Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 691-700 of 700 questions.
Which expression is a quadratic trinomial polynomial?
A. \(x^2-5x+6\)
\(x^2-5x+6\) की घात (2) है और इसमें तीन पद हैं। इसलिए यह द्विघात त्रिपदी है। / \(x^2-5x+6\) has degree (2) and three terms. Therefore, it is a quadratic trinomial.
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Which expression is not a polynomial because (x) is hidden in the denominator?
B. \(\frac{x^2+4}{x^2}\)
\(\frac{x^2+4}{x^2}=1+\frac{4}{x^2}\) है। \(\frac{4}{x^2}=4x^{-2}\), इसलिए यह बहुपद नहीं है। / \(\frac{x^2+4}{x^2}=1+\frac{4}{x^2}\). Since \(\frac{4}{x^2}=4x^{-2}\), it is not a polynomial.
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If (p(x)=x-4+cx-3+dx-2+e), under what condition is its degree definitely (4)?
A. किसी भी (c), (d), (e) के लिएFor any (c), (d), (e)
\(x^4\) का गुणांक (1) है, जो कभी शून्य नहीं होता। इसलिए घात हमेशा (4) रहेगी। / The coefficient of \(x^4\) is (1), which is never zero. Therefore, the degree is always (4).
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Which expression is a polynomial in (x) but not a linear polynomial in (x)?
B. \(x^3+1\)
\(x^3+1\) बहुपद है, पर इसकी घात (3) है। रैखिक बहुपद की घात (1) होती है। / \(x^3+1\) is a polynomial, but its degree is (3). A linear polynomial has degree (1).
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If (p(x)=(a-1)x-3+(a-1)x-2+(a-1)x+5) is a constant polynomial, what is (a)?
A. (1)
स्थिर बहुपद के लिए सभी चर पदों के गुणांक शून्य होने चाहिए। (a-1=0) से (a=1) मिलता है और (5) बचता है। / For a constant polynomial, all variable-term coefficients must be zero. From (a-1=0), (a=1), and (5) remains.
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If (q(x)=(a+2)x-6+(a-4)x-5+3) has degree exactly (5), what is the value of (a)?
B. (-2)
घात (5) के लिए \(x^6\) का गुणांक शून्य और \(x^5\) का गुणांक अशून्य होना चाहिए। (a=-2) पर (a-4=-6) अशून्य रहता है। / For degree (5), the \(x^6\) coefficient must be zero and the \(x^5\) coefficient must be non-zero. At (a=-2), (a-4=-6) remains non-zero.
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After simplifying \(\frac{x^4+x^2+x}{x}\) for \(x\neq0\), which polynomial is obtained?
A. \(x^3+x+1\)
हर पद को (x) से भाग देने पर \(x^3+x+1\) मिलता है। इसमें सभी घातें शून्य या धनात्मक पूर्णांक हैं। / Dividing each term by (x) gives \(x^3+x+1\). All its powers are non-negative integers.
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Which expression is not a polynomial in (x) because it contains a term like \(\cos x\)?
B. \(3x^2+\cos x\)
बहुपद के पद चर की निश्चित शून्य या धनात्मक पूर्णांक घातों में होते हैं। \(\cos x\) ऐसा पद नहीं है। / Polynomial terms use fixed non-negative integer powers of the variable. \(\cos x\) is not such a term.
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If (p(x)=(k-3)x-2+(2k-6)x+11) has degree (0), what is (k)?
C. (3)
घात (0) के लिए चर वाले दोनों गुणांक शून्य होने चाहिए। (k-3=0) और (2k-6=0) दोनों से (k=3) मिलता है। / For degree (0), both variable-term coefficients must be zero. Both (k-3=0) and (2k-6=0) give (k=3).
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If (p(x)=\(a^2-4\)x-4+(a+2)x-3+5x+1) has degree exactly (3), what is the value of (a)?
B. (2)
घात (3) के लिए \(x^4\) का गुणांक शून्य और \(x^3\) का गुणांक अशून्य होना चाहिए। (a=2) पर \(a^2-4=0\) और (a+2=4) है। / For degree (3), the \(x^4\) coefficient must be zero and the \(x^3\) coefficient must be non-zero. At (a=2), \(a^2-4=0\) and (a+2=4).
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