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 \(c\neq0\), what will be the degree of \(cx^5+2x^2-7\)?
C. (5)
\(c\neq0\) होने पर \(x^5\) पद मौजूद रहेगा। इसलिए सबसे बड़ी घात (5) होगी। / When \(c\neq0\), the \(x^5\) term remains present. Therefore the highest power will be (5).
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Which expression is a polynomial and has coefficient of \(x^2\) equal to (0)?
A. \(x^3+4x-2\)
\(x^3+4x-2\) बहुपद है और उसमें \(x^2\) पद नहीं है। इसलिए \(x^2\) का गुणांक (0) है। / \(x^3+4x-2\) is a polynomial and it has no \(x^2\) term. So the coefficient of \(x^2\) is (0).
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Is \(2x^2+3|x|+1\) a polynomial or not?
B. नहीं क्योंकि (|x|) बहुपद पद नहीं हैNo because (|x|) is not a polynomial term
(|x|) को (x) की अऋणात्मक पूर्णांक घातों के रूप में नहीं लिखा जाता। इसलिए यह बहुपद नहीं है। / The term (|x|) is not written using non-negative integer powers of (x). Therefore it is not a polynomial.
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Which option correctly gives the leading term of \(3x^4-2x^2+x-5\)?
A. \(3x^4\)
अग्रणी पद सबसे बड़ी घात वाला पद होता है। यहां सबसे बड़ी घात (4) है। / The leading term is the term with the highest power. Here the highest power is (4).
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If the degree of (p(x)=(2d-6)x-4+x-2+1) is (2), what is the value of (d)?
B. (3)
डिग्री (2) के लिए \(x^4\) का गुणांक (0) होना चाहिए। (2d-6=0) से (d=3)। / For degree (2), the coefficient of \(x^4\) must be (0). From (2d-6=0), (d=3).
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What is obtained by simplifying \(x^2+\frac{x}{x}\) for \(x\neq0\)?
B. \(x^2+1\)
\(x\neq0\) पर \(\frac{x}{x}=1\) होता है। इसलिए सरल रूप \(x^2+1\) है। / For \(x\neq0\), \(\frac{x}{x}=1\). Therefore the simplified form is \(x^2+1\).
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Which statement about \(x^2+\frac{x}{x}\) is the most accurate?
B. यह \(x\neq0\) पर \(x^2+1\) के बराबर है पर मूल रूप में चर हर में हैIt equals \(x^2+1\) for \(x\neq0\) but originally has variable in denominator
मूल व्यंजक में \(\frac{x}{x}\) में चर हर में है। सरल रूप डोमेन को ध्यान में रखकर लिया जाता है। / In the original expression, \(\frac{x}{x}\) has a variable in the denominator. The simplified form is taken with domain in mind.
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In which option is the degree of the polynomial (0)?
B. (-13)
अशून्य नियतांक बहुपद की डिग्री (0) होती है। शून्य बहुपद की डिग्री परिभाषित नहीं होती। / A non-zero constant polynomial has degree (0). The degree of the zero polynomial is not defined.
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What is the degree of \(x^4+x^2+x^0\)?
C. (4)
\(x^0=1\) होता है और सबसे बड़ी घात (4) है। इसलिए डिग्री (4) है। / \(x^0=1\), and the highest power is (4). Therefore the degree is (4).
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Which expression is not a polynomial because the variable is inside a radical sign?
C. \(\sqrt{x+1}+2\)
\(\sqrt{x+1}\) में चर मूल चिह्न के अंदर है। इसे बहुपद की मान्य घातों में नहीं लिखा जाता। / In \(\sqrt{x+1}\), the variable is inside a radical sign. It is not written using valid polynomial powers.
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