यदि बहुपद (p(x)=2x-3 +kx-2 -8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=2x-3 +kx-2 -8x+3) is (0), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (3). The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 3
Exam Tip
गुणांकों का योग (2+k-8+3=k-3) है, इसलिए (k=3)। गुणांकों का योग (p(1)) से भी मिलता है।
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(p(x)=5x-3 -2x-2 +x-4) में सभी गुणांकों का योग क्या है?
What is the sum of all coefficients in (p(x)=5x-3 -2x-2 +x-4)?
#sum of coefficients
#evaluation
#polynomial
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).
Step 2
Why this answer is correct
The correct answer is A. (0). The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).
Step 3
Exam Tip
सभी गुणांकों का योग (5-2+1-4=0) है। यह (p(1)) के बराबर भी होता है।
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यदि (p(x)) की घात (4) और (q(x)) की घात (3) है, तो सामान्यतः (p(x)q(x)) की घात क्या होगी?
If the degree of (p(x)) is (4) and the degree of (q(x)) is (3), what will generally be the degree of (p(x)q(x))?
#degree
#product
#polynomial
A (1)
B (7)
C (12)
D (4)
Explanation opens after your attempt
Step 1
Concept
In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.
Step 2
Why this answer is correct
The correct answer is B. (7). In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.
Step 3
Exam Tip
दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (4+3=7)। गुणन में घातों का योग याद रखें।
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यदि (p(x)=kx-2 -5x+6) और (p(-1)=14), तो (k) का मान क्या है?
If (p(x)=kx-2 -5x+6) and (p(-1)=14), what is the value of (k)?
#evaluation
#parameter
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.
Step 3
Exam Tip
(p(-1)=k+5+6=14), इसलिए (k=3)। ऋणात्मक मान रखते समय संकेत सावधानी से देखें।
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यदि (p(x)=(a-5)x-5 +2x-3 -7x+4) की घात (3) है, तो (a) क्या होगा?
If the degree of (p(x)=(a-5)x-5 +2x-3 -7x+4) is (3), what is (a)?
#degree
#parameter
#polynomial
A (0)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 2
Why this answer is correct
The correct answer is C. (5). For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 3
Exam Tip
घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए, इसलिए (a-5=0)। उच्चतम घात वाले पद को पहले शून्य करें।
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((2x+3)2 ) का विस्तृत बहुपद रूप क्या है?
What is the expanded polynomial form of ((2x+3)2 )?
#expansion
#identity
#polynomial
A \(4x^2+12x+9\)
B \(4x^2+9\)
C \(2x^2+12x+3\)
D \(4x^2-12x+9\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+12x+9\)
Step 1
Concept
((2x+3)2 =4x-2 +12x+9). Do not skip the middle term (2ab) while squaring.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+12x+9\). ((2x+3)2 =4x-2 +12x+9). Do not skip the middle term (2ab) while squaring.
Step 3
Exam Tip
((2x+3)2 =4x-2 +12x+9)। वर्ग करते समय मध्य पद (2ab) को न छोड़ें।
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यदि (p(x)=(k-4)x-4 +3x-2 -5x+2) की घात (2) है, तो (k) का मान क्या होगा?
If the degree of (p(x)=(k-4)x-4 +3x-2 -5x+2) is (2), what will be the value of (k)?
#degree
#parameter
#polynomial
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 2
Why this answer is correct
The correct answer is C. (4). For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 3
Exam Tip
घात (2) होने के लिए \(x^4\) का गुणांक (0) होना चाहिए, इसलिए (k-4=0) और (k=4)। सबसे बड़ी घात वाले पद का गुणांक पहले जांचें।
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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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एक चर के बहुपद में चर की घातें कैसी होनी चाहिए?
What should the powers of the variable be in a polynomial in one variable?
