\(3x^2-2x+1\) और \(x^2+4x+7\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(3x^2-2x+1\) and \(x^2+4x+7\)?
#coefficients
#like terms
#polynomials
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is A. (2). The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 3
Exam Tip
पहले बहुपद में (x) का गुणांक (-2) और दूसरे में (4) है, योग (2) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=5x-2 +3x-2) से (r(x)=2x-2 -x+4) घटाने पर क्या मिलेगा?
What is obtained when (r(x)=2x-2 -x+4) is subtracted from (p(x)=5x-2 +3x-2)?
#subtraction
#polynomials
#like terms
A \(3x^2+4x-6\)
B \(7x^2+2x+2\)
C \(3x^2+2x+2\)
D \(7x^2+4x-6\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+4x-6\)
Step 1
Concept
(p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6). Change all signs while subtracting.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+4x-6\). (p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6). Change all signs while subtracting.
Step 3
Exam Tip
(p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6)। घटाते समय सभी संकेत बदलें।
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(p(x)=3x-2 -4x+1) और (q(x)=x-2 +2x-5) का योग क्या है?
What is the sum of (p(x)=3x-2 -4x+1) and (q(x)=x-2 +2x-5)?
#addition
#like terms
#polynomials
A \(4x^2-2x-4\)
B \(2x^2-6x+6\)
C \(4x^2+6x-4\)
D \(3x^4-8x^2-5\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-2x-4\)
Step 1
Concept
Adding like terms gives \(4x^2-2x-4\). Combine only like terms.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-2x-4\). Adding like terms gives \(4x^2-2x-4\). Combine only like terms.
Step 3
Exam Tip
समान घात वाले पद जोड़ने पर \(4x^2-2x-4\) मिलता है। केवल समान पदों को मिलाएं।
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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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बहुपद \(7x^3-4x+9\) की घात क्या है?
What is the degree of the polynomial \(7x^3-4x+9\)?
#degree
#polynomials
#class10
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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(p(x)=x-2 +3x+2) के लिए (p(1)) का मान क्या है?
For (p(x)=x-2 +3x+2), what is the value of (p(1))?
#polynomials
#one-variable
#value
#substitution
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(p(1)=12 +3\cdot1+2=6). While evaluating, replace every (x) with the given number.
Step 2
Why this answer is correct
The correct answer is C. (6). (p(1)=12 +3\cdot1+2=6). While evaluating, replace every (x) with the given number.
Step 3
Exam Tip
(p(1)=12 +3\cdot1+2=6) है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें।
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यदि (p(x)=2x-3 -5x+9) है, तो इसमें \(x^2\) का गुणांक क्या है?
If (p(x)=2x-3 -5x+9), what is the coefficient of \(x^2\)?
#polynomials
#one-variable
#coefficient
#missing-term
A (2)
B (-5)
C (9)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक हमेशा (0) माना जाता है।
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एक छात्र \(x^2+2x+1\) की घात (3) बताता है क्योंकि इसमें (3) पद हैं। सही घात क्या है?
A student says the degree of \(x^2+2x+1\) is (3) because it has (3) terms. What is the correct degree?
#polynomials
#common-mistake
#degree
#easy
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.
Step 2
Why this answer is correct
The correct answer is B. (2). Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.
Step 3
Exam Tip
घात पदों की संख्या से नहीं, सबसे बड़ी घात (2) से तय होती है। यह सामान्य गलती परीक्षा में न करें।
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यदि (p(x)=x-2 +4x+4) है, तो (p(-2)) कितना है?
If (p(x)=x-2 +4x+4), what is (p(-2))?
#polynomials
#value
#zero
#easy
A (0)
B (2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=(-2)2 +4(-2)+4=4-8+4=0). Be careful with signs when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-2)=(-2)2 +4(-2)+4=4-8+4=0). Be careful with signs when substituting a negative value.
Step 3
Exam Tip
(p(-2)=(-2)2 +4(-2)+4=4-8+4=0) है। ऋणात्मक मान रखते समय चिह्न सावधानी से लिखें।
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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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\(x^4+3x^2+2\) में कौन सा पद अनुपस्थित है?
Which term is missing in \(x^4+3x^2+2\)?
#polynomials
#missing-term
#easy
#standard-form
A \(x^4\)
B \(x^3\)
C \(3x^2\)
D (2)
Explanation opens after your attempt
Correct Answer
B. \(x^3\)
Step 1
Concept
The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^3\). The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जा सकता है।
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निम्न में से कौन सा बहुपद मानक रूप में व्यवस्थित है?
Which of the following polynomials is arranged in standard form?
