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (m+1=0) and (m-2 =0) are needed, which is impossible together. All variable terms must vanish.
Step 3
Exam Tip
अचर बहुपद के लिए (m+1=0) और (m-2 =0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।
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((2x-3)\(x^2+x+1\)) में अचर पद क्या है?
What is the constant term in ((2x-3)\(x^2+x+1\))?
#constant term
#multiplication
#polynomial
A (-3)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
Step 2
Why this answer is correct
The correct answer is A. (-3). The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.
Step 3
Exam Tip
अचर पद केवल ((-3)\cdot1=-3) से आता है। अचर पद के लिए अचर पदों का गुणन देखें।
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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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अशून्य अचर बहुपद (p(x)=-18) की घात क्या है?
What is the degree of the non-zero constant polynomial (p(x)=-18)?
#constant polynomial
#degree
#definition
A (0)
B (1)
C (18)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).
Step 3
Exam Tip
अशून्य अचर बहुपद की घात (0) होती है। अचर संख्या का अर्थ घात (0) से जुड़ा है।
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बहुपद (p(t)=4t-5 -6t-2 +t+15) में अचर पद कौन सा है?
Which is the constant term in the polynomial (p(t)=4t-5 -6t-2 +t+15)?
#constant term
#polynomial
#basic
A (4)
B (-6)
C (1)
D (15)
Explanation opens after your attempt
Step 1
Concept
The term without (t) is the constant term. Here the constant term is (15).
Step 2
Why this answer is correct
The correct answer is D. (15). The term without (t) is the constant term. Here the constant term is (15).
Step 3
Exam Tip
जिस पद में (t) नहीं है वह अचर पद है। यहां अचर पद (15) है।
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कौन सा विकल्प \(2x^3-5x^2+x-4\) की घात और नियत पद को सही बताता है?
Which option correctly gives the degree and constant term of \(2x^3-5x^2+x-4\)?
#degree
#constant-term
#cubic-polynomial
A घात (3), नियत पद (-4) / Degree (3), constant term (-4)
B घात (2), नियत पद (1) / Degree (2), constant term (1)
C घात (1), नियत पद (-5) / Degree (1), constant term (-5)
D घात (4), नियत पद (2) / Degree (4), constant term (2)
Explanation opens after your attempt
Correct Answer
A. घात (3), नियत पद (-4) / Degree (3), constant term (-4)
Step 1
Concept
The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 2
Why this answer is correct
The correct answer is A. घात (3), नियत पद (-4) / Degree (3), constant term (-4). The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 3
Exam Tip
सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है।
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यदि (p(x)=x-2 +5x+c) में नियत पद (-6) है, तो (p(0)) क्या होगा?
If the constant term in (p(x)=x-2 +5x+c) is (-6), what will (p(0)) be?
#constant-term
#p-of-zero
#polynomial-value
A (6)
B (-6)
C (0)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(0)) is always equal to the constant term. Here the constant term is (-6).
Step 2
Why this answer is correct
The correct answer is B. (-6). (p(0)) is always equal to the constant term. Here the constant term is (-6).
Step 3
Exam Tip
(p(0)) हमेशा नियत पद के बराबर होता है। यहाँ नियत पद (-6) है।
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यदि किसी गैर-शून्य नियत बहुपद की घात पूछी जाए, तो सही उत्तर क्या होगा?
If the degree of a non-zero constant polynomial is asked, what will be the correct answer?
#constant-polynomial
#degree
#concept
A (0)
B (1)
C परिभाषित नहीं / Not defined
D बहुपद नहीं / Not a polynomial
Explanation opens after your attempt
Step 1
Concept
The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.
Step 3
Exam Tip
गैर-शून्य नियत बहुपद की घात (0) होती है। इसे शून्य बहुपद से अलग रखें।
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निम्न में से कौन सा बहुपद नियत बहुपद नहीं है?
Which of the following is not a constant polynomial?
#constant-polynomial
#classification
A (8)
B (-3)
C (0)
D (2x+1)
Explanation opens after your attempt
Step 1
Concept
(2x+1) contains the variable (x), so it is not a constant polynomial. A constant polynomial has no variable term.
Step 2
Why this answer is correct
The correct answer is D. (2x+1). (2x+1) contains the variable (x), so it is not a constant polynomial. A constant polynomial has no variable term.
Step 3
Exam Tip
(2x+1) में चर (x) है इसलिए यह नियत बहुपद नहीं है। नियत बहुपद में चर वाला पद नहीं होता।
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बहुपद \(12x^2-9x+4\) में नियत पद कौन सा है?
Which is the constant term in \(12x^2-9x+4\)?
#constant-term
#polynomial-terms
#easy
A (12)
B (-9)
C (4)
D (2)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). The term without (x) is the constant term. Here the constant term is (4).
Step 3
Exam Tip
जिस पद में (x) नहीं है वह नियत पद होता है। यहाँ नियत पद (4) है।
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अशून्य अचर बहुपद (p(x)=12) की घात क्या होती है?
What is the degree of the non-zero constant polynomial (p(x)=12)?
#constant polynomial
#degree
#definition
A (0)
B (1)
C (12)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.
Step 3
Exam Tip
अशून्य अचर बहुपद की घात (0) होती है। शून्य बहुपद से इसे अलग रखें।
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व्यंजक \(5x^4-8x+11\) में अचर पद कौन सा है?
Which is the constant term in \(5x^4-8x+11\)?
#constant term
#polynomial
#basic
A (5)
B (-8)
C (11)
D (4)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (11).
Step 2
Why this answer is correct
The correct answer is C. (11). The term without (x) is the constant term. Here the constant term is (11).
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह अचर पद है। यहां अचर पद (11) है।
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बहुपद \(2x^2+3x-11\) में नियत पद कौन सा है?
Which is the constant term in \(2x^2+3x-11\)?
#constant-term
#polynomials
A (2)
B (3)
C (-11)
D (11x)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (-11).
Step 2
Why this answer is correct
The correct answer is C. (-11). The term without (x) is the constant term. Here the constant term is (-11).
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह नियत पद होता है। यहाँ नियत पद (-11) है।
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(p(x)=7x-2 ) में नियत पद क्या है?
What is the constant term in (p(x)=7x-2 )?
#polynomials
#constant-term
#easy
#missing-term
A (7)
B (2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 2
Why this answer is correct
The correct answer is C. (0). There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 3
Exam Tip
कोई अलग नियत पद नहीं है, इसलिए नियत पद (0) है। केवल (x) वाले पद को नियत पद न मानें।
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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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कौन सा बहुपद नियत बहुपद है?
Which is a constant polynomial?
#polynomials
#constant-polynomial
#easy
A (6)
B (x+6)
C (6x)
D \(x^2+6\)
Explanation opens after your attempt
Step 1
Concept
A polynomial with no variable is a constant polynomial. (6) has no (x).
Step 2
Why this answer is correct
The correct answer is A. (6). A polynomial with no variable is a constant polynomial. (6) has no (x).
Step 3
Exam Tip
जिस बहुपद में चर नहीं होता वह नियत बहुपद है। (6) में (x) नहीं है।
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\(6x^2-3x+10\) में नियत पद क्या है?
What is the constant term in \(6x^2-3x+10\)?
#polynomials
#constant-term
#easy
#coefficient
A (6)
B (-3)
C (10)
D (2)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here it is (10).
Step 2
Why this answer is correct
The correct answer is C. (10). The term without (x) is the constant term. Here it is (10).
Step 3
Exam Tip
जिस पद में (x) नहीं है वह नियत पद होता है। यहाँ वह (10) है।
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किस विकल्प में स्थिर पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the constant term absent but the equation is quadratic?
#quadratic-equations
#missing-constant-term
#identify
#medium
A \(2x^2+7x=0\)
B (2x+7=0)
C \(2x^3+7x=0\)
D \(\frac{2}{x^2}+7x=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+7x=0\)
Step 1
Concept
In \(2x^2+7x=0\), the \(x^2\) term is present and the constant term is absent. An equation can be quadratic even without a constant term.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+7x=0\). In \(2x^2+7x=0\), the \(x^2\) term is present and the constant term is absent. An equation can be quadratic even without a constant term.
