Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
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If (a=2) in (p(x)=(a-2)x-4+5x-2-3), what will be the degree of (p(x))?
C. (2)
(a=2) पर \(x^4\) का गुणांक (0) हो जाता है। इसलिए सबसे बड़ी बची घात (2) है। / At (a=2), the coefficient of \(x^4\) becomes (0). Therefore, the highest remaining power is (2).
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Which option gives both the correct identification and degree of the polynomial?
C. \(3x^5-2x^2+7\), बहुपद, घात (5)\(3x^5-2x^2+7\), polynomial, degree (5)
\(3x^5-2x^2+7\) में सभी घातें मान्य हैं और सबसे बड़ी घात (5) है। बाकी विकल्पों में अमान्य घातें हैं। / In \(3x^5-2x^2+7\), all powers are valid and the highest power is (5). The other options have invalid powers.
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Which expression is not a polynomial because the variable is hidden in the denominator?
B. \(\frac{x^2+4}{x}\)
\(\frac{x^2+4}{x}=x+\frac{4}{x}\) में \(\frac{4}{x}\) की घात (-1) है। इसलिए यह बहुपद नहीं है। / \(\frac{x^2+4}{x}=x+\frac{4}{x}\) contains \(\frac{4}{x}\), whose power is (-1). Hence it is not a polynomial.
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What is the correct identification of \(2x^6-4x^4+x^2-9\)?
B. घात (6) का चार-पदी बहुपदFour-term polynomial of degree (6)
इसमें चार पद हैं और सबसे बड़ी घात (6) है। इसलिए यह घात (6) का चार-पदी बहुपद है। / It has four terms and the highest power is (6). Therefore, it is a four-term polynomial of degree (6).
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Which expression is a polynomial in (x), if (a) and (b) are constants?
A. \(ax^3+b x+9\)
(a) और (b) गुणांक की तरह हैं। (x) की घातें (3), (1) और (0) मान्य हैं। / (a) and (b) act like coefficients. The powers of (x) are (3), (1), and (0), which are valid.
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If the degree of (r(x)=kx-3+2x-2+1) is (2), what is correct about (k)?
C. (k=0)
घात (2) होने के लिए \(x^3\) वाला पद हटना चाहिए। इसलिए (k=0) होना जरूरी है। / For the degree to be (2), the \(x^3\) term must disappear. Therefore, (k=0) is required.
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Which expression is not a polynomial because its power is not an integer?
C. (x^{52}+3x)
\(x^{5/2}\) में घात \(\frac{5}{2}\) है जो पूर्णांक नहीं है। बहुपद में ऐसी घात मान्य नहीं होती। / In \(x^{5/2}\), the power is \(\frac{5}{2}\), which is not an integer. Such a power is not valid in a polynomial.
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Which expression is a polynomial with only odd powers along with a constant term?
A. \(x^5-2x^3+7x-4\)
इसमें (x) की घातें (5), (3), (1) और (0) हैं। ये सभी मान्य हैं और चर घातें विषम हैं। / It has powers (5), (3), (1), and (0). All are valid, and the variable powers are odd.
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What is the degree of \(0x^4+0x^2+6\)?
C. (0)
शून्य गुणांक वाले पद हट जाते हैं और बहुपद (6) बचता है। अशून्य स्थिर बहुपद की घात (0) होती है। / Terms with zero coefficients disappear and the polynomial (6) remains. A non-zero constant polynomial has degree (0).
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Which expression is not a polynomial because the variable's power depends on the variable?
B. \(3^x+x^2\)
\(3^x\) में चर घात में है। बहुपद में चर की घात निश्चित शून्य या धनात्मक पूर्णांक होनी चाहिए। / In \(3^x\), the variable is in the exponent. In a polynomial, variable powers must be fixed non-negative integers.
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