इनमें से कौन सा एक चर में बहुपद है?
Which of the following is a polynomial in one variable?
#polynomial
#one variable
#identification
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A (p(x)=3x-2 -5x+7)
B (p(x)=\frac{2}{x}+1)
C (p(x)=\sqrt{x}+4)
D (p(x)=x^{-2}+3)
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Correct Answer
A. (p(x)=3x-2 -5x+7)
Explanation
Simple Explanation
एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें। / In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
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बहुपद (p(x)=4x-5 -3x-2 +9) की घात क्या है?
What is the degree of the polynomial (p(x)=4x-5 -3x-2 +9)?
#degree
#polynomial
#powers
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A (2)
B (3)
C (5)
D (9)
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Explanation
Simple Explanation
सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। हमेशा सबसे ऊंची घात देखें। / The highest power is (5), so the degree is (5). Always check the highest exponent.
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व्यंजक \(7x^3+2x^2-x+6\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(7x^3+2x^2-x+6\)?
#coefficient
#term
#polynomial
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A (7)
B (2)
C (-1)
D (6)
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Explanation
Simple Explanation
\(x^2\) के साथ लगा संख्या गुणक (2) है। गुणांक पूछने पर उसी पद को पहचानें। / The numerical factor attached to \(x^2\) is (2). When coefficient is asked, identify the exact term.
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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
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A (5)
B (-8)
C (11)
D (4)
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Explanation
Simple Explanation
जिस पद में (x) नहीं होता वह अचर पद है। यहां अचर पद (11) है। / The term without (x) is the constant term. Here the constant term is (11).
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बहुपद (p(x)=2x-3 -5x-2 +4x-1) में कितने पद हैं?
How many terms are there in (p(x)=2x-3 -5x-2 +4x-1)?
#terms
#polynomial
#counting
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
अलग अलग पद \(2x^3\), \(-5x^2\), (4x) और (-1) हैं। चिह्न के साथ पद गिनें। / The separate terms are \(2x^3\), \(-5x^2\), (4x), and (-1). Count terms with their signs.
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(p(x)=3x-2 -2x+5) के लिए (p(2)) का मान क्या है?
For (p(x)=3x-2 -2x+5), what is the value of (p(2))?
#evaluation
#substitution
#polynomial
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A (9)
B (11)
C (13)
D (15)
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Explanation
Simple Explanation
(p(2)=3(2)2 -2(2)+5=13)। मान निकालते समय (x) की जगह दी गई संख्या रखें। / (p(2)=3(2)2 -2(2)+5=13). Substitute the given number for (x) carefully.
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(q(x)=x-3 -4x-2 +x+6) के लिए (q(-1)) क्या होगा?
For (q(x)=x-3 -4x-2 +x+6), what is (q(-1))?
#evaluation
#negative value
#polynomial
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
(q(-1)=-1-4-1+6=0)। ऋणात्मक संख्या की घात लगाते समय संकेत पर ध्यान दें। / (q(-1)=-1-4-1+6=0). Pay attention to signs while using powers of a negative number.
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बहुपद \(8x^2-3x+1\) किस प्रकार का है?
What type of polynomial is \(8x^2-3x+1\)?
#trinomial
#classification
#terms
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A एकपदी / Monomial
B द्विपदी / Binomial
C त्रिपदी / Trinomial
D शून्य बहुपद / Zero polynomial
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Correct Answer
C. त्रिपदी / Trinomial
Explanation
Simple Explanation
इसमें तीन पद हैं इसलिए यह त्रिपदी है। पदों की संख्या से प्रकार पहचानें। / It has three terms, so it is a trinomial. Identify the type by counting terms.
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(p(x)=ax-2 +bx+c) कब द्विघात बहुपद होगा?
When will (p(x)=ax-2 +bx+c) be a quadratic polynomial?
#quadratic condition
#coefficient
#concept
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A (a=0)
B \(a\ne0\)
C (b=0)
D (c=0)
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Correct Answer
B. \(a\ne0\)
Explanation
Simple Explanation
द्विघात बहुपद के लिए \(x^2\) का गुणांक शून्य नहीं होना चाहिए। इसलिए \(a\ne0\) जरूरी है। / For a quadratic polynomial, the coefficient of \(x^2\) must not be zero. Hence \(a\ne0\) is necessary.
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(p(x)=0) को किस नाम से जाना जाता है?
What is (p(x)=0) called?
#zero polynomial
#degree
#definition
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A अचर बहुपद / Constant polynomial
B रैखिक बहुपद / Linear polynomial
C शून्य बहुपद / Zero polynomial
D द्विघात बहुपद / Quadratic polynomial
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Correct Answer
C. शून्य बहुपद / Zero polynomial
Explanation
Simple Explanation
(p(x)=0) शून्य बहुपद कहलाता है। इसकी घात परिभाषित नहीं मानी जाती। / (p(x)=0) is called the zero polynomial. Its degree is considered undefined.
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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
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A (0)
B (1)
C (12)
D परिभाषित नहीं / Undefined
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Explanation
Simple Explanation
अशून्य अचर बहुपद की घात (0) होती है। शून्य बहुपद से इसे अलग रखें। / A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.
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\(3x^4+0x^3-2x+5\) की घात क्या है?
What is the degree of \(3x^4+0x^3-2x+5\)?
#degree
#zero coefficient
#polynomial
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A (1)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
\(0x^3\) पद प्रभावी नहीं है और सबसे बड़ी अशून्य घात (4) है। शून्य गुणांक वाले पद को नजरअंदाज करें। / The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.
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बहुपद (p(t)=6t-2 -7t+3) में चर कौन सा है?
What is the variable in the polynomial (p(t)=6t-2 -7t+3)?
#variable
#one variable
#polynomial
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A (p)
B (t)
C (6)
D (3)
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Explanation
Simple Explanation
जिस अक्षर का मान बदल सकता है वह चर है। यहां चर (t) है। / The letter whose value can vary is the variable. Here the variable is (t).
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(p(x)=2x-2 +kx+8) में (x) का गुणांक (5) हो तो (k) क्या है?
If the coefficient of (x) in (p(x)=2x-2 +kx+8) is (5), what is (k)?
#coefficient
#parameter
#polynomial
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A (2)
B (5)
C (8)
D (10)
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Explanation
Simple Explanation
(kx) में (x) का गुणांक (k) है। दिया है (k=5)। / In (kx), the coefficient of (x) is (k). It is given that (k=5).
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यदि (p(x)=x-2 -9), तो (p(3)) का मान क्या है?
If (p(x)=x-2 -9), what is the value of (p(3))?
#zero of polynomial
#evaluation
#substitution
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A (0)
B (3)
C (6)
D (9)
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Explanation
Simple Explanation
(p(3)=32 -9=0)। ऐसे मान को बहुपद का शून्य भी कहा जा सकता है। / (p(3)=32 -9=0). Such a value can also be called a zero of the polynomial.
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(x=2) किस बहुपद का शून्य है?
For which polynomial is (x=2) a zero?
#zero
#linear polynomial
#evaluation
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A (p(x)=x-2)
B (p(x)=x+2)
C (p(x)=2x+1)
D (p(x)=x-2 +2)
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Correct Answer
A. (p(x)=x-2)
Explanation
Simple Explanation
(p(2)=2-2=0), इसलिए (x=2) इसका शून्य है। शून्य जांचने के लिए मान रखकर (0) देखें। / (p(2)=2-2=0), so (x=2) is its zero. To test a zero, substitute and check for (0).
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(p(x)=x-2 +2x-8) के लिए (p(2)) क्या है?
For (p(x)=x-2 +2x-8), what is (p(2))?
#evaluation
#zero
#quadratic
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A (0)
B (2)
C (4)
D (8)
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Explanation
Simple Explanation
(p(2)=4+4-8=0)। इसलिए (2) इस बहुपद का शून्य है। / (p(2)=4+4-8=0). Hence (2) is a zero of this polynomial.
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किसी रैखिक बहुपद (ax+b) में \(a\ne0\) हो तो उसकी घात क्या है?
If \(a\ne0\) in a linear polynomial (ax+b), what is its degree?
#linear polynomial
#degree
#general form
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A (0)
B (1)
C (2)
D परिभाषित नहीं / Undefined
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Explanation
Simple Explanation
(ax+b) में \(a\ne0\) होने पर (x) की सबसे बड़ी घात (1) है। इसलिए घात (1) होगी। / When \(a\ne0\) in (ax+b), the highest power of (x) is (1). So the degree is (1).
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बहुपद (p(y)=9y-4 -y-2 +5y-6) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(y)=9y-4 -y-2 +5y-6)?
#leading coefficient
#degree
#polynomial
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A (9)
B (-1)
C (5)
D (-6)
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Explanation
Simple Explanation
सबसे बड़ी घात \(y^4\) के पद का गुणांक (9) है। अग्र गुणांक वही होता है। / The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
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(p(x)=4x-3 -2x-2 +7x-1) में \(x^3\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^3\) term in (p(x)=4x-3 -2x-2 +7x-1)?