Step 3
Exam Tip
\(2x^2+7x=0\) में \(x^2\) पद है और स्थिर पद अनुपस्थित है। स्थिर पद न होने पर भी समीकरण द्विघात हो सकता है।
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समीकरण \(2x^2+3x-8=0\) में स्थिर पद कौन-सा है?
What is the constant term in \(2x^2+3x-8=0\)?
#quadratic-equations
#constant-term
#easy
A (2)
B (3)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (-8).
Step 2
Why this answer is correct
The correct answer is D. (-8). The term without (x) is the constant term. Here the constant term is (-8).
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह स्थिर पद होता है। यहाँ स्थिर पद (-8) है।
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कौन सा विकल्प \(6x^2+x-8=0\) में स्थिर पद है?
Which option is the constant term in \(6x^2+x-8=0\)?
#quadratic equations
#constant term
#term identification
A \(6x^2\)
B (x)
C (-8)
D (0)
Explanation opens after your attempt
Step 1
Concept
The constant term has no variable. Here the constant term is (-8).
Step 2
Why this answer is correct
The correct answer is C. (-8). The constant term has no variable. Here the constant term is (-8).
Step 3
Exam Tip
स्थिर पद में चर नहीं होता। यहां स्थिर पद (-8) है।
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कौन सा विकल्प \(2x^2+3x+1=0\) में स्थिर पद है?
Which option is the constant term in \(2x^2+3x+1=0\)?
#quadratic equations
#constant term
#term identification
A \(2x^2\)
B (3x)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The constant term does not contain (x). Hence (1) is the constant term.
Step 2
Why this answer is correct
The correct answer is C. (1). The constant term does not contain (x). Hence (1) is the constant term.
Step 3
Exam Tip
स्थिर पद में (x) नहीं होता। इसलिए (1) स्थिर पद है।
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यदि (p(x)=x-2 -2x-3\sqrt{2}) है, तो स्थिर पद का शून्यकों से संबंध क्या बताता है?
If (p(x)=x-2 -2x-3\sqrt{2}), what does the constant term tell about the zeroes?
#constant-term
#product-of-zeroes
#irrational
A शून्यकों का गुणनफल \(-3\sqrt{2}\) है / The product of zeroes is \(-3\sqrt{2}\)
B शून्यकों का योग \(-3\sqrt{2}\) है / The sum of zeroes is \(-3\sqrt{2}\)
C दोनों शून्यक परिमेय हैं / Both zeroes are rational
D विविक्तकर \(-3\sqrt{2}\) है / The discriminant is \(-3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. शून्यकों का गुणनफल \(-3\sqrt{2}\) है / The product of zeroes is \(-3\sqrt{2}\)
Step 1
Concept
In a monic quadratic, the constant term is the product of zeroes. Here \(\alpha\beta=-3\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. शून्यकों का गुणनफल \(-3\sqrt{2}\) है / The product of zeroes is \(-3\sqrt{2}\). In a monic quadratic, the constant term is the product of zeroes. Here \(\alpha\beta=-3\sqrt{2}\).
Step 3
Exam Tip
एकक द्विघात में स्थिर पद शून्यकों का गुणनफल होता है। यहाँ \(\alpha\beta=-3\sqrt{2}\) है।
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यदि \(a+\sqrt{b}\) और \(a-\sqrt{b}\) किसी एकक द्विघात बहुपद के शून्यक हैं, तो स्थिर पद क्या होगा?
If \(a+\sqrt{b}\) and \(a-\sqrt{b}\) are zeroes of a monic quadratic polynomial, what is the constant term?
#general-form
#conjugates
#constant-term
A \(a^2-b\)
B \(a^2+b\)
C (2a)
D (-2a)
Explanation opens after your attempt
Correct Answer
A. \(a^2-b\)
Step 1
Concept
In a monic polynomial, the constant term is the product of zeroes. Here the product is (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b).
Step 2
Why this answer is correct
The correct answer is A. \(a^2-b\). In a monic polynomial, the constant term is the product of zeroes. Here the product is (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b).
Step 3
Exam Tip
एकक बहुपद में स्थिर पद शून्यकों का गुणनफल होता है। यहाँ गुणनफल (\(a+\sqrt{b}\)\(a-\sqrt{b}\)=a-2 -b) है।
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यदि शून्यक \(2\sqrt{2}\) और \(3\sqrt{2}\) हैं, तो बहुपद का स्थिर पद क्या होगा यदि अग्र गुणांक (1) है?
If the zeroes are \(2\sqrt{2}\) and \(3\sqrt{2}\), what is the constant term if the leading coefficient is (1)?
#constant-term
#product
#irrational-zeroes
A (12)
B \(5\sqrt{2}\)
C \(6\sqrt{2}\)
D (10)
Explanation opens after your attempt
Step 1
Concept
The constant term equals the product of the zeroes. (\(2\sqrt{2}\)\(3\sqrt{2}\)=12).
Step 2
Why this answer is correct
The correct answer is A. (12). The constant term equals the product of the zeroes. (\(2\sqrt{2}\)\(3\sqrt{2}\)=12).
Step 3
Exam Tip
स्थिर पद शून्यकों के गुणनफल के बराबर है। (\(2\sqrt{2}\)\(3\sqrt{2}\)=12) है।
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स्थिर बहुपद (p(x)=5) के ग्राफ के वास्तविक शून्यक कितने हैं?
How many real zeroes does the constant polynomial (p(x)=5) have?
#constant-polynomial
#no-zero
#graph
A शून्य / Zero
B एक / One
C पाँच / Five
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
The line (y=5) is parallel to the (x)-axis and does not meet it. So it has no real zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. The line (y=5) is parallel to the (x)-axis and does not meet it. So it has no real zero.
Step 3
Exam Tip
रेखा (y=5) (x)-अक्ष के समानांतर है और उससे नहीं मिलती। इसलिए कोई वास्तविक शून्यक नहीं है।
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अशून्य स्थिर बहुपद (p(x)=5) के आलेख का (x)-अक्ष से संबंध क्या है?
What is the relation of the graph of the non-zero constant polynomial (p(x)=5) with the (x)-axis?
#constant polynomial graph
A यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
B यह (x)-अक्ष को दो बार काटता है / It cuts the (x)-axis twice
C यह मूल बिंदु से गुजरता है / It passes through the origin
D यह (y)-अक्ष के समांतर है / It is parallel to the (y)-axis
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
Step 1
Concept
The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it. The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 3
Exam Tip
(p(x)=5) कभी (0) नहीं होता इसलिए शून्यक नहीं है। टिप: अशून्य स्थिर बहुपद का शून्यक नहीं होता।
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किसी स्थिर अशून्य बहुपद (p(x)=-3) का ग्राफ (x)-अक्ष को क्यों नहीं काटता?
Why does the graph of the non-zero constant polynomial (p(x)=-3) not cut the (x)-axis?
#constant-polynomial
#no-zero
#x-axis
#easy
A क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
B क्योंकि (x) हमेशा (-3) रहता है / Because (x) always remains (-3)
C क्योंकि ग्राफ पर कोई बिंदु नहीं होता / Because the graph has no point
D क्योंकि यह परवलय है / Because it is a parabola
Explanation opens after your attempt
Correct Answer
A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
Step 1
Concept
For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3). For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 3
Exam Tip
(p(x)=-3) का (y)-मान कभी (0) नहीं होता। इसलिए ग्राफ (x)-अक्ष को नहीं काटता और कोई शून्यक नहीं है।
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किसी स्थिर अशून्य बहुपद जैसे (p(x)=5) के ग्राफ से शून्यकों के बारे में क्या पता चलता है?
What does the graph of a non-zero constant polynomial like (p(x)=5) show about its zeroes?
#constant-polynomial
#no-zero
#graph
#easy
A कोई शून्यक नहीं / No zero
B एक शून्यक / One zero
C दो शून्यक / Two zeroes
D अनंत शून्यक / Infinite zeroes
Explanation opens after your attempt
Correct Answer
A. कोई शून्यक नहीं / No zero
Step 1
Concept
The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 2
Why this answer is correct
The correct answer is A. कोई शून्यक नहीं / No zero. The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 3
Exam Tip
(p(x)=5) का ग्राफ (x)-अक्ष के समानांतर रेखा है जो (x)-अक्ष को नहीं काटती। इसलिए इसका कोई शून्यक नहीं है।
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किसी सूची में क्रमागत पदों का अंतर समान हो तो उस सूची को क्या कहते हैं?
