बहुपद \(7x^3-4x+9\) की घात क्या है?
What is the degree of the polynomial \(7x^3-4x+9\)?
#degree
#polynomials
#class10
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A (1)
B (2)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
The highest power is (3), so the degree is (3). Always check the highest power of the variable.
Step 2
Why this answer is correct
The correct answer is C. (3). The highest power is (3), so the degree is (3). Always check the highest power of the variable.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। हमेशा चर की सबसे बड़ी घात देखें।
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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
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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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बहुपद \(2x^2+3x-11\) में नियत पद कौन सा है?
Which is the constant term in \(2x^2+3x-11\)?
#constant-term
#polynomials
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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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बहुपद \(4x^3+x^2-7x+1\) में कितने पद हैं?
How many terms are there in \(4x^3+x^2-7x+1\)?
#number-of-terms
#polynomial
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The terms are \(4x^3\), \(x^2\), (-7x), and (1). Separate terms by plus or minus signs.
Step 2
Why this answer is correct
The correct answer is C. (4). The terms are \(4x^3\), \(x^2\), (-7x), and (1). Separate terms by plus or minus signs.
Step 3
Exam Tip
पद \(4x^3\), \(x^2\), (-7x) और (1) हैं। पदों को जोड़ या घटाव के चिह्नों से अलग करें।
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(9) किस प्रकार का बहुपद है?
What type of polynomial is (9)?
#constant-polynomial
#degree-zero
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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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निम्न में से रैखिक बहुपद कौन सा है?
Which of the following is a linear polynomial?
#linear-polynomial
#degree
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A (3x+4)
B \(x^2+1\)
C \(x^3-2\)
D (5)
Explanation opens after your attempt
Step 1
Concept
A linear polynomial has degree (1). In (3x+4), the highest power is (1).
Step 2
Why this answer is correct
The correct answer is A. (3x+4). A linear polynomial has degree (1). In (3x+4), the highest power is (1).
Step 3
Exam Tip
रैखिक बहुपद की घात (1) होती है। (3x+4) में सबसे बड़ी घात (1) है।
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निम्न में से त्रिघात बहुपद कौन सा है?
Which of the following is a cubic polynomial?
#cubic-polynomial
#degree
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A \(x^3-4x+2\)
B \(x^2+9\)
C (6x-1)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(x^3-4x+2\)
Step 1
Concept
A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-4x+2\). A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 3
Exam Tip
त्रिघात बहुपद की घात (3) होती है। \(x^3-4x+2\) में सबसे बड़ी घात (3) है।
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क्या \(2x^2+\frac{3}{x}+1\) (x) में बहुपद है?
Is \(2x^2+\frac{3}{x}+1\) a polynomial in (x)?
#not-polynomial
#negative-power
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A हाँ क्योंकि इसमें \(x^2\) है / Yes because it has \(x^2\)
B नहीं क्योंकि इसमें \(\frac{3}{x}\) है / No because it has \(\frac{3}{x}\)
C हाँ क्योंकि इसमें नियत पद है / Yes because it has a constant term
D नहीं क्योंकि इसमें (2) है / No because it has (2)
Explanation opens after your attempt
Correct Answer
B. नहीं क्योंकि इसमें \(\frac{3}{x}\) है / No because it has \(\frac{3}{x}\)
Step 1
Concept
\(\frac{3}{x}\) means \(3x^{-1}\), which is not allowed in a polynomial. Powers of the variable must be whole numbers.
Step 2
Why this answer is correct
The correct answer is B. नहीं क्योंकि इसमें \(\frac{3}{x}\) है / No because it has \(\frac{3}{x}\). \(\frac{3}{x}\) means \(3x^{-1}\), which is not allowed in a polynomial. Powers of the variable must be whole numbers.
Step 3
Exam Tip
\(\frac{3}{x}\) का अर्थ \(3x^{-1}\) है जो बहुपद में मान्य नहीं है। बहुपद में चर की घातें पूर्ण संख्याएँ होनी चाहिए।
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बहुपद (p(x)=x-2 +2x+1) में (p(1)) का मान क्या है?