#coefficient
#cubic term
#polynomial
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A (4)
B (-2)
C (7)
D (-1)
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Explanation
Simple Explanation
\(x^3\) के साथ गुणांक (4) जुड़ा है। घात और गुणांक को अलग अलग पहचानें। / The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
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कौन सा बहुपद मानक रूप में अवरोही घातों में लिखा गया है?
Which polynomial is written in standard form with descending powers?
#standard form
#descending powers
#polynomial
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A \(2x+5x^3-1\)
B \(5x^3+2x-1\)
C \(7+3x^2-x^4\)
D \(x+x^2+x^3\)
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Correct Answer
B. \(5x^3+2x-1\)
Explanation
Simple Explanation
मानक रूप में बड़ी घात से छोटी घात की ओर लिखते हैं। \(5x^3+2x-1\) इसी क्रम में है। / In standard form, terms are written from highest power to lowest power. \(5x^3+2x-1\) follows this order.
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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
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A \(4x^2-2x-4\)
B \(2x^2-6x+6\)
C \(4x^2+6x-4\)
D \(3x^4-8x^2-5\)
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Correct Answer
A. \(4x^2-2x-4\)
Explanation
Simple Explanation
समान घात वाले पद जोड़ने पर \(4x^2-2x-4\) मिलता है। केवल समान पदों को मिलाएं। / Adding like terms gives \(4x^2-2x-4\). Combine only like terms.
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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
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A \(3x^2+4x-6\)
B \(7x^2+2x+2\)
C \(3x^2+2x+2\)
D \(7x^2+4x-6\)
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Correct Answer
A. \(3x^2+4x-6\)
Explanation
Simple Explanation
(p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6)। घटाते समय सभी संकेत बदलें। / (p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6). Change all signs while subtracting.
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(2x\(3x^2-5x+1\)) का सरल रूप क्या है?
What is the simplified form of (2x\(3x^2-5x+1\))?
#multiplication
#distributive property
#polynomial
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A \(6x^3-10x^2+2x\)
B \(6x^2-10x+2\)
C \(5x^3-7x^2+x\)
D \(6x^3+10x^2+2x\)
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Correct Answer
A. \(6x^3-10x^2+2x\)
Explanation
Simple Explanation
प्रत्येक पद को (2x) से गुणा करने पर \(6x^3-10x^2+2x\) मिलता है। वितरण नियम का प्रयोग करें। / Multiplying each term by (2x) gives \(6x^3-10x^2+2x\). Use the distributive property.
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((x+3)(x-4)) का बहुपद रूप क्या है?
What is the polynomial form of ((x+3)(x-4))?
#multiplication
#binomials
#polynomial
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A \(x^2-x-12\)
B \(x^2+7x-12\)
C \(x^2-x+12\)
D \(x^2-7x-12\)
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Correct Answer
A. \(x^2-x-12\)
Explanation
Simple Explanation
((x+3)(x-4)=x-2 -4x+3x-12=x-2 -x-12)। मध्य पद जोड़ते समय संकेत देखें। / ((x+3)(x-4)=x-2 -4x+3x-12=x-2 -x-12). Watch signs while combining middle terms.
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((2x-1)(x+5)) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying ((2x-1)(x+5))?
#binomial multiplication
#polynomial
#expansion
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A \(2x^2+9x-5\)
B \(2x^2+10x-1\)
C \(2x^2-9x-5\)
D \(2x^2+9x+5\)
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Correct Answer
A. \(2x^2+9x-5\)
Explanation
Simple Explanation
((2x-1)(x+5)=2x-2 +10x-x-5=2x-2 +9x-5)। हर पद का हर पद से गुणा करें। / ((2x-1)(x+5)=2x-2 +10x-x-5=2x-2 +9x-5). Multiply each term by each term.
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(p(x)=x-3 -6x-2 +11x-6) में (p(1)) का मान क्या है?
What is the value of (p(1)) in (p(x)=x-3 -6x-2 +11x-6)?
#evaluation
#cubic polynomial
#zero
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A (0)
B (1)
C (6)
D (11)
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Explanation
Simple Explanation
(p(1)=1-6+11-6=0)। इसलिए (1) इस बहुपद का शून्य है। / (p(1)=1-6+11-6=0). Therefore (1) is a zero of this polynomial.
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यदि (p(x)=x-2 +kx+6) और (p(2)=0), तो (k) क्या है?
If (p(x)=x-2 +kx+6) and (p(2)=0), what is (k)?
#parameter
#zero condition
#polynomial
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A (-5)
B (-4)
C (4)
D (5)
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Explanation
Simple Explanation
(p(2)=4+2k+6=0), इसलिए (2k=-10) और (k=-5)। शून्य की शर्त में मान रखकर समीकरण बनाएं। / (p(2)=4+2k+6=0), so (2k=-10) and (k=-5). Substitute the zero and form an equation.
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यदि (p(x)=x-2 -ax+10) और (p(5)=0), तो (a) का मान क्या है?
If (p(x)=x-2 -ax+10) and (p(5)=0), what is the value of (a)?
#parameter
#evaluation
#quadratic polynomial
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A (5)
B (7)
C (10)
D (15)
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Explanation
Simple Explanation
(p(5)=25-5a+10=0), इसलिए (35=5a) और (a=7)। दिए गए शून्य का उपयोग करें। / (p(5)=25-5a+10=0), so (35=5a) and (a=7). Use the given zero.
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किस मान के लिए \(x^2-4x+m\) में (x=1) शून्य होगा?
For what value of (m) will (x=1) be a zero of \(x^2-4x+m\)?
#zero
#parameter
#quadratic
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(1-4+m=0), इसलिए (m=3)। शून्य मिलने पर बहुपद का मान (0) रखें। / (1-4+m=0), so (m=3). When a zero is given, set the polynomial value equal to (0).
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बहुपद (p(x)=2x-2 -3x+1) में (x=1) रखने पर क्या निष्कर्ष है?
What conclusion follows when (x=1) is substituted in (p(x)=2x-2 -3x+1)?
#zero
#evaluation
#concept
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A (1) शून्य है / (1) is a zero
B (1) गुणांक है / (1) is a coefficient
C (1) घात है / (1) is a degree
D (1) पद है / (1) is a term
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Correct Answer
A. (1) शून्य है / (1) is a zero
Explanation
Simple Explanation
(p(1)=2-3+1=0), इसलिए (1) शून्य है। शून्य के लिए परिणाम (0) होना चाहिए। / (p(1)=2-3+1=0), so (1) is a zero. For a zero, the result must be (0).
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(p(x)=x-2 +4x+4) में (p(-2)) क्या है?
What is (p(-2)) for (p(x)=x-2 +4x+4)?
#evaluation
#negative zero
#quadratic
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A (0)
B (2)
C (4)
D (8)
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Explanation
Simple Explanation
(p(-2)=4-8+4=0)। ऋणात्मक मान रखते समय संकेतों को सावधानी से लिखें। / (p(-2)=4-8+4=0). Write signs carefully when substituting a negative value.
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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?
Which option is a polynomial in one variable but not quadratic?
#classification
#cubic
#not quadratic
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A \(x^2+2x+1\)
B \(4x^3+x-9\)
C \(\frac{1}{x}+2\)
D \(\sqrt{x}+3\)
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Correct Answer
B. \(4x^3+x-9\)
Explanation
Simple Explanation
\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है। / \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
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(p(x)=7x-14) का शून्य क्या है?
What is the zero of (p(x)=7x-14)?
#linear zero
#equation
#polynomial
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A (1)
B (2)
C (7)
D (14)
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Explanation
Simple Explanation
(7x-14=0) से (x=2) मिलता है। रैखिक बहुपद का शून्य जल्दी निकालने के लिए समीकरण हल करें। / From (7x-14=0), we get (x=2). Solve the equation to find the zero of a linear polynomial.
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(p(x)=3x+12) का शून्य कौन सा है?
Which is the zero of (p(x)=3x+12)?
#linear polynomial
#zero
#solution
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A (4)
B (-4)
C (3)
D (-3)
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Explanation
Simple Explanation
(3x+12=0) से (x=-4) मिलता है। शून्य वह मान है जिससे बहुपद (0) हो जाए। / From (3x+12=0), we get (x=-4). A zero is the value that makes the polynomial equal to (0).
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यदि (p(x)=ax+b) और \(a\ne0\), तो इसका शून्य क्या होगा?
If (p(x)=ax+b) and \(a\ne0\), what will be its zero?
#linear zero
#general form
#formula
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A \(\frac{b}{a}\)
B \(-\frac{b}{a}\)
C (ab)
D (a+b)
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Correct Answer
B. \(-\frac{b}{a}\)
Explanation
Simple Explanation
(ax+b=0) से \(x=-\frac{b}{a}\) मिलता है। सामान्य सूत्र याद रखें लेकिन संकेत न भूलें। / From (ax+b=0), we get \(x=-\frac{b}{a}\). Remember the general formula but do not miss the sign.
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बहुपद (p(x)=2x-2 +0x+3) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-2 +0x+3)?