What is a list called when the difference between consecutive terms is constant?
#arithmetic progression
#ap
#introduction
#common difference
A अंकगणितीय श्रेणी / Arithmetic progression
B ज्यामितीय श्रेणी / Geometric progression
C समुच्चय / Set
D समीकरण / Equation
Explanation opens after your attempt
Correct Answer
A. अंकगणितीय श्रेणी / Arithmetic progression
Step 1
Concept
A constant difference between consecutive terms is the key sign of an arithmetic progression. In exams first check the differences.
Step 2
Why this answer is correct
The correct answer is A. अंकगणितीय श्रेणी / Arithmetic progression. A constant difference between consecutive terms is the key sign of an arithmetic progression. In exams first check the differences.
Step 3
Exam Tip
क्रमागत पदों का समान अंतर अंकगणितीय श्रेणी की मुख्य पहचान है। परीक्षा में पहले अंतर जांचें।
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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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समीकरण (2x+3y=13) और (4x+6y=26) के लिए \(a_1/a_2\), \(b_1/b_2\) और स्थिर पद अनुपात का संबंध क्या है?
For (2x+3y=13) and (4x+6y=26), what is the relation among \(a_1/a_2\), \(b_1/b_2\), and the constant ratio?
#linear equations
#ratio relation
#coincident
A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (2/4=3/6=13/26)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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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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कौन-सा बहुपद स्थिर बहुपद है?
Which polynomial is a constant polynomial?
#constant_polynomial
#classification
#basics
A (3x+2)
B \(x^2-1\)
C \(-7\)
D \(x^3\)
Explanation opens after your attempt
Step 1
Concept
A constant polynomial has no variable. The number (-7) is a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(-7\). A constant polynomial has no variable. The number (-7) is a non-zero constant polynomial.
Step 3
Exam Tip
स्थिर बहुपद में चर नहीं होता। (-7) शून्य से भिन्न स्थिर बहुपद है।
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स्थिर बहुपद (p(x)=9) की घात क्या है?
What is the degree of the constant polynomial (p(x)=9)?
#constant_polynomial
#degree
#basics
A (0)
B (1)
C (9)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).
Step 3
Exam Tip
शून्य से भिन्न स्थिर बहुपद की घात (0) होती है। (9) को \(9x^0\) माना जा सकता है।
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बहुपद \(7x^2+5x-11\) में स्थिर पद क्या है?
What is the constant term in the polynomial \(7x^2+5x-11\)?
#constant_term
#polynomials
#basics
A (7)
B (5)
C \(-11\)
D (2)
Explanation opens after your attempt
Correct Answer
C. \(-11\)
Step 1
Concept
The constant term is the term without (x). Here the constant term is (-11).
Step 2
Why this answer is correct
The correct answer is C. \(-11\). The constant term is the term without (x). Here the constant term is (-11).
Step 3
Exam Tip
स्थिर पद वह होता है जिसमें (x) नहीं होता। यहाँ स्थिर पद (-11) है।
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यदि किसी एकक द्विघात बहुपद के शून्यक \(4+\sqrt{11}\) और \(4-\sqrt{11}\) हैं, तो स्थिर पद क्या होगा?
If the zeroes of a monic quadratic polynomial are \(4+\sqrt{11}\) and \(4-\sqrt{11}\), what will be the constant term?
#conjugate-zeroes
#constant-term
#quadratic
A (5)
B (27)
C (8)
D \(16+\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 2
Why this answer is correct
The correct answer is A. (5). The constant term is the product, and (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5). In conjugate products, the irrational middle part cancels.
Step 3
Exam Tip
स्थिर पद गुणनफल है और (\(4+\sqrt{11}\)\(4-\sqrt{11}\)=16-11=5)। संयुग्मी गुणनफल में बीच का अपरिमेय भाग हट जाता है।
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लैंगिक प्रजनन में गुणसूत्र संख्या पीढ़ी दर पीढ़ी समान कैसे बनी रहती है?
How does chromosome number remain constant generation after generation in sexual reproduction?
#sexual-reproduction
#chromosomes
#gametes
#fertilization
A युग्मकों में आधी संख्या होती है और निषेचन से पूरी संख्या लौटती है / Gametes have half the number and fertilization restores the full number
B सभी कोशिकाएँ गुणसूत्र खो देती हैं / All cells lose chromosomes
C निषेचन के बाद गुणसूत्र समाप्त हो जाते हैं / Chromosomes disappear after fertilization
D संतति में केवल एक जनक के गुणसूत्र जाते हैं / Offspring receive chromosomes from only one parent
Explanation opens after your attempt
Correct Answer
A. युग्मकों में आधी संख्या होती है और निषेचन से पूरी संख्या लौटती है / Gametes have half the number and fertilization restores the full number
Step 1
Concept
Gametes have half the chromosome number compared with body cells.
Step 2
Why this answer is correct
Male and female gametes fuse during fertilization.
Step 3
Exam Tip
This fusion restores the normal chromosome number. चरण 1: युग्मकों में सामान्य शरीर कोशिकाओं की तुलना में आधी गुणसूत्र संख्या होती है। चरण 2: निषेचन में नर और मादा युग्मक मिलते हैं। चरण 3: इस मिलन से सामान्य गुणसूत्र संख्या फिर से बन जाती है।
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मेसोपोटामिया में इनन्ना देवी किस क्षेत्र से विशेष रूप से जुड़ी थीं?
In Mesopotamia the goddess Inanna was especially associated with which domain?
#world history
#ancient civilizations
#mesopotamia
#inanna
A लिखित कानून / Written law
B लौह रेल / Iron rail
C प्रेम युद्ध और सत्ता / Love war and power
D नील बाढ़ / Nile flood
Explanation opens after your attempt
Correct Answer
C. प्रेम युद्ध और सत्ता / Love war and power
Step 1
Concept
Inanna was associated with love war and power. For exams domains of deities reveal beliefs of a civilization.
Step 2
Why this answer is correct
The correct answer is C. प्रेम युद्ध और सत्ता / Love war and power. Inanna was associated with love war and power. For exams domains of deities reveal beliefs of a civilization.
Step 3
Exam Tip
इनन्ना को प्रेम युद्ध और शक्ति से जोड़ा जाता था। परीक्षा में देवताओं के कार्यक्षेत्र सभ्यता की मान्यताएं बताते हैं।
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यदि \(9,9,9,\ldots\) को \(2,5,8,\ldots\) से पद-दर-पद जोड़ा जाए तो नए अनुक्रम का (d) क्या होगा?
If \(9,9,9,\ldots\) is added term by term to \(2,5,8,\ldots\), what will be (d) of the new sequence?
#ap
#constant sequence
#sum
#hard
A (0)
B (3)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
The constant sequence has (d=0), and the second has (d=3), so the sum has (d=3). Adding a constant sequence does not change (d).
Step 2
Why this answer is correct
The correct answer is B. (3). The constant sequence has (d=0), and the second has (d=3), so the sum has (d=3). Adding a constant sequence does not change (d).
Step 3
Exam Tip
स्थिर अनुक्रम का (d=0) है और दूसरे का (d=3) है, इसलिए योग का (d=3)। स्थिर अनुक्रम जोड़ने से (d) नहीं बदलता।
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यदि \(13, 13, 13,\ldots\) को \(1, 4, 7,\ldots\) से पद-दर-पद घटाया जाए, तो नए अनुक्रम का (d) क्या होगा?
If \(1, 4, 7,\ldots\) is subtracted term by term from \(13, 13, 13,\ldots\), what will be (d) of the new sequence?
#ap
#constant sequence
#difference
#expert
A (-3)
B (0)
C (3)
D (13)
Explanation opens after your attempt
Step 1
Concept
The constant sequence has (d=0), and the second has (d=3), so the new (d=0-3=-3). Even with a constant sequence, subtraction can change (d).