#polynomials
#standard-form
#easy
#arrangement
A \(2x^3+x^2+5x+1\)
B \(5x+2x^3+1+x^2\)
C \(1+5x+x^2+2x^3\)
D \(x^2+2x^3+5x+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3+x^2+5x+1\)
Step 1
Concept
In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 2
Why this answer is correct
The correct answer is A. \(2x^3+x^2+5x+1\). In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 3
Exam Tip
मानक रूप में घातें घटते क्रम में लिखी जाती हैं। \(2x^3+x^2+5x+1\) में यही क्रम है।
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(p(x)=x-2 -1) के लिए (p(-1)) क्या है?
For (p(x)=x-2 -1), what is (p(-1))?
#polynomials
#value
#zero
#easy
A (0)
B (-2)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=(-1)2 -1=1-1=0). Use brackets when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=(-1)2 -1=1-1=0). Use brackets when substituting a negative value.
Step 3
Exam Tip
(p(-1)=(-1)2 -1=1-1=0) है। कोष्ठक लगाकर ऋणात्मक मान रखें।
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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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यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?
If a polynomial has degree (3), what is it called?
#polynomials
#cubic
#easy
#degree
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रैखिक बहुपद / Linear polynomial
D नियत बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 3
Exam Tip
घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।
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यदि किसी बहुपद की घात (2) है, तो उसे क्या कहते हैं?
If a polynomial has degree (2), what is it called?
#polynomials
#quadratic
#easy
#degree
A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C घन बहुपद / Cubic polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.
Step 2
Why this answer is correct
The correct answer is B. द्विघात बहुपद / Quadratic polynomial. A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.
Step 3
Exam Tip
घात (2) वाला बहुपद द्विघात कहलाता है। \(x^2\) का अशून्य पद होना जरूरी है।
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यदि किसी बहुपद की घात (1) है, तो उसे क्या कहते हैं?
If a polynomial has degree (1), what is it called?
#polynomials
#degree
#type
#easy
A नियत बहुपद / Constant polynomial
B रैखिक बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D घन बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
B. रैखिक बहुपद / Linear polynomial
Step 1
Concept
A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.
Step 2
Why this answer is correct
The correct answer is B. रैखिक बहुपद / Linear polynomial. A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.
Step 3
Exam Tip
घात (1) वाले बहुपद को रैखिक बहुपद कहते हैं। नाम हमेशा घात से जोड़कर याद करें।
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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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किस विकल्प में (x) की घात बहुपद के लिए स्वीकार्य है?
In which option is the power of (x) acceptable for a polynomial?
#polynomials
#powers
#easy
#concept
A \(x^{-1}\)
B \(x^{\frac{1}{2}}\)
C \(x^0\)
D \(x^{-3}\)
Explanation opens after your attempt
Correct Answer
C. \(x^0\)
Step 1
Concept
In a polynomial, powers of (x) must be \(0,1,2,\ldots\). \(x^0\) is acceptable.
Step 2
Why this answer is correct
The correct answer is C. \(x^0\). In a polynomial, powers of (x) must be \(0,1,2,\ldots\). \(x^0\) is acceptable.
Step 3
Exam Tip
बहुपद में (x) की घात \(0,1,2,\ldots\) जैसी होनी चाहिए। \(x^0\) स्वीकार्य है।
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(p(x)=4x-8) में (x=2) रखने पर क्या निष्कर्ष निकलेगा?
What conclusion follows when (x=2) is substituted in (p(x)=4x-8)?
#polynomials
#zero
#reasoning
#easy
A (2) शून्यक है / (2) is a zero
B (2) घात है / (2) is the degree
C (2) गुणांक है / (2) is the coefficient
D (2) नियत पद है / (2) is the constant term
Explanation opens after your attempt
Correct Answer
A. (2) शून्यक है / (2) is a zero
Step 1
Concept
(p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
Step 2
Why this answer is correct
The correct answer is A. (2) शून्यक है / (2) is a zero. (p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
Step 3
Exam Tip
(p(2)=4\cdot2-8=0), इसलिए (2) शून्यक है। शून्यक जांचने के लिए मान (0) आना चाहिए।
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(p(x)=x-3 +2x-2 +x) में अग्र पद कौन सा है?
What is the leading term of (p(x)=x-3 +2x-2 +x)?
#polynomials
#leading-term
#easy
A \(x^3\)
B \(2x^2\)
C (x)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(x^3\)
Step 1
Concept
The term with the highest power is \(x^3\). To identify the leading term, look for the highest power.
Step 2
Why this answer is correct
The correct answer is A. \(x^3\). The term with the highest power is \(x^3\). To identify the leading term, look for the highest power.