#coefficient
#missing term
#polynomial
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A (0)
B (2)
C (3)
D (5)
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Explanation
Simple Explanation
(x) वाला पद (0x) है इसलिए (x) का गुणांक (0) है। अनुपस्थित पद का गुणांक (0) मानें। / The (x)-term is (0x), so the coefficient of (x) is (0). Treat a missing term as having coefficient (0).
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(p(x)=x-4 +2x-2 +1) में कौन सी घात अनुपस्थित है?
Which power is missing in (p(x)=x-4 +2x-2 +1)?
#missing power
#coefficient zero
#polynomial
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A \(x^4\)
B \(x^3\)
C \(x^2\)
D \(x^0\)
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Correct Answer
B. \(x^3\)
Explanation
Simple Explanation
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है। / The term \(x^3\) is not present in this polynomial. A missing term has coefficient (0).
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किसी बहुपद में (x) की घातें कैसी होनी चाहिए?
What should the powers of (x) be in a polynomial?
#powers
#definition
#polynomial
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A केवल ऋणात्मक पूर्णांक / Only negative integers
B केवल भिन्न / Only fractions
C अऋणात्मक पूर्णांक / Non-negative integers
D केवल अपरिमेय संख्याएं / Only irrational numbers
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Correct Answer
C. अऋणात्मक पूर्णांक / Non-negative integers
Explanation
Simple Explanation
बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही सबसे महत्वपूर्ण पहचान नियम है। / In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the key identification rule.
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निम्न में से एक चर वाला बहुपद कौन सा नहीं है?
Which of the following is not a polynomial in one variable?
#one variable
#two variables
#identification
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A \(2x^2+3x+1\)
B \(5t^3-t\)
C \(x^2+y+1\)
D (9z-4)
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Correct Answer
C. \(x^2+y+1\)
Explanation
Simple Explanation
\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है। / \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
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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
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A (0)
B (1)
C (5)
D (6)
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Explanation
Simple Explanation
(p(0)=0-0+6=6)। (x=0) रखने पर केवल अचर पद बचता है। / (p(0)=0-0+6=6). When (x=0), only the constant term remains.
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(p(x)=4x-2 -12x+9) में (p\left\(\frac{3}{2}\right\)) का मान क्या है?
What is the value of (p\left\(\frac{3}{2}\right\)) for (p(x)=4x-2 -12x+9)?
#fraction substitution
#evaluation
#zero
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A (0)
B (1)
C (3)
D (9)
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Explanation
Simple Explanation
(p\left\(\frac{3}{2}\right\)=4\cdot\frac{9}{4}-18+9=0)। भिन्न मान रखते समय पहले वर्ग ठीक से निकालें। / (p\left\(\frac{3}{2}\right\)=4\cdot\frac{9}{4}-18+9=0). While substituting a fraction, square it carefully first.
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(p(x)=2x-3 +3x-2 -5) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-3 +3x-2 -5)?
#coefficient
#missing term
#cubic
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A (2)
B (3)
C (0)
D (-5)
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Explanation
Simple Explanation
इसमें (x) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को (0x) समझें। / There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
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\(3x^2-2x+1\) 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
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A (2)
B (4)
C (6)
D (8)
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Explanation
Simple Explanation
पहले बहुपद में (x) का गुणांक (-2) और दूसरे में (4) है, योग (2) है। समान घात के गुणांक ही जोड़ें। / 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.
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कौन सा कथन (p(x)=x-2 +1) के बारे में सही है?
Which statement about (p(x)=x-2 +1) is correct?
#quadratic
#degree
#classification
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A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह बहुपद नहीं है / It is not a polynomial
D इसकी घात (1) है / Its degree is (1)
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Correct Answer
B. यह द्विघात बहुपद है / It is a quadratic polynomial
Explanation
Simple Explanation
(p(x)=x-2 +1) में सबसे बड़ी घात (2) है इसलिए यह द्विघात बहुपद है। घात से वर्गीकरण करें। / In (p(x)=x-2 +1), the highest power is (2), so it is a quadratic polynomial. Classify by degree.
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यदि (p(x)=(m-2 )x-3 +4x-2 -7) की घात (2) है, तो (m) का मान क्या होगा?
If the degree of (p(x)=(m-2 )x-3 +4x-2 -7) is (2), what will be the value of (m)?
#degree
#parameter
#polynomial
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
घात (2) होने के लिए \(x^3\) का गुणांक (0) होना चाहिए, इसलिए (m-2 =0) और (m=2)। परीक्षा में सबसे ऊंची घात के गुणांक को पहले देखें। / For the degree to be (2), the coefficient of \(x^3\) must be (0), so (m-2 =0) and (m=2). In exams, check the coefficient of the highest power first.
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(p(x)=2x-3 -5x-2 +7x-4) में (p(0)+p(1)) का मान क्या है?
What is the value of (p(0)+p(1)) for (p(x)=2x-3 -5x-2 +7x-4)?
#evaluation
#substitution
#polynomial
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A (0)
B (-1)
C (1)
D (4)
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Explanation
Simple Explanation
(p(0)=-4) और (p(1)=2-5+7-4=0), इसलिए योग (-4+4=0) नहीं बल्कि (-4+0=-4)। सही गणना में (p(0)+p(1)=-4) होता है। / (p(0)=-4) and (p(1)=2-5+7-4=0), so (p(0)+p(1)=-4). Always substitute each value separately before adding.
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बहुपद (p(x)=x-3 -3x-2 +3x-1) का कौन सा मान (0) देता है?
Which value gives (0) for the polynomial (p(x)=x-3 -3x-2 +3x-1)?
#zero
#cubic polynomial
#evaluation
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A (0)
B (1)
C (2)
D (3)
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Explanation
Simple Explanation
(p(1)=1-3+3-1=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखने से शून्य जल्दी मिल सकता है। / (p(1)=1-3+3-1=0), so (1) is a zero of this polynomial. Substituting options can quickly identify the zero.
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यदि (p(x)=kx-2 +6x+9) और (p(-3)=0), तो (k) क्या है?
If (p(x)=kx-2 +6x+9) and (p(-3)=0), what is (k)?
#parameter
#zero condition
#quadratic polynomial
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(-3)=9k-18+9=0), इसलिए (9k-9=0) और (k=1)। दिए गए शून्य को रखकर अज्ञात गुणांक निकालें। / (p(-3)=9k-18+9=0), so (9k-9=0) and (k=1). Substitute the given zero to find the unknown coefficient.
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यदि (p(x)=3x-2 +bx-10) में (x=2) एक शून्य है, तो (b) का मान क्या होगा?
If (x=2) is a zero of (p(x)=3x-2 +bx-10), what will be the value of (b)?
#zero
#parameter
#quadratic polynomial
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A (-1)
B (-2)
C (1)
D (2)
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Explanation
Simple Explanation
(p(2)=12+2b-10=0), इसलिए (2b=-2) और (b=-1)। शून्य दिए होने पर बहुपद का मान (0) रखें। / (p(2)=12+2b-10=0), so (2b=-2) and (b=-1). When a zero is given, set the polynomial value equal to (0).
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यदि (p(x)=ax-2 +3x+5) की घात (1) है, तो (a) का मान क्या होगा?
If (p(x)=ax-2 +3x+5) has degree (1), what will be the value of (a)?
#polynomials
#degree
#parameter
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A (0)
B (1)
C (3)
D (5)
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Explanation
Simple Explanation
घात (1) होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a=0) है। / For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).
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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
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A (-11)
B (-7)
C (7)
D (11)
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Explanation
Simple Explanation
\(x^2\) का गुणांक (-2) और नियत पद (-9) है। उनका योग (-11) है। / The coefficient of \(x^2\) is (-2) and the constant term is (-9). Their sum is (-11).
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यदि (q(x)=x-2 -kx+6) और (q(2)=0), तो (k) का मान क्या है?
If (q(x)=x-2 -kx+6) and (q(2)=0), what is the value of (k)?
#zero-of-polynomial
#parameter
#substitution
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A (3)
B (4)
C (5)
D (6)
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Explanation
Simple Explanation
(q(2)=4-2k+6=0) से (10-2k=0) मिलता है। इसलिए (k=5) है। / (q(2)=4-2k+6=0) gives (10-2k=0). So (k=5).
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निम्न में से कौन सा व्यंजक (x) में बहुपद नहीं है?
Which of the following expression is not a polynomial in (x)?
#not-polynomial
#negative-power
#definition
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A \(3x^2-5x+1\)
B \(\sqrt{3}x^2+2x-8\)
C \(x^4+\frac{1}{2}x^2-7\)
D \(x^2+\frac{4}{x}+1\)
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Correct Answer
D. \(x^2+\frac{4}{x}+1\)
Explanation
Simple Explanation
\(\frac{4}{x}=4x^{-1}\) में चर की घात ऋणात्मक है। बहुपद में चर की घातें पूर्ण संख्याएँ होनी चाहिए। / \(\frac{4}{x}=4x^{-1}\) has a negative power of the variable. In a polynomial, powers of the variable must be whole numbers.