Step 2
Why this answer is correct
The correct answer is A. (-3). The constant sequence has (d=0), and the second has (d=3), so the new (d=0-3=-3). Even with a constant sequence, subtraction can change (d).
Step 3
Exam Tip
स्थिर अनुक्रम का (d=0) और दूसरे का (d=3) है, इसलिए नया (d=0-3=-3)। स्थिर अनुक्रम घटाव में भी (d) बदल सकता है।
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यदि \(5, 5, 5,\ldots\) को \(2, 4, 6,\ldots\) से पद-दर-पद जोड़ा जाए, तो नए अनुक्रम का (d) क्या होगा?
If \(5, 5, 5,\ldots\) is added term by term to \(2, 4, 6,\ldots\), what will be (d) of the new sequence?
#ap
#constant sequence
#sum
#hard
A (0)
B (2)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The first sequence has (d=0) and the second has (d=2), so the new (d=2). Adding a constant sequence does not change (d).
Step 2
Why this answer is correct
The correct answer is B. (2). The first sequence has (d=0) and the second has (d=2), so the new (d=2). Adding a constant sequence does not change (d).
Step 3
Exam Tip
पहले अनुक्रम का (d=0) और दूसरे का (d=2) है, इसलिए नया (d=2)। स्थिर अनुक्रम जोड़ने से (d) नहीं बदलता।
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किस अनुक्रम में सार्व अंतर (0) है?
Which sequence has common difference (0)?
#ap
#zero common difference
#constant sequence
#medium
A \(0,1,2,3,\ldots\)
B \(5,0,-5,-10,\ldots\)
C \(7,14,21,28,\ldots\)
D \(11,11,11,11,\ldots\)
Explanation opens after your attempt
Correct Answer
D. \(11,11,11,11,\ldots\)
Step 1
Concept
All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is D. \(11,11,11,11,\ldots\). All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। स्थिर अनुक्रम भी अंकगणितीय श्रेणी माना जाता है।
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यदि कोई अनुक्रम \(12,12,12,12,\ldots\) है, तो वह किस प्रकार की समांतर श्रेढ़ी है?
If a sequence is \(12,12,12,12,\ldots\), what type of arithmetic progression is it?
#arithmetic-progression
#constant-ap
#class10
A बढ़ती हुई / Increasing
B घटती हुई / Decreasing
C समान पदों वाली / Constant terms
D समांतर श्रेढ़ी नहीं / Not an arithmetic progression
Explanation opens after your attempt
Correct Answer
C. समान पदों वाली / Constant terms
Step 1
Concept
All terms are equal, so (d=0). It is called an arithmetic progression with constant terms.
Step 2
Why this answer is correct
The correct answer is C. समान पदों वाली / Constant terms. All terms are equal, so (d=0). It is called an arithmetic progression with constant terms.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कहते हैं।
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अनुक्रम \(3,3,3,3,\ldots\) के बारे में सही कथन क्या है?
Which statement is correct about the sequence \(3,3,3,3,\ldots\)?
#ap
#constant ap
#zero difference
#easy
A यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
B यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0)
C इसका (d=3) है / Its (d=3)
D इसका (a=0) है / Its (a=0)
Explanation opens after your attempt
Correct Answer
B. यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0)
Step 1
Concept
All terms are equal, so the common difference is (0). A constant sequence is also an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0). All terms are equal, so the common difference is (0). A constant sequence is also an arithmetic progression.
Step 3
Exam Tip
सभी पद समान हैं इसलिए सार्व अंतर (0) है। स्थिर अनुक्रम भी अंकगणितीय श्रेणी होता है।
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अनुक्रम \(8,8,8,8,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(8,8,8,8,\ldots\)?
#ap
#constant sequence
#common difference
#class ten
A (8)
B (0)
C (1)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The common difference is (8-8=0). A sequence with equal terms has difference (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The common difference is (8-8=0). A sequence with equal terms has difference (0).
Step 3
Exam Tip
सार्व अंतर (8-8=0) है। समान पदों वाली श्रेणी में अंतर (0) होता है।
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यदि सार्व अंतर (0) हो तो अंकगणितीय श्रेणी कैसी होती है?
If the common difference is (0), what type of arithmetic progression is formed?
#ap
#zero common difference
#constant sequence
#easy
A सभी पद समान होते हैं / All terms are equal
B सभी पद शून्य होते हैं / All terms are zero
C सभी पद ऋणात्मक होते हैं / All terms are negative
D सभी पद भिन्न होते हैं / All terms are different
Explanation opens after your attempt
Correct Answer
A. सभी पद समान होते हैं / All terms are equal
Step 1
Concept
When (d=0), each next term remains the same. This can also be an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. सभी पद समान होते हैं / All terms are equal. When (d=0), each next term remains the same. This can also be an arithmetic progression.
Step 3
Exam Tip
(d=0) होने पर प्रत्येक अगला पद पहले जैसा रहता है। यह भी अंकगणितीय श्रेणी हो सकती है।
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यदि कोई अनुक्रम \(5,5,5,5,\ldots\) है, तो वह किस प्रकार की समांतर श्रेढ़ी है?
If a sequence is \(5,5,5,5,\ldots\), what type of arithmetic progression is it?
#arithmetic-progression
#constant-ap
#class10
A घटती हुई / Decreasing
B बढ़ती हुई / Increasing
C समान पदों वाली / Constant terms
D समांतर श्रेढ़ी नहीं / Not an arithmetic progression
Explanation opens after your attempt
Correct Answer
C. समान पदों वाली / Constant terms
Step 1
Concept
All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
Step 2
Why this answer is correct
The correct answer is C. समान पदों वाली / Constant terms. All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कह सकते हैं।
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कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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यदि (p(x)=x-5 +ax-3 +b) में (p(0)=0), तो कौन सा निष्कर्ष निश्चित है?
If (p(x)=x-5 +ax-3 +b) has (p(0)=0), which conclusion is certain?
#constant term
#zero
#evaluation
A (b=0)
B (a=0)
C (1) शून्य है / (1) is a zero
D घात (3) है / Degree is (3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 2
Why this answer is correct
The correct answer is A. (b=0). (p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 3
Exam Tip
(p(0)=b) होता है, इसलिए (p(0)=0) से (b=0) निश्चित है। बाकी निष्कर्ष जरूरी नहीं हैं।
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यदि (p(x)=5x-2 +bx+c), (p(0)=-4) और (p(1)=3), तो (b) क्या है?
If (p(x)=5x-2 +bx+c), (p(0)=-4), and (p(1)=3), what is (b)?
#parameter
#constant term
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=c=-4) and (p(1)=5+b-4=3), so (b=2). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is B. (2). (p(0)=c=-4) and (p(1)=5+b-4=3), so (b=2). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=c=-4) और (p(1)=5+b-4=3), इसलिए (b=2)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-2 +ax+b), (p(-4)=0) और (p(1)=0), तो (b) का मान क्या है?
If (p(x)=x-2 +ax+b), (p(-4)=0), and (p(1)=0), what is the value of (b)?
#zeros
#quadratic
#constant term
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
With zeros (-4) and (1), the polynomial is ((x+4)(x-1)=x-2 +3x-4). Hence (b=-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). With zeros (-4) and (1), the polynomial is ((x+4)(x-1)=x-2 +3x-4). Hence (b=-4).
Step 3
Exam Tip
शून्य (-4) और (1) होने पर बहुपद ((x+4)(x-1)=x-2 +3x-4) है। इसलिए (b=-4)।
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कौन सा बहुपद (x=0) को शून्य बनाता है?
Which polynomial makes (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^2+5\)
B \(3x^3-2x\)
C \(x^4+1\)
D \(2x^2-7x+9\)
Explanation opens after your attempt
Correct Answer
B. \(3x^3-2x\)
Step 1
Concept
Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^3-2x\). Substituting (x=0) in \(3x^3-2x\) gives (0). To make (x=0) a zero, the constant term must be (0).
Step 3
Exam Tip
(x=0) रखने पर \(3x^3-2x=0\) मिलता है। (x=0) को शून्य बनाने के लिए अचर पद (0) होना चाहिए।
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यदि (p(x)=x-4 +ax-2 +b) में (p(0)=0), तो कौन सा निष्कर्ष निश्चित है?