For (p(x)=x-2 +2x+1), what is the value of (p(1))?
#value-of-polynomial
#substitution
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(1)=12 +2(1)+1=4). Substitute the given number for every (x).
Step 2
Why this answer is correct
The correct answer is C. (4). (p(1)=12 +2(1)+1=4). Substitute the given number for every (x).
Step 3
Exam Tip
(p(1)=12 +2(1)+1=4) होता है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें।
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यदि (p(x)=3x-5), तो (p(2)) क्या होगा?
If (p(x)=3x-5), what is (p(2))?
#polynomial-value
#linear-polynomial
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A (1)
B (2)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=3(2)-5=1). Use direct substitution in a simple linear polynomial.
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=3(2)-5=1). Use direct substitution in a simple linear polynomial.
Step 3
Exam Tip
(p(2)=3(2)-5=1) है। सरल रैखिक बहुपद में सीधे प्रतिस्थापन करें।
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यदि (q(x)=x-3 -x), तो (q(0)) का मान क्या है?
If (q(x)=x-3 -x), what is the value of (q(0))?
#substitution
#zero-value
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A (-1)
B (0)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(q(0)=03 -0=0). When substituting (0), check each term containing (x).
Step 2
Why this answer is correct
The correct answer is B. (0). (q(0)=03 -0=0). When substituting (0), check each term containing (x).
Step 3
Exam Tip
(q(0)=03 -0=0) है। (0) रखने पर हर (x) वाला पद सावधानी से देखें।
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\(6x^4-2x^2+x-8\) की घात क्या है?
What is the degree of \(6x^4-2x^2+x-8\)?
#degree
#highest-power
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A (1)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.
Step 3
Exam Tip
सबसे बड़ी घात (4) है इसलिए घात (4) है। पदों की संख्या नहीं, सबसे बड़ी घात महत्वपूर्ण 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
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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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क्या \(\sqrt{2}x^2+5x-1\) (x) में बहुपद है?
Is \(\sqrt{2}x^2+5x-1\) a polynomial in (x)?
#real-coefficient
#polynomial
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A हाँ क्योंकि \(\sqrt{2}\) वास्तविक गुणांक है / Yes because \(\sqrt{2}\) is a real coefficient
B नहीं क्योंकि \(\sqrt{2}\) है / No because \(\sqrt{2}\) is present
C नहीं क्योंकि इसमें \(x^2\) है / No because it has \(x^2\)
D हाँ केवल तब जब (x=0) / Yes only when (x=0)
Explanation opens after your attempt
Correct Answer
A. हाँ क्योंकि \(\sqrt{2}\) वास्तविक गुणांक है / Yes because \(\sqrt{2}\) is a real coefficient
Step 1
Concept
\(\sqrt{2}\) is a real number and the powers of the variable are whole numbers. Real coefficients are allowed in polynomials.
Step 2
Why this answer is correct
The correct answer is A. हाँ क्योंकि \(\sqrt{2}\) वास्तविक गुणांक है / Yes because \(\sqrt{2}\) is a real coefficient. \(\sqrt{2}\) is a real number and the powers of the variable are whole numbers. Real coefficients are allowed in polynomials.
Step 3
Exam Tip
\(\sqrt{2}\) वास्तविक संख्या है और चर की घातें पूर्ण संख्याएँ हैं। वास्तविक गुणांक बहुपद में मान्य होते हैं।
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क्या \(x^{\frac{1}{2}}+3\) (x) में बहुपद है?
Is \(x^{\frac{1}{2}}+3\) a polynomial in (x)?
#not-polynomial
#fractional-power
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A हाँ / Yes
B नहीं / No
C केवल (x=1) पर / Only at (x=1)
D केवल (x=0) पर / Only at (x=0)
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Step 1
Concept
In \(x^{\frac{1}{2}}\), the power of the variable is not a whole number. In a polynomial, powers must be \(0,1,2,\ldots\).