#powers
#definition
#polynomial
A ऋणात्मक पूर्णांक / Negative integers
B भिन्न संख्याएं / Fractions
C अऋणात्मक पूर्णांक / Non-negative integers
D केवल अभाज्य संख्याएं / Only prime numbers
Explanation opens after your attempt
Correct Answer
C. अऋणात्मक पूर्णांक / Non-negative integers
Step 1
Concept
In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
Step 2
Why this answer is correct
The correct answer is C. अऋणात्मक पूर्णांक / Non-negative integers. In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
Step 3
Exam Tip
बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है।
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(p(x)=x-5 +3x-3 -2) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-5 +3x-3 -2)?
#missing power
#coefficient zero
#polynomial
A \(x^5\)
B \(x^4\)
C \(x^3\)
D \(x^0\)
Explanation opens after your attempt
Correct Answer
B. \(x^4\)
Step 1
Concept
The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^4\). The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
Step 3
Exam Tip
इस बहुपद में \(x^4\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है।
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बहुपद (p(x)=5x-3 +0x-2 -4x+12) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 +0x-2 -4x+12)?
#coefficient
#missing term
#polynomial
A (0)
B (5)
C (-4)
D (12)
Explanation opens after your attempt
Step 1
Concept
The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
Step 3
Exam Tip
\(x^2\) वाला पद \(0x^2\) है इसलिए गुणांक (0) है। अनुपस्थित या शून्य पद का गुणांक (0) माना जाता है।
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(p(x)=9x-27) का शून्य क्या है?
What is the zero of (p(x)=9x-27)?
#linear zero
#equation
#polynomial
A (2)
B (3)
C (9)
D (27)
Explanation opens after your attempt
Step 1
Concept
From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 2
Why this answer is correct
The correct answer is B. (3). From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
Step 3
Exam Tip
(9x-27=0) से (x=3) मिलता है। रैखिक बहुपद का शून्य समीकरण हल करके निकालें।
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((3x+2)(x-4)) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying ((3x+2)(x-4))?
#binomial multiplication
#polynomial
#expansion
A \(3x^2-10x-8\)
B \(3x^2+14x-8\)
C \(3x^2-12x+2\)
D \(3x^2-10x+8\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-10x-8\)
Step 1
Concept
((3x+2)(x-4)=3x-2 -12x+2x-8=3x-2 -10x-8). Multiply each term by each term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-10x-8\). ((3x+2)(x-4)=3x-2 -12x+2x-8=3x-2 -10x-8). Multiply each term by each term.
Step 3
Exam Tip
((3x+2)(x-4)=3x-2 -12x+2x-8=3x-2 -10x-8)। प्रत्येक पद का हर पद से गुणा करें।
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((x-5)(x+2)) का बहुपद रूप क्या है?
What is the polynomial form of ((x-5)(x+2))?
#binomial multiplication
#expansion
#polynomial
A \(x^2-3x-10\)
B \(x^2+7x-10\)
C \(x^2-3x+10\)
D \(x^2-7x-10\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10\)
Step 1
Concept
((x-5)(x+2)=x-2 +2x-5x-10=x-2 -3x-10). Combine the middle terms with signs.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10\). ((x-5)(x+2)=x-2 +2x-5x-10=x-2 -3x-10). Combine the middle terms with signs.
Step 3
Exam Tip
((x-5)(x+2)=x-2 +2x-5x-10=x-2 -3x-10)। मध्य पदों को संकेत सहित जोड़ें।
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(-3x\(2x^2-4x+5\)) का सरल रूप क्या है?
What is the simplified form of (-3x\(2x^2-4x+5\))?
#multiplication
#distributive property
#polynomial
A \(-6x^3+12x^2-15x\)
B \(-6x^3-12x^2-15x\)
C \(6x^3+12x^2-15x\)
D \(-6x^2+12x-15\)
Explanation opens after your attempt
Correct Answer
A. \(-6x^3+12x^2-15x\)
Step 1
Concept
Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
Step 2
Why this answer is correct
The correct answer is A. \(-6x^3+12x^2-15x\). Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
Step 3
Exam Tip
प्रत्येक पद को (-3x) से गुणा करने पर \(-6x^3+12x^2-15x\) मिलता है। ऋणात्मक गुणक के संकेत ध्यान से लगाएं।
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(p(x)=8x-4 -5x-3 +2x-6) में \(x^4\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^4\)-term in (p(x)=8x-4 -5x-3 +2x-6)?