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यदि (p(x)=2x-3 +mx-2 -x+4) में \(x^2\) का गुणांक (-5) है, तो (m) क्या है?
If the coefficient of \(x^2\) in (p(x)=2x-3 +mx-2 -x+4) is (-5), what is (m)?
#coefficient
#parameter
#polynomial
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A (5)
B (-5)
C (2)
D (-1)
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Explanation
Simple Explanation
\(x^2\) के साथ लगा गुणक (m) है। दिया है (m=-5), इसलिए उत्तर (-5) है। / The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
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बहुपद \(7x^5-3x^4+x^2-11\) में अनुपस्थित \(x^3\) पद का गुणांक क्या है?
What is the coefficient of the missing \(x^3\) term in \(7x^5-3x^4+x^2-11\)?
#missing-term
#coefficient
#degree
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A (7)
B (-3)
C (0)
D (1)
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Explanation
Simple Explanation
इस बहुपद में \(x^3\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जाता है। / There is no \(x^3\) term in this polynomial. The coefficient of a missing term is taken as (0).
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यदि (f(x)=x-2 +2x-8), तो निम्न में से कौन (f(x)) का शून्य है?
If (f(x)=x-2 +2x-8), which of the following is a zero of (f(x))?
#zero-of-polynomial
#substitution
#quadratic
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A (4)
B (2)
C (1)
D (-1)
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Explanation
Simple Explanation
(f(2)=4+4-8=0) है। इसलिए (2) इस बहुपद का शून्य है। / (f(2)=4+4-8=0). Therefore (2) is a zero of this polynomial.
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यदि (p(x)=3x-2 -2x+1), तो (p(2)-p(1)) का मान क्या है?
If (p(x)=3x-2 -2x+1), what is the value of (p(2)-p(1))?
#polynomial-value
#substitution
#difference
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A (5)
B (6)
C (7)
D (8)
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Explanation
Simple Explanation
(p(2)=9) और (p(1)=3) है। इसलिए (p(2)-p(1)=6) है। / (p(2)=9) and (p(1)=3). Therefore (p(2)-p(1)=6).
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यदि \(2x^2+5x-3\) को अवरोही घातों में लिखा जाए, तो प्रमुख पद कौन सा है?
If \(2x^2+5x-3\) is written in descending powers, which is the leading term?
#leading-term
#descending-order
#quadratic
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A \(2x^2\)
B (5x)
C (-3)
D \(x^2\)
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Correct Answer
A. \(2x^2\)
Explanation
Simple Explanation
सबसे बड़ी घात (2) वाला पद \(2x^2\) है। प्रमुख पद हमेशा सबसे बड़ी घात वाला पूरा पद होता है। / The term with highest power (2) is \(2x^2\). The leading term is always the full term with the greatest power.
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किस मान के लिए (p(x)=(a-2)x-3 +4x-2 +1) की घात (2) हो जाएगी?
For which value will (p(x)=(a-2)x-3 +4x-2 +1) have degree (2)?
#degree
#parameter
#highest-power
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A (a=0)
B (a=1)
C (a=2)
D (a=4)
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Explanation
Simple Explanation
घात (2) के लिए \(x^3\) का गुणांक (0) होना चाहिए। (a-2=0) से (a=2) मिलता है। / For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).
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निम्न में से किस बहुपद में (x) का गुणांक (0) है?
In which of the following polynomials is the coefficient of (x) equal to (0)?
#coefficient
#missing-x-term
#polynomial
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A \(x^2+5x+6\)
B \(3x^2-4\)
C \(2x^3+x-1\)
D (7x-9)
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Correct Answer
B. \(3x^2-4\)
Explanation
Simple Explanation
\(3x^2-4\) में (x) का पद नहीं है। इसलिए (x) का गुणांक (0) है। / In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
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यदि (r(x)=x-3 -4x), तो (r(-2)) का मान क्या है?
If (r(x)=x-3 -4x), what is the value of (r(-2))?
#substitution
#cubic-polynomial
#zero
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A (0)
B (2)
C (4)
D (-4)
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Explanation
Simple Explanation
(r(-2)=(-2)3 -4(-2)=-8+8=0) है। ऋणात्मक मानों में कोष्ठक लगाना जरूरी है। / (r(-2)=(-2)3 -4(-2)=-8+8=0). Brackets are important for negative values.
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कौन सा कथन \(5x^2-3x+7\) के लिए सही है?
Which statement is correct for \(5x^2-3x+7\)?
#quadratic-polynomial
#classification
#degree
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A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह त्रिघात बहुपद है / It is a cubic polynomial
D यह शून्य बहुपद है / It is the zero polynomial
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Correct Answer
B. यह द्विघात बहुपद है / It is a quadratic polynomial
Explanation
Simple Explanation
इसमें (x) की सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है। / The highest power of (x) is (2). Therefore it is a quadratic polynomial.
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यदि (p(x)=kx+12) का शून्य (3) है, तो (k) का मान क्या है?
If (3) is a zero of (p(x)=kx+12), what is the value of (k)?
#linear-polynomial
#zero
#parameter
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A (4)
B (-4)
C (9)
D (-9)
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Explanation
Simple Explanation
(p(3)=0) से (3k+12=0) मिलता है। इसलिए (k=-4) है। / From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
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\(x^4-6x^2+9\) में कितने गैर-शून्य पद हैं?
How many non-zero terms are there in \(x^4-6x^2+9\)?
#number-of-terms
#nonzero-terms
#polynomial
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
गैर-शून्य पद \(x^4\), \(-6x^2\) और (9) हैं। इसलिए कुल (3) गैर-शून्य पद हैं। / The non-zero terms are \(x^4\), \(-6x^2\), and (9). So there are (3) non-zero terms.
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यदि (p(x)=x-2 +ax+a) और (p(1)=5), तो (a) का मान क्या है?
If (p(x)=x-2 +ax+a) and (p(1)=5), what is the value of (a)?
#parameter
#polynomial-value
#substitution
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(1)=1+a+a=5) से (1+2a=5) मिलता है। इसलिए (a=2) है। / (p(1)=1+a+a=5) gives (1+2a=5). Therefore (a=2).
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यदि (p(x)=x-2 -9), तो कौन सी संख्या (p(x)) का शून्य नहीं है?
If (p(x)=x-2 -9), which number is not a zero of (p(x))?
#zero-of-polynomial
#quadratic
#checking
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A (3)
B (-3)
C (0)
D इनमें से कोई नहीं / None of these
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Explanation
Simple Explanation
(p(0)=02 -9=-9) है जो (0) नहीं है। इसलिए (0) शून्य नहीं है। / (p(0)=02 -9=-9), which is not (0). So (0) is not a zero.
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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
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A (3)
B (-5)
C (2)
D (-8)
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Explanation
Simple Explanation
प्रमुख पद \(3x^4\) है। इसलिए प्रमुख गुणांक (3) है। / The leading term is \(3x^4\). Therefore the leading coefficient is (3).
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यदि (p(x)=2x-2 -7x+3), तो (p(3)) का मान क्या है?
If (p(x)=2x-2 -7x+3), what is the value of (p(3))?
#substitution
#zero
#quadratic
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A (0)
B (3)
C (6)
D (9)
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Explanation
Simple Explanation
(p(3)=2(3)2 -7(3)+3=18-21+3=0) है। अतः (3) इसका शून्य है। / (p(3)=2(3)2 -7(3)+3=18-21+3=0). Hence (3) is its zero.
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यदि \(x^3+2x^2+cx+5\) में (x) का गुणांक (6) है, तो (c+5) क्या होगा?
If the coefficient of (x) in \(x^3+2x^2+cx+5\) is (6), what will be (c+5)?
#coefficient
#parameter
#evaluation
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A (6)
B (9)
C (11)
D (15)
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Explanation
Simple Explanation
(x) का गुणांक (c=6) है। इसलिए (c+5=11) होगा। / The coefficient of (x) is (c=6). Therefore (c+5=11).
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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
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A (8)
B (-3)
C (0)
D (2x+1)
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Explanation
Simple Explanation
(2x+1) में चर (x) है इसलिए यह नियत बहुपद नहीं है। नियत बहुपद में चर वाला पद नहीं होता। / (2x+1) contains the variable (x), so it is not a constant polynomial. A constant polynomial has no variable term.
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(p(x)=x-2 +4x+4) के लिए निम्न में से कौन सा सत्य है?
Which of the following is true for (p(x)=x-2 +4x+4)?
#zero-of-polynomial
#perfect-square
#substitution
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A (p(-2)=0)
B (p(0)=0)
C (p(2)=0)
D (p(4)=0)
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Correct Answer
A. (p(-2)=0)
Explanation
Simple Explanation
(p(-2)=4-8+4=0) है। इसलिए (-2) इस बहुपद का शून्य है। / (p(-2)=4-8+4=0). Therefore (-2) is a zero of this polynomial.
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यदि (p(x)=5x-2 -3x+2), तो (p(0)+p(1)) का मान क्या है?
If (p(x)=5x-2 -3x+2), what is the value of (p(0)+p(1))?