If (p(x)=x-4 +ax-2 +b) has (p(0)=0), which conclusion is certain?
#constant term
#zero
#evaluation
A (b=0)
B (a=0)
C (1) शून्य है / (1) is a zero
D घात (2) है / Degree is (2)
Explanation opens after your attempt
Step 1
Concept
(p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 2
Why this answer is correct
The correct answer is A. (b=0). (p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 3
Exam Tip
(p(0)=b) होता है, इसलिए (p(0)=0) से (b=0) निश्चित है। बाकी निष्कर्ष जरूरी नहीं हैं।
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यदि (p(x)=3x-2 +bx+c), (p(0)=7) और (p(1)=2), तो (b) क्या है?
If (p(x)=3x-2 +bx+c), (p(0)=7), and (p(1)=2), what is (b)?
#parameter
#constant term
#evaluation
A (-8)
B (-7)
C (-6)
D (-5)
Explanation opens after your attempt
Step 1
Concept
(p(0)=c=7) and (p(1)=3+b+7=2), so (b=-8). (x=0) gives the constant term directly.
Step 2
Why this answer is correct
The correct answer is A. (-8). (p(0)=c=7) and (p(1)=3+b+7=2), so (b=-8). (x=0) gives the constant term directly.
Step 3
Exam Tip
(p(0)=c=7) और (p(1)=3+b+7=2), इसलिए (b=-8)। (x=0) अचर पद तुरंत देता है।
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यदि (p(x)=x-2 +ax+b), (p(-1)=0) और (p(5)=0), तो (b) का मान क्या है?
If (p(x)=x-2 +ax+b), (p(-1)=0), and (p(5)=0), what is the value of (b)?
#zeros
#quadratic
#constant term
A (-5)
B (-4)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
With zeros (-1) and (5), the polynomial is ((x+1)(x-5)=x-2 -4x-5). Hence (b=-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). With zeros (-1) and (5), the polynomial is ((x+1)(x-5)=x-2 -4x-5). Hence (b=-5).
Step 3
Exam Tip
शून्य (-1) और (5) होने पर बहुपद ((x+1)(x-5)=x-2 -4x-5) है। इसलिए (b=-5)।
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कौन सा बहुपद (x=0) को शून्य नहीं बनाता?
Which polynomial does not make (x=0) a zero?
#zero at zero
#constant term
#polynomial
A \(x^3-2x\)
B \(5x^2+x\)
C \(x^4\)
D \(x^2+1\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+1\)
Step 1
Concept
On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 2
Why this answer is correct
The correct answer is D. \(x^2+1\). On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).
Step 3
Exam Tip
(x=0) रखने पर \(x^2+1=1\), इसलिए (0) इसका शून्य नहीं है। (x=0) पर अचर पद निर्णायक होता है।
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यदि (p(x)=2x-2 +bx+c), (p(0)=5) और (p(1)=1), तो (b) क्या है?
If (p(x)=2x-2 +bx+c), (p(0)=5), and (p(1)=1), what is (b)?
#parameter
#constant term
#evaluation
A (-6)
B (-5)
C (-4)
D (-3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).
Step 2
Why this answer is correct
The correct answer is A. (-6). (p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).
Step 3
Exam Tip
(p(0)=c=5) और (p(1)=2+b+5=1), इसलिए (b=-6)। (x=0) से अचर पद तुरंत मिलता है।
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यदि (p(x)=x-2 +ax+b), (p(1)=0) और (p(3)=0), तो (b) का मान क्या है?
If (p(x)=x-2 +ax+b), (p(1)=0), and (p(3)=0), what is the value of (b)?
#zeros
#quadratic
#constant term
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
With zeros (1) and (3), the polynomial is ((x-1)(x-3)=x-2 -4x+3). Hence (b=3).
Step 2
Why this answer is correct
The correct answer is C. (3). With zeros (1) and (3), the polynomial is ((x-1)(x-3)=x-2 -4x+3). Hence (b=3).
Step 3
Exam Tip
शून्य (1) और (3) होने पर बहुपद ((x-1)(x-3)=x-2 -4x+3) है। इसलिए (b=3)।
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यदि (p(x)=2x-2 -5x+c) और (p(4)=7), तो (c) का मान क्या है?
If (p(x)=2x-2 -5x+c) and (p(4)=7), what is the value of (c)?
#evaluation
#parameter
#constant term
A (-5)
B (-3)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(4)=32-20+c=7), so (12+c=7) and (c=-5). Substitute the given value to find the unknown constant term.
Step 2
Why this answer is correct
The correct answer is A. (-5). (p(4)=32-20+c=7), so (12+c=7) and (c=-5). Substitute the given value to find the unknown constant term.
Step 3
Exam Tip
(p(4)=32-20+c=7), इसलिए (12+c=7) और (c=-5)। दिए गए मान को रखकर अज्ञात अचर पद निकालें।
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यदि (p(x)=ax-3 +bx-2 +cx+d) और (p(0)=-7), तो (d) का मान क्या है?
If (p(x)=ax-3 +bx-2 +cx+d) and (p(0)=-7), what is the value of (d)?
#polynomial-value
#constant-term
#parameter
A (7)
B (-7)
C (0)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (p(0)=d). Therefore (d=-7).
Step 2
Why this answer is correct
The correct answer is B. (-7). Putting (x=0) gives (p(0)=d). Therefore (d=-7).
Step 3
Exam Tip
(x=0) रखने पर (p(0)=d) मिलता है। इसलिए (d=-7) है।
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(p(x)=x-2 -8x+13) के लिए (p(0)) क्या है?
For (p(x)=x-2 -8x+13), what is (p(0))?
#evaluation
#constant term
#polynomial
A (0)
B (8)
C (13)
D (21)
Explanation opens after your attempt
Step 1
Concept
(p(0)=0-0+13=13). When (x=0), only the constant term remains.
Step 2
Why this answer is correct
The correct answer is C. (13). (p(0)=0-0+13=13). When (x=0), only the constant term remains.
Step 3
Exam Tip
(p(0)=0-0+13=13)। (x=0) रखने पर अचर पद ही बचता है।
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बहुपद (p(x)=2x-2 +3) में (p(0)) का मान क्या है?
For the polynomial (p(x)=2x-2 +3), what is the value of (p(0))?
#polynomials
#substitution
#constant-term
A (0)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(0)=2(0)2 +3=3). When (x=0), the constant term remains.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(0)=2(0)2 +3=3). When (x=0), the constant term remains.
Step 3
Exam Tip
(p(0)=2(0)2 +3=3) है। (x=0) रखने पर नियत पद बचता है।
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(p(x)=x-2 -5x+6) के लिए (p(0)) क्या है?
For (p(x)=x-2 -5x+6), what is (p(0))?
#evaluation
#constant term
#polynomial
A (0)
B (1)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(0)=0-0+6=6). When (x=0), only the constant term remains.
Step 2
Why this answer is correct
The correct answer is D. (6). (p(0)=0-0+6=6). When (x=0), only the constant term remains.
Step 3
Exam Tip
(p(0)=0-0+6=6)। (x=0) रखने पर केवल अचर पद बचता है।
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(9) किस प्रकार का बहुपद है?
What type of polynomial is (9)?
#constant-polynomial
#degree-zero
A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C नियत बहुपद / Constant polynomial
D त्रिघात बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
C. नियत बहुपद / Constant polynomial
Step 1
Concept
(9) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 2
Why this answer is correct
The correct answer is C. नियत बहुपद / Constant polynomial. (9) has no variable, so it is a constant polynomial. A non-zero constant polynomial has degree (0).
Step 3
Exam Tip
(9) में चर नहीं है इसलिए यह नियत बहुपद है। गैर-शून्य नियत बहुपद की घात (0) होती है।
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\(3x^2+2x+1\) में (x=0) रखने पर किस पद का मान बचता है?
When (x=0) is put in \(3x^2+2x+1\), which term remains?
#polynomials
#value
#constant-term
#easy
A \(3x^2\)
B (2x)
C (1)
D \(3x^2+2x\)
Explanation opens after your attempt
Step 1
Concept
At (x=0), \(3x^2\) and (2x) become zero. Only the constant term (1) remains.