Step 2
Why this answer is correct
The correct answer is B. नहीं / No. In \(x^{\frac{1}{2}}\), the power of the variable is not a whole number. In a polynomial, powers must be \(0,1,2,\ldots\).
Step 3
Exam Tip
\(x^{\frac{1}{2}}\) में चर की घात पूर्ण संख्या नहीं है। बहुपद में चर की घात \(0,1,2,\ldots\) होनी चाहिए।
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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
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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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शून्य बहुपद (0) की घात के बारे में सही कथन कौन सा है?
Which statement about the degree of the zero polynomial (0) is correct?
#zero-polynomial
#degree
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A घात (0) है / Degree is (0)
B घात (1) है / Degree is (1)
C घात परिभाषित नहीं है / Degree is not defined
D घात (2) है / Degree is (2)
Explanation opens after your attempt
Correct Answer
C. घात परिभाषित नहीं है / Degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. घात परिभाषित नहीं है / Degree is not defined. The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। इसे गैर-शून्य नियत बहुपद से अलग याद रखें।
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(p(x)=2x-2 -3x+4) में (p(-1)) का मान क्या है?
For (p(x)=2x-2 -3x+4), what is (p(-1))?
#substitution
#negative-value
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=2(-1)2 -3(-1)+4=9). Use brackets when squaring a negative number.
Step 2
Why this answer is correct
The correct answer is D. (9). (p(-1)=2(-1)2 -3(-1)+4=9). Use brackets when squaring a negative number.
Step 3
Exam Tip
(p(-1)=2(-1)2 -3(-1)+4=9) है। ऋणात्मक संख्या का वर्ग रखते समय कोष्ठक लगाएँ।
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बहुपद \(x^4+2x^3+x^2+x+1\) में प्रमुख पद कौन सा है?
What is the leading term in \(x^4+2x^3+x^2+x+1\)?
#leading-term
#highest-degree
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A (1)
B (x)
C \(2x^3\)
D \(x^4\)
Explanation opens after your attempt
Correct Answer
D. \(x^4\)
Step 1
Concept
The term with the highest power is \(x^4\). To identify the leading term, check the powers.
Step 2
Why this answer is correct
The correct answer is D. \(x^4\). The term with the highest power is \(x^4\). To identify the leading term, check the powers.
Step 3
Exam Tip
सबसे बड़ी घात वाला पद \(x^4\) है। प्रमुख पद पहचानने के लिए घातों को देखें।
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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
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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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\(4x^2+0x+9\) 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
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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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यदि (p(a)=0), तो (a) को (p(x)) का क्या कहा जाता है?
If (p(a)=0), what is (a) called for (p(x))?
#zero-of-polynomial
#definition
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A गुणांक / Coefficient
B घात / Degree
C शून्य / Zero
D पद / Term
Explanation opens after your attempt
Correct Answer
C. शून्य / Zero
Step 1
Concept
If (p(a)=0), then (a) is called a zero of the polynomial. To test a zero, substitute that number for (x).
Step 2
Why this answer is correct
The correct answer is C. शून्य / Zero. If (p(a)=0), then (a) is called a zero of the polynomial. To test a zero, substitute that number for (x).
Step 3
Exam Tip
यदि (p(a)=0), तो (a) बहुपद का शून्य कहलाता है। शून्य जाँचने के लिए उस संख्या को (x) में रखें।
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निम्न में से कौन सा (x) में बहुपद नहीं है?
Which of the following is not a polynomial in (x)?
#not-polynomial
#negative-exponent
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A \(x^2+1\)
B \(4x^3-2\)
C \(\frac{5}{x^2}+1\)
D (7x+8)
Explanation opens after your attempt
Correct Answer
C. \(\frac{5}{x^2}+1\)
Step 1
Concept
\(\frac{5}{x^2}=5x^{-2}\) has a negative power. Such powers are not allowed in a polynomial.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{5}{x^2}+1\). \(\frac{5}{x^2}=5x^{-2}\) has a negative power. Such powers are not allowed in a polynomial.