#coefficient
#quartic term
#polynomial
A (8)
B (-5)
C (2)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (8). The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
Step 3
Exam Tip
\(x^4\) वाले पद \(8x^4\) का गुणांक (8) है। घात और गुणांक को अलग पहचानें।
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बहुपद (p(z)=-6z-5 +4z-4 -z+8) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(z)=-6z-5 +4z-4 -z+8)?
#leading coefficient
#degree
#polynomial
A (-6)
B (4)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-6). The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 3
Exam Tip
सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है।
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यदि (p(x)=9x-2 +cx-5) में (x) का गुणांक (-4) है, तो (c) क्या है?
If the coefficient of (x) in (p(x)=9x-2 +cx-5) is (-4), what is (c)?
#coefficient
#parameter
#polynomial
A (-9)
B (-5)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 2
Why this answer is correct
The correct answer is C. (-4). In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 3
Exam Tip
(cx) में (x) का गुणांक (c) है। दिया है कि (c=-4)।
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बहुपद (p(u)=13u-3 -2u+9) में चर कौन सा है?
What is the variable in the polynomial (p(u)=13u-3 -2u+9)?
#variable
#one variable
#polynomial
A (p)
B (u)
C (13)
D (9)
Explanation opens after your attempt
Step 1
Concept
The letter whose values can change is the variable. Here the variable is (u).
Step 2
Why this answer is correct
The correct answer is B. (u). The letter whose values can change is the variable. Here the variable is (u).
Step 3
Exam Tip
जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है।
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(p(x)=0x-5 +7x-3 -2x+1) की घात क्या है?
What is the degree of (p(x)=0x-5 +7x-3 -2x+1)?
#degree
#zero coefficient
#polynomial
A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 3
Exam Tip
\(0x^5\) का गुणांक (0) है इसलिए वह पद नहीं गिना जाएगा। सबसे बड़ी प्रभावी घात (3) है।
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यदि (p(x)=2x-2 +3x-11), तो (p(2)) का मान क्या है?
If (p(x)=2x-2 +3x-11), what is the value of (p(2))?
#evaluation
#substitution
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=2(2)2 +3(2)-11=3). While evaluating, calculate the power first.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(2)=2(2)2 +3(2)-11=3). While evaluating, calculate the power first.
Step 3
Exam Tip
(p(2)=2(2)2 +3(2)-11=3)। मान निकालते समय पहले घात का मान निकालें।
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बहुपद \(7x^4-3x^3+0x^2+5\) में प्रभावी पदों की संख्या कितनी है?
How many effective terms are there in the polynomial \(7x^4-3x^3+0x^2+5\)?
#terms
#zero coefficient
#polynomial
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term \(0x^2\) is not effective, so the terms are \(7x^4\), \(-3x^3\), and (5). Do not count a term with zero coefficient.
Step 2
Why this answer is correct
The correct answer is B. (3). The term \(0x^2\) is not effective, so the terms are \(7x^4\), \(-3x^3\), and (5). Do not count a term with zero coefficient.
Step 3
Exam Tip
\(0x^2\) प्रभावी पद नहीं है इसलिए पद \(7x^4\), \(-3x^3\) और (5) हैं। शून्य गुणांक वाले पद को न गिनें।
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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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(p(x)=5x-3 -8x-2 +13x-21) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in (p(x)=5x-3 -8x-2 +13x-21)?
#coefficient
#sign
#polynomial
A (5)
B (-8)
C (13)
D (-21)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 2
Why this answer is correct
The correct answer is B. (-8). The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
Step 3
Exam Tip
\(x^2\) वाले पद \(-8x^2\) का गुणांक (-8) है। संकेत सहित गुणांक लिखना जरूरी है।
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बहुपद (p(x)=11x-6 -4x-3 +x-9) की घात क्या है?