Step 2
Why this answer is correct
The correct answer is C. (1). At (x=0), \(3x^2\) and (2x) become zero. Only the constant term (1) remains.
Step 3
Exam Tip
(x=0) पर \(3x^2\) और (2x) शून्य हो जाते हैं। केवल नियत पद (1) बचता है।
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बहुपद (5) की घात क्या है?
What is the degree of the polynomial (5)?
#polynomials
#constant-polynomial
#easy
#degree
A (0)
B (1)
C (5)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.
Step 3
Exam Tip
अशून्य नियत बहुपद की घात (0) होती है। याद रखें \(5=5x^0\) माना जा सकता है।
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समीकरण (x-2 -2(a-5)x+a-2 -10a+21=0) के मूलों की प्रकृति क्या है?
What is the nature of roots of (x-2 -2(a-5)x+a-2 -10a+21=0)?
#quadratic equations
#constant discriminant
#real distinct roots
A हमेशा वास्तविक और भिन्न / Always real and distinct
B हमेशा वास्तविक और समान / Always real and equal
C वास्तविक मूल नहीं / No real roots
D प्रकृति (a) पर निर्भर है / Nature depends on (a)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और भिन्न / Always real and distinct
Step 1
Concept
Here (D=4(a-5)2 -4\(a^2-10a+21\)=16>0). Therefore the roots are real and distinct for every real (a).
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=4(a-5)2 -4\(a^2-10a+21\)=16>0). Therefore the roots are real and distinct for every real (a).
Step 3
Exam Tip
यहाँ (D=4(a-5)2 -4\(a^2-10a+21\)=16>0) है। इसलिए हर वास्तविक (a) के लिए मूल वास्तविक और भिन्न हैं।
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यदि (x-2 -2(a+4)x+a-2 +8a+16=0) है, तो मूलों की प्रकृति क्या होगी?
If (x-2 -2(a+4)x+a-2 +8a+16=0), what will be the nature of roots?
#quadratic equations
#equal roots
#constant D
A हमेशा वास्तविक और समान / Always real and equal
B हमेशा वास्तविक और भिन्न / Always real and distinct
C हमेशा वास्तविक नहीं / Always not real
D केवल (a=-4) पर समान / Equal only when (a=-4)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और समान / Always real and equal
Step 1
Concept
Here (D=4(a+4)2 -4(a+4)2 =0). Therefore roots are always real and equal.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और समान / Always real and equal. Here (D=4(a+4)2 -4(a+4)2 =0). Therefore roots are always real and equal.
Step 3
Exam Tip
यहाँ (D=4(a+4)2 -4(a+4)2 =0) है। इसलिए मूल हमेशा वास्तविक और समान हैं।
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यदि (x-2 -2(a+4)x+a-2 +8a+15=0) है, तो मूलों की प्रकृति क्या होगी?
If (x-2 -2(a+4)x+a-2 +8a+15=0), what will be the nature of roots?
#quadratic equations
#rational distinct roots
#constant D
A हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक नहीं / Always not real
D प्रकृति (a) पर निर्भर है / Nature depends on (a)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct
Step 1
Concept
Here (D=4(a+4)2 -4\(a^2+8a+15\)=4). Therefore roots are always real, rational and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct. Here (D=4(a+4)2 -4\(a^2+8a+15\)=4). Therefore roots are always real, rational and distinct.
Step 3
Exam Tip
यहाँ (D=4(a+4)2 -4\(a^2+8a+15\)=4) है। इसलिए मूल हमेशा वास्तविक, परिमेय और भिन्न हैं।
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समीकरण (x-2 +2(n+2)x+n-2 +4n+8=0) के मूलों के बारे में सही कथन क्या है?
What is the correct statement about roots of (x-2 +2(n+2)x+n-2 +4n+8=0)?
#quadratic equations
#no real roots
#constant discriminant
A वास्तविक मूल नहीं हैं / No real roots
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक और भिन्न / Always real and distinct
D प्रकृति (n) पर निर्भर है / Nature depends on (n)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं हैं / No real roots
Step 1
Concept
Here (D=4(n+2)2 -4\(n^2+4n+8\)=-16<0). Therefore real roots do not exist.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं हैं / No real roots. Here (D=4(n+2)2 -4\(n^2+4n+8\)=-16<0). Therefore real roots do not exist.
Step 3
Exam Tip
यहाँ (D=4(n+2)2 -4\(n^2+4n+8\)=-16<0) है। इसलिए वास्तविक मूल नहीं हैं।
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समीकरण (x-2 +2(n+2)x+n-2 +4n+1=0) के मूलों की प्रकृति क्या है?
What is the nature of roots of (x-2 +2(n+2)x+n-2 +4n+1=0)?
#quadratic equations
#constant positive D
#real distinct
A हमेशा वास्तविक और भिन्न / Always real and distinct
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक नहीं / Always not real
D केवल (n=0) पर वास्तविक / Real only when (n=0)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और भिन्न / Always real and distinct
Step 1
Concept
Here (D=4(n+2)2 -4\(n^2+4n+1\)=12>0). Hence roots are always real and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=4(n+2)2 -4\(n^2+4n+1\)=12>0). Hence roots are always real and distinct.
Step 3
Exam Tip
यहाँ (D=4(n+2)2 -4\(n^2+4n+1\)=12>0) है। इसलिए मूल हमेशा वास्तविक और भिन्न हैं।
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यदि (x-2 -2(k-3)x+k-2 -6k+8=0) है, तो मूलों की प्रकृति क्या है?
If (x-2 -2(k-3)x+k-2 -6k+8=0), what is the nature of roots?
#quadratic equations
#always real distinct
#constant D
A हमेशा वास्तविक और भिन्न / Always real and distinct
B हमेशा वास्तविक और समान / Always real and equal
C वास्तविक मूल नहीं / No real roots
D प्रकृति (k) पर निर्भर / Nature depends on (k)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और भिन्न / Always real and distinct
Step 1
Concept
Here (D=4(k-3)2 -4\(k^2-6k+8\)=4>0). Therefore roots are always real and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=4(k-3)2 -4\(k^2-6k+8\)=4>0). Therefore roots are always real and distinct.
Step 3
Exam Tip
यहाँ (D=4(k-3)2 -4\(k^2-6k+8\)=4>0) है। इसलिए मूल हमेशा वास्तविक और भिन्न हैं।
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समीकरण (x-2 -(2r+5)x+\(r^2+5r+7\)=0) के वास्तविक मूलों के बारे में क्या सही है?
What is correct about real roots of (x-2 -(2r+5)x+\(r^2+5r+7\)=0)?
#quadratic equations
#constant negative D
#no real roots
A वास्तविक मूल नहीं हैं / No real roots
B हमेशा वास्तविक और भिन्न / Always real and distinct
C हमेशा वास्तविक और समान / Always real and equal
D केवल (r=0) पर वास्तविक / Real only when (r=0)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं हैं / No real roots
Step 1
Concept
Here (D=(2r+5)2 -4\(r^2+5r+7\)=-3<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं हैं / No real roots. Here (D=(2r+5)2 -4\(r^2+5r+7\)=-3<0). Therefore there are no real roots.
Step 3
Exam Tip
यहाँ (D=(2r+5)2 -4\(r^2+5r+7\)=-3<0) है। इसलिए वास्तविक मूल नहीं हैं।
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समीकरण (x-2 -(2r+5)x+\(r^2+5r+4\)=0) के मूलों की प्रकृति क्या है?
What is the nature of roots of (x-2 -(2r+5)x+\(r^2+5r+4\)=0)?
#quadratic equations
#constant D
#rational roots
A हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक नहीं / Always not real
D प्रकृति (r) पर निर्भर है / Nature depends on (r)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct
Step 1
Concept
Here (D=(2r+5)2 -4\(r^2+5r+4\)=9). Since (9>0) and is a perfect square, roots are rational and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक, परिमेय और भिन्न / Always real, rational and distinct. Here (D=(2r+5)2 -4\(r^2+5r+4\)=9). Since (9>0) and is a perfect square, roots are rational and distinct.