Step 3
Exam Tip
\(\frac{5}{x^2}=5x^{-2}\) में ऋणात्मक घात है। बहुपद में ऐसी घात मान्य नहीं होती।
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(p(x)=x-6) का शून्य क्या है?
What is the zero of (p(x)=x-6)?
#zero
#linear-polynomial
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A (6)
B (-6)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Setting (x-6=0) gives (x=6). The zero of (x-a) is (a).
Step 2
Why this answer is correct
The correct answer is A. (6). Setting (x-6=0) gives (x=6). The zero of (x-a) is (a).
Step 3
Exam Tip
(x-6=0) करने पर (x=6) आता है। (x-a) का शून्य (a) होता है।
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\(2x^3-7\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(2x^3-7\)?
#coefficient
#missing-power
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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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निम्न में से किस बहुपद की घात (1) है?
Which polynomial has degree (1)?
#degree-one
#linear
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A \(4x^2+1\)
B (9x-3)
C \(x^3+2\)
D (11)
Explanation opens after your attempt
Step 1
Concept
In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).
Step 2
Why this answer is correct
The correct answer is B. (9x-3). In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).
Step 3
Exam Tip
(9x-3) में (x) की सबसे बड़ी घात (1) है। इसलिए यह घात (1) का बहुपद है।
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निम्न में से किस बहुपद की घात (2) है?
Which polynomial has degree (2)?
#degree-two
#quadratic
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A \(x^2+4x\)
B \(x^4+1\)
C (6x+5)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x\)
Step 1
Concept
The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x\). The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).
Step 3
Exam Tip
\(x^2+4x\) में सबसे बड़ी घात (2) है। इसलिए इसकी घात (2) 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
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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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क्या \(4x^2-3\sqrt{x}+1\) (x) में बहुपद है?
Is \(4x^2-3\sqrt{x}+1\) a polynomial in (x)?
#not-polynomial
#root-variable
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A हाँ / Yes
B नहीं / No
C केवल जब (x) धनात्मक हो / Only when (x) is positive
D केवल जब (x=1) हो / Only when (x=1)
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Step 1
Concept
\(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).
Step 2
Why this answer is correct
The correct answer is B. नहीं / No. \(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).
Step 3
Exam Tip
\(\sqrt{x}=x^{\frac{1}{2}}\) है और \(\frac{1}{2}\) पूर्ण संख्या नहीं है। इसलिए यह (x) में बहुपद नहीं है।
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(p(x)=x-2 +5) में (p(-2)) का मान क्या है?
For (p(x)=x-2 +5), what is (p(-2))?
#substitution
#quadratic
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A (1)
B (7)
C (9)
D (25)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=(-2)2 +5=9). The square of a negative value is positive.
Step 2
Why this answer is correct
The correct answer is C. (9). (p(-2)=(-2)2 +5=9). The square of a negative value is positive.
Step 3
Exam Tip
(p(-2)=(-2)2 +5=9) है। ऋणात्मक मान का वर्ग धनात्मक होता है।
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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
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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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यदि (p(x)=2x+1), तो (p(3)-p(1)) का मान क्या है?
If (p(x)=2x+1), what is the value of (p(3)-p(1))?
#polynomial-value
#difference
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(3)=7) and (p(1)=3), so the difference is (4). Find both values separately first.
Step 2
Why this answer is correct
The correct answer is B. (4). (p(3)=7) and (p(1)=3), so the difference is (4). Find both values separately first.
Step 3
Exam Tip
(p(3)=7) और (p(1)=3), इसलिए अंतर (4) है। पहले दोनों मान अलग-अलग निकालें।
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\(3x^2+2x+1\) में (x=1) रखने पर कौन सा मान मिलेगा?
What value is obtained by putting (x=1) in \(3x^2+2x+1\)?
#substitution
#evaluation
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(3(1)2 +2(1)+1=6). After substitution, simplify the sum carefully.
Step 2
Why this answer is correct
The correct answer is D. (6). (3(1)2 +2(1)+1=6). After substitution, simplify the sum carefully.