#polynomial-value
#sum
#substitution
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A (4)
B (5)
C (6)
D (8)
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Explanation
Simple Explanation
(p(0)=2) और (p(1)=4) है। इसलिए योग (6) है। / (p(0)=2) and (p(1)=4). Therefore the sum is (6).
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कौन सा विकल्प \(x^2-5x+6\) को पदों के सही समूह के रूप में दिखाता है?
Which option shows the correct group of terms of \(x^2-5x+6\)?
#terms
#signs
#trinomial
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A \(x^2\), (-5x), (6)
B \(x^2\), (5x), (6)
C (x), (-5), (6)
D \(x^2-5\), (x+6)
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Correct Answer
A. \(x^2\), (-5x), (6)
Explanation
Simple Explanation
चिह्न सहित पद \(x^2\), (-5x) और (6) हैं। पद पहचानते समय ऋण चिह्न साथ रखें। / The terms with signs are \(x^2\), (-5x), and (6). Keep the negative sign with the term while identifying terms.
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यदि (p(x)=x-3 +ax-2 +bx+1) में (a=0) और (b=-2), तो बहुपद क्या होगा?
If (a=0) and (b=-2) in (p(x)=x-3 +ax-2 +bx+1), what will the polynomial be?
#parameter
#substitution
#polynomial-form
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A \(x^3-2x+1\)
B \(x^3+2x+1\)
C \(x^3-2x^2+1\)
D \(x^3+x^2-2x\)
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Correct Answer
A. \(x^3-2x+1\)
Explanation
Simple Explanation
(a=0) से \(x^2\) पद हटता है और (b=-2) से (-2x) मिलता है। इसलिए बहुपद \(x^3-2x+1\) है। / With (a=0), the \(x^2\) term vanishes, and with (b=-2), we get (-2x). So the polynomial is \(x^3-2x+1\).
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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
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A \(x^2+3x+1\)
B \(y^2+3y+1\)
C (xy+1)
D (x+y+1)
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Correct Answer
A. \(x^2+3x+1\)
Explanation
Simple Explanation
\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है। / \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
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यदि (p(x)=4x-12), तो किस मान पर (p(x)=0) होगा?
If (p(x)=4x-12), for which value will (p(x)=0)?
#linear-polynomial
#zero
#equation
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A (2)
B (3)
C (4)
D (12)
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Explanation
Simple Explanation
(4x-12=0) से (4x=12) और (x=3) मिलता है। यह बहुपद का शून्य है। / From (4x-12=0), we get (4x=12) and (x=3). This is the zero of the polynomial.
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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
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A (0)
B (1)
C परिभाषित नहीं / Not defined
D बहुपद नहीं / Not a polynomial
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Explanation
Simple Explanation
गैर-शून्य नियत बहुपद की घात (0) होती है। इसे शून्य बहुपद से अलग रखें। / The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.
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\(x^2+1\), \(x^3+x\), (5x-2) में सबसे कम घात वाला बहुपद कौन सा है?
Among \(x^2+1\), \(x^3+x\), and (5x-2), which polynomial has the least degree?
#compare-degree
#linear-polynomial
#classification
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A \(x^2+1\)
B \(x^3+x\)
C (5x-2)
D तीनों की घात समान है / All three have the same degree
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Explanation
Simple Explanation
इनकी घातें क्रमशः (2), (3) और (1) हैं। सबसे कम घात (1) है। / Their degrees are (2), (3), and (1) respectively. The least degree is (1).
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यदि (p(x)=x-2 +x+1), तो (p(-1)) का मान क्या है?
If (p(x)=x-2 +x+1), what is the value of (p(-1))?
#substitution
#negative-value
#quadratic
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A (0)
B (1)
C (2)
D (3)
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Explanation
Simple Explanation
(p(-1)=(-1)2 +(-1)+1=1) है। चिह्नों को सावधानी से जोड़ें। / (p(-1)=(-1)2 +(-1)+1=1). Add the signs carefully.
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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
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A \(6x^3-2x+9\)
B \(6x^3+2x+9\)
C \(6x^3+x^2-2x+9\)
D \(6x^3-2x\)
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Correct Answer
A. \(6x^3-2x+9\)
Explanation
Simple Explanation
\(0x^2\) का मान (0) है इसलिए वह पद हट जाता है। बाकी पद जैसे हैं वैसे रहते हैं। / The value of \(0x^2\) is (0), so that term vanishes. The remaining terms stay unchanged.
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यदि (p(x)=x-2 -3x+2), तो (p(1)) और (p(2)) के बारे में सही कथन कौन सा है?
If (p(x)=x-2 -3x+2), which statement about (p(1)) and (p(2)) is correct?
#zeros
#quadratic
#substitution
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A दोनों (0) हैं / Both are (0)
B केवल (p(1)=0) है / Only (p(1)=0)
C केवल (p(2)=0) है / Only (p(2)=0)
D दोनों (0) नहीं हैं / Both are not (0)
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Correct Answer
A. दोनों (0) हैं / Both are (0)
Explanation
Simple Explanation
(p(1)=1-3+2=0) और (p(2)=4-6+2=0) है। इसलिए दोनों शून्य हैं। / (p(1)=1-3+2=0) and (p(2)=4-6+2=0). So both are zeros.
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निम्न में से किस बहुपद में प्रमुख गुणांक (1) नहीं है?
Which of the following polynomials does not have leading coefficient (1)?
#leading-coefficient
#monic-polynomial
#classification
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A \(x^3+2x+5\)
B \(x^2-4\)
C \(3x^2+x+1\)
D \(x^5-x\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+x+1\)
Explanation
Simple Explanation
\(3x^2+x+1\) का प्रमुख पद \(3x^2\) है। इसका प्रमुख गुणांक (3) है, (1) नहीं। / The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
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यदि (p(x)=2x-2 +bx-10) और (p(2)=4), तो (b) का मान क्या है?
If (p(x)=2x-2 +bx-10) and (p(2)=4), what is the value of (b)?
#parameter
#polynomial-value
#linear-equation
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(2)=8+2b-10=4) से (2b-2=4) मिलता है। इसलिए (b=3) है। / (p(2)=8+2b-10=4) gives (2b-2=4). Therefore (b=3).
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कौन सा विकल्प \(x^3-1\) के प्रकार को सही बताता है?
Which option correctly describes the type of \(x^3-1\)?
#cubic-binomial
#classification
#terms
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A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी / Quadratic trinomial
C त्रिघात द्विपदी / Cubic binomial
D नियत एकपदी / Constant monomial
Explanation opens after your attempt
Correct Answer
C. त्रिघात द्विपदी / Cubic binomial
Explanation
Simple Explanation
\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है। / \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
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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
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A (6)
B (-6)
C (0)
D (5)
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Explanation
Simple Explanation
(p(0)) हमेशा नियत पद के बराबर होता है। यहाँ नियत पद (-6) है। / (p(0)) is always equal to the constant term. Here the constant term is (-6).
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निम्न में से कौन सा (t) में बहुपद है?
Which of the following is a polynomial in (t)?
#polynomial-in-t
#definition
#real-coefficient
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A \(t^2+\sqrt{t}+1\)
B \(t^{-2}+3\)
C \(4t^3-\frac{1}{2}t+7\)
D \(\frac{2}{t}+t\)
Explanation opens after your attempt
Correct Answer
C. \(4t^3-\frac{1}{2}t+7\)
Explanation
Simple Explanation
\(4t^3-\frac{1}{2}t+7\) में (t) की घातें (3), (1) और (0) हैं। ये सभी पूर्ण संख्याएँ हैं। / In \(4t^3-\frac{1}{2}t+7\), the powers of (t) are (3), (1), and (0). All are whole numbers.
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यदि (p(x)=x-2 -2x+3), तो (p(2)+p(-1)) का मान क्या है?
If (p(x)=x-2 -2x+3), what is the value of (p(2)+p(-1))?
#polynomial-value
#sum
#substitution
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A (8)
B (9)
C (10)
D (11)
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Explanation
Simple Explanation
(p(2)=3) और (p(-1)=6) है। इसलिए योग (9) है। / (p(2)=3) and (p(-1)=6). Therefore the sum is (9).
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यदि \(a\neq0\), तो (ax+b) के बारे में सही कथन कौन सा है?
If \(a\neq0\), which statement is correct about (ax+b)?
#linear-polynomial
#standard-form
#degree
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A यह नियत बहुपद है / It is a constant polynomial
B यह रैखिक बहुपद है / It is a linear polynomial
C यह द्विघात बहुपद है / It is a quadratic polynomial
D यह शून्य बहुपद है / It is the zero polynomial
Explanation opens after your attempt
Correct Answer
B. यह रैखिक बहुपद है / It is a linear polynomial
Explanation
Simple Explanation
\(a\neq0\) होने पर (x) का पद मौजूद रहता है। इसलिए (ax+b) की घात (1) होती है। / When \(a\neq0\), the (x)-term is present. So (ax+b) has degree (1).
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बहुपद \(2x^4+3x^2-5x+7\) में \(x^3\) के गुणांक और (x) के गुणांक का योग क्या है?