Step 3
Exam Tip
सबसे बड़ी घात वाला पद \(x^3\) है। अग्र पद पहचानने के लिए सबसे बड़ी घात देखें।
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(p(x)=ax-2 +bx+c) में यदि \(a\ne0\) है, तो यह किस प्रकार का बहुपद है?
In (p(x)=ax-2 +bx+c), if \(a\ne0\), what type of polynomial is it?
#polynomials
#quadratic-form
#easy
#degree
A रैखिक / Linear
B द्विघात / Quadratic
C घन / Cubic
D नियत / Constant
Explanation opens after your attempt
Correct Answer
B. द्विघात / Quadratic
Step 1
Concept
Since \(a\ne0\), the \(x^2\)-term remains, so the degree is (2). A degree (2) polynomial is quadratic.
Step 2
Why this answer is correct
The correct answer is B. द्विघात / Quadratic. Since \(a\ne0\), the \(x^2\)-term remains, so the degree is (2). A degree (2) polynomial is quadratic.
Step 3
Exam Tip
\(a\ne0\) होने से \(x^2\) पद रहता है, इसलिए घात (2) है। घात (2) वाला बहुपद द्विघात होता है।
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(p(x)=ax+b) में यदि \(a\ne0\) है, तो इसकी घात क्या होती है?
In (p(x)=ax+b), if \(a\ne0\), what is its degree?
#polynomials
#linear-form
#easy
#degree
A (0)
B (1)
C (2)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.
Step 2
Why this answer is correct
The correct answer is B. (1). When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.
Step 3
Exam Tip
\(a\ne0\) होने पर (x) वाला पद मौजूद है, इसलिए घात (1) है। यही रैखिक बहुपद का रूप है।
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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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बहुपद \(x^2-5x+6\) में पदों की संख्या कितनी है?
How many terms are in the polynomial \(x^2-5x+6\)?
#polynomials
#terms
#easy
#trinomial
A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
It has three terms: \(x^2\), (-5x), and (6). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (3). It has three terms: \(x^2\), (-5x), and (6). Count terms with their signs.
Step 3
Exam Tip
इसमें \(x^2\), (-5x) और (6) तीन पद हैं। चिह्न सहित पद गिनें।
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(p(x)=2x-2 -8) के लिए (p(2)) का मान क्या है?
For (p(x)=2x-2 -8), what is the value of (p(2))?
#polynomials
#value
#easy
#substitution
A (0)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(2)=2\cdot22 -8=8-8=0). Square first, then multiply.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(2)=2\cdot22 -8=8-8=0). Square first, then multiply.
Step 3
Exam Tip
(p(2)=2\cdot22 -8=8-8=0) है। पहले वर्ग करें फिर गुणा करें।
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यदि (p(x)=x-2 +x) है, तो (p(-1)) क्या होगा?
If (p(x)=x-2 +x), what is (p(-1))?
#polynomials
#value
#negative-input
#easy
A (0)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=(-1)2 +(-1)=1-1=0). The square of a negative number is positive.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=(-1)2 +(-1)=1-1=0). The square of a negative number is positive.
Step 3
Exam Tip
(p(-1)=(-1)2 +(-1)=1-1=0) है। ऋणात्मक संख्या का वर्ग धनात्मक होता है।
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बहुपद \(x^3-1\) में (x=1) रखने पर मान क्या है?
What is the value of \(x^3-1\) when (x=1)?
#polynomials
#value
#zero
#easy
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(1^3-1=0\). So (1) is also a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). \(1^3-1=0\). So (1) is also a zero of this polynomial.
Step 3
Exam Tip
\(1^3-1=0\) है। इसलिए (1) इस बहुपद का शून्यक भी है।
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बहुपद \(11x^5-3x^2+8\) की घात क्या है?
What is the degree of \(11x^5-3x^2+8\)?
#polynomials
#degree
#easy
#highest-power
A (2)
B (3)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.
Step 3
Exam Tip
सबसे बड़ी घात (5) है इसलिए घात (5) होगी। पदों की संख्या नहीं बल्कि सबसे बड़ी घात देखें।
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कौन सा बहुपद एक चर (x) में है?
Which polynomial is in one variable (x)?
#polynomials
#one-variable
#easy
#concept
A \(x^2+2x+1\)
B (x+y+1)
C \(a^2+b^2\)
D (xy+3)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1\)
Step 1
Concept
A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+1\). A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.
Step 3
Exam Tip
एक चर (x) में बहुपद में केवल (x) चर होता है। अन्य विकल्पों में एक से अधिक चर हैं।
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