Step 3
Exam Tip
(3(1)2 +2(1)+1=6) है। प्रतिस्थापन के बाद सरल जोड़ करें।
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निम्न में से कौन सा बहुपद (2) पदों वाला है?
Which of the following is a polynomial with (2) terms?
#binomial
#number-of-terms
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A \(x^2+x+1\)
B \(5x^3-4\)
C (7x)
D \(x^4+x^3+x^2+x\)
Explanation opens after your attempt
Correct Answer
B. \(5x^3-4\)
Step 1
Concept
\(5x^3-4\) has (2) terms. A polynomial with two terms is called a binomial.
Step 2
Why this answer is correct
The correct answer is B. \(5x^3-4\). \(5x^3-4\) has (2) terms. A polynomial with two terms is called a binomial.
Step 3
Exam Tip
\(5x^3-4\) में (2) पद हैं। दो पदों वाला बहुपद द्विपदी कहलाता है।
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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
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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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\(x^5+1\) की घात क्या है?
What is the degree of \(x^5+1\)?
#degree
#highest-power
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A (1)
B (2)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5), so the degree is (5). The constant term does not increase the degree.
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5), so the degree is (5). The constant term does not increase the degree.
Step 3
Exam Tip
सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। नियत पद घात को नहीं बढ़ाता।
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निम्न में से (y) में बहुपद कौन सा है?
Which of the following is a polynomial in (y)?
#polynomial-in-y
#one-variable
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A \(y^2-3y+2\)
B \(\frac{1}{y}+4\)
C \(\sqrt{y}+5\)
D \(y^{-2}+1\)
Explanation opens after your attempt
Correct Answer
A. \(y^2-3y+2\)
Step 1
Concept
In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).
Step 2
Why this answer is correct
The correct answer is A. \(y^2-3y+2\). In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).
Step 3
Exam Tip
\(y^2-3y+2\) में (y) की घातें पूर्ण संख्याएँ हैं। बहुपद किसी एक चर जैसे (y) में भी हो सकता है।
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यदि (r(x)=4x-2 ), तो (r\left\(\frac{1}{2}\right\)) क्या है?
If (r(x)=4x-2 ), what is (r\left\(\frac{1}{2}\right\))?
#substitution
#fraction-value
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A (1)
B (2)
C (4)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
(r\left\(\frac{1}{2}\right\)=4\left\(\frac{1}{2}\right\)2 =1). Use brackets when substituting fractions.
Step 2
Why this answer is correct
The correct answer is A. (1). (r\left\(\frac{1}{2}\right\)=4\left\(\frac{1}{2}\right\)2 =1). Use brackets when substituting fractions.
Step 3
Exam Tip
(r\left\(\frac{1}{2}\right\)=4\left\(\frac{1}{2}\right\)2 =1) है। भिन्न रखते समय कोष्ठक का प्रयोग करें।
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बहुपद \(7x^2+5\) में कितने पद हैं?
How many terms are there in \(7x^2+5\)?
#terms
#binomial
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A (1)
B (2)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
The terms are \(7x^2\) and (5). Therefore it has (2) terms.
Step 2
Why this answer is correct
The correct answer is B. (2). The terms are \(7x^2\) and (5). Therefore it has (2) terms.
Step 3
Exam Tip
पद \(7x^2\) और (5) हैं। इसलिए इसमें (2) पद हैं।
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\(ax^2+bx+c\) में यदि \(a\neq0\), तो यह किस प्रकार का बहुपद है?
In \(ax^2+bx+c\), if \(a\neq0\), what type of polynomial is it?
#standard-form
#quadratic
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A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C त्रिघात बहुपद / Cubic polynomial
D नियत बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
When \(a\neq0\), the \(x^2\) term is present. So the degree of the polynomial is (2).
Step 2
Why this answer is correct
The correct answer is B. द्विघात बहुपद / Quadratic polynomial. When \(a\neq0\), the \(x^2\) term is present. So the degree of the polynomial is (2).