Step 3
Exam Tip
यहाँ (D=(2r+5)2 -4\(r^2+5r+4\)=9) है। (9>0) और पूर्ण वर्ग है, इसलिए मूल परिमेय और भिन्न हैं।
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समीकरण \(2x^2-4vx+2v^2+5=0\) के वास्तविक मूलों के बारे में सही कथन क्या है?
What is the correct statement about real roots of \(2x^2-4vx+2v^2+5=0\)?
#quadratic equations
#no real roots
#constant negative D
A वास्तविक मूल नहीं हैं / No real roots
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक और भिन्न / Always real and distinct
D प्रकृति (v) पर निर्भर है / Nature depends on (v)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं हैं / No real roots
Step 1
Concept
Here (D=(-4v)2 -4(2)\(2v^2+5\)=-40<0). Hence there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं हैं / No real roots. Here (D=(-4v)2 -4(2)\(2v^2+5\)=-40<0). Hence there are no real roots.
Step 3
Exam Tip
यहाँ (D=(-4v)2 -4(2)\(2v^2+5\)=-40<0) है। इसलिए वास्तविक मूल नहीं हैं।
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यदि \(x^2-2\ell x+\ell^2-9=0\) है, तो मूलों की प्रकृति क्या है?
If \(x^2-2\ell x+\ell^2-9=0\), what is the nature of roots?
#quadratic equations
#constant discriminant
#real distinct
A हमेशा वास्तविक और भिन्न / Always real and distinct
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक नहीं / Always not real
D \(\ell=3\) पर ही वास्तविक / Real only when \(\ell=3\)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और भिन्न / Always real and distinct
Step 1
Concept
Here (D=\(-2\ell\)2 -4\(\ell^2-9\)=36>0). So for every real \(\ell\), roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=\(-2\ell\)2 -4\(\ell^2-9\)=36>0). So for every real \(\ell\), roots are real and distinct.
Step 3
Exam Tip
यहाँ (D=\(-2\ell\)2 -4\(\ell^2-9\)=36>0) है। इसलिए हर वास्तविक \(\ell\) के लिए मूल वास्तविक और भिन्न हैं।
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समीकरण \(x^2-3x-1=0\) के मूलों की प्रकृति बताइए।
State the nature of roots of \(x^2-3x-1=0\).
#quadratic-equations
#irrational-roots
#negative-constant
A दो वास्तविक अपरिमेय और असमान ((D=13)) / Two real irrational and distinct ((D=13))
B दो वास्तविक परिमेय और असमान ((D=9)) / Two real rational and distinct ((D=9))
C दो वास्तविक समान ((D=0)) / Two real and equal ((D=0))
D कोई वास्तविक मूल नहीं ((D<0)) / No real roots ((D<0))
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक अपरिमेय और असमान ((D=13)) / Two real irrational and distinct ((D=13))
Step 1
Concept
Here (D=(-3)2 -4(1)(-1)=13). Since (13) is not a perfect square, the roots are irrational.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक अपरिमेय और असमान ((D=13)) / Two real irrational and distinct ((D=13)). Here (D=(-3)2 -4(1)(-1)=13). Since (13) is not a perfect square, the roots are irrational.
Step 3
Exam Tip
यहाँ (D=(-3)2 -4(1)(-1)=13) है। (13) पूर्ण वर्ग नहीं है, इसलिए मूल अपरिमेय हैं।
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समीकरण \(3x^2+5x-2=0\) के लिए सही मूल प्रकृति चुनिए।
Choose the correct root nature for \(3x^2+5x-2=0\).
#quadratic-equations
#rational-roots
#negative-constant
A दो वास्तविक परिमेय और असमान ((D=49)) / Two real rational and distinct ((D=49))
B दो वास्तविक समान ((D=0)) / Two real and equal ((D=0))
C कोई वास्तविक मूल नहीं ((D=-49)) / No real roots ((D=-49))
D दो अपरिमेय मूल ((D=5)) / Two irrational roots ((D=5))
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक परिमेय और असमान ((D=49)) / Two real rational and distinct ((D=49))
Step 1
Concept
Here (D=52 -4(3)(-2)=49). (D=49) gives two rational distinct roots.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक परिमेय और असमान ((D=49)) / Two real rational and distinct ((D=49)). Here (D=52 -4(3)(-2)=49). (D=49) gives two rational distinct roots.
Step 3
Exam Tip
यहाँ (D=52 -4(3)(-2)=49) है। (D=49) से दो परिमेय असमान मूल मिलते हैं।
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समीकरण (x-2 +2(a+1)x+a-2 +2a+5=0) के मूलों की प्रकृति क्या है?
What is the nature of roots of (x-2 +2(a+1)x+a-2 +2a+5=0)?
#quadratic equations
#no real roots
#constant negative
A वास्तविक मूल नहीं / No real roots
B वास्तविक और समान / Real and equal
C वास्तविक और भिन्न / Real and distinct
D प्रकृति (a) के चिन्ह पर निर्भर / Nature depends on the sign of (a)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं / No real roots
Step 1
Concept
Here (D=4(a+1)2 -4\(a^2+2a+5\)=-16<0). So there will be no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / No real roots. Here (D=4(a+1)2 -4\(a^2+2a+5\)=-16<0). So there will be no real roots.
Step 3
Exam Tip
यहाँ (D=4(a+1)2 -4\(a^2+2a+5\)=-16<0) है। इसलिए वास्तविक मूल नहीं होंगे।
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समीकरण (3x-2 -6ax+\(3a^2+2\)=0) के वास्तविक मूलों के बारे में क्या सही है?
What is correct about the real roots of (3x-2 -6ax+\(3a^2+2\)=0)?
#quadratic equations
#no real roots
#constant D
A वास्तविक मूल नहीं हैं / No real roots
B वास्तविक और समान मूल हैं / Real and equal roots
C वास्तविक और भिन्न मूल हैं / Real and distinct roots
D प्रकृति (a) पर निर्भर है / Nature depends on (a)
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं हैं / No real roots
Step 1
Concept
Here (D=(-6a)2 -4(3)\(3a^2+2\)=-24<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं हैं / No real roots. Here (D=(-6a)2 -4(3)\(3a^2+2\)=-24<0). Therefore there are no real roots.
Step 3
Exam Tip
यहाँ (D=(-6a)2 -4(3)\(3a^2+2\)=-24<0) है। इसलिए वास्तविक मूल नहीं हैं।
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समीकरण (2x-2 -4ax+\(2a^2-3\)=0) के मूलों की प्रकृति क्या है?
What is the nature of roots of (2x-2 -4ax+\(2a^2-3\)=0)?
#quadratic equations
#always real distinct
#constant D
A हमेशा वास्तविक और भिन्न / Always real and distinct
B हमेशा वास्तविक और समान / Always real and equal
C हमेशा वास्तविक नहीं / Always not real
D सिर्फ (a=0) पर वास्तविक / Real only when (a=0)
Explanation opens after your attempt
Correct Answer
A. हमेशा वास्तविक और भिन्न / Always real and distinct
Step 1
Concept
Here (D=(-4a)2 -4(2)\(2a^2-3\)=24>0). Thus roots are always real and distinct.
Step 2
Why this answer is correct
The correct answer is A. हमेशा वास्तविक और भिन्न / Always real and distinct. Here (D=(-4a)2 -4(2)\(2a^2-3\)=24>0). Thus roots are always real and distinct.
Step 3
Exam Tip
यहाँ (D=(-4a)2 -4(2)\(2a^2-3\)=24>0) है। इसलिए मूल हमेशा वास्तविक और भिन्न हैं।
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समीकरण \(x^2+2px+p^2+1=0\) के मूलों के बारे में सही कथन क्या है?
What is the correct statement about the roots of \(x^2+2px+p^2+1=0\)?
#quadratic equations
#no real roots
#constant negative D
A किसी भी वास्तविक (p) के लिए वास्तविक मूल नहीं हैं / There are no real roots for any real (p)
B हर (p) पर समान मूल हैं / Equal roots for every (p)
C हर (p) पर भिन्न वास्तविक मूल हैं / Distinct real roots for every (p)
D (p=0) पर दो वास्तविक मूल हैं / Two real roots when (p=0)
Explanation opens after your attempt
Correct Answer
A. किसी भी वास्तविक (p) के लिए वास्तविक मूल नहीं हैं / There are no real roots for any real (p)
Step 1
Concept
Here (D=4p-2 -4\(p^2+1\)=-4<0). Therefore real roots do not exist.