What is the degree of the polynomial (p(x)=11x-6 -4x-3 +x-9)?
#degree
#highest power
#polynomial
A (1)
B (3)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.
Step 2
Why this answer is correct
The correct answer is C. (6). The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.
Step 3
Exam Tip
सबसे बड़ी घात (6) है इसलिए घात (6) होगी। गुणांक नहीं बल्कि चर की सबसे ऊंची घात देखें।
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\(x^2+\sqrt{5}x-7\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(x^2+\sqrt{5}x-7\)?
#real-coefficient
#polynomial
#definition
A यह बहुपद नहीं है क्योंकि \(\sqrt{5}\) है / It is not a polynomial because \(\sqrt{5}\) is present
B यह (x) में बहुपद है / It is a polynomial in (x)
C यह केवल नियत बहुपद है / It is only a constant polynomial
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
B. यह (x) में बहुपद है / It is a polynomial in (x)
Step 1
Concept
\(\sqrt{5}\) is a real coefficient and the powers of (x) are whole numbers. So it is a polynomial in (x).
Step 2
Why this answer is correct
The correct answer is B. यह (x) में बहुपद है / It is a polynomial in (x). \(\sqrt{5}\) is a real coefficient and the powers of (x) are whole numbers. So it is a polynomial in (x).
Step 3
Exam Tip
\(\sqrt{5}\) वास्तविक गुणांक है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह (x) में बहुपद है।
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कौन सा विकल्प बहुपद \(8-3x+2x^2\) को अवरोही घातों में सही लिखता है?
Which option correctly writes the polynomial \(8-3x+2x^2\) in descending powers?
#descending-order
#rearrangement
#polynomial
A \(2x^2-3x+8\)
B \(8+3x+2x^2\)
C \(2x^2+3x+8\)
D \(8-2x^2-3x\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-3x+8\)
Step 1
Concept
In descending order, the term with greater power comes first. So the correct form is \(2x^2-3x+8\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-3x+8\). In descending order, the term with greater power comes first. So the correct form is \(2x^2-3x+8\).
Step 3
Exam Tip
अवरोही क्रम में बड़ी घात वाला पद पहले आता है। इसलिए सही रूप \(2x^2-3x+8\) है।
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किस विकल्प में बहुपद \(6x^3+0x^2-2x+9\) को सरल रूप में सही लिखा गया है?
Which option correctly writes \(6x^3+0x^2-2x+9\) in simplified form?
#zero-coefficient
#simplification
#polynomial
A \(6x^3-2x+9\)
B \(6x^3+2x+9\)
C \(6x^3+x^2-2x+9\)
D \(6x^3-2x\)
Explanation opens after your attempt
Correct Answer
A. \(6x^3-2x+9\)
Step 1
Concept
The value of \(0x^2\) is (0), so that term vanishes. The remaining terms stay unchanged.
Step 2
Why this answer is correct
The correct answer is A. \(6x^3-2x+9\). The value of \(0x^2\) is (0), so that term vanishes. The remaining terms stay unchanged.
Step 3
Exam Tip
\(0x^2\) का मान (0) है इसलिए वह पद हट जाता है। बाकी पद जैसे हैं वैसे रहते हैं।
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निम्न में से कौन सा बहुपद (x) में है लेकिन (y) में नहीं है?
Which of the following is a polynomial in (x) but not in (y)?
#one-variable
#variable-identification
#polynomial
A \(x^2+3x+1\)
B \(y^2+3y+1\)
C (xy+1)
D (x+y+1)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+1\)
Step 1
Concept
\(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+1\). \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 3
Exam Tip
\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है।
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बहुपद \(3x^4-5x^2+2x-8\) का प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^4-5x^2+2x-8\)?
#leading-coefficient
#degree-four
#polynomial
A (3)
B (-5)
C (2)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 3
Exam Tip
प्रमुख पद \(3x^4\) है। इसलिए प्रमुख गुणांक (3) है।
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