In \(2x^4+3x^2-5x+7\), what is the sum of the coefficient of \(x^3\) and the coefficient of (x)?
#coefficients
#missing-term
#sum
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A (-5)
B (0)
C (5)
D (3)
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Explanation
Simple Explanation
\(x^3\) का गुणांक (0) और (x) का गुणांक (-5) है। योग (-5) है। / The coefficient of \(x^3\) is (0) and the coefficient of (x) is (-5). The sum is (-5).
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यदि (p(x)=3x-2 +2x-1), तो (p\left\(\frac{1}{3}\right\)) का मान क्या है?
If (p(x)=3x-2 +2x-1), what is the value of (p\left\(\frac{1}{3}\right\))?
#fraction-substitution
#zero
#polynomial-value
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A (0)
B \(\frac{1}{3}\)
C \(\frac{2}{3}\)
D (1)
Explanation opens after your attempt
Explanation
Simple Explanation
(p\left\(\frac{1}{3}\right\)=3\left\(\frac{1}{3}\right\)2 +2\left\(\frac{1}{3}\right\)-1=0) है। भिन्न रखते समय कोष्ठक लगाएँ। / (p\left\(\frac{1}{3}\right\)=3\left\(\frac{1}{3}\right\)2 +2\left\(\frac{1}{3}\right\)-1=0). Use brackets while substituting fractions.
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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
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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. \(2x^2-3x+8\)
Explanation
Simple Explanation
अवरोही क्रम में बड़ी घात वाला पद पहले आता है। इसलिए सही रूप \(2x^2-3x+8\) है। / In descending order, the term with greater power comes first. So the correct form is \(2x^2-3x+8\).
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यदि (p(x)=x-2 +px+16) और (4) इसका शून्य है, तो (p) का मान क्या है?
If (4) is a zero of (p(x)=x-2 +px+16), what is the value of (p)?
#zero
#parameter
#quadratic
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A (-8)
B (-4)
C (4)
D (8)
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Explanation
Simple Explanation
\(4^2+4p+16=0\) से (32+4p=0) मिलता है। इसलिए (p=-8) है। / \(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
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निम्न में से कौन सा कथन शून्य बहुपद के लिए सही है?
Which statement is correct for the zero polynomial?
#zero-polynomial
#degree
#concept
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A इसकी घात (0) होती है / Its degree is (0)
B इसकी घात (1) होती है / Its degree is (1)
C इसकी घात परिभाषित नहीं होती / Its degree is not defined
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. इसकी घात परिभाषित नहीं होती / Its degree is not defined
Explanation
Simple Explanation
शून्य बहुपद की घात परिभाषित नहीं होती। गैर-शून्य नियत बहुपद की घात (0) होती है। / The degree of the zero polynomial is not defined. A non-zero constant polynomial has degree (0).
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यदि (p(x)=x-3 -2x-2 +x), तो (p(1)) का मान क्या है?
If (p(x)=x-3 -2x-2 +x), what is the value of (p(1))?
#cubic-polynomial
#zero
#substitution
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A (0)
B (1)
C (2)
D (-1)
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Explanation
Simple Explanation
(p(1)=1-2+1=0) है। इसलिए (1) इस बहुपद का शून्य है। / (p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
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यदि (p(x)=2x-2 +3x+4), तो (p(-1)) और (p(0)) का अंतर (p(-1)-p(0)) क्या है?
If (p(x)=2x-2 +3x+4), what is the difference (p(-1)-p(0))?
#polynomial-value
#difference
#substitution
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A (-1)
B (0)
C (1)
D (2)
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Explanation
Simple Explanation
(p(-1)=3) और (p(0)=4) है। इसलिए (p(-1)-p(0)=-1) है। / (p(-1)=3) and (p(0)=4). Therefore (p(-1)-p(0)=-1).
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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
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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)
Explanation
Simple Explanation
\(\sqrt{5}\) वास्तविक गुणांक है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह (x) में बहुपद है। / \(\sqrt{5}\) is a real coefficient and the powers of (x) are whole numbers. So it is a polynomial in (x).
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यदि (p(x)=x-2 -ax+12) और (p(3)=0), तो (a) का मान क्या है?
If (p(x)=x-2 -ax+12) and (p(3)=0), what is the value of (a)?
#parameter
#zero
#quadratic
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A (5)
B (6)
C (7)
D (8)
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Explanation
Simple Explanation
(9-3a+12=0) से (21-3a=0) मिलता है। इसलिए (a=7) है। / (9-3a+12=0) gives (21-3a=0). Therefore (a=7).
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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
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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)
Explanation
Simple Explanation
सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है। / The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
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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
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A (7)
B (-7)
C (0)
D (a+b+c)
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Explanation
Simple Explanation
(x=0) रखने पर (p(0)=d) मिलता है। इसलिए (d=-7) है। / Putting (x=0) gives (p(0)=d). Therefore (d=-7).
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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
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A (1)
B (3)
C (6)
D (11)
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Explanation
Simple Explanation
सबसे बड़ी घात (6) है इसलिए घात (6) होगी। गुणांक नहीं बल्कि चर की सबसे ऊंची घात देखें। / The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.
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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
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A (5)
B (-8)
C (13)
D (-21)
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Explanation
Simple Explanation
\(x^2\) वाले पद \(-8x^2\) का गुणांक (-8) है। संकेत सहित गुणांक लिखना जरूरी है। / The coefficient of the \(x^2\)-term \(-8x^2\) is (-8). Write the coefficient with its sign.
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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
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A (4)
B (-6)
C (1)
D (15)
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Explanation
Simple Explanation
जिस पद में (t) नहीं है वह अचर पद है। यहां अचर पद (15) है। / The term without (t) is the constant term. Here the constant term is (15).
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निम्न में से कौन सा (y) में बहुपद नहीं है?
Which of the following is not a polynomial in (y)?
#not polynomial
#negative power
#concept
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A \(3y^4-y+2\)
B \(7y^2+5y^0\)
C \(6y+\sqrt{3}\)
D \(y^2+\frac{4}{y}\)
Explanation opens after your attempt
Correct Answer
D. \(y^2+\frac{4}{y}\)
Explanation
Simple Explanation
\(y^2+\frac{4}{y}\) में \(\frac{4}{y}=4y^{-1}\) है इसलिए घात ऋणात्मक है। ऋणात्मक घात वाला चर बहुपद नहीं बनाता। / In \(y^2+\frac{4}{y}\), \(\frac{4}{y}=4y^{-1}\), so the power is negative. A variable with a negative power is not a polynomial.
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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
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
\(0x^2\) प्रभावी पद नहीं है इसलिए पद \(7x^4\), \(-3x^3\) और (5) हैं। शून्य गुणांक वाले पद को न गिनें। / 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.
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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
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(2)=2(2)2 +3(2)-11=3)। मान निकालते समय पहले घात का मान निकालें। / (p(2)=2(2)2 +3(2)-11=3). While evaluating, calculate the power first.
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(q(x)=x-3 +2x-2 -5x-6) के लिए (q(-2)) क्या होगा?
For (q(x)=x-3 +2x-2 -5x-6), what is (q(-2))?
#evaluation
#negative input
#cubic
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
(q(-2)=-8+8+10-6=4)। ऋणात्मक मान रखते समय प्रत्येक पद का संकेत अलग जांचें। / (q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.
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\(12x^2-7x+4\) किस प्रकार का बहुपद है?
What type of polynomial is \(12x^2-7x+4\)?
#trinomial
#terms
#classification
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A एकपदी / Monomial
B द्विपदी / Binomial
C त्रिपदी / Trinomial
D शून्य बहुपद / Zero polynomial
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Correct Answer
C. त्रिपदी / Trinomial
Explanation
Simple Explanation
इसमें (3) प्रभावी पद हैं इसलिए यह त्रिपदी है। पदों की संख्या से नाम पहचाना जाता है। / It has (3) effective terms, so it is a trinomial. The name is identified by the number of terms.
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यदि (p(x)=(a+3)x-2 +5x-1) रैखिक बहुपद है, तो (a) क्या होगा?
If (p(x)=(a+3)x-2 +5x-1) is a linear polynomial, what is (a)?
#linear condition
#parameter
#degree
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A (-3)
B (0)
C (3)
D (5)
Explanation opens after your attempt
Explanation
Simple Explanation
रैखिक होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a+3=0) और (a=-3)। / For it to be linear, the coefficient of \(x^2\) must be (0). Hence (a+3=0) and (a=-3).
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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
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A (0)
B (1)
C (18)
D परिभाषित नहीं / Undefined
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Explanation
Simple Explanation
अशून्य अचर बहुपद की घात (0) होती है। अचर संख्या का अर्थ घात (0) से जुड़ा है। / A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).
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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
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A (1)
B (3)
C (5)
D (7)
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Explanation
Simple Explanation
\(0x^5\) का गुणांक (0) है इसलिए वह पद नहीं गिना जाएगा। सबसे बड़ी प्रभावी घात (3) है। / The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
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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
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A (p)
B (u)
C (13)
D (9)
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Explanation
Simple Explanation
जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है। / The letter whose values can change is the variable. Here the variable is (u).