Step 3
Exam Tip
\(a\neq0\) होने पर \(x^2\) का पद मौजूद रहता है। इसलिए बहुपद की घात (2) होती 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
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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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निम्न में से कौन सा (x) में बहुपद है जिसकी घात (4) है?
Which of the following is a polynomial in (x) with degree (4)?
#degree
#highest-power
#polynomial
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A \(x^4-2x+7\)
B \(x^3+4\)
C \(5x^2-1\)
D (9x+6)
Explanation opens after your attempt
Correct Answer
A. \(x^4-2x+7\)
Step 1
Concept
In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.
Step 2
Why this answer is correct
The correct answer is A. \(x^4-2x+7\). In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.
Step 3
Exam Tip
\(x^4-2x+7\) में सबसे बड़ी घात (4) है। घात पहचानने के लिए सबसे बड़ी शक्ति देखें।
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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
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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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यदि (f(x)=x-2 +4x), तो (f(-4)) का मान क्या है?
If (f(x)=x-2 +4x), what is the value of (f(-4))?
#substitution
#zero-of-polynomial
#easy
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A (0)
B (4)
C (-4)
D (16)
Explanation opens after your attempt
Step 1
Concept
(f(-4)=(-4)2 +4(-4)=16-16=0). Pay attention to signs while substituting negative values.
Step 2
Why this answer is correct
The correct answer is A. (0). (f(-4)=(-4)2 +4(-4)=16-16=0). Pay attention to signs while substituting negative values.
Step 3
Exam Tip
(f(-4)=(-4)2 +4(-4)=16-16=0) है। ऋणात्मक मान रखते समय चिह्नों पर ध्यान दें।
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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
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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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(p(x)=x+9) का शून्य क्या है?
What is the zero of (p(x)=x+9)?
#linear-polynomial
#zero
#easy
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A (9)
B (-9)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Setting (x+9=0) gives (x=-9). The zero of (x+a) is (-a).
Step 2
Why this answer is correct
The correct answer is B. (-9). Setting (x+9=0) gives (x=-9). The zero of (x+a) is (-a).
Step 3
Exam Tip
(x+9=0) करने पर (x=-9) मिलता है। (x+a) का शून्य (-a) होता है।
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\(4x^2-6x+1\) में कुल कितने पद हैं?
How many terms are there in \(4x^2-6x+1\)?
#trinomial
#number-of-terms
#polynomial
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
It has the terms \(4x^2\), (-6x), and (1). Therefore it is a trinomial.
Step 2
Why this answer is correct
The correct answer is C. (3). It has the terms \(4x^2\), (-6x), and (1). Therefore it is a trinomial.
Step 3
Exam Tip
इसमें पद \(4x^2\), (-6x) और (1) हैं। इसलिए यह त्रिपदी है।
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यदि (g(x)=3x-2 -x), तो (g(1)) का मान क्या है?
If (g(x)=3x-2 -x), what is the value of (g(1))?
#polynomial-value
#substitution
#class10
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(g(1)=3(1)2 -1=2). Substitute (1) for each (x) and simplify.
Step 2
Why this answer is correct
The correct answer is B. (2). (g(1)=3(1)2 -1=2). Substitute (1) for each (x) and simplify.
Step 3
Exam Tip
(g(1)=3(1)2 -1=2) है। प्रत्येक (x) की जगह (1) रखकर सरल करें।
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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
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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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यदि (h(x)=x-2 +2x), तो (h(-2)) का मान क्या है?
If (h(x)=x-2 +2x), what is the value of (h(-2))?
#polynomial-value
#substitution
#zero-of-polynomial
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A (0)
B (2)
C (-2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(h(-2)=(-2)2 +2(-2)=4-4=0). Use brackets and check signs when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (0). (h(-2)=(-2)2 +2(-2)=4-4=0). Use brackets and check signs when substituting a negative value.
Step 3
Exam Tip
(h(-2)=(-2)2 +2(-2)=4-4=0) है। ऋणात्मक मान रखते समय कोष्ठक और चिह्नों का ध्यान रखें।
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