Step 2
Why this answer is correct
The correct answer is A. किसी भी वास्तविक (p) के लिए वास्तविक मूल नहीं हैं / There are no real roots for any real (p). Here (D=4p-2 -4\(p^2+1\)=-4<0). Therefore real roots do not exist.
Step 3
Exam Tip
यहाँ (D=4p-2 -4\(p^2+1\)=-4<0) है। इसलिए वास्तविक मूल नहीं हैं।
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समीकरण (4x-2 -4(k+1)x+\(k^2+2k\)=0) के वास्तविक मूलों के लिए (k) पर क्या शर्त है?
What is the condition on (k) for real roots of (4x-2 -4(k+1)x+\(k^2+2k\)=0)?
#quadratic equations
#all real parameters
#constant discriminant
A सभी वास्तविक (k) / All real (k)
B (k>0)
C (k<0)
D कोई वास्तविक (k) नहीं / No real (k)
Explanation opens after your attempt
Correct Answer
A. सभी वास्तविक (k) / All real (k)
Step 1
Concept
Here (D=16(k+1)2 -16\(k^2+2k\)=16). Thus (D>0) for every real (k).
Step 2
Why this answer is correct
The correct answer is A. सभी वास्तविक (k) / All real (k). Here (D=16(k+1)2 -16\(k^2+2k\)=16). Thus (D>0) for every real (k).
Step 3
Exam Tip
यहाँ (D=16(k+1)2 -16\(k^2+2k\)=16) है। इसलिए (D>0) हर वास्तविक (k) के लिए है।
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यदि किसी द्विघात समीकरण के मूल (c) और (-c) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{d}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (c) and (-c), what is the value of the ratio \(\frac{d}{a}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-c^2\)
B \(c^2\)
C (0)
D (2c)
Explanation opens after your attempt
Correct Answer
A. \(-c^2\)
Step 1
Concept
\(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-c^2\). \(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2 ).
Step 3
Exam Tip
\(\frac{d}{a}\) मूलों का गुणनफल होता है। यहां (c(-c)=-c-2 ) है।
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यदि किसी द्विघात समीकरण के मूल (b) और (-b) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (b) and (-b), what is the value of the ratio \(\frac{c}{a}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-b^2\)
B \(b^2\)
C (0)
D (2b)
Explanation opens after your attempt
Correct Answer
A. \(-b^2\)
Step 1
Concept
\(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-b^2\). \(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2 ).
Step 3
Exam Tip
\(\frac{c}{a}\) मूलों का गुणनफल होता है। यहां (b(-b)=-b-2 ) है।
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यदि किसी द्विघात समीकरण के मूल (a) और (-a) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a_1}\) का मान क्या होगा?
If the roots of a quadratic equation are (a) and (-a), what is the value of the ratio \(\frac{c}{a_1}\) of constant term to leading coefficient?
#roots
#opposite_roots
#product
A \(-a^2\)
B \(a^2\)
C (0)
D (2a)
Explanation opens after your attempt
Correct Answer
A. \(-a^2\)
Step 1
Concept
\(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2 ).
Step 2
Why this answer is correct
The correct answer is A. \(-a^2\). \(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2 ).
Step 3
Exam Tip
\(\frac{c}{a_1}\) मूलों का गुणनफल होता है। यहां (a(-a)=-a-2 ) है।
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यदि किसी मोनिक द्विघात समीकरण के मूल (3r) और (4r) हैं तथा उनका योग (28) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (3r) and (4r), and their sum is (28), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (192)
B (28)
C (112)
D (84)
Explanation opens after your attempt
Step 1
Concept
From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 2
Why this answer is correct
The correct answer is A. (192). From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 3
Exam Tip
(3r+4r=28) से (r=4) मिलता है, इसलिए मूल (12) और (16) हैं। स्थिर पद मूलों का गुणनफल (192) होगा।
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यदि किसी मोनिक द्विघात समीकरण के मूल (2r) और (5r) हैं तथा उनका योग (21) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (2r) and (5r), and their sum is (21), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (90)
B (21)
C (45)
D (63)
Explanation opens after your attempt
Step 1
Concept
From (2r+5r=21), we get (r=3), so the roots are (6) and (15). The constant term is the product of roots (90).
Step 2
Why this answer is correct
The correct answer is A. (90). From (2r+5r=21), we get (r=3), so the roots are (6) and (15). The constant term is the product of roots (90).
Step 3
Exam Tip
(2r+5r=21) से (r=3) मिलता है, इसलिए मूल (6) और (15) हैं। स्थिर पद मूलों का गुणनफल (90) होगा।
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यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (3r) हैं तथा उनका योग (16) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (r) and (3r), and their sum is (16), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (48)
B (16)
C (64)
D (32)
Explanation opens after your attempt
Step 1
Concept
From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).
Step 2
Why this answer is correct
The correct answer is A. (48). From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).
Step 3
Exam Tip
(r+3r=16) से (r=4) मिलता है, इसलिए मूल (4) और (12) हैं। स्थिर पद मूलों का गुणनफल (48) होगा।
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यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (2r) हैं तथा उनका योग (9) है, तो उस समीकरण में स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (r) and (2r), and their sum is (9), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#hard
A (18)
B (9)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
From (r+2r=9), we get (r=3), so the roots are (3) and (6). The constant term will be the product of roots (18).
Step 2
Why this answer is correct
The correct answer is A. (18). From (r+2r=9), we get (r=3), so the roots are (3) and (6). The constant term will be the product of roots (18).
Step 3
Exam Tip
(r+2r=9) से (r=3) मिलता है, इसलिए मूल (3) और (6) हैं। स्थिर पद मूलों का गुणनफल (18) होगा।
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समीकरण \(x^2+1=0\) की घात क्या है?
What is the degree of \(x^2+1=0\)?
#quadratic-equations
#degree
#constant-term
A (1)
B (2)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
The highest power of (x) is (2). The constant term does not change the degree.
Step 2
Why this answer is correct
The correct answer is B. (2). The highest power of (x) is (2). The constant term does not change the degree.
Step 3
Exam Tip
इसमें (x) की सबसे बड़ी घात (2) है। स्थिर पद घात को नहीं बदलता।
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समीकरण \(x^2-13x=0\) में कौन सा पद अनुपस्थित है?
Which term is absent in \(x^2-13x=0\)?
#quadratic equations
#missing term
#constant
A द्विघात पद / Quadratic term
B रैखिक पद / Linear term
C स्थिर पद / Constant term
D चर पद / Variable term
Explanation opens after your attempt
Correct Answer
C. स्थिर पद / Constant term
Step 1
Concept
It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 2
Why this answer is correct
The correct answer is C. स्थिर पद / Constant term. It can be written as \(x^2-13x+0=0\). So the constant term is absent.
Step 3
Exam Tip
इसे \(x^2-13x+0=0\) लिखा जा सकता है। इसलिए स्थिर पद अनुपस्थित है।
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समीकरण \(11x^2-6x=0\) में (c) का मान क्या होगा?
What will be the value of (c) in \(11x^2-6x=0\)?
#quadratic equations
#missing constant
#standard form
A (11)
B (-6)
C (0)
D (6)
Explanation opens after your attempt
Step 1
Concept
It can be written as \(11x^2-6x+0=0\). So (c=0).
Step 2
Why this answer is correct
The correct answer is C. (0). It can be written as \(11x^2-6x+0=0\). So (c=0).
Step 3
Exam Tip
इसे \(11x^2-6x+0=0\) लिखा जा सकता है। इसलिए (c=0) है।
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समीकरण \(8x^2+3x+12=0\) में (c) का मान क्या है?
What is the value of (c) in \(8x^2+3x+12=0\)?
#quadratic equations
#constant term
#c value
A (8)
B (3)
C (12)
D (0)
Explanation opens after your attempt
Step 1
Concept
In standard form, (c) is the constant term. Here the constant term is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). In standard form, (c) is the constant term. Here the constant term is (12).
Step 3
Exam Tip
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (12) है।
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