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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
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A (-9)
B (-5)
C (-4)
D (4)
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Explanation
Simple Explanation
(cx) में (x) का गुणांक (c) है। दिया है कि (c=-4)। / In (cx), the coefficient of (x) is (c). It is given that (c=-4).
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यदि (p(x)=x-2 -16), तो (p(4)) का मान क्या है?
If (p(x)=x-2 -16), what is the value of (p(4))?
#zero
#evaluation
#substitution
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A (0)
B (4)
C (8)
D (16)
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Explanation
Simple Explanation
(p(4)=42 -16=0)। इसलिए (4) इस बहुपद का शून्य है। / (p(4)=42 -16=0). Hence (4) is a zero of this polynomial.
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(x=-3) किस बहुपद का शून्य है?
For which polynomial is (x=-3) a zero?
#zero
#linear polynomial
#evaluation
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A (p(x)=x+3)
B (p(x)=x-3)
C (p(x)=3x+1)
D (p(x)=x-2 +3)
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Correct Answer
A. (p(x)=x+3)
Explanation
Simple Explanation
(p(-3)=-3+3=0), इसलिए (x=-3) इसका शून्य है। शून्य जांचने के लिए मान रखकर परिणाम (0) देखें। / (p(-3)=-3+3=0), so (x=-3) is its zero. To test a zero, substitute the value and check for (0).
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(p(x)=x-2 -7x+12) के लिए (p(3)) क्या है?
For (p(x)=x-2 -7x+12), what is (p(3))?
#quadratic
#zero
#evaluation
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A (0)
B (2)
C (3)
D (6)
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Explanation
Simple Explanation
(p(3)=9-21+12=0)। इसलिए (3) इस बहुपद का शून्य है। / (p(3)=9-21+12=0). Hence (3) is a zero of this polynomial.
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किसी रैखिक बहुपद (mx+n) में \(m\ne0\) हो तो उसकी घात क्या है?
If \(m\ne0\) in a linear polynomial (mx+n), what is its degree?
#linear polynomial
#degree
#general form
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A (0)
B (1)
C (2)
D परिभाषित नहीं / Undefined
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Explanation
Simple Explanation
\(m\ne0\) होने पर (mx) पद मौजूद रहता है और सबसे बड़ी घात (1) होती है। इसलिए घात (1) है। / When \(m\ne0\), the term (mx) exists and the highest power is (1). So the degree is (1).
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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
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A (-6)
B (4)
C (-1)
D (8)
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Explanation
Simple Explanation
सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है। / The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
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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
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A (8)
B (-5)
C (2)
D (-6)
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Explanation
Simple Explanation
\(x^4\) वाले पद \(8x^4\) का गुणांक (8) है। घात और गुणांक को अलग पहचानें। / The coefficient of the \(x^4\)-term \(8x^4\) is (8). Identify the power and coefficient separately.
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(p(x)=4x-2 -9x+2) और (q(x)=3x-2 +x-7) का योग क्या है?
What is the sum of (p(x)=4x-2 -9x+2) and (q(x)=3x-2 +x-7)?
#addition
#like terms
#polynomials
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A \(7x^2-8x-5\)
B \(x^2-10x+9\)
C \(7x^2+8x-5\)
D \(12x^4-9x-14\)
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Correct Answer
A. \(7x^2-8x-5\)
Explanation
Simple Explanation
समान घात वाले पद जोड़ने पर \(7x^2-8x-5\) मिलता है। केवल समान पदों को ही जोड़ें। / Adding like terms gives \(7x^2-8x-5\). Add only like terms.
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(p(x)=6x-2 -x+3) से (r(x)=2x-2 +5x-8) घटाने पर क्या मिलेगा?
What is obtained when (r(x)=2x-2 +5x-8) is subtracted from (p(x)=6x-2 -x+3)?
#subtraction
#like terms
#polynomials
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A \(4x^2-6x+11\)
B \(8x^2+4x-5\)
C \(4x^2+6x+11\)
D \(8x^2-6x-11\)
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Correct Answer
A. \(4x^2-6x+11\)
Explanation
Simple Explanation
(p(x)-r(x)=6x-2 -x+3-\(2x^2+5x-8\)=4x-2 -6x+11)। घटाते समय कोष्ठक के सभी संकेत बदलें। / (p(x)-r(x)=6x-2 -x+3-\(2x^2+5x-8\)=4x-2 -6x+11). Change all signs inside the bracket while subtracting.
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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
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A \(-6x^3+12x^2-15x\)
B \(-6x^3-12x^2-15x\)
C \(6x^3+12x^2-15x\)
D \(-6x^2+12x-15\)
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Correct Answer
A. \(-6x^3+12x^2-15x\)
Explanation
Simple Explanation
प्रत्येक पद को (-3x) से गुणा करने पर \(-6x^3+12x^2-15x\) मिलता है। ऋणात्मक गुणक के संकेत ध्यान से लगाएं। / Multiplying each term by (-3x) gives \(-6x^3+12x^2-15x\). Apply signs carefully with a negative multiplier.
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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
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A \(x^2-3x-10\)
B \(x^2+7x-10\)
C \(x^2-3x+10\)
D \(x^2-7x-10\)
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Correct Answer
A. \(x^2-3x-10\)
Explanation
Simple Explanation
((x-5)(x+2)=x-2 +2x-5x-10=x-2 -3x-10)। मध्य पदों को संकेत सहित जोड़ें। / ((x-5)(x+2)=x-2 +2x-5x-10=x-2 -3x-10). Combine the middle terms with signs.
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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
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A \(3x^2-10x-8\)
B \(3x^2+14x-8\)
C \(3x^2-12x+2\)
D \(3x^2-10x+8\)
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Correct Answer
A. \(3x^2-10x-8\)
Explanation
Simple Explanation
((3x+2)(x-4)=3x-2 -12x+2x-8=3x-2 -10x-8)। प्रत्येक पद का हर पद से गुणा करें। / ((3x+2)(x-4)=3x-2 -12x+2x-8=3x-2 -10x-8). Multiply each term by each term.
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(p(x)=x-3 -4x-2 +x+6) में (p(-1)) का मान क्या है?
What is the value of (p(-1)) in (p(x)=x-3 -4x-2 +x+6)?
#cubic polynomial
#evaluation
#zero
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
(p(-1)=-1-4-1+6=0)। इसलिए (-1) इस बहुपद का शून्य है। / (p(-1)=-1-4-1+6=0). Therefore (-1) is a zero of this polynomial.
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यदि (p(x)=x-2 +kx-15) और (p(3)=0), तो (k) क्या है?
If (p(x)=x-2 +kx-15) and (p(3)=0), what is (k)?
#parameter
#zero condition
#quadratic
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
(p(3)=9+3k-15=0), इसलिए (3k=6) और (k=2)। शून्य की शर्त लगाकर अज्ञात निकालें। / (p(3)=9+3k-15=0), so (3k=6) and (k=2). Use the zero condition to find the unknown.
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यदि (p(x)=x-2 -ax+18) और (p(3)=0), तो (a) का मान क्या है?
If (p(x)=x-2 -ax+18) and (p(3)=0), what is the value of (a)?
#parameter
#evaluation
#quadratic polynomial
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A (7)
B (8)
C (9)
D (10)
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Explanation
Simple Explanation
(p(3)=9-3a+18=0), इसलिए (27=3a) और (a=9)। मान रखने के बाद सरल रैखिक समीकरण हल करें। / (p(3)=9-3a+18=0), so (27=3a) and (a=9). After substitution, solve the simple linear equation.
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किस मान के लिए \(x^2-6x+m\) में (x=2) शून्य होगा?
For what value of (m) will (x=2) be a zero of \(x^2-6x+m\)?
#zero
#parameter
#quadratic
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A (6)
B (8)
C (10)
D (12)
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Explanation
Simple Explanation
(4-12+m=0), इसलिए (m=8)। शून्य दिए होने पर बहुपद का मान (0) रखें। / (4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
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बहुपद (p(x)=3x-2 -10x+7) में (x=1) रखने पर क्या निष्कर्ष है?
What conclusion follows when (x=1) is substituted in (p(x)=3x-2 -10x+7)?
#zero
#evaluation
#concept
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A (1) शून्य है / (1) is a zero
B (1) घात है / (1) is a degree
C (1) गुणांक है / (1) is a coefficient
D (1) अचर पद है / (1) is a constant term
Explanation opens after your attempt
Correct Answer
A. (1) शून्य है / (1) is a zero
Explanation
Simple Explanation
(p(1)=3-10+7=0), इसलिए (1) शून्य है। शून्य के लिए बहुपद का मान (0) आना चाहिए। / (p(1)=3-10+7=0), so (1) is a zero. For a zero, the polynomial value must be (0).
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(p(x)=x-2 +6x+9) में (p(-3)) क्या है?
What is (p(-3)) for (p(x)=x-2 +6x+9)?
#evaluation
#negative zero
#quadratic
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A (0)
B (3)
C (6)
D (9)
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Explanation
Simple Explanation
(p(-3)=9-18+9=0)। इसलिए (-3) इस बहुपद का शून्य है। / (p(-3)=9-18+9=0). Hence (-3) is a zero of this polynomial.
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कौन सा विकल्प एक चर में बहुपद है लेकिन रैखिक नहीं है?
Which option is a polynomial in one variable but not linear?
#classification
#quadratic
#not linear
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A (5x-8)
B \(x^2+2x+3\)
C \(x+\frac{1}{x}\)
D \(\sqrt{x}+2\)
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Correct Answer
B. \(x^2+2x+3\)
Explanation
Simple Explanation
\(x^2+2x+3\) बहुपद है और इसकी घात (2) है। इसलिए यह रैखिक नहीं है। / \(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.
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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
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A (2)
B (3)
C (9)
D (27)
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Explanation
Simple Explanation
(9x-27=0) से (x=3) मिलता है। रैखिक बहुपद का शून्य समीकरण हल करके निकालें। / From (9x-27=0), we get (x=3). Find the zero of a linear polynomial by solving the equation.
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(p(x)=4x+20) का शून्य कौन सा है?
Which is the zero of (p(x)=4x+20)?
#linear polynomial
#zero
#solution
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A (5)
B (-5)
C (4)
D (-4)
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Explanation
Simple Explanation
(4x+20=0) से (x=-5) मिलता है। शून्य वह मान है जिससे बहुपद (0) हो जाए। / From (4x+20=0), we get (x=-5). A zero is the value that makes the polynomial equal to (0).
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यदि (p(x)=cx+d) और \(c\ne0\), तो इसका शून्य क्या होगा?
If (p(x)=cx+d) and \(c\ne0\), what will be its zero?
#linear zero
#general form
#formula
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A \(\frac{d}{c}\)
B \(-\frac{d}{c}\)
C (cd)
D (c-d)
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Correct Answer
B. \(-\frac{d}{c}\)
Explanation
Simple Explanation
(cx+d=0) से \(x=-\frac{d}{c}\) मिलता है। सूत्र में ऋण चिह्न ध्यान रखें। / From (cx+d=0), we get \(x=-\frac{d}{c}\). Remember the negative sign in the formula.
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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
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A (0)
B (5)
C (-4)
D (12)
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Explanation
Simple Explanation
\(x^2\) वाला पद \(0x^2\) है इसलिए गुणांक (0) है। अनुपस्थित या शून्य पद का गुणांक (0) माना जाता है। / The \(x^2\)-term is \(0x^2\), so the coefficient is (0). A missing or zero term has coefficient (0).
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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
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A \(x^5\)
B \(x^4\)
C \(x^3\)
D \(x^0\)
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Correct Answer
B. \(x^4\)
Explanation
Simple Explanation
इस बहुपद में \(x^4\) का पद नहीं है। अनुपस्थित पद का गुणांक (0) होता है। / The term \(x^4\) is not present in this polynomial. A missing term has coefficient (0).
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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
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A ऋणात्मक पूर्णांक / Negative integers
B भिन्न संख्याएं / Fractions
C अऋणात्मक पूर्णांक / Non-negative integers
D केवल अभाज्य संख्याएं / Only prime numbers
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Correct Answer
C. अऋणात्मक पूर्णांक / Non-negative integers
Explanation
Simple Explanation
बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है। / In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
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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
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A (0)
B (8)
C (13)
D (21)
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Explanation
Simple Explanation
(p(0)=0-0+13=13)। (x=0) रखने पर अचर पद ही बचता है। / (p(0)=0-0+13=13). When (x=0), only the constant term remains.
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(p(x)=9x-2 -12x+4) में (p\left\(\frac{2}{3}\right\)) का मान क्या है?
What is the value of (p\left\(\frac{2}{3}\right\)) for (p(x)=9x-2 -12x+4)?
#fraction substitution
#evaluation
#zero
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A (0)
B (1)
C (2)
D (4)
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Explanation
Simple Explanation
(p\left\(\frac{2}{3}\right\)=9\cdot\frac{4}{9}-8+4=0)। भिन्न मान रखते समय वर्ग और गुणा सावधानी से करें। / (p\left\(\frac{2}{3}\right\)=9\cdot\frac{4}{9}-8+4=0). While substituting a fraction, square and multiply carefully.
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(p(x)=7x-4 -2x-2 +9) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in (p(x)=7x-4 -2x-2 +9)?
#coefficient
#missing term
#quartic
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A (7)
B (-2)
C (0)
D (9)
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Explanation
Simple Explanation
\(x^3\) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^3\) समझें। / There is no \(x^3\)-term, so its coefficient is (0). Treat the missing term as \(0x^3\).
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\(5x^2-6x+2\) और \(2x^2+9x-1\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(5x^2-6x+2\) and \(2x^2+9x-1\)?
#coefficients
#like terms
#polynomials
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
पहले बहुपद में (x) का गुणांक (-6) और दूसरे में (9) है, योग (3) है। समान घात के गुणांक ही जोड़ें। / The coefficient of (x) is (-6) in the first polynomial and (9) in the second, so the sum is (3). Add coefficients of like powers only.
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कौन सा कथन (p(x)=x-3 +1) के बारे में सही है?
Which statement about (p(x)=x-3 +1) is correct?
#cubic
#degree
#classification
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A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह घन बहुपद है / It is a cubic polynomial
D यह बहुपद नहीं है / It is not a polynomial
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Correct Answer
C. यह घन बहुपद है / It is a cubic polynomial
Explanation
Simple Explanation
(p(x)=x-3 +1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें। / In (p(x)=x-3 +1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.
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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
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A (0)
B (2)
C (4)
D (6)
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Explanation
Simple Explanation
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। / 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.
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कौन सा व्यंजक (x) में बहुपद है लेकिन (x) में द्विघात नहीं है?
Which expression is a polynomial in (x) but not quadratic in (x)?
#classification
#cubic
#not quadratic
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A \(4x^2-3x+1\)
B \(6x^3-2x+9\)
C \(x^2+\frac{5}{x}\)
D \(7\sqrt{x}+2\)
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Correct Answer
B. \(6x^3-2x+9\)
Explanation
Simple Explanation
\(6x^3-2x+9\) बहुपद है और इसकी घात (3) है, इसलिए यह द्विघात नहीं है। घात से वर्गीकरण करें। / \(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.
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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
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A (-5)
B (-3)
C (3)
D (5)
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Explanation
Simple Explanation
(p(4)=32-20+c=7), इसलिए (12+c=7) और (c=-5)। दिए गए मान को रखकर अज्ञात अचर पद निकालें। / (p(4)=32-20+c=7), so (12+c=7) and (c=-5). Substitute the given value to find the unknown constant term.
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(p(x)=x-3 -2x-2 -5x+6) के लिए कौन सा मान (p(x)=0) बनाता है?
For (p(x)=x-3 -2x-2 -5x+6), which value makes (p(x)=0)?
#zero
#cubic polynomial
#evaluation
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(1)=1-2-5+6=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखकर जांचना तेज तरीका है। / (p(1)=1-2-5+6=0), so (1) is a zero of this polynomial. Substituting options is a quick method.
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यदि (p(x)=ax-2 +4x-12) और (x=2) इसका शून्य है, तो (a) क्या होगा?
If (p(x)=ax-2 +4x-12) and (x=2) is its zero, what is (a)?
#zero condition
#parameter
#quadratic
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A (1)
B (2)
C (3)
D (4)
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Explanation
Simple Explanation
(p(2)=4a+8-12=0), इसलिए (4a=4) और (a=1)। शून्य दिए होने पर बहुपद का मान (0) रखें। / (p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
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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
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A (-18)
B (-11)
C (-7)
D (4)
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Explanation
Simple Explanation
\(x^2\) का गुणांक (-7) और अचर पद (-11) है, इसलिए योग (-18) है। संकेत सहित जोड़ना न भूलें। / 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.
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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
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A \(4x^2+12x+9\)
B \(4x^2+9\)
C \(2x^2+12x+3\)
D \(4x^2-12x+9\)
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Correct Answer
A. \(4x^2+12x+9\)
Explanation
Simple Explanation
((2x+3)2 =4x-2 +12x+9)। वर्ग करते समय मध्य पद (2ab) को न छोड़ें। / ((2x+3)2 =4x-2 +12x+9). Do not skip the middle term (2ab) while squaring.
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यदि (p(x)=x-2 -10x+21), तो (p(7)) का मान क्या है?
If (p(x)=x-2 -10x+21), what is the value of (p(7))?
#evaluation
#zero
#quadratic polynomial
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A (0)
B (7)
C (14)
D (21)
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Explanation
Simple Explanation
(p(7)=49-70+21=0), इसलिए (7) इस बहुपद का शून्य है। मान रखते समय सभी पदों को क्रम से सरल करें। / (p(7)=49-70+21=0), so (7) is a zero of this polynomial. Simplify all terms in order after substitution.
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