\(3x^2+2x+1\) 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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\(6x^2-3x+10\) 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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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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यदि (p(x)=5x-3), तो (p(0)) का मान क्या है?
If (p(x)=5x-3), what is the value of (p(0))?
#evaluation
#constant_term
#linear_polynomial
A (5)
B \(-3\)
C (0)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=5(0)-3=-3). In exams, when (x=0), only the constant term remains.
Step 2
Why this answer is correct
The correct answer is B. \(-3\). (p(0)=5(0)-3=-3). In exams, when (x=0), only the constant term remains.
Step 3
Exam Tip
(p(0)=5(0)-3=-3)। परीक्षा में (x=0) रखने पर केवल स्थिर पद बचता 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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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 \(2x^2+3x-8=0\) 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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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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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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समीकरण \(4x^2-8x+1=0\) में (c) का मान क्या है?
What is the value of (c) in \(4x^2-8x+1=0\)?
#quadratic equations
#constant term
#standard form
A (4)
B \(-8\)
C (1)
D \(-1\)
Explanation opens after your attempt
Step 1
Concept
In standard form, (c) is the constant term. Here the constant term is (1).
Step 2
Why this answer is correct
The correct answer is C. (1). In standard form, (c) is the constant term. Here the constant term is (1).
Step 3
Exam Tip
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (1) 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 \(x^2-2x+m\) के शून्यक \(1+\sqrt{6}\) और \(1-\sqrt{6}\) हैं, तो (m) क्या है?
If the zeroes of \(x^2-2x+m\) are \(1+\sqrt{6}\) and \(1-\sqrt{6}\), what is (m)?
#parameter
#constant-term
#conjugates
A (-5)
B (5)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The product is (1-6=-5), so (m=-5). In a monic polynomial, the constant term is the product of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-5). The product is (1-6=-5), so (m=-5). In a monic polynomial, the constant term is the product of zeroes.
Step 3
Exam Tip
गुणनफल (1-6=-5) है, इसलिए (m=-5)। एकक बहुपद में स्थिर पद शून्यकों का गुणनफल होता 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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यदि \(x^2+bx+12\) के शून्यक \(2+\sqrt{7}\) और \(2-\sqrt{7}\) हैं, तो त्रुटि क्या है?
If the zeroes of \(x^2+bx+12\) are \(2+\sqrt{7}\) and \(2-\sqrt{7}\), what is the error?
#error-finding
#constant-term
#conjugates
A स्थिर पद (12) होना सही है / Constant term (12) is correct
B गुणनफल (-3) है, इसलिए स्थिर पद (12) नहीं हो सकता / Product is (-3), so constant term cannot be (12)
C योग अपरिमेय है / Sum is irrational
D शून्यक वास्तविक नहीं हैं / Zeroes are not real
Explanation opens after your attempt
Correct Answer
B. गुणनफल (-3) है, इसलिए स्थिर पद (12) नहीं हो सकता / Product is (-3), so constant term cannot be (12)
Step 1
Concept
The product of these zeroes is (4-7=-3). In a monic polynomial, the constant term must equal the product.
Step 2
Why this answer is correct
The correct answer is B. गुणनफल (-3) है, इसलिए स्थिर पद (12) नहीं हो सकता / Product is (-3), so constant term cannot be (12). The product of these zeroes is (4-7=-3). In a monic polynomial, the constant term must equal the product.
Step 3
Exam Tip
इन शून्यकों का गुणनफल (4-7=-3) है। एकक बहुपद में स्थिर पद गुणनफल के बराबर होना चाहिए।